Counting to Calculus

Counting
to Calculus
Deanne Crawford
Consultant, Rainbow Resource Center
[email protected]
Compiled by Rainbow Consulting Staff:
Deanne Crawford
Donna Krahn
Gina Burmeier
Janice Price
Sara Rask
Contact us at [email protected]
Counting to Calculus
Definitions:
• Algebra: is defined as a branch of mathematics that substitutes letters for numbers. An
algebraic equation represents a scale, what is done on one side of the scale with a number
is also done to the other side of the scale. The numbers are the constants. Algebra can
include real numbers, complex numbers, matrices, vectors etc.
• Arithmetic: is defined as the branch of mathematics usually concerned with the four operations (adding, subtracting, multiplication and division) of positive numbers.
• Common Core Standards: The Common Core State Standards define the rigorous skills
and knowledge in English Language Arts and Mathematics that need to be effectively
taught and learned for students to be ready to succeed academically in credit-bearing,
college-entry courses and in workforce training programs.
• Constructivism: theory of learning and an approach to education that lays emphasis on
the ways that people create meaning of the world through a series of individual constructs.
In mathematics, students construct their own understanding of mathematical concepts, so
that the primary role of teaching is not to lecture, explain, or otherwise attempt to ‘transfer’ mathematical knowledge, but to create situations for students that will foster their
making the necessary mental constructions.
• Discovery Learning: a minimization of both teacher instruction and repetitive drills and
a disdain for standard procedures (algorithms) such as addition/subtraction or multiplication/division facts.
• Exercises: the teaching of mathematical skills by completing a large number of exercises
of a similar type.
• Mathematics: is defined as the abstract science of number, quantity, and space, either as
abstract concepts ( pure mathematics), or as applied to other disciplines such as physics
and engineering ( applied mathematics).
• Place value: is defined as the value of a digit as determined by its position in a number,
the name of the place or location of a digit in a number.
• Reform (or Standards Based) Math: often called the “new, new” math based on constructivism (learning theory) and formalized by the National Council of Teachers of Mathematics (NTCM) which created the Principles and Standards for School Mathematics.
Published in 1989, these were an extensive set of mathematics standards for grades K-12,
which de-emphasized memorization of number facts, the learning of proofs, and algebraic
skills but encouraged the use of calculators and “discovery learning”. In 2000 and 2006, the
same NCTM released additional standards which many considered an admission that the
previous standards had mistakenly de-emphasized instruction of basic skills.
Continued…
2
Deanne Crawford • [email protected]
Counting to Calculus
• Rote Learning: teaching of mathematical results, definitions, and concepts by repetition
and memorization. Typically used to teach multiplication tables. Sometimes referred to as
drill to instill or by the negative terms: Drill and Kill or Parrot Math.
• Scope and Sequence: a listing of the learning objectives and skills covered by a curriculum product(s) by subject and grade level.
• Traditional Math: Method of instruction where the teacher presents a mathematical concept, reviews the procedures required to find the solution, and then has students practice
these procedures with additional problems.
MATH BUILDING BLOCKS :
Basic math skills provide the floor of your math house, and the advanced math courses
(Algebra, Geometry, Calculus) provide the ceiling in your house. In between your floor joists
and the roof, lie five building blocks, which provide the cornerstones of your math house.
1. Numbers
2. Place Value System
3. Whole Number Operations
4. Fractions and Decimals
5. Problem Solving
Notes:
3
Deanne Crawford • [email protected]
Counting to Calculus
Activities you can do to prepare your child for Elementary math:
q Teach shapes/colors including larger than/smaller than; number of sides, distinctives.
q Teach how to recognize numbers and counting.
q Teach how to count forwards and backwards. Skip count.
q Count and Sort Activities with blocks and shapes.
q Cook Together.
q Telling Time.
q Calendar skills-day of week, number of days, months, weeks in months etc.
q Teach Place Value using M&Ms, Cuisenaire Rods/Unifix Rods.
4
Deanne Crawford • [email protected]
Counting to Calculus
Resources for Math Games:
24
Learning Wrap Ups
Math Dice (add/subtract, Place Value etc)
Snap It Up
Monkey Math
Equate Muggins Math Games
Build & Block (add/subtraction and multiply/divide games)
S’Math Game
Monopoly
Yahtzee
Life
Pay Day
Check Math
Math File Games (grade specific)
Math Bingo
Math Hopscotch
Math War
Place Value Hat Trick
Math Games book by Peggy Kaye
Resources for Grade Level Standards:
World Book Typical Course of Study:
http://worldbook.com/typical-course-of-study
A-Beka CurriculumScope and Sequence:
http://www.abeka.com/HomeSchool/ScopeAndSequence.aspx
Bob Jones Curriculum Scope and Sequence:
http://www.bjupress.com/pdfs/catalogs/2013-287102-scope-and-sequence.pdf
5
“On Core” Mathematics—which is based on the common core standards.
Common Core Standards: www.corestandards.org
Grade Appropriate Test Prep Books—like Spectrum are written to core standards.
What Your __________ Grader Needs to Know—books by E.D. Hirsch
Deanne Crawford • [email protected]