Meaningful Math Activities in Pre-K: Part 1

Transcription

Apples
produced by
STARnet Regions I & III
Video Magazine
#179
April 11, 2012
Meaningful Math Activities in Pre-K:
Part 1
Featuring
Sally Moomaw, Ed.D
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Number Sense Activities Ten-‐Frame Cookie Sheet: Teachers can construct a 10-‐frame by using tape on a cookie sheet. Using magnets, represent a number on the cookie sheet and ask children to look quickly and tell the number by showing the same number on their hands. The sound of the magnets being added to or removed from the metal helps children keep count. Children learn to tell the number of magnets by simply looking. -‐ The Young Child and Mathematics (2nd Ed.) Colored Bead Strands: Blue beads – Single beads (1) Green beads – String of 2 Orange beads – String of 3 Yellow beads – String of 4 Red beads – String of 5 With these beads, children can make sets of 6,7,8,9, or 10, using the beads as another way to emphasize the part-‐part-‐whole model. Children can describe their sets of 6 as “2 greens and 4 yellows” or “1 blue and 5 reds”. -‐ The Young Child and Mathematics (2nd Ed.) The Snake Game: This game requires a game board in the shape of a snake that you make or you make it with the help of the students. It consists of twenty spaces from the snake’s head to the snake’s tail. Two players progress from the head of the snake to the tail by moving their counters from space to space. In each round of play, one child is the guesser and the other child is the hider, and then the roles switch. During a turn, the hider selects zero, one, two, or three objects to hide in her hand. The guesser then guesses how many objects she is hiding. If the guesser is correct, he moves that number of spaces. But if the guesser is incorrect, the hider moves that number of spaces. Children learn that if they put 3 objects in their hand, they can move quickly if the guesser is incorrect. They may try to really “fool” their partner with zero, but then realize this doesn’t get them anywhere! -‐ The Young Child and Mathematics (2nd Ed.) Make Four Elbows! Children form a circle and begin walking slowly in one direction. At a signal from the leader, they stop and listen to the instructions. When the leader states, “Make four elbows”, the children touch one or both of their elbows to other children’s elbows to make a total of four connected elbows. After everyone shares their methods of accomplishing this task, new directions can be given: “Make 3 ankles”; “Make 6 fingers”; “Make 7 feet”; and “Make 9 shoulders”. -‐ The Young Child and Mathematics (2nd Ed.) Where’s the Bear? Upside down plastic cups are labeled with numbers and displayed in order. A child/teacher hides a small plastic bear under one of the cups and then gives clues to help the other child figure out where the bear is. Many position words are modeled, learned, and used (between, before, after, in front of, behind) during this game. Children also discover problem-‐solving strategies. In addition, they learn terms like “first, second, third, etc.” -‐ The Young Child and Mathematics (2nd Ed.) Bears in a Cave: Using an overturned plastic bowl to represent a cave and 7 or 8 counting bears, two children act out a scenario in which several bears having a picnic decide to play hide-‐and-‐seek. While one child covers her eyes, the other child hides some of the bears in the cave (leaving the others in plain sight). The child now tries to guess how many bears are hiding in the cave – a highly motivating and challenging task for preschoolers, who tend to focus on the visible bears rather than on the hidden ones. -‐ The Young Child and Mathematics (2nd Ed.) Block Towers A die with two 1s, two 2s, and two 3s is added to the block center. The teacher may want to explain that this die is special, and that a regular die has pips for 1 to 6. The children throw the die and build towers with the indicated number of blocks. The towers are then compared by height. Number cards representing 1, 2, and 3 in a variety of different ways can also be used instead of a die. Children’s thinking is very evident in this activity, which is excellent for prekindergartners. Often, children change the activity by throwing the die a number of times and building many towers before comparing. They also figure out that the way the blocks are stacked affects how tall the towers are. Two blocks stacked “the tall way” are taller than three blocks stacked “the wide way”. -‐ The Young Child and Mathematics (2nd Ed.) 2/2012 Algebra Activities People Patterns: Half of a group of children stands in a line, while the other half observes. The teacher (or child) leading the activity whispers instructions that follow a pattern to each person in line – for example, the first person in line is told to smile, the second to frown, the third to smile, etc. The observers try to guess the pattern. -‐The Young Child and Mathematics (2nd Ed.) Pattern Dance: Children take turns creating a dance using three different motions in sequence – for example, kick-‐spin-‐wiggle. The steps are repeated over and over again in an abc pattern. The child who creates the dance serves at the class’s dance director, teaching the steps to the other children. -‐The Young Child and Mathematics (2nd Ed.) Picture Patterns: Take a walk around the school and go on a “pattern hunt.” Take a digital camera and snap photos of patterns when the children find them. Then create a classroom pattern book. “Leo found a pattern on a gate, it goes……… circle, rectangle, circle rectangle.” -‐Creative Curriculum (4th Ed.) Block Center Photo Patterns: Photographs featuring patterns on buildings, sidewalks, and monuments around town are displayed in the block center. Children create their own versions of the structures in the photos by setting up block creations with similar patterns. -‐The Young Child and Mathematics (2nd Ed.) The Line Up: Hold up cards with symbols for features such as shoe type, pet ownerships, clothing color, etc. Some cards have symbols with large black X through it and mean “Those children NOT wearing red should line up.” Initially, not characteristics are very difficult for young children to understand. To best teach this, pick one characteristic and divide the children into two groups. WEARING RED and NOT WEARING RED -‐The Young Child and Mathematics (2nd Ed.) Sing Chants & Songs with Growing Patterns: •There was an Old Lady Who Swallowed a Fly •The Green Grass Grew All Around •B-‐I-‐N-‐G-‐O •Don’t throw Your Junk In my Backyard •Tooty Ta After you do this activity in the classroom several times, have the children help you make up new stories. It can be an activity that can be sent home with fish crackers (after the children have done this several times). We use straight pretzels in February for Lincoln’s Birthday. A variety of snack items can be used to go along with a story. Fish Story Children could cut out a pond or use a blue rectangle (piece of construction paper) for an aquarium. They will need to start with 5 fish crackers (may need to give them more as story continues). The children will follow the story as the story is read/told to them and they will act the story out with the fish crackers. Once upon a time there was a little fish. (Children will place one fish cracker on the “water”.) He was very lonely. Then one day 2 friends came to visit. (Children will place two fish crackers on the “water”.) Now there are _____ fish. (Encourage children to answer “3”.) Yes, 1 fish and 2 more fish make 3 fish. Now the 3 fish were very happy swimming in their pond until one day a very large fish came along. The large fish ate one of the little fish. (The children pretend to be the large fish and they get to eat one of the fish in the water.) How many fish are left? (2) As the 2 fish swim around the pond, they meet 2 more fish. Now, how many fish are there? (4) Yes, 2 fish and 2 more fish are 4. Four little fish are swimming in the pond. One is caught by a fisherman (Children eat one.) and now there are _____ (3). The 3 little fish swim through the weeds and one jumped out (Children eat one.) and then there were _____ (2). We had 3 fish and lost 1 fish and that leaves 2 fish. The last 2 fish were swimming by a net. One got scared and swam home. (Children eat one.) There is now ____ (1) fish left. There were 2 fish and 1 left which leaves 1 fish. Our lonely little fish was swimming by himself when all of a sudden a little child caught him! Now there are _____ (zero) fish left. Geometry Activities Where’s the Egg/Teddy Bear? (Any small items can be used that come in various colors.) Materials: 5-‐6 plastic colored eggs or small stuffed teddy bears (each one a different color). -‐Give a child a direction on where to place an egg or bear such as “Put the red bear under the table.” Continue with different position words. -‐Can also have eggs or bears placed in the room and give a child a hint where to find the item. (Example: “Find the blue bear on top of a chair.”) Continue with different position words. -‐Can make a game with index cards listing a variety of directions as previously mentioned. Children can take turns drawing a card and teacher/adult can read the card to the child or group and child does what the card says. String Shapes Have three or four children share a string (yarn or fabric) which is tied to make a loop. (Need supervision) They make a variety of shapes by pulling the loop taunt to see what shapes they can make. They also can move the shape-‐high, low, turn, or flip. Children enjoy making shapes as the leader of the activity names them. They find that a triangle is easy to make because it can be skinny, fat, or “just right” and still be a triangle. A square is harder because all the sides must be exactly the same. Children are often surprised that a circle is one of the hardest shapes to make with string as it is easy to draw. As one child explained, “Circles are easy to draw because you don’t have anyone holding the line and making a point. They are much harder to hold.” -‐The Young Child and Mathematics Reenacting Stories Children can reenact stories that they are familiar with and a variety of position words can be used such as above, below, down, up, right, left, under, top, and bottom. They can act the story by portraying the characters themselves or they can use storyboards, dolls, etc. to demonstrate the story. The story, The Three Billy Goats Gruff, is an excellent story to act out. Props can be used such as the bridge on the playground equipment or the paper bridge made in the classroom, or a classroom table. Have someone tell the story and the children act out the story as it is told using position words. Geoboard Flash Materials: Each child should have a geoboard and geobands (rubber bands) of various colors. Teacher or child will lead by making a shape on the geoboard secretly. Then when he has everyone’s attention reveals the geoboard for a few seconds (the time can vary depending on the group or child) then quickly covers or removes the geoboard so they no longer see the shape or design. Then the children try to reproduce what they saw on the leader’s geoboard. When everyone is finished the leader can show his/her design and the group can compare their design to the leader’s. Paint Stick Puzzles Materials: 6-‐8 paint sticks (paint stirrers from paint store). Picture of an animal or something appealing to young children. Place paint sticks in a row and glue portion of the picture on the stick. Children are given all of the paint sticks and are to put in order to see the picture it makes. When the sticks are put in the correct order the entire picture will be formed just like a puzzle. Numerals with a corresponding number of dots can also be place on one end of the stick to make a connection to number sense. -‐from Linda Bessler, Illinois Measurement Activities Walking the Circle: This activity illustrates the meaning of comparison words, an important aspect of understanding measurement. Children walk in a circle. Teacher calls out commands: “Walk faster!” “Walk slower” “Walk higher (on tiptoes)” “Lower” “More heavily (like an elephant)” “More lightly (like a mouse)” “noisily” “quietly” “sway back and forth” *For a greater challenge, the children can hold dowels and combine different instructions, such as “Hold the stick higher and walk faster!” -‐The Young Child and Mathematics (2nd Ed.) Body Balances: Have children experiment using balances to compare a variety of items in the classroom. Discuss the terms “heavier,” “lighter,” “weighs more,” and “weighs less.” Then let the children use their bodies as scales by holding their arms straight out to the side with a different object (or number of objects) in each hand. Have them determine which item is heavier and they can tilt their arm down in the direction of the heavier object and raise the opposite arm up for the lighter object. -‐Navigating through Measurement Oobleck: Children mix 2 parts cornstarch with one part water to make a substance called oobleck. This is a strange mixture that shifts between a liquid and a solid state. When cornstarch and water are mixed together, children have an opportunity to measure both a powder and a liquid as accurately as possible. They can also practice measuring various amounts of oobleck while they explore it’s properties. -‐The Young Child and Mathematics (2nd Ed.) Actual Size Footprints: Actual Size by Steve Jenkin’s illustrates the foot of the largest land animal, the African elephant. Children can use adding-‐machine tape to make measuring tape that illustrates their own footprints placed end-‐to-‐end, a baby’s footprint, and the footprint of the elephant. Children then measure their heights with all three measures and compare results. The Young Child and Mathematics (2nd Ed.) Shoe Store: Transforming the dramatic play area into a shoe store provides preschool children with many opportunities to measure. Children can take off their shoes and measure feet to determine the right size of shoe. Boxes of various sizes can be used as shoeboxes. Children can decide which shoes can fit into certain boxes. Items you might want to include: -‐Shoes of various sizes and styles Shoe boxes of various sizes -‐Ruler or foot measure -‐Order forms and receipt pads -‐Sticky labels or price tags -‐Cash register -‐Play money, checkbooks, credit cards -‐Wallets and purses -‐Paper, cardboard, markers and tape (for making signs) -‐-‐The Young Child and Mathematics (2nd Ed.) and The Creative Curriculum for Preschool (Volume 4) Mathematics MATH TERMS Note these terms have been compiled and adapted from Principles and Standards for School Mathematics; Math Dictionary: Homework Help for Families; Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity; Wikipedia.org; Mathisfun.com; and Webster’s Dictionary. These terms are terms that children through Pre-‐K through third grade will be exposed to in classrooms. This list is to help parents and teachers when there is a question in terminology. This list is just a partial list of Math Terms. Addition Add, adding Symbol + Joining two or more numbers together to make a larger number. Example: 1 + 3 = 4, 10 + 30 = 40 Addend The number being added. Addend Addend 3 + 2 = 5 Algebra An area of mathematics that begins by understanding sorting, classifying and order of objects by size, number, and other properties. It also includes recognizing, describing, and extending patterns which includes repeating and growing patterns. These help young children develop algebraic thinking. Example: Sorting a group of teddy bear counters by color—all the red bears in one pile and all the blue bears in another pile. Classifying a group of seashells into groups of small shells, middle-‐sized shells, and large shells. Order objects such as socks by size from smallest to largest. Patterns-‐repeating pattern such as red button, blue button, red button, blue button . . . Growing pattern-‐ pattern is increasing in a consistent manner. Example: Increase by 1 each time. 
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 Illinois STARNET Regions I & III • Center for Best Practices in Early Childhood Education Western Illinois University • 1 University Circle • Horrabin Hall 32 • Macomb, Illinois 61455 800-‐227-‐7537 • www.starnet.org Angle The amount of turn around a fixed point (vertex). Angles are measured in degrees (°). vertex angle Attribute A characteristic of an object, such as size, shape, or color. Balance An even or equal distribution of weight. Observed using balance scales. Basic Facts Operations: Adding, Subtracting, Multiplying, and Division Operations are performed with numbers, 0 to 9. 1 + 4 = 5 9 – 7 = 2 0 x 8 = 0 Calculate Calculate means to find the answer by working the problem. Cardinal Number It is the number of all the items. It tells how many. Cardinality This refers to the number of items in a group (set). Circle Circle is a shape that 2-‐D that does not have any straight lines only a curved line. Each part of the curve is equal distance from the center of the shape. Illinois STARNET Regions I & III • Center for Best Practices in Early Childhood Education Western Illinois University • 1 University Circle • Horrabin Hall 32 • Macomb, Illinois 61455 800-‐227-‐7537 • www.starnet.org Classification Organizing objects into sets or groups according to the attributes (color, shape, size, texture, etc). Closed figure A 2-‐D shape with sides that begin and end from the same point. Commutative Property: Two or more numbers can add or multiply in any order and the answer will always be the same. 3 + 1 = 4 2 x 5 = 10 1 + 3 = 4 5 x 2 = 10 Comparison Comparing objects, quantities, or measurements to see if they are the same or different. Composing/Decomposing Refers to putting together and taking apart and applies to numbers, geometry and measurement. Examples: 20 ones are composed to form 2 groups of 10 7 can be decomposed into 3 + 4 2 identical squares can compose to make 1 rectangle. A hexagon can be decomposed into 6 triangles. Computation—Compute or computing To work (calculate) out a problem using addition, subtraction, multiplication, and/or division and find an answer to the math question/problem. Computation can be done with paper and pencil, using a calculator or computer, with manipulatives, and/or mentally. Cone Refers to a 3-‐D solid that has a circular base that comes to a point at the top. It looks like an ice cream cone. Consecutive Numbers These are numbers that follow each one in a sequence and continuously. 1, 2, 3, 4, 5, 6, 7, 8, 9 Illinois STARNET Regions I & III • Center for Best Practices in Early Childhood Education Western Illinois University • 1 University Circle • Horrabin Hall 32 • Macomb, Illinois 61455 800-‐227-‐7537 • www.starnet.org Counting Means giving one number to each item in a group or set. The numbers are in sequence beginning with 1. Example-‐ 1, 2, 3, 4, 5 . . . Note: Zero is not a counting number. Cube A 3-‐D solid that looks like a box. It has 6 equal sides called faces. It also has 12 equal edges. Cup A type of measurement used when we cook. One cup holds 8 ounces. Curve This is a line with no straight parts. A circle is a closed curve. Customary Measurement System This is the main measurement system in the United States. It began in England and is called the Imperial measurement system. Instead of liters, we have pints and quarts. Instead of kilometers, we have miles. Cylinder This is a 3-‐D solid that looks like a can. It has two circular sides (faces) and has a curved surface. Data A group or collection of numbers, measurements, facts, or symbols. Decimal It contains 10 parts. Decimal number is a fraction that is written as a decimal. Example: Fraction Decimal Number 3 ______________ = 0. 3 10 Illinois STARNET Regions I & III • Center for Best Practices in Early Childhood Education Western Illinois University • 1 University Circle • Horrabin Hall 32 • Macomb, Illinois 61455 800-‐227-‐7537 • www.starnet.org Decimal point is a point, dot, or period that is placed to separate a whole number from a part of number (a decimal number). Decrease To make something smaller or reduce it. Example: The number of squares was decreased by 3 which meant it went from4 squares to 3 squares which left 1 square. − = Degree Symbol ° A degree is a unit used to measure angles in geometry and geometric shapes. Diagonal ⁄ It is a slanting straight line. Diameter A straight line passing from side to side through the center of a circle or sphere. The diameter is the length of this straight line. 
Diamond (The correct name is rhombus.) A 2-‐D shape with 4 sides and they are equal in length. It also has four angles but they are not right angles. Die (Dice if you have 2 or more die) It is usually a cube (3-‐D), It is marked with dots usually representing 1 through 6. Sometimes a die may have numerals. There are 6 sides or faces normally but have more. Difference It is a quantity (number or dimension) by which amounts differ. One quantity is bigger or smaller than another. You can find the difference by subtracting the smaller number from the bigger number. Example: 7 – 3 = 4 (The difference between 7 and 3 is 4.) Illinois STARNET Regions I & III • Center for Best Practices in Early Childhood Education Western Illinois University • 1 University Circle • Horrabin Hall 32 • Macomb, Illinois 61455 800-‐227-‐7537 • www.starnet.org Digit It is a single numeral. The numerals 0 through 9 are called digits. They make up other numbers. Examples: One-‐digit number is 7. Two-‐digit number is 38. Three-‐digit number is 129. Dimension It is a measure of size that includes length, width, and height. • One-‐dimensional (1-‐D) items have only length. Examples: Lines and curves • Two-‐dimensional (2-‐D) objects have length and width. Examples: Circles and polygons (squares, rhombus, etc. ) • Three-‐dimensional (3-‐D) objects have length, width, and height. Examples: Cubes and pyramids Note: A point (a dot) has no dimension. Direction The course that must be taken in order to reach a destination or a way to go. Examples: • Position/Location words – Left, right, up, down, above, below, inside, outside, near, forward, etc. • Compass Directions North, South, East, West, Northwest, Southeast, etc. Distance It is the length between two objects or two points. Distribute Give a share of something to each person or each set. Example: The teacher distributes the snack to the children. Division This is separating something into parts-‐-‐ equal and smaller groups. • Grouping Example: How many groups of 4 can be made with 12 crayons? The crayons are placed into equal groups of 4. 12 ÷ 4 = 3 Illinois STARNET Regions I & III • Center for Best Practices in Early Childhood Education Western Illinois University • 1 University Circle • Horrabin Hall 32 • Macomb, Illinois 61455 800-‐227-‐7537 • www.starnet.org Sharing A teacher has 12 crayons to give each child 4 crayons. How many children (groups) can she give crayons to? The crayons can be grouped into a groups of 3. 12 ÷ 4 = 3 The teacher has 4 groups of 3 crayons. Divisible Divisible means a number is divided by another number without a remainder.
54 ÷ 9 = 6 54 is divisible by 6 and by 9. Ellipse It is a curved shape that looks like a stretched-‐out circle. Example: a football Equal Symbol = (means equals or is equal to) • Quantity or amount is identical. • Items have the same value. • Sums that show the same amount in different ways. Equation It is a statement that has two amounts that are equal. On each side of the equal side are two sides that have to be the same or balanced . 2 + 3 = 5 3 + 1 = 2 + 2 Equilateral It is shape having all sides of equal length. Example: Equilateral triangle Equivalent Means having the same amount or value. Example: $5 bill is equivalent to $1 bill, $1 bill, $1 bill, $1bill, and $1 bill. Even number It is a number that is divisible by two. All even numbers end with 0, 2, 4, 6, or 8. •
Illinois STARNET Regions I & III • Center for Best Practices in Early Childhood Education Western Illinois University • 1 University Circle • Horrabin Hall 32 • Macomb, Illinois 61455 800-‐227-‐7537 • www.starnet.org Face Face is the flat side or part of the surface of a 3-‐D shape. First The first one is the one at the beginning or the one before any other item or number. Flip It means to turn over. (Geometry term) Examples: You flip a puzzle piece to fit. You flip a card to see other side. Fraction It is not a whole number. It is part of the whole number or quantity. Example: A large pizza is cut into 8 equal pieces. One piece would be ⅛. If you ate 3 pieces of the pizza. You ate ⅜ of the pizza. Gallon It is measure of volume. It is in the Imperial system. Geoboard A geoboard is usually a square board made of plastic or wood. It has pegs or nails that are equally spaced to form a grid. Rubber bands are placed on the geoboard to form shapes. Geometry It is an area of math that pertains to shapes, solids, lines, angles, and surfaces. Graph It is a diagram or drawing that shows information about different items. There are a variety of types of graphs. • Real Items Graph For young children, it is important to start with actual items on a graph (tablecloth with tape making a grid, large squares on a table or pad, a commercial graph, etc.). Example: Making a graph with different types of fruit such as apples, bananas, and oranges by using real fruit. (Not pictures or words) • Pictograph-‐ This type of graph uses photographs or pictures of real objects in place of the actual objects. Illinois STARNET Regions I & III • Center for Best Practices in Early Childhood Education Western Illinois University • 1 University Circle • Horrabin Hall 32 • Macomb, Illinois 61455 800-‐227-‐7537 • www.starnet.org •
Bar Graph This is a graph with horizontal or vertical bars or columns. This graph is more appropriate for older children. Example of horizontal bar graph: (from Google Images) Illinois STARNET Regions I & III • Center for Best Practices in Early Childhood Education Western Illinois University • 1 University Circle • Horrabin Hall 32 • Macomb, Illinois 61455 800-‐227-‐7537 • www.starnet.org Other types of graphs for older children circle (pie) graph, histogram, and line graph. Heptagon This is a 2-‐D shape with 7 sides and 7 angles. Hexagon This is a 2-‐D shape with 6 sides and 6 angles. This shape is one of the shapes in a set of pattern blocks. Horizontal Line This is a line that is parallel to the horizon or bottom of the page. Identical This means items are exactly alike. Imperial System The Imperial System is a system of measurements. It was originally developed in England. Examples: Length – inches, feet, yards, miles Weight – ounces, pounds Volume – fluid ounces, quarts, gallons Inch An inch is a measure of length. 12 inches = 1 foot Infinite This means without bounds of number or size. It is endless. Intersect This means lines cross each other. Illinois STARNET Regions I & III • Center for Best Practices in Early Childhood Education Western Illinois University • 1 University Circle • Horrabin Hall 32 • Macomb, Illinois 61455 800-‐227-‐7537 • www.starnet.org Length It is how long something is from each end. Less than ( < ) It is a number or item that is smaller than. 2 < 4 Two is less than 4 Line The line is a thin mark with only one dimension. Maximum This is the greatest or largest amount or value. Measure This is finding the amount, size, or degree of something. It can be done with standard and nonstandard measurement tools/items. Minimum It is the smallest amount or value. Minus ( -‐ ) It means to subtract or take away. Example: 10 minus 4 equals 6 or 10 – 4 = 6 Multiplication This is a way to add up many groups of the same number. Example: 3 groups of 4 * * * * * * * * * * * * 3 x 4 = 12 Not equal ( ≠ ) It stands for items or numbers that are not the same. It is also called unequal. 3 ≠ 1 Three is not equal to 1. Illinois STARNET Regions I & III • Center for Best Practices in Early Childhood Education Western Illinois University • 1 University Circle • Horrabin Hall 32 • Macomb, Illinois 61455 800-‐227-‐7537 • www.starnet.org Number Number is a quantity or amount. When children count items they will determine the number of items they have. Number line A number line is a picture of a straight line on which every point corresponds to a number. The numbers are space equally on the number line. Number sentence This is a sentence with numbers instead of words Examples of number sentence: 5 + 3 = 8 7 – 6 = 1 2 x 4 = 8 Numeral The numeral is actually a symbol that represents a number. 3 represents the number three such as 3 squares    Octagon This is a 2-‐D shape with 8 straight sides and 8 angles. Odd number This is a number that cannot be divided by 2. Odd numbers are 1, 3, 5, 7, and 9. Illinois STARNET Regions I & III • Center for Best Practices in Early Childhood Education Western Illinois University • 1 University Circle • Horrabin Hall 32 • Macomb, Illinois 61455 800-‐227-‐7537 • www.starnet.org One-‐dimensional • One-‐dimensional (1-‐D) items have only length. Examples: Lines and curves One-‐to-‐one (1-‐to-‐1) Correspondence This refers to a connection (correspondence) between two collections. It is the ability to match items either group to group or with a number such as counting 4 items. Placing an item next to another or on top of it. 
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 1 2 3 4 Touching an item and stating the number of that item when counting. Order Order refers to arranging items in a pattern or a sequence according to size or value. Example: Teddy bear counters are ordered from smallest to largest. Ordinal Number This is a number that tells the position of a person or object. Example: Five children in line to get on the bus. Tom is the first child to get on the bus. Joe is the second child to get on the bus. Mary is third to get on. Jose is the fourth one to get on, and Mary is the fifth child to get on the bus. Oval An oval is an egg-‐shaped figure. It has one end that is more pointed than the other end. It can also be an ellipse – like a football or race track. Pair A pair is two things that belong together such as a pair of socks or pair of gloves. Parallel Lines These lines never meet. Parallel lines always remain the same distance apart. Illinois STARNET Regions I & III • Center for Best Practices in Early Childhood Education Western Illinois University • 1 University Circle • Horrabin Hall 32 • Macomb, Illinois 61455 800-‐227-‐7537 • www.starnet.org Parallelogram It has opposite sides that are parallel. Opposite sides are the same length, and opposite angles are equal. Pattern It is a repeated arrangement or design. It can include shapes, colors, numbers, and various items. Example: Red square, blue square, red square, blue square, red square, blue square . . . Patterns are all around us in our world. (Stripes on fabric, rows of corn in a field, a painting, etc.) Pentagon It is a 2-‐D shape with five straight sides and five angles. Perpendicular It is lines that meet or intersect to make right angles. Polygon A 2-‐D shape that has 3 or more straight sides. Probability The chance of something or event happening. Illinois STARNET Regions I & III • Center for Best Practices in Early Childhood Education Western Illinois University • 1 University Circle • Horrabin Hall 32 • Macomb, Illinois 61455 800-‐227-‐7537 • www.starnet.org Problem It is a question that needs to be solved. Quantity It is the amount of something-‐ the number of something. Rectangle It is a 4-‐side flat shape with straight sides and 4 right angles. Rhombus It is a parallelogram with 4 equal sides and 2 pairs of equal angles. It is commonly called a diamond. Right Angle It is an angle that is exactly 90°. Rule It is an instruction to do something in a particular way. Example: Sort a tub of buttons by color. Illinois STARNET Regions I & III • Center for Best Practices in Early Childhood Education Western Illinois University • 1 University Circle • Horrabin Hall 32 • Macomb, Illinois 61455 800-‐227-‐7537 • www.starnet.org Same Two or more items that are exactly the same. They are identical or alike. Slide Change the position of the item. (Geometric Term) Example: When you slide a puzzle piece across the table but did not turn upside down. Solid It is a figure with all three dimensions – length, width, and height. Examples: Cubes, spheres, pyramids, cylinders Some A part of an object. It is not the whole item. 1 piece of pizza is some of the pizza. Sorting This is where objects are grouped by a certain way. (Size, shape, color, etc.) Spatial Orientation This is knowing where one is and how to move in the world. Children learn through their experiences with their own position and movements. Sphere A 3-‐D shape with curves and no corners. Example: A ball Square It is a 4-‐sided shape with 4 equal sides and 4 right angles. Illinois STARNET Regions I & III • Center for Best Practices in Early Childhood Education Western Illinois University • 1 University Circle • Horrabin Hall 32 • Macomb, Illinois 61455 800-‐227-‐7537 • www.starnet.org Children’s Books Relating to Math Concepts
Numbers
Counting:
Anno, Mitsumasa. Anno’s Counting Book. Crowell, 1975.
Aylesworth, Jim. One Crow A-Counting Book. Harper J. Publishing Co. 1990.
Bucknall, Caroline. One Bear All Alone. Dial, 1985.
Butler, Christina. Too Many Eggs: A Counting Book. David R. Godine Publishing, 1988.
Carle, Eric. 1, 2, 3 to the Zoo: A Counting Book. W. Collins & World Publishing, 1968.
Carle, Eric. Rooster’s Off to See the World. Simon & Schuster, 2002.
Carle, Eric. Ten Little Rubber Ducks. HarperCollins, 2005.
Carle, Eric. The Very Hungry Caterpillar. Putnam, 1986
Cave, Kathryn. One Child, One See: A South African Counting Book.
Clement, Rod. Counting on Frank. Gareth Stevens, 1991.
Crews, Donald. Ten Black Dots. Greenwillow Books, 1986.
Cristelow, Eileen. Five Little Monkeys Jumping on the Bed. Clarion Books. 1989.
Cristelow, Eileen. Don’t Wake Up Mama!. Trumpet Club, 1992.
Dee, Ruby, Two Ways to Count to Ten. Holt, 1988.
deRegniers, Beatrice Schenk. So Many Cats. Clarion Books, 1985.
Dijs, Carla. How Many Fingers? Pop-Up Book. Random House. 1994.
Dunbar, Joyce. Ten Little Mice. Harcourt Brace & Co., 1990.
Ehlert, Lois. Fish Eyes: A Book You Can Count On. Harcourt Brace & Co., 1990.
Galdone, Paul. Over in the Meadow. Prentice Hall, 1986.
Giganti, Paul. Each Orange Has Eight Slices. Greenwillow Books, 1992.
Giganti, Paul. How Many Snails? A Counting Book. Greenwillow Books, 1988.
Hague, Kathleen. Numbears. Henry Holt & Co., 1986.
Hoban, Tana. Count and See. MacMillan, 1972.
Hoban, Tana. 26 Letters and 99 Cents. Greenwillow Books, 1982.
Hutchins, Pat. The Doorbell Rang. Greenwillow Books, 1994.
Kitamura, Satashi. When Sheep Cannot Sleep: The Counting Book. Sunburst. 1986.
McMillan, Bruce. Counting Wildflowers. Lathrop, Lee & Shepard Books, 1986.
Miller, Jane. Farm Counting Book. Prentice Hall, 1984.
Mosel, Arlene. Tikki, Tikki, Tembo. Holt & Co., 1968 (original version).
Mosel, Arlene. Tikki, Tikki, Tembo. Square Fish Books, 2007.
Pallotta, Jerry. The Icky Bug Counting Book. Charlesbridge Publishing, 1992.
Ross, H. L. Not Counting Monsters. Platt & Munk, 1978.
Saul, Carol. Barn Cat. Little, Brown & Co., 2000.
Schade, Susan. The Noisy Counting Book. Random House, 1987.
Schiein, Miriam, More Than One. Greenwillow Books, 1996.
Schwartz, David. How Much Is a Million? Lorthrop, Lee & Shepard, 1985.
Wahl, John & Stacy. I Can Count the Petals of a Flower. NCTM, 1976.
Walsh, Ellen Stohl. Mouse Count. Harcourt Brace, 1991.
Walton, Rick. How Many, How Many, How Many. Candlewick, 1996.
Wildsmith, Brian. Brian Wildsmith’s 1, 2, 3’s. Franklin Watts, 1965.
Wood, Audrey & Don. Piggies. Harcourt Brace & Co., 1991.
Young, Ed. Seven Blind Mice. Philomel Books, 1992.
Addition:
Adams, Pam. (Illustrator). There Was an Old Lady Who Swallowed a Fly. Playspaces
International, 1973.
Balin, Lorna. Amelia’s Nine Lives. Abingdon Press, 1986.
Bogart, JoEllen. 10 for Dinner. Scholastic, 1989.
Boynton, Sandra. Hippos Go Berserk! Little Simon, 2000. (Board Book)
Brenner, Barbara. The Snow Parade. Crown, 1984.
Burningham, John. Pigs Plus. Viking Press. 1983.
Burningham, John. John Burningham’s 1, 2, 3. Crown, 1985.
Burningham, John. Hey! Get Off Our Train. Crown, 1990.
Carle, Eric. The Very Busy Spider. Putnam, 1984.
Carle, Eric. A House for Hermit Crab. Picture Books Studio, 1987.
de Paola, Tomie. Too Many Hopkins. Putnam, 1989.
de Regniers, Beatrice S. So Many Cats! Clarion, 1985.
Dubanevich, Arlene. Pigs in Hiding. Scholastic, 1983.
Ginsburg, Mirra. Mushroom in the Rain. MacMillan, 1974.
Gray, Catherine. One, Two, Three, and Four. No More? Houghton Mifflin, 1988.
Hellen, Nancy. Bus Stop. Orchard Books. 1988.
Hooper, Meredith. Seven Eggs. Harper & Row, 1985.
Kent, Jack. Twelve Days of Christmas. Scholastic, 1973.
Lewin, Betsy, Cat Count. Henry Holt & Co., 2003.
MacDonald, Elizabeth. Mike’s Kite. Orchard, 1990.
Morgan, Pierr (Illustrator). The Turnip. Putnam, 1996.
Owen, Annie. Annie’s One to Ten. Knopf, 1988.
Pomerantz, Charlotte. One Duck, Another Duck. Greenwillow, 1984.
Punnett, Dick. Count the Possums. Children’s Press, 1982.
Russell, Sandra. A Farmer’s Dozen. HarperCollins, 1982.
Sendak, Maurice. One Was Johnny. HarperCollins, 1991.
Silverstein, Shel. “Band-aids”. In Where the Sidewalk Ends. HarperCollins 1975.
Walsh, Ellen Stohl. Mouse Count. Harcourt Brace, 1991.
Wood, Audrey. The Napping House. Harcourt Brace, 1984.
Subtraction:
Asch, Frank. The Last Puppy. Prentice-Hall, 1980.
Barrett, Judi. What’s Left? Atheneum, 1983.
Bate, Lucy. Little Rabbit’s Loose Tooth. Crown, 1975.
Becker, John. Seven Little Rabbits. Walker Books, 2007.
Burningham, John. Mr. Grumpy’s Outing. Henry Holt & Co., 1995.
Burningham, John. The Shopping Basket. Crowell, 1980.
Cristelow, Eileen. Five Little Monkeys Jumping on the Bed. Clarion Books. 1989.
Cristelow, Eileen. Five Little Monkeys Sitting in a Tree. Clarion Books. 1989.
Coats, Laura. Ten Little Animals. MacMillan, 1990.
Dale, Penny. Ten in the Bed. Black Pursuit, 1988.
Dale, Penny. Ten Out of Bed. Candlewick Press, 1993.
Dunbar, Joyce. Ten Little Mice. Harcourt Brace, 1990.
Gerstein Mordicai. Roll Over! Crown, 1984.
Hawkins, Colin. Take Away Monsters. Putnam, 1984.
Hayes, Sarah. Nine Ducks Nine. Candlewick Press, 2008.
Kellogg, Steven. Much Bigger than Martin. Dial, 1976.
Leydenfrost, Robert. Ten Little Elephants. Doubleday, 1975.
Mack Stan. 10 Bears in My Bed: A Goodnight Countdown. Pantheon, 1974.
Mathews, Louise, The Great Take-away. Dodd Mead, 1980.
Peek, Merie. Roll Over! Clarion, 1981.
Raffi, Five Little Ducks. Crown, 1992.
Tafuri, Nancy. Have You Seen My Duckling? Greenwillow, 1984.
Thaler, Mike. Seven Little Hippos. Aladdin, 1994.
Viorst, Judith. Alexander Who Used to be Rich Last Sunday. Atheneum, 1978.
Wood, Audrey, Ten Little Fish. Blue Sky Press, 2004.
Measurement:
Base, Graeme. The Water Hole. Abrams, 2001.
Carter, David A. How Many Bugs in a Box? Simon & Schuster, 1988.
Jenkins, Steve. Actual Size. Houghton Mifflin, 2004.
Jenkins, Steve. Biggest, Strongest, Fastest. Sandpiper, 1997.
Leedy, Loreen. Measuring Penny. Henry Holt, 1997.
Lionni, Leo. Inch by Inch. Knopf Books, 2010.
McBratney, Sam. Guess How Much I Love You. Candlewick, 1995.
Miller, Margaret. Now I’m Big. Greenwillow, 1996. Myller, Rolf. How Big Is a Foot. Yearling, 1991.
Schwartz, David. If You Hopped Like a Frog. Scholastic Press, 1999.
Silverstein, Shel. "One Inch Tall" from Where the Sidewalk Ends. HarperCollins, 1974.
Silverstein, Shel. A Giraffe and a Half. HarperCollins, 1964.
Wells, Robert E. Is a Blue Whale the Biggest Thing There Is? Albert Whitman & Company,
1993.
Algebra:
Classification:
Aliki. Dinosaurs are Different. Crowell, 1985.
Carle, Eric. The Mixed-up Chameleon. Crowell, 1975.
Ehlert, Lois. Planting a Rainbow. Harcourt Brace & Co., 1988.
Giganti, Paul. How Many Snails? A Counting Book. Greenwillow Books, 1988.
Hoban, Tana. Is It Red? Is It Blue. Mulberry, 1978.
Hoban, Tana. Is It Rough? Is It Smooth? Is It Shiny? Greenwillow Books, 1984.
Hoban, Tana. A Children’s Zoo. Greenwillow Books, 1985.
Hoban, Tana. Dots, Freckles, and Stripes. Greenwillow Books, 1987.
Hoban, Tana. Of Colors and Things. Greenwillow Books, 1989.
Hoban, Tana. Exactly the Opposite Greenwillow Books, 1990.
Imershein, Betsy. Finding Red, Finding Yellow. Harcourt Brace & Co., 1989.
Konigsburg, E. L. Samuel Todd’s Book of Great Colors. Atheneum, 1990.
Lionni, Leo. A Color of his Own. Pantheon. 1975.
Lobel, Arnold. “ The Lost Button”. In Frog and Toad are Friend. Harper & Row, 1970.
Mayer, Mercer. Just a Mess. Western, 1987.
Morris, Ann. Bread, Bread, Bread. HarperCollins, 1993.
Morris, Ann. Hats, Hats, Hats. HarperCollins 1993.
Morris, Ann. Shoes, Shoes, Shoes. Mulberry Books, 1995.
Reid, Margaretta S. The Button Box. Dutton, 1990.
Roy, Ron. Whose Hat is That? Clarion, 1987.
Roy, Ron. Whose Shoes are These? Clarion, 1988.
Ruben, Patricia. What Is New? What Is Missing? What Is Different? Lippincott, 1978.
Scarry, Richard. Rabbit and His Friends. Western. 1973.
Selsam, Millicent. Benny’s Animals, and How He Put Them in Order. Harper & Row. 1966.
Sis, Peter. Beach Ball. Greenwillow, 1990.
Slobodkina, Esphyr. Caps for Sale. Scholastic, 1976.
Spier, Peter. People. Doubleday, 1990.
Spier, Peter. Fast-Slow, High-Low. Doubleday, 1988.
Tafuri, Nancy. Spots, Feathers adn Curly Tails. Greenwillow, 1988.
Thomson, Ruth. All About 1, 2, 3. Gareth Stevens, 1987.
Winthrop, Elizabeth. Shoes. Harper & Row, 1986.
Patterns:
Aardema, Verna. Why Mosquitoes Buzz in People’s Ears. Dial Books, 2008.
Harris, Trudy. Pattern Bugs. Millbrook Press, 2001.
Harris, Trudy. Pattern Fish. Millbrook Press, 2000.
Jocelyn, Marthe. Hannah’s Collections. Tundra Books, 2004.
Murphey, Stuart. A Pair of Socks. HarperCollins Publishers, 1999.
Slobodkima, Esphyr. Caps for Sale. HarperFestival, 1996.
Swinburne, Stephen R. Lots and Lots of Zebra Stripes: Patterns in Nature. Boyds Mill Press,
1998.
Growing Patterns:
Adams, Pam. (Illustrator). The House That Jack Built.
Carle, Eric. The Grouchy Ladybug.
Carle, Eric. The Very Hungry Caterpillar.
Carle, Eric. Rooster’s Off to See the World.
Parkinson, Kathy. The Enormous Turnip.
Wilson, Karma. A Frog in the Bog.
Wood, Audrey. The Napping House.
Geometry:
Burns, Marilyn. The Greedy Triangle. Scholastic Paperbacks, 2008.
Carle, Eric. Draw Me a Star. Putnam, 1998.
Chesanow, Neil. Where Do I Live? Barron’s Educational Series, 1995.
Dotlich, Rebecca Kai. What Is a Triangle? Scholastic, 2000.
Greene, Rhonda. When a Line Bends: A Shape Begins. Sandpiper, 2001.
Hartman, Gail. As the Crow Flies: A First Book of Maps. Aladdin, 1993.
Hoban, Tana. Cubes, Cones, Cylinders, & Spheres. Greenwillow Books. 2000.
Hoban, Tana. Over, Under and Through. Simon & Schuster, 1973.
Hoban, Tana. Shapes, Shapes, Shapes. Greenwillow Books, 1996.
Hoban, Tana. So Many Circles, So Many Squares. Greenwillow Books, 1998.
Micklethwait, Lucy. I Spy Shapes in Art. Greenwillow Books, 2004.
Pallotta, Jerry. Icky Bug Shapes. Scholastic, 2004.
The Metropolitan Museum of Art. Museum Shapes. Little, Brown & Co., 2005.
Walsh, Ellen Stohl. Mouse Shapes. Harcourt Inc., 2007.
Data Analysis/Probability:
Barrett, Judy. Cloudy With a Chance of Meatballs. Atheneum, 1978.
Nagda, Ann Whitehead & Cindy Bickel. Tiger Math: Learning to Graph from a Baby Tiger.
Henry Holt, 2000.
Stinson, Kathy. Red Is Best. Annick Press, 1998.
Tabback, Simms. There Was an Old Lady Who Swallowed a Fly. (prediction)
Tally It is a way of counting things by making a mark for each item. They are straight lines and the fifth mark crosses the 4 lines. This helps make it easy to count. Trapezoid It is a 4-‐sided shape with 2 sides being parallel and the other 2 sides are not parallel. Whole numbers Zero along with all counting numbers. (0, 1, 2, 3, 4….). Whole numbers do not include fractions or decimals. Width This means the measurement of an object from side to side. The width of the swimming pool is 15 feet. Zero ( 0 ) Zero means nothing but can also be a place holder in a numeral such as 20. 20 is 2 tens and 0 means no ones or single units. Illinois STARNET Regions I & III • Center for Best Practices in Early Childhood Education Western Illinois University • 1 University Circle • Horrabin Hall 32 • Macomb, Illinois 61455 800-‐227-‐7537 • www.starnet.org Data Analysis/Probability Activities Nursery Rhyme Game Pick a nursery rhyme that children are familiar with such as “Hickory Dickory Dock”. Have a graph with Possible and Impossible at the top. Go through the rhyme a line at a time and determine if it is possible or impossible. Such as “Hickory Dickory Dock the mouse ran up the clock.” Discuss with the children if it is possible for a mouse to run up the clock. If it is it will go under Possible. Continue through the rhyme. (Lines can be preprinted on paper to make it easier to place on graph. An example for Impossible is “The cow jumped over the moon.” Water Graph Materials: Two clear, plastic cups are labeled “YES” and “NO”. The teacher asks the class yes/no questions, and the children individually answerby using a turkey baster filled with colored water to place a drop in the appropriate cup. The water levels in the two cups are then compared to determine the most common answer. (This activity would be geared for 5 year-‐olds. Can also use an eye dropper.) For a greater challenge, the eye dropper can be used only for “NO” and the turkey baster is used for the “YES” answers. The children will quickly see that it is unfair to use both the eyedropper and the baster. This indicates a developing understanding of the importance of a consistent unit of measurement. -‐The Young Child and Mathematics Photos on Sticks for Graphing Take photos of children –entire body-‐ and cut around the photo. Then place the photo on metal clip. The clip can them be stood up so it appears as a miniature child is standing. These can be used for graphing in place of actual children. Can also be used in an ice cube tray. where we STAND
naeyc
and
nctm
on early childhood mathematics
T
o succeed in school and in life, young children need
a strong foundation in mathematics. Yet U.S. children’s
mathematical proficiency is far below that of many other countries, and the mathematics gap is widest for
children living in poverty and those who are members
of ethnic, cultural, and linguistic minority groups.
Early childhood is the place to start addressing the mathematics achievement gap: Preschoolers
already enjoy and are keenly interested in the mathematical aspects of their everyday world. Families
and early childhood programs can play a crucial part
in nurturing these interests. Drawing on the latest
research, the National Association for the Education
of Young Children (NAEYC) and the National Council of Teachers of Mathematics (NCTM) have come
together with a joint position statement: Early Childhood Mathematics: Promoting Good Beginnings.
NAEYC and NCTM take the position that all young
children should experience high-quality, challenging,
and accessible mathematics experiences. They make
specific recommendations to guide curriculum and
teaching practices in programs for 3- to 6-year-old
children, and they recommend actions for policies,
systems changes, and other steps needed to support
high-quality mathematics education.
2. build on children’s varying experiences, including their family, linguistic, and cultural backgrounds;
their individual approaches to learning; and their
informal knowledge
Recommendations
9. actively introduce mathematical concepts, methods, and language through a range of appropriate
experiences and teaching strategies
In high-quality mathematics education for 3- to
6-year-old children, teachers and other key professionals should . . .
1. enhance children’s natural interest in mathematics
and their disposition to use it to make sense of their
physical and social worlds
3. base mathematics curriculum and teaching practices on current knowledge of young children’s
cognitive, linguistic, physical, and social-emotional
development
4. use curriculum and teaching practices that
strengthen children’s problem-solving and reasoning
processes as well as representing, communicating,
and connecting mathematical ideas
5. ensure that the curriculum is coherent and compatible with known relationships and sequences of
important mathematical ideas
6. provide for children’s deep and sustained interaction with mathematical ideas
7. integrate mathematics with other activities and
other activities with mathematics
8. provide ample time, materials, and teacher support
for children to engage in play, a context in which they
explore and manipulate mathematical ideas with keen
interest
10. support children’s learning by thoughtfully and
continually assessing all children’s mathematical
knowledge, skills, and strategies
National Association for the Education of Young Children and
National Council of Teachers of Mathematics
To support high-quality mathematics education,
institutions, program developers, and policymakers
should . . .
1. create more effective early childhood teacher
preparation and continuing professional development
in mathematics
2. use collaborative processes to develop well aligned
systems of appropriate, high-quality standards, mathematics curriculum, and assessment
3. design institutional structures and policies that
support teachers’ mathematics learning, teamwork,
and planning
4. provide resources necessary to overcome the barriers to young children’s mathematical proficiency at
the classroom, community, institutional, and systemwide levels
A positive attitude toward mathematics and a
strong foundation for mathematics learning begin
in early childhood. Working together, educators,
administrators, policymakers and families can raise
awareness about the importance of early childhood
mathematics, inform others about sound approaches
to mathematical teaching and learning, and develop
resources that support high-quality, equitable mathematical experiences for all young children.
The complete position statement, with research
and references, is available online at www.naeyc.org/
positionstatements/mathematics
Beyond Early Childhood Mathematics:
What Else Matters?
Learn more about…
• early learning standards, as described in NAEYC
and NAECS/SDE’s 2002 position statement, online at
www.naeyc.org/positionstatements/learning_standards.
• teaching strategies and other elements of developmentally appropriate practice. See C. Copple &
S. Bredekamp (eds.), Developmentally Appropriate
Practice in Early Childhood Programs Serving Children
from Birth through Age 8, 3d ed., Washington, DC:
NAEYC, 2009. Access the position statement online
at www.naeyc.org/positionstatements/dap.
• standards for early childhood programs and accreditation performance criteria, online at www.
naeyc.org/academy/primary/standardsintro.
• standards for early childhood professional preparation programs as updated by NAEYC in 2009, online
at www.naeyc.org/positionstatements/ppp.
• implementation of professional standards. See M.
Hyson (ed.), Preparing Early Childhood Professionals:
NAEYC’s Standards for Programs, Washington, DC:
NAEYC, 2003.
The National Research Council and Early Childhood Mathematics
Affirming the critical need for improved mathematics
education in early childhood, in 2009 the National Research Council released a report summarizing the evidence and making key recommendations for practice,
policy, and research. The report’s recommendations
strongly align with those in the NAEYC/NCTM position
statement.
“Providing young children with extensive, high-quality
early mathematics instruction can serve as a sound
foundation for later learning in mathematics and contribute to addressing long-term systemic inequities in
educational outcomes” (Cross, Woods, & Schweingruber
2009, 2).
Cross, C.T., T.A. Woods, & H. Schweingruber (eds.); Committee
on Early Childhood Mathematics; National Research Council.
(2009). Mathematics learning in early childhood: Paths toward
excellence and equity. Washington, DC: National Academies
Press. Online: www.nap.edu/catalog.php?record_id=12519.
where we STAND
naeyc
and
nctm
Copyright © 2009 by the National Association for the Education of Young Children. All rights reserved.
POSITION STATEMENT
Early Childhood Mathematics:
Promoting Good Beginnings
A joint position statement of the National Association for the Education of Young Children (NAEYC)
and the National Council of Teachers of Mathematics (NCTM). Adopted in 2002. Updated in 2010.
Position
solid foundation for success in school. In elementary and middle school, children need mathematical understanding and skills not only in math
courses but also in science, social studies, and
other subjects. In high school, students need
mathematical proficiency to succeed in course
work that provides a gateway to technological
literacy and higher education [1–4]. Once out
of school, all adults need a broad range of basic
mathematical understanding to make informed
decisions in their jobs, households, communities,
and civic lives.
Besides ensuring a sound mathematical
foundation for all members of our society, the
nation also needs to prepare increasing numbers
of young people for work that requires a higher
proficiency level [5, 6]. The National Commission
on Mathematics and Science Teaching for the
21st Century (known as the Glenn Commission)
asks this question: “As our children move toward
the day when their decisions will be the ones
shaping a new America, will they be equipped
with the mathematical and scientific tools needed
to meet those challenges and capitalize on those
opportunities?” [7, p. 6]
The National Council of Teachers of Mathematics (NCTM) and the National Association for the
Education of Young Children (NAEYC) affirm that
high-quality, challenging, and accessible mathematics education for 3- to 6-year-old children is a
vital foundation for future mathematics learning.
In every early childhood setting, children should
experience effective, research-based curriculum
and teaching practices. Such high-quality classroom practice requires policies, organizational
supports, and adequate resources that enable
teachers to do this challenging and important
work.
The challenges
Throughout the early years of life, children notice
and explore mathematical dimensions of their
world. They compare quantities, find patterns,
navigate in space, and grapple with real problems
such as balancing a tall block building or sharing
a bowl of crackers fairly with a playmate. Mathematics helps children make sense of their world
outside of school and helps them construct a
Copyright © 2002 National Association for the Education of Young Children
1
Early Childhood Mathematics
Since the 1970s a series of assessments of
U.S. students’ performance has revealed an overall level of mathematical proficiency well below
what is desired and needed [5, 8, 9]. In recent
years NCTM and others have addressed these
challenges with new standards and other resources to improve mathematics education, and
progress has been made at the elementary and
middle school levels—especially in schools that
have instituted reforms [e.g., 10–12]. Yet achievement in mathematics and other areas varies
widely from state to state [13] and from school
district to school district. There are many encouraging indicators of success but also areas of
continuing concern. In mathematics as in
literacy, children who live in poverty and who are
members of linguistic and ethnic minority groups
demonstrate significantly lower levels of achievement [14–17].
If progress in improving the mathematics
proficiency of Americans is to continue, much
greater attention must be given to early mathematics experiences. Such increased awareness
and effort recently have occurred with respect to
early foundations of literacy. Similarly, increased
energy, time, and wide-scale commitment to the
early years will generate significant progress in
mathematics learning.
The opportunity is clear: Millions of young
children are in child care or other early education settings where they can have significant
early mathematical experiences. Accumulating
research on children’s capacities and learning
in the first six years of life confirms that early
experiences have long-lasting outcomes [14, 18].
Although our knowledge is still far from complete, we now have a fuller picture of the mathematics young children are able to acquire and
the practices to promote their understanding.
This knowledge, however, is not yet in the hands
of most early childhood teachers in a form to effectively guide their teaching. It is not surprising
then that a great many early childhood programs
have a considerable distance to go to achieve
high-quality mathematics education for children
age 3-6.
In 2000, with the growing evidence that the
early years significantly affect mathematics learning and attitudes, NCTM for the first time included the prekindergarten year in its Principles and
Standards for School Mathematics (PSSM) [19].
Guided by six overarching principles—regarding
equity, curriculum, teaching, learning, assessment, and technology—PSSM describes for each
mathematics content and process area what children should be able to do from prekindergarten
through second grade.
NCTM Principles for School
Mathematics
Equity: Excellence in mathematics education
requires equally high expectations and
strong support for all students.
Curriculum: A curriculum is more than a collection of activities; it must be coherent,
focused on important mathematics, and well
articulated across the grades.
Teaching: Effective mathematics teaching requires understanding of what students know
and need to learn and then challenging and
supporting them to learn it well.
Learning: Students must learn mathematics
with understanding, actively building new
knowledge from experience and prior knowledge.
Assessment: Assessment should support the
learning of important mathematics and furnish useful information to both teachers and
students.
Technology: Technology is essential to teaching and learning mathematics; it influences
the mathematics that is taught and enhances
students’ learning.
Note: These principles are relevant across all
grade levels, including early childhood.
The present statement focuses on children
over 3, in large part because the knowledge
base on mathematical learning is more robust
for this age group. Available evidence, however,
2
NAEYC/NCTM Joint Position Statement
indicates that children under 3 enjoy and benefit
from various kinds of mathematical explorations
and experiences. With respect to mathematics
education beyond age 6, the recommendations
on classroom practice presented here remain
relevant. Further, closely connecting curriculum
and teaching for children age 3–6 with what is
done with students over 6 is essential to achieve
the seamless mathematics education that children need.
Recognition of the importance of good beginnings, shared by NCTM and NAEYC, underlies
this joint position statement. The statement describes what constitutes high-quality mathematics education for children 3–6 and what is necessary to achieve such quality. To help achieve
this goal, the position statement sets forth 10
research-based, essential recommendations to
guide classroom1 practice, as well as four recommendations for policies, systems changes, and
other actions needed to support these practices.
8. provide ample time, materials, and teacher
support for children to engage in play, a
context in which they explore and manipulate
mathematical ideas with keen interest
In high-quality mathematics education
for 3- to 6-year-old children, teachers and
other key professionals should
1. enhance children’s natural interest in mathematics and their disposition to use it to make
sense of their physical and social worlds
9. actively introduce mathematical concepts,
methods, and language through a range of appropriate experiences and teaching strategies
2. build on children’s experience and knowledge, including their family, linguistic, cultural,
and community backgrounds; their individual
approaches to learning; and their informalknowledge
10. support children’s learning by thoughtfully
and continually assessing all children’s mathematical knowledge, skills, and strategies.
To support high quality mathematics education, institutions, program developers,
and policy makers should
3. base mathematics curriculum and teaching
practices on knowledge of young children’s
cognitive, linguistic, physical, and socialemotional development
1. create more effective early childhood teacher preparation and continuing professional
development
4. use curriculum and teaching practices that
strengthen children’s problem-solving and
reasoning processes as well as representing,
communicating, and connecting mathematical
ideas
2. use collaborative processes to develop well
aligned systems of appropriate high-quality
standards, curriculum, and assessment
5. ensure that the curriculum is coherent and
compatible with known relationships and sequences of important mathematical ideas
3. design institutional structures and policies
that support teachers’ ongoing learning, teamwork, and planning
6. provide for children’s deep and sustained
interaction with key mathematical ideas
4. provide resources necessary to overcome
the barriers to young children’s mathematical
proficiency at the classroom, community, institutional, and system-wide levels.
7. integrate mathematics with other activities
and other activities with mathematics
1
Classroom refers to any group setting for 3- to 6-year-olds
(e.g., child care program, family child care, preschool, or
public school classroom).
3
Recommendations
2. Build on children’s experience and knowledge, including their family, linguistic,
cultural, and community backgrounds;
their individual approaches to learning;
and their informal knowledge.
Within the classroom
To achieve high-quality mathematics education for 3- to 6-year-old children, teachers2 and other key professionals should
Recognizing and building on children’s individual experiences and knowledge are central to
effective early childhood mathematics education [e.g., 20, 22, 29, 30]. While striking similarities are evident in the mathematical issues that
interest children of different backgrounds [31],
it is also true that young children have varying
cultural, linguistic, home, and community experiences on which to build mathematics learning
[16, 32]. For example, number naming is regular
in Asian languages such as Korean (the Korean
word for “eleven” is ship ill, or “ten one”), while
English uses the irregular word eleven. This
difference appears to make it easier for Korean
children to learn or construct certain numerical concepts [33, 34]. To achieve equity and
educational effectiveness, teachers must know
as much as they can about such differences
and work to build bridges between children’s
varying experiences and new learning [35–37].
1. Enhance children’s natural interest in
mathematics and their disposition to use it
to make sense of their physical and social
worlds.
Young children show a natural interest in and
enjoyment of mathematics. Research evidence
indicates that long before entering school children spontaneously explore and use mathematics—at least the intuitive beginnings—and their
mathematical knowledge can be quite complex
and sophisticated [20]. In play and daily activities, children often explore mathematical ideas
and processes; for example, they sort and classify, compare quantities, and notice shapes and
patterns [21–27].
Mathematics helps children make sense of the
physical and social worlds around them, and
children are naturally inclined to use mathematics in this way (“He has more than I do!”
“That won’t fit in there—it’s too big”). By capitalizing on such moments and by carefully planning a variety of experiences with mathematical ideas in mind, teachers cultivate and extend
children’s mathematical sense and interest.
In mathematics, as in any knowledge domain,
learners benefit from having a variety of ways
to understand a given concept [5, 14]. Building
on children’s individual strengths and learning styles makes mathematics curriculum and
instruction more effective. For example, some
children learn especially well when instructional materials and strategies use geometry to
convey number concepts [38].
Because young children’s experiences fundamentally shape their attitude toward
mathematics, an engaging and encouraging
climate for children’s early encounters with
mathematics is important [19]. It is vital for
young children to develop confidence in their
ability to understand and use mathematics—
in other words, to see mathematics as within
their reach. In addition, positive experiences
with using mathematics to solve problems
help children to develop dispositions such as
curiosity, imagination, flexibility, inventiveness,
and persistence that contribute to their future
success in and out of school [28].
Children’s confidence, competence, and interest in mathematics flourish when new experiences are meaningful and connected with
their prior knowledge and experience [19, 39].
At first, young children’s understanding of a
mathematical concept is only intuitive. Lack of
explicit concepts sometimes prevents the child
from making full use of prior knowledge and
connecting it to school mathematics. Therefore, teachers need to find out what young
children already understand and help them
begin to understand these things mathematical-
2
Teachers refers to adults who care for and educate
groups of young children.
4
opment and her sensitivity to the individual
child’s frustration tolerance and persistence
[45, 46].
ly. From ages 3 through 6, children need many
experiences that call on them to relate their
knowledge to the vocabulary and conceptual
frameworks of mathematics—in other words,
to “mathematize” what they intuitively grasp.
Toward this end, effective early childhood
programs provide many such opportunities
for children to represent, reinvent, reorganize,
quantify, abstract, generalize, and refine that
which they grasp at an experiential or intuitive
level [28].
For some mathematical topics, researchers have
identified a developmental continuum or learning path—a sequence indicating how particular
concepts and skills build on others [44, 47, 48].
Snapshots taken from a few such sequences are
given in the accompanying chart (pp. 19–21).
Research-based generalizations about what
many children in a given grade or age range can
do or understand are key in shaping curriculum
and instruction, although they are only a starting point. Even with comparable learning opportunities, some children will grasp a concept
earlier and others somewhat later. Expecting
and planning for such individual variation are
always important.
3. Base mathematics curriculum and teaching
practices on knowledge of young children’s
cognitive, linguistic, physical, and socialemotional development.
All decisions regarding mathematics curriculum and teaching practices should be grounded
in knowledge of children’s development and
learning across all interrelated areas—cognitive, linguistic, physical, and social-emotional.
First, teachers need broad knowledge of
children’s cognitive development—concept
development, reasoning, and problem solving,
for instance—as well as their acquisition of
particular mathematical skills and concepts.
Although children display mathematical ideas
at early ages [e.g., 40–43] their ideas are often
very different from those of adults [e.g., 26, 44].
For example, young children tend to believe
that a long line of pennies has more coins than
a shorter line with the same number.
With the enormous variability in young children’s development, neither policymakers nor
teachers should set a fixed timeline for children
to reach each specific learning objective [49].
In addition to the risk of misclassifying individual children, highly specific timetables for
skill acquisition pose another serious threat,
especially when accountability pressures are
intense. They tend to focus teachers’ attention
on getting children to perform narrowly defined
skills by a specified time, rather than on laying
the conceptual groundwork that will serve
children well in the long run. Such prescriptions often lead to superficial teaching and rote
learning at the expense of real understanding.
Under these conditions, children may develop
only a shaky foundation for further mathematics learning [50–52].
Beyond cognitive development, teachers need
to be familiar with young children’s social, emotional, and motor development, all of which
are relevant to mathematical development.
To determine which puzzles and manipulative
materials are helpful to support mathematical
learning, for instance, teachers combine their
knowledge of children’s cognition with the
knowledge of fine7 motor development [45].
In deciding whether to let a 4-year-old struggle
with a particular mathematical problem or to
offer a clue, the teacher draws on more than
an understanding of the cognitive demands involved. Important too are the teacher’s understanding of young children’s emotional devel-
4. Use curriculum and teaching practices that
strengthen children’s problem-solving and
reasoning processes as well as representing, communicating, and connecting mathematical ideas.
Problem solving and reasoning are the heart of
mathematics. Teaching that promotes proficiency in these and other mathematical processes is consistent with national reports on
5
The big ideas or vital understandings in early
childhood mathematics are those that are
mathematically central, accessible to children
at their present level of understanding, and
generative of future learning [28]. Research and
expert practice indicate that certain concepts
and skills are both challenging and accessible
to young children [19]. National professional
standards outline core ideas in each of five
major content areas: number and operations,
geometry, measurement, algebra (including patterns), and data analysis [19]. For example, the
idea that the same pattern can describe different situations is a “big idea” within the content
area of algebra and patterning.
mathematics education [5, 19, 53] and recommendations for early childhood practice [14,
46]. While content represents the what of early
childhood mathematics education, the processes—problem solving, reasoning, communication, connections, and representation—make it
possible for children to acquire content know
edge [19]. These processes develop over time
and when supported by well designed opportunities to learn.
Children’s development and use of these
processes are among the most longlasting and
important achievements of mathematics education. Experiences and intuitive ideas become
truly mathematical as the children reflect on
them, represent them in various ways, and connect them to other ideas [19, 47].
These content areas and their related big ideas,
however, are just a starting point. Where does
one begin to build understanding of an idea
such as “counting” or “symmetry,” and where
does one take this understanding over the
early years of school? Articulating goals and
standards for young children as a developmental or learning continuum is a particularly
useful strategy in ensuring engagement with
and mastery of important mathematical ideas
[49]. In the key areas of mathematics, researchers have at least begun to map out trajectories
or paths of learning—that is, the sequence in
which young children develop mathematical
understanding and skills [21, 58, 59]. The accompanying chart provides brief examples of
learning paths in each content area and a few
teaching strategies that promote children’s
progress along these paths. Information about
such learning paths can support developmentally appropriate teaching, illuminating various
avenues to understanding and guiding teachers
in providing activities appropriate for children
as individuals and as a group.
The process of making connections deserves
special attention. When children connect
number to geometry (for example, by counting the sides of shapes, using arrays to understand number combinations, or measuring the
length of their classroom), they strengthen
concepts from both areas and build knowledge
and beliefs about mathematics as a coherent
system [19, 47]. Similarly, helping children connect mathematics to other subjects, such as
science, develops knowledge of both subjects
as well as knowledge of the wide applicability
of mathematics. Finally and critically, teaching
concepts and skills in a connected, integrated
fashion tends to be particularly effective not
only in the early childhood years [14, 23] but
also in future learning [5, 54].
5. Ensure that the curriculum is coherent
and compatible with known relationships
and sequences of important mathematical
ideas.
In developing early mathematics curriculum,
teachers need to be alert to children’s experiences, ideas, and creations [55, 56]. To create
coherence and power in the curriculum, however, teachers also must stay focused on the
“big ideas” of mathematics and on the connections and sequences among those ideas
[23, 57].
6. Provide for children’s deep and sustained
interaction with key mathematical ideas.
In many early childhood programs, mathematics makes only fleeting, random appearances.
Other programs give mathematics adequate
time in the curriculum but attempt to cover
so many mathematical topics that the result
6
is superficial and uninteresting to children.
In a more effective third alternative, children
encounter concepts in depth and in a logical
sequence. Such depth and coherence allow
children to develop, construct, test, and reflect
on their mathematical understandings [10,
23, 59, 60]. This alternative also enhances
teachers’ opportunities to determine gaps in
children’s understanding and to take time to
address these.
7. Integrate mathematics with other activities
and other activities with mathematics.
Young children do not perceive their world as if
it were divided into separate cubbyholes such
as “mathematics” or “literacy” [61]. Likewise,
effective practice does not limit mathematics
to one specified period or time of day. Rather,
early childhood teachers help children develop
mathematical knowledge throughout the day
and across the curriculum. Children’s everyday
activities and routines can be used to introduce
and develop important mathematical ideas [55,
59, 60, 62–67]. For example, when children are
lining up, teachers can build in many opportunities to develop an understanding of mathematics. Children wearing something red can be
asked to get in line first, those wearing blue to
get in line second, and so on. Or children wearing both something red and sneakers can be
asked to head up the line. Such opportunities
to build important mathematical vocabulary
and concepts abound in any classroom, and
the alert teacher takes full advantage of them.
Because curriculum depth and coherence
are important, unplanned experiences with
mathematics are clearly not enough. Effective
programs also include intentionally organized
learning experiences that build children’s
understanding over time. Thus, early childhood
educators need to plan for children’s in-depth
involvement with mathematical ideas, including helping families extend and develop these
ideas outside of school.
Depth is best achieved when the program focuses on a number of key content areas rather
than trying to cover every topic or skill with
equal weight. As articulated in professional
standards, researchers have identified number
and operations, geometry, and measurement
as areas particularly important for 3- to 6-yearolds [19]. These play an especially significant
role in building the foundation for mathematics learning [47]. For this reason, researchers
recommend that algebraic thinking and data
analysis/probability receive somewhat less
emphasis in the early years. The beginnings of
ideas in these two areas, however, should be
woven into the curriculum where they fit most
naturally and seem most likely to promote
understanding of the other topic areas [19].
Within this second tier of content areas, patterning (a component of algebra) merits special
mention because it is accessible and interesting
to young children, grows to undergird all algebraic thinking, and supports the development
of number, spatial sense, and other conceptual
areas.
Also important is weaving mathematics into
children’s experiences with literature, language,
science, social studies, art, movement, music,
and all parts of the classroom environment. For
example, there are books with mathematical
concepts in the reading corner, and clipboards
and wall charts are placed where children are
engaged in science observation and recording (e.g., measuring and charting the weekly
growth of plants) [65, 66, 68–71]. Projects
also reach across subject-matter boundaries.
Extended investigations offer children excellent opportunities to apply mathematics as well
as to develop independence, persistence, and
flexibility in making sense of real-life problems
[19]. When children pursue a project or investigation, they encounter many mathematical
problems and questions. With teacher guidance, children think about how to gather and
record information and develop representations to help them in understanding and using
the information and communicating their work
to others [19, 72].
7
have emerged in their play. Teachers enhance
children’s mathematics learning when they ask
questions that provoke clarifications, extensions, and development of new understandings
[19].
Another rationale for integrating mathematics
throughout the day lies in easing competition
for time in an increasingly crowded curriculum.
Heightened attention to literacy is vital but can
make it difficult for teachers to give mathematics and other areas their due. With a strong
interdisciplinary curriculum, teachers can still
focus on one area at times but also find ways
to promote children’s competence in literacy,
mathematics, and other subjects within integrated learning experiences [73].
Block building offers one example of play’s
value for mathematical learning. As children
build with blocks, they constantly accumulate
experiences with the ways in which objects
can be related, and these experiences become
the foundation for a multitude of mathematical
concepts—far beyond simply sorting and seriating. Classic unit blocks and other construction materials such as connecting blocks give
children entry into a world where objects have
predictable similarities and relationships [66,
76]. With these materials, children reproduce
objects and structures from their daily lives
and create abstract designs by manipulating
pattern, symmetry, and other elements [77].
Children perceive geometric notions inherent
in the blocks (such as two square blocks as the
equivalent of one rectangular unit block) and
the structures they build with them (such as
symmetric buildings with parallel sides). Over
time, children can be guided from an intuitive
to a more explicit conceptual understanding of
these ideas [66].
An important final note: As valuable as integration is within early childhood curriculum, it
is not an end in itself. Teachers should ensure
that the mathematics experiences woven
throughout the curriculum follow logical
sequences, allow depth and focus, and help
children move forward in knowledge and skills.
The curriculum should not become, in the
name of integration, a grab bag of any mathematics-related experiences that seem to relate
to a theme or project. Rather, concepts should
be developed in a coherent, planful manner.
8. Provide ample time, materials, and teacher
support for children to engage in play, a
context in which they explore and manipulate mathematical ideas with keen interest.
Children become intensely engaged in play.
Pursuing their own purposes, they tend to tackle problems that are challenging enough to be
engrossing yet not totally beyond their capacities. Sticking with a problem—puzzling over it
and approaching it in various ways—can lead
to powerful learning. In addition, when several children grapple with the same problem,
they often come up with different approaches,
discuss, and learn from one another [74, 75].
These aspects of play tend to prompt and promote thinking and learning in mathematics and
in other areas.
A similar progression from intuitive to explicit
knowledge takes place in other kinds of play.
Accordingly, early childhood programs should
furnish materials and sustained periods of
time that allow children to learn mathematics through playful activities that encourage
counting, measuring, constructing with blocks,
playing board and card games, and engaging in
dramatic play, music, and art [19, 64].
Finally, the teacher can observe play to learn
more about children’s development and interests and use this knowledge to inform curriculum and instruction. With teacher guidance, an
individual child’s play interest can develop into
a classroom-wide, extended investigation or
project that includes rich mathematical learning [78–82]. In classrooms in which teachers
are alert to all these possibilities, children’s
Play does not guarantee mathematical development, but it offers rich possibilities. Significant
benefits are more likely when teachers follow up by engaging children in reflecting on
and representing the mathematical ideas that
8
game more mathematically powerful and more
appropriate for children of differing developmental levels [55, 83].
play continually stimulates and enriches mathematical explorations and learning.
9. Actively introduce mathematical concepts,
methods, and language through a range
of appropriate experiences and teaching
strategies.
Use of materials also requires intentional planning and involvement on the teacher’s part.
Computer technology is a good example [84].
Teachers need to intentionally select and use
research-based computer tools that complement and expand what can be done with other
media [59]. As with other instructional materials, choosing software and determining how
best to incorporate computer use in the day-today curriculum requires thoughtful, informed
decision-making in order for children’s learning
experiences to be rich and productive.
A central theme of this position statement is
that early childhood curriculum needs to go
beyond sporadic, hit-or-miss mathematics. In
effective programs, teachers make judicious
use of a variety of approaches, strategies, and
materials to support children’s interest and
ability in mathematics.
Besides embedding significant mathematics learning in play, classroom routines, and
learning experiences across the curriculum, an
effective early mathematics program also provides carefully planned experiences that focus
children’s attention on a particular mathematical idea or set of related ideas. Helping children
name such ideas as horizontal or even and odd
as they find and create many examples of these
categories provides children with a means to
connect and refer to their just-emerging ideas
[35, 37]. Such concepts can be introduced and
explored in large- and small-group activities
and learning centers. Small groups are particularly well suited to focusing children’s attention
on an idea. Moreover, in this setting the teacher
is able to observe what each child does and
does not understand and engage each child in
the learning experience at his own level.
In short, mathematics is too important to be
left to chance, and yet it must also be connected to children’s lives. In making all of these
choices, effective early childhood teachers
build on children’s informal mathematical
knowledge and experiences, always taking children’s cultural background and language into
consideration [23].
10. Support children’s learning by thoughtfully and continually assessing all children’s
mathematical knowledge, skills, and strategies.
Assessment is crucial to effective teaching
[85]. Early childhood mathematics assessment is most useful when it aims to help young
children by identifying their unique strengths
and needs so as to inform teacher planning.
Beginning with careful observation, assessment
uses multiple sources of information gathered systematically over time—for example, a
classroom book documenting the graphs made
by children over several weeks. Mathematics
assessment should follow widely accepted principles for varied and authentic early childhood
assessment [85]. For instance, the teacher
needs to use multiple assessment approaches
to find out what each child understands—and
may misunderstand. Child observation, documentation of children’s talk, interviews, collections of children’s work over time, and the use
In planning for new investigations and activities, teachers should think of ways to engage
children in revisiting concepts they have
previously explored. Such experiences enable
children to forge links between previously
encountered mathematical ideas and new applications [19].
Even the way that teachers introduce and
modify games can promote important mathematical concepts and provide opportunities for
children to practice skills [55, 57]. For example,
teachers can modify any simple board game in
which players move along a path to make the
9
of open-ended questions and appropriate performance assessments to illuminate children’s
thinking are positive approaches to assessing
mathematical strengths and needs [86, 87].
and ongoing professional development is an
urgent priority. In mathematics, as in literacy
and other areas, the challenges are formidable,
but research-based solutions are available [14,
92–95]. To support children’s mathematical
proficiency, every early childhood teacher’s
professional preparation should include these
connected components: (1) knowledge of the
mathematical content and concepts most
relevant for young children—including in-depth
understanding of what children are learning
now and how today’s learning points toward
the horizons of later learning [5]; (2) knowledge
of young children’s learning and development
in all areas—including but not limited to cognitive development—and knowledge of the issues
and topics that may engage children at different points in their development; (3) knowledge
of effective ways of teaching mathematics to
all young learners; (4) knowledge and skill in
observing and documenting young children’s
mathematical activities and understanding;
and (5) knowledge of resources and tools that
promote mathematical competence and enjoyment [96].
Careful assessment is especially important
when planning for ethnically, culturally, and linguistically diverse young children and for children with special needs or disabilities. Effective
teachers use information and insights gathered
from assessment to plan and adapt teaching
and curriculum. They recognize that even
young children invent their own mathematical
ideas and strategies and that children’s ideas
can be quite different from those of adults [44].
They interpret what the child is doing and
thinking, and they attempt to see the situation
from the child’s point of view. With this basis
in thoughtful assessment, teachers are able to
make informed decisions about what the child
might be able to learn from new experiences.
Reliance on a single group-administered test to
document 3- to 6-year-old children’s mathematical competence is counter to expert recommendations on assessment of young children
[85, 88–91]. Educators must take care that assessment does not narrow the curriculum and
inappropriately label children. If assessment
results exclude some children from challenging
learning activities, they undercut educational
equity. Teachers and education policy makers
need to stay in control of the assessment process, ensuring that it helps build mathematical
competence and confidence. Well conceived,
well implemented, continuous assessment is an
indispensable tool in facilitating all children’s
engagement and success in mathematics.
Essential as this knowledge is, it can be
brought to life only when teachers themselves
have positive attitudes about mathematics.
Lack of appropriate preparation may cause
both preservice and experienced teachers to
fail to see mathematics as a priority for young
children and to lack confidence in their ability
to teach mathematics effectively [97]. Thus,
both preservice education and continuing
professional development experiences need to
place greater emphasis on encouraging teachers’ own enjoyment and confidence, building
positive mathematical attitudes and dispositions.
Beyond the classroom
To support excellent early mathematics
education, institutions, program developers, and policy makers should
Even graduates of four-year early childhood
programs with state licensure usually lack
adequate preparation in mathematics. State
legislatures often address their concern over
teachers’ weak background in mathematics by
simply increasing the number of required mathematics courses needed for teacher licensure.
1. Create more effective early childhood
teacher preparation and continuing professional development.
Improving early childhood teacher preparation
10
ticipation of staff who work in similar settings;
content focused both on what and how to
teach; active learning techniques; and professional development as part of a coherent program of teacher learning [5, 99]. Innovative and
effective professional development models may
use a variety of research-based approaches. In
addition, classroom-based inquiry, team teaching by mathematics and early childhood education specialists, discussion of case studies, and
analysis of young children’s work samples tend
to strengthen teachers’ confidence and engagement in early childhood mathematics [5, 97, 99,
100].
This remedy lacks research support [5, 92].
Credit hours or yearly training requirements do
little or nothing unless the content and delivery
of professional development are designed to
produce desired outcomes for teachers and
children [93].
Teachers of young children should learn the
mathematics content that is directly relevant to
their professional role. But content alone is not
enough. Effective professional programs weave
together mathematics content, pedagogy, and
knowledge of child development and family
relationships [98]. When high-quality, well
supervised field work is integrated throughout
a training program, early childhood teachers
can apply their knowledge in realistic contexts. Courses or inservice training should
be designed to help teachers develop a deep
understanding of the mathematics they will
teach and the habits of mind of a mathematical
thinker. Courses, practicum experiences, and
other training should strengthen teachers’ ability to ask young children the kinds of questions
that stimulate mathematical thinking. Effective
professional development, whether preservice
or inservice, should also model the kind of flexible, interactive teaching styles that work well
with children [92].
Delivering this kind of ongoing professional
development requires a variety of innovative
strategies. For early childhood staff living in
isolated communities or lacking knowledgeable
trainers, distance learning with local facilitators is a promising option. Literacy initiatives
are increasingly using itinerant or school-wide
specialists; similarly, mathematics education
specialists could offer resources to a number
of early childhood programs. Partnerships
between higher education institutions and local
early childhood programs can help provide this
support. Finally, school-district-sponsored professional development activities that include
participants from community child care centers, family child care, and Head Start programs
along with public school kindergarten/primary
teachers would build coherence and continuity
for teachers and for children’s mathematical
experiences.
Preservice and inservice professional development present somewhat differing challenges. In
preservice education, the major challenge is to
build a sound, well integrated knowledge base
about mathematics, young children’s development and learning, and classroom practices [5].
Inservice training shares this challenge but also
carries risks of superficiality and fragmentation.
2. Use collaborative processes to develop
well aligned systems of appropriate
high-quality standards, curriculum, and
assessment.
To avoid these risks, inservice professional
development needs to move beyond the onetime workshop to deeper exploration of key
mathematical topics as they connect with
young children’s thinking and with classroom
practices. Inservice professional development
in mathematics appears to have the greatest
impact on teacher learning if it incorporates six
features: teacher networking or study groups;
sustained, intensive programs; collective par-
In mathematics, as in other domains, the task
of developing curriculum and related goals and
assessments has become the responsibility not
only of the classroom teacher but also of other
educators and policy makers. State agencies,
school districts, and professional organizations
are engaged in standards setting, defining desired educational and developmental outcomes
11
the principles articulated by national groups
concerned with appropriate assessment for
young children [88–91].
for children below kindergarten age [13]. This
trend represents an opportunity to improve
early childhood mathematics education but
also presents a challenge. The opportunity is
to develop a coherent, developmentally appropriate, and well aligned system that offers
teachers a framework to guide their work. The
challenge, especially at the preschool and kindergarten levels, is to ensure that such a framework does not stifle innovation, put children
into inappropriate categories, ignore important
individual or cultural differences, or result in
narrowed and superficial teaching that fails to
give children a solid foundation of understanding [49].
District- or program-level educators are often
responsible for selecting or developing curriculum. Decision makers can be guided by the
general criteria for curriculum adoption articulated in the position statement jointly adopted
by NAEYC and the National Association of Early
Childhood Specialists in State Departments of
Education [85]. In addition, decision makers
should insist that any mathematics curriculum
considered for adoption has been extensively
field tested and evaluated with young children.
3. Design institutional structures and policies
that support teachers’ ongoing learning,
teamwork, and planning.
To avoid these risks, state agencies and others
must work together to develop more coherent
systems of standards, curriculum, instruction,
and assessment that support the development
of mathematical proficiency. To build coherence between preschool and early elementary
mathematics, the processes of setting standards and developing early childhood curriculum and assessment systems must include the
full range of stakeholders. Participants should
include not only public school teachers and
administrators but also personnel from centerbased programs and family child care, private
and public prekindergarten, and Head Start, as
well as others who serve young children and
their families. Families too should participate
as respected partners. Relevant expertise
should be sought from professional associations and other knowledgeable sources.
National reports stress the need for teacher
planning and collaboration [5, 7, 101, 102], yet
few early childhood programs have the structures and supports to enable these processes to
take place regularly. Teachers of young children
face particular challenges in planning mathematics activities. Early childhood teachers work
in diverse settings, and some of these settings
pose additional obstacles to teamwork and collaboration. Many early childhood programs, in
or out of public school settings, have little or no
time available for teacher planning, either individually or in groups. Team meetings and staff
development activities occur infrequently.
The institutional divide between teachers in
child care, Head Start, or preschool programs
and those in public kindergarten and primary
programs presents a barrier to the communication necessary for a coherent mathematics
curriculum. Without communication opportunities, preschool teachers often do not know
what kindergarten programs expect, and early
elementary teachers may have little idea of the
content or pedagogy used in prekindergarten
mathematics education. New strategies and
structures, such as joint inservice programs
and classroom visits, could support these
linkages.
As in all effective standards-setting efforts,
early childhood mathematics standards should
be coupled with an emphasis on children’s
opportunities to learn, not just on expectations
for their performance. Standards also should
be accompanied by descriptions of what young
children might be expected to accomplish
along a flexible developmental continuum [49].
Standards for early childhood mathematics
should connect meaningfully but not rigidly
with curriculum. Assessment also should align
with curriculum and with standards, following
12
To support effective teaching and learning,
mathematics-rich classrooms require a wide
array of materials for young children to explore
and manipulate [45, 59, 107]. Equity requires
that all programs, not just those serving affluent communities, have these resources.
In addition, many programs have limited access to specialists who might help teachers
as they try to adopt new approaches to early
childhood mathematics. Administrators need
to reexamine their allocation of resources and
their scheduling practices, keeping in mind the
value of investing in teacher planning time.
Finally, resources are needed to support
families as partners in developing their young
children’s mathematical proficiency. The growing national awareness of families’ central role
in literacy development is a good starting point
from which to build awareness of families’
equally important role in mathematical development [108, 109]. Public awareness campaigns, distribution of materials in ways similar
to the successful Reach Out and Read initiative, computer-linked as well as school-based
meetings for families, Family Math Nights,
and take-home activities such as mathematics
games and manipulative materials tailored to
the ages, interests, languages, and cultures of
the children—these are only a few examples of
the many ways in which resources can support
families’ engagement in their young children’s
mathematical learning [110, see also the online
“Family Math” materials at www.lhs.berkeley.
edu/equals/FMnetwork.htm and other resources at www.nctm.org/corners/family/index.htm].
4. Provide the resources necessary to overcome the barriers to young children’s
mathematical proficiency at the classroom,
community, institutional, and system-wide
levels.
A variety of resources, some financial and some
less tangible, are needed to support implementation of this position statement’s recommendations. Partnerships among the business,
philanthropic, and government sectors at the
national, state, and local levels will improve
teaching and learning in all communities,
including those that lack equitable access to
mathematics education. Universally available
early childhood mathematics education can
occur only in the context of a comprehensive,
well financed system of high-quality early
education, including child care, Head Start, and
prekindergarten programs [103–106]. To support universal mathematical proficiency, access
to developmentally and educationally effective
programs of early education, supported by
adequate resources, should be available to all
children.
Conclusion
A positive attitude toward mathematics and a
strong foundation for mathematics learning begin
in early childhood. These good beginnings reflect
all the characteristics of good early childhood
education: deep understanding of children’s
development and learning; a strong community of
teachers, families, and children; research-based
knowledge of early childhood curriculum and
teaching practices; continuous assessment in
the service of children’s learning; and an abiding
respect for young children’s families, cultures,
and communities.
To realize this vision, educators, administrators, policy makers, and families must work
together—raising awareness of the importance
of mathematics in early education, informing
Improvement of early childhood mathematics
education also requires substantial investment
in teachers’ professional development. The
mathematics knowledge gap must be bridged
with the best tools, including resources for disseminating models of effective practice, videos
showing excellent mathematics pedagogy in
real-life settings, computer-based professional
development resources, and other materials.
In addition, resources are needed to support
teachers’ involvement in professional conferences, college courses, summer institutes, and
visits to model sites.
13
others about sound approaches to mathematical
teaching and learning, and developing essential
resources to support high-quality, equitable
mathematical experiences for all young children.
13. Education Week. 2002. Quality Counts 2002: Building blocks for success: State efforts in early-childhood education. Education Week (Special issue) 21
(17).
14. Bowman, B.T., M.S. Donovan, & M.S. Burns, eds.
2001. Eager to learn: Educating our preschoolers.
Washington, DC: National Academy Press.
15. Denton, K., & J. West. 2002. Children’s reading and
mathematics achievement in kindergarten and first
grade. Washington, DC: National Center for Education Statistics.
16. Natriello, G., E.L. McDill, & A.M. Pallas. 1990. Schooling disadvantaged children: Racing against catastrophe. New York: Teachers College Press.
17. Starkey, P., & A. Klein. 1992. Economic and cultural
influence on early mathematical development. In
New directions in child and family research: Shaping
Head Start in the nineties, eds. F. Lamb-Parker, R.
Robinson, S. Sambrano, C. Piotrkowski, J. Hagen, S.
Randolph, & A. Baker, 440. Washington, DC: Administration on Children, Youth and Families (DHHS).
18. Shonkoff, J.P., & D.A. Phillips, eds. 2000. From neurons to neighborhoods: The science of early childhood
development. Washington, DC: National Academy
Press.
19. National Council of Teachers of Mathematics. 2000.
Principles and standards for school mathematics.
Reston, VA: Author.
20. Seo, K.-H., & H.P. Ginsburg. 2004. What is developmentally appropriate in early childhood mathematics education? In Engaging young children in mathematics: Standards for early childhood mathematics
education, eds. D.H. Clements, J. Sarama, & A.-M.
DiBiase, 91–104. Mahwah, NJ: Lawrence Erlbaum.
21. Baroody, A.J. 2004. The role of psychological research in the development of early childhood mathematics standards. In Engaging young children in
mathematics: Standards for early childhood mathematics education, eds. D.H. Clements, J. Sarama, & A.-M.
22. Clements, D.H., S. Swaminathan, M.-A. Hannibal, &
J. Sarama. 1999. Young children’s concepts of shape.
Journal for Research in Mathematics Education 30:
192–212.
23. Fuson, K.C. 2004. Pre-K to grade 2 goals and standards: Achieving 21st century mastery for all. In
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early childhood mathematics education, eds. D.H. Clements, J. Sarama, & A.-M. DiBiase, 105–48. Mahwah,
NJ: Lawrence Erlbaum.
24. Gelman, R. 1994. Constructivism and supporting
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18
Learning PATHS and Teaching
STRATEGIES in Early Mathematics
early and late in the 3–6 age range. These are, then,
simply two points along the learning path that may
have many steps in between. For each content area,
the Sample Teaching Strategies column shows a few
of the many teacher actions that promote learning
when used within a classroom context that reflects
the recommendations set forth in this NAEYC/NCTM
position statement. In general, they are helpful strategies, with minor adaptations, across the age range.
The research base for sketching a picture of children’s mathematical development varies considerably from one area of mathematics to another. Outlining a learning path, moreover, does not mean we
can predict with confidence where a child of a given
age will be in that sequence. Developmental variation is the norm, not the exception. However, children do tend to follow similar sequences, or learning
paths, as they develop. This chart illustrates in each
area some things that many children know and do—
Content
Area
Number and
operations
Examples of Typical Knowledge and Skills
From Age 3
Counts a collection of one
to four items and begins
to understand that the last
counting word tells
how many.
Age 6
Counts and produces (counts
out) collections up to 100
using groups of 10.
Sample Teaching
Strategies
Models counting of small
collections and guides children’s counting in everyday situations, emphasizing
that we use one counting
word for each object:
“One . . . two . . . three . . .”
Models counting by 10s while
making groups of 10s (e.g.,
10, 20, 30 . . . or 14, 24, 34 . . . ).
Quickly “sees” and labels
collections of one to three
with a number.
Quickly “sees” and labels
with the correct number
“patterned” collections
(e.g., dominoes) and unpatterned collections of up to
about six items.
Gives children a brief
glimpse (a couple of
seconds) of a small collection of items and asks how
many there are.
19
Content
Area
Number and
operations
Age 6
From Age 3
Adds and subtracts nonverbally when numbers
are very low. For example,
when one ball and then
another are put into the
box, expects the box to
contain two balls.
Adds or subtracts using
counting-based strategies
such as counting on (e.g.,
adding 3 to 5, says “Five . . . ,
six, seven, eight”), when
numbers and totals do not
go beyond 10.
Sample Teaching
Strategies
Tells real-life stories involving numbers and a problem. Asks how many questions (e.g., “How many are
left?” “How many are there
now?” “How many did they
start with?” “How many
were added?”).
Shows children the use of
objects, fingers, counting
on, guessing, and checking
to solve problems.
Geometry
and spatial
sense
Begins to match and name
2-D and 3-D shapes, first
only with same size and
orientation, then shapes
that differ in size and
orientation (e.g., a large
triangle sitting on its point
versus a small one sitting
on its side).
Recognizes and names a
variety of 2-D and 3-D
shapes (e.g., quadrilaterals, trapezoids, rhombi,
hexagons, spheres, cubes)
in any orientation.
Uses shapes, separately, to
create a picture.
Makes a picture by combining shapes.
Describes basic features of
shapes (e.g., number of
sides or angles).
Introduces and labels a wide
variety of shapes (e.g., skinny triangles, fat rectangles,
prisms) that are in a variety
of positions (e.g., a square
or a triangle standing on a
corner, a cylinder “standing
up” or horizontal).
Involves children in constructing shapes and talking about their features.
Encourages children to
make pictures or models of
familiar objects using shape
blocks, paper shapes, or
other materials.
Encourages children to make
and talk about models with
blocks and toys.
Describes object locations
with spatial words such
as under and behind and
builds simple but meaningful “maps” with toys
such as houses, cars, and
trees.
Builds, draws, or follows
simple maps of familiar
places, such as the classroom or playground.
Challenges children to mark
a path from a table to the
wastebasket with masking
tape, then draw a map of
the path, adding pictures
of objects appearing along
the path, such as a table or
easel.
20
Content
Area
Measurement
Age 6
From Age 3
Recognizes and labels
measurable attributes
of objects (e.g., “I need
a long string,” “Is this
heavy?”).
Begins to compare and
sort according to these
attributes (e.g., more/
less, heavy/light; “This
block is too short to be
the bridge”).
Tries out various processes and units for
measurement and begins
to notice different results
of one method or another
(e.g., what happens when
we don’t use a standard
unit).
Makes use of nonstandard
measuring tools or uses
conventional tools such
as a cup or ruler in nonstandard ways (e.g., “It’s
three rulers long”).
Sample Teaching
Strategies
Uses comparing words to
model and discuss measuring
(e.g. “This book feels heavier
than that block,” “I wonder if
this block tower is taller than
the desk?”).
Uses and creates situations
that draw children’s attention
to the problem of measuring
something with two different
units (e.g., making garden
rows “four shoes” apart, first
using a teacher’s shoe and
then a child’s shoe).
Pattern/
algebraic
thinking
Notices and copies simple
repeating patterns, such
as a wall of blocks with
long, short, long, short,
long, short, long. . . .
Notices and discusses patterns in arithmetic (e.g.,
adding one to any number results in the next
“counting number”).
Encourages, models, and discusses patterns (e.g., “What’s
missing?” “Why do you think
that is a pattern?” “I need a
blue next”). Engages children
in finding color and shape
patterns in the environment,
number patterns on calendars
and charts (e.g., with the
numerals 1–100), patterns in
arithmetic (e.g., recognizing
that when zero is added to
a number, the sum is always
that number).
Displaying
and analyzing data
Sorts objects and counts
and compares the groups
formed.
Organizes and displays
data through simple
numerical representations such as bar graphs
and counts the number in
each group.
Invites children to sort and
organize collected materials
by color, size, shape, etc. Asks
them to compare groups to
find which group has the most.
Helps to make simple
graphs (e.g., a pictograph
formed as each child
places her own photo in
the row indicating her
preferred treat—pretzels
or crackers).
Uses “not” language to help
children analyze their data
(e.g., “All of these things are
red, and these things are NOT
red”).
Works with children to make
simple numerical summaries such as tables and bar
graphs, comparing parts of
the data.
21
Mathematic Resources: (Those with an (*) are in STARNET Regions I & III Resource Library) Baratta-‐Lorton, Mary. 1995. Mathematics their way: an activity-‐centered mathematics program for early childhood education (20th anniversary edition). Menlo Park, CA: Addison-‐Wesley Publishing Co. Bickmore-‐Brand, J. 1990. Language in mathematics. Portsmouth, NH: Heinemann. Braddon, K.L., N.J. Hall, & D. Taylor. 1993. Math through children’s literature: Making the NCTM standards come alive. Englewood, CO: Teacher Ideas Press. *Bredenkamp, S. & C. Copple. (Eds.). 1997. Developmentally appropriate practice in early childhood programs. Washington, DC: National Association for the Education of Young Children. Bredenkamp, S. & T. Rosegrant. (Eds.). 1992. Reaching potentials: Appropriate curriculum and assessment for young children. Washington, DC: National Association for the Education of Young Children. Burns, M. 1992. Math and literature: (K-‐3). White Plains, NY: Math Solutions Publications. Burns, M. 1982. Math for smarty pants. New York, NY: Scholastic. *Copley, J.V., C. Jones & J. Dighe. 2010. The creative curriculum for preschool, fifth edition, volume 4: mathematics. Washington, D.C.: Teaching Strategies, Inc. Copley, J.V. (Ed). 1999. Mathematics in the early years. Reston, VA: The National Council of Teachers of Mathematics. Copley, J.V., C. Jones & J. Dighe. 2007. Mathematics: the creative curriculum approach. Washington, D.C.: Teaching Strategies, Inc. Copley, J.V. 2000. The young child and mathematics. Washington, DC: National Association for the Education of Young Children. *Copley, J.V. 2010. The young child and mathematics (2nd Ed.). Washington, DC: National Association for the Education of Young Children. *Copley, J.V. (Ed). 2004. Showcasing mathematics for the young child: activities for three-‐, four-‐, and five-‐year-‐olds. Reston, VA: The National Council of Teachers of Mathematics. Dacey, L., M. Cavanagh, C.R. Findell, C.E. Greenes, L.J. Sheffield, & M. Small. 2003. Principles and standards for school mathematics: navigating through measurement in prekindergarten – Grade 2. Reston, VA: The National Council of Teachers of Mathematics. Epstein, A.S. & S. Gainsley. 2011. “I’m Older Than You. I’m Five!” Math in the
Preschool Classroom, 2nd Ed. Ypsilanti, MI: High Scope Press.
Fuson, K.C., D.H. Clements & S. Beckmann. 2010. Focus in prekindergarten: teaching with curriculum focal points. Reston, VA: The National Council of Teachers of Mathematics. Greenes, C., M. Cavanagh, L. Dacey, C.R. Findell, & M. Small. 2001. Principles and standards for school mathematics: navigating through algebra in prekindergarten – Grade 2. Reston, VA: The National Council of Teachers of Mathematics. Illinois State Board of Education: Division of Early Childhood Education. 2004. Illinois early learning standards. Springfield, IL: Illinois State Board of Education. Katz, L.G., & S.C. Chard. 1990. Engaging children’s minds: The project approach. Norwood, NJ: Ablex Publishing Corporation. Kolakowski, J.S. 1994. Linking math with literature: Math activities to accompany 51 pieces of children’s literature. Greensboro, NC: Carson-‐Dellosa Publishing Company. Kolakowski, J.S. 1992. Linking math with literature: Math activities to accompany 50 pieces of children’s literature. Greensboro, NC: Carson-‐Dellosa Publishing Company. Koralek, Derry. (Ed.). 2003. Spotlight on young children and math. Washington, DC: National Association for the Education of Young Children. Krogh, S. 1990. The integrated early childhood curriculum. New York, NY: McGraw-‐Hill Publishing Company. *Moomaw, S. & B. Hieronymus. 2011. More than counting: Math activities for preschool and kindergarten-‐standards edition. St. Paul, MN: Redleaf Press. *Moomaw, S. & B. Hieronymus. 1995. More than counting: Whole math activities for preschool and kindergarten. St. Paul, MN: Redleaf Press. Moomaw, S. & B. Hieronymus. 1999. Much more than counting: More math activities for preschool and kindergarten. St. Paul, MN: Redleaf Press. *Moomaw, S. 2011. Teaching Mathematics in Early Childhood. Baltimore, MD: Brookes Publishing. *Moomaw, S. 2013. Teaching STEM in the Early Years: Activities for Integrating Science, Technology, Engineering, and Mathematics. St. Paul, MN: Redleaf Press. National Council of Teachers of Mathematics. 2006. Curriculum focal points for prekindergarten through grade 8 mathematics: a quest for coherence. Reston, VA: The National Council of Teachers of Mathematics. National Council of Teachers of Mathematics. 1989. Curriculum and evaluation standards for school mathematics. Reston, VA: The National Council of Teachers of Mathematics. National Council of Teachers of Mathematics. 2004. Principles and standards for school mathematics: navigating through number and 0perations in prekindergarten-‐grade 2. Reston, VA: The National Council of Teachers of Mathematics. National Council of Teachers of Mathematics. 2001. Principles and standards for school mathematics: navigating through geometry in prekindergarten-‐grade 2. Reston, VA: The National Council of Teachers of Mathematics. *National Council of Teachers of Mathematics. 2000. Principles and standards for school mathematics. Reston, VA: The National Council of Teachers of Mathematics Newburger, A. & E. Vaughan. 2006. Teaching numeracy, language, and literacy with blocks. St. Paul, MN: Redleaf Press. Raines, S.C., & R.J. Canady. 1989. Story S-‐T-‐R-‐E-‐T-‐C-‐H-‐E-‐R-‐S: Activities to expand children’s favorite books. Mt. Rainier, MD: Gryphon House. Rowan, T., & B. Bourne. 1994. Thinking like mathematicians: Putting the K-‐4 NCTM Standards into Practice. Portsmouth, NH: Heinemann. Schickedanz, J.A. 2008. Increasing the power of instruction: Integration of language, literacy, and math across the preschool day. Washington, DC: National Association for the Education of Young Children. *Stenmark, J. K., & G. D. Coates. 1997. Family math for young children. Berkeley, CA: University of California. Tangorra, Joanne. (Ed.). 2009. Small-‐Group Times to Scaffold Early Learning. Ypsilanti, MI: High Scope Press. Theissen, D. & M. Matthias. (Eds.) 1992. The wonderful world of mathematics. Reston, VA: National Council of Teachers of Mathematics. Whitin, D.J., & S. Wilde. 1992. Read any good math lately? Portsmouth, NH: Heinemann. Revised – 4/2013 STAR net
Regions I & III
presents Apples Video Magazine
#179
STARnet is pleased to offer this program as part of the
Apples Video Magazine series. Apples Video Magazine is a
monthly inservice training program designed specifically
around early childhood issues for practitioners, parents,
and families. For viewing options, visit our website.
To purchase Apples Video Magazines, call:
(800) 227-7537 ext 251 or visit “Products” on our website.
Meaningful Math Activities in Pre-K: Part 1
Description: Early childhood teachers and families provide young children the foundation for strong
math skills and concepts. In this Apples Video Magazine, Sally Moomaw explains the five math content
standards and what that looks like in a Pre-K classroom. She gives some ideas of how parents and
teachers can incorporate math concepts into the child’s day.
Featuring:
Sally Moomaw, Ed.D
STARnet Regions I & III
Western Illinois University • Horrabin Hall 32 • Macomb, IL 61455
800/227-7537 • 309/298-1634 • Fax 309/298-2305
www.starnet.org

Meaningful Math Activities in Pre-K: Part 1

Transcription

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