Teach it All Workshop - American Montessori Society

Transcription

ST. CATHERINE UNIVERSITY
The Center for Contemporary Montessori Programs
2004 Randolph Ave.
Mail # 4100
St. Paul, MN 55105
(651) 690-6001
FAX (651) 690-6039
You Can Teach it All
Elementary Level
Michael Dorer
1. Introduction:
2. What is the problem?
•
Are there any solutions?
•
Can they work?
3. Start with a curriculum plan.
•
What is a curriculum? Is it an album?
•
How should it be leveled?
•
Plan 30-33 lessons//subject/year/age group.
4. Create careful lesson plans on a weekly basis
•
Have a designated day for each subject area.
•
Create careful follow-up work for each lesson: two choices
•
Keep lessons brisk and crisp; Do NOT have children do the work at the lesson.
5. Have a Great Period.
•
2 ½ to 3 hour Work block in the morning.
•
Topics lessons in the afternoon.
•
Open lesson Policy
From Michael Dorer
Spring, 2011 1
6. Use Guided Discovery
•
Only present key lessons, avoiding details.
•
Have self created problems
•
Plan that children will engage with issues that emerge.
•
Do not focus on mastery
7. Questions
From Michael Dorer
Spring, 2011 2
3/21/11
What is the problem?
•  I can’t get it all done!
•  Too many lessons? Too
little time? The drive for
mastery? Too much
detail?
•  Are there any
solutions?
•  Can they work?
Solutions
•  There are some solutions, many
of which will work. They will
require some changes in how you
do business.
•  You can teach successfully,
offering children the whole
curriculum.
1
3/21/11
Start with a curriculum
plan.
•  What is a curriculum?
Is it an album?
•  How should it be
leveled?
•  Plan 30-33 lessons/
subject/year/age
group.
A Curriculum Plan
A curriculum plan should
contain:
• A year by year sequence
• Vertical articulation
• A complete scope
• It can be very detailed or
simple.
The Elementary Subject Areas
Six major subjects
Supporting subjects
•  Arithmetic
•  Practical Life
•  Biology/Science
•  Art
•  Geography
•  Music
•  Geometry
•  Physical Education
•  History
•  Language/Literacy
2
3/21/11
Weekly Lesson Plans
•  Cover the six major subjects carefully
•  You may alternate or mix Geography and History
•  Create careful follow-up work for each lesson:
two choices, differentiated.
•  Keep lessons brisk and crisp; Do NOT have
children do the work at the lesson.
How Often
•  One morning curriculum lesson per day for
each age group.
•  Cover all of the six major subjects weekly.
•  It is possible to have as many as seven
lessons per week, some weeks – but
rarely!
Designated Days
Have a designated day for presenting lessons in each subject area.
First Year and Early Second Year
3
3/21/11
The Numbers Game
Presenting according to this schedule means:
• 
• 
• 
• 
One lesson/week in a subject area for each age group.
Approximately 30-35 lessons in a subject area for each
age group annually – somewhat fewer in cultural
subjects, somewhat more in math and language.
This averages to about about 160 lessons per age
group.
That makes about 480 total lessons annually in a full
range class.
This sounds daunting, but is still only one daily lesson per age group on
average.
The Great Period
  Every morning allow 2½ to 3
hours of work time.
  This is not to be interrupted by
recess, group snack, class
meetings, pull outs, etc.
  During this time present your
three lessons, totaling NO MORE
than 1½ hours at the most.
  Implement an Open Lesson
Policy.
Topics or Focus Groups
  Topics lessons belong in the afternoons.
There are two kinds: interest groups and
task forces.
  Interest groups are mixed age groups
formed around common interests.
  Task Forces are groups formed by the
adult to focus on specific curriculum
needs or remediation.
4
3/21/11
Guided Discovery
•  Only present key lessons, avoiding details.
•  Offer 2-5 examples at the most.
•  Encourage self created problems
•  Plan that children will engage with issues that
arise in exploration.
•  Avoid task cards, many problem cards, many
example cards, Keep it simple (KISS)
•  Do not focus on mastery, focus on technique or
process.
Guided Discovery: An
Advantage
In My Album: Stamp Game Division
•  Division with a One Digit Divisor
•  Introducing the Remainder
•  Division with a Two Digit Divisor
•  Division with a Three Digit Divisor
•  Division with a Zero in the Dividend
•  Division with more than one Zero in
the Dividend
Guided Discovery: Stamp Game
Division
•  Division with a One Digit Divisor
•  Division with a Two Digit Divisor
 Lots of practice with self
created problems.
 The children discover every
special case.
•  Division with a Zero in the Divisor
•  Division with a Zero in the Units
Place of the Divisor
•  Division with Two Zeros in the
Divisor
Summary
•  Curriculum plan
•  Weekly lesson plans
•  Designated Days
•  One lesson per group, per subject, per week.
•  The Great Period
•  Open Lesson Policy
•  Focus Groups in the Afternoon
•  Guided Discovery
5
3/21/11
6
2004 Randolph Ave.
Mail # 4100
St. Paul, MN 55105
(651) 690-6001
FAX (651) 690-6039
History Plan for Lower Elementary
Year in School
Every Year
First Great Lesson: Story of Creation
Second Great Lesson: Life Comes to Earth
Third Great Lesson: Human Beings Come to Earth
Major Theme
First Year
Second Year
Third Year
Time:
• Personal Time Lines
• Calendars
• Clocks
• BC/AD Timelines
• Fundamental Tenses
The Story Of Life:
• Long Black Line
• Clock of the Eras
• Time Line of Life
The Story of Humans:
• Time Line of Human Beings
• The Significance of the Appearance of
Humanity
• The Difference between Society and
Civilization
Minor theme
Human Needs:
Culture Folders
Human Needs:
• Culture Folders
• Organizing the Chart of Fundamental
Needs
• The Fundamental Needs of People
• Stages in the Progress of Human
Civilization
Human Needs:
• The Development and Ways of Meeting
Human Needs through History
1
History Plan for Upper Elementary
Year in School
Every Year
First Great Lesson: Story of Creation
Second Great Lesson: Life Comes to Earth
Third Great Lesson: Human Beings Come to Earth
NOTE: Both Themes are integrated in Upper Elementary
Fourth Year
Fifth Year
Sixth Year
•
Time Line of Life (Second Level)
•
Time Line of Human Beings (Second Level)
•
The Significance of the Appearance of Humanity (Second Level)
•
The Difference between Society and Civilization (Second Level)
•
Great Civilizations/Time Line of Humanity
•
The Middle Ages and the Renaissance
•
Time Line of the Child's Own Country
•
The Child's Own State or Province
2
1
2004 Randolph Ave.
Mail # 4100
St. Paul, MN 55105
(651) 690-6001
FAX (651) 690-6039
Simple Arithmetic Curriculum Plan for Montessori
Written by Michael Dorer © 2010
#
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
Lessons for Preschool and Kindergarten
Grade
Number Rods
PK
Sandpaper Numerals
PK
Association of Rods and Numerals
PK
Spindle Boxes
PK
Zero Activity
PK
Cards and Counters
PK
The Memory Game
PK
Snake Game for Tens
PK
Golden Bead Quantity and Symbols
PK
First Presentation of Quantity
PK
First Presentation of Decimal Symbols
PK
Association of Quantity and Symbol
PK
The Nines Layout of Numerals
PK
The Composition of Numbers
PK
The Birdʼs Eye View
PK
First Seguin Boards - The Teen Boards
PK
Second Seguin Boards – The Tens Boards
PK
The Hundred Chain
PK
The Hundred Board
PK
Linear Counting the Short Chains
PK
The Thousand Chain
PK
Skip Counting
PK
Static Addition with the Golden Beads
PK
Static Multiplication Golden Beads
PK
Static Subtraction Golden Beads
PK
2
#
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
Lessons for Preschool and Kindergarten
Grade
Static Division Golden Beads
PK
The Change Game
PK
Dynamic Addition Golden Beads
PK
Dynamic Multiplication Golden Beads
PK
Dynamic Subtraction Golden Beads
PK
Dynamic Division Golden Beads
PK
Addition with the Stamp Game
PK
Multiplication with the Stamp Game
PK
Subtraction with the Stamp Game
PK
Dot Game Addition
PK
Addition Strip Board: Booklet of Combinations
PK
Addition Strip Board: Cut Tables
PK
Addition Strip Board: Families of Numbers
PK
Finger Chart: The Whole Chart
PK
Finger Chart:: The Half Chart
PK
Ninth Exercise: The Addition Bingo Game
PK
Subtraction Strip Board: Booklet of Combinations
PK
Subtraction Strip Board: Cut Tables or Equations
PK
Finger Chart: The Second Chart
PK
Finger Chart: The Bingo Game
PK
Memorization of Multiplication
PK
Multiplication Board: The Booklet of Combinations
PK
Cut Tables or Equations
PK
Finger Chart: The Multiplication Bingo Game
PK
Bead Bar Multiplication: Memorizing the Tables
PK
Division Board: Families of Dividends
PK
Division Finger Chart: Cut Tables
PK
Fraction Skittles
PK
The Small Bead Frame: The Composition of Numbers
PK
The Small Bead Frame: Addition
PK
The Small Bead Frame: Subtraction
PK
The Small Bead Frame: Multiplication as Repeated Addition
PK
3
#
NA
NA
NA
NA
1.
Lesson for Elementary School
Grade
Notes
Spindle Boxes
1
Optional
Zero Activity
1
Optional
Cards and Counters
1
Optional
The Memory Game
1
Optional
Snake Game for the Research of Ten: Dynamic
1
Snake
2.
Golden Beads: First Presentation of Quantity First
1
Presentation of Decimal Symbols Association of
Quantity and Symbol
3.
The Nines Layout of Numerals
1
4.
The Birdʼs Eye View
1
The Change Game
NA
NA
5.
First Seguin Boards - The Teen Boards
1
Optional
Second Seguin Boards – The Tens Boards
1
Optional
The Hundred Chain
1
The Hundred Board
6.
Linear Counting the Short Chains
1
The Thousand Chain
7.
8.
Skip Counting
1
Golden Beads: Addition: Impressionistic Approach
1
Addition with the Golden Beads: Usual Approach
9.
10.
Golden Beads: Multiplication
1
Golden Beads: Subtraction: Impressionistic
1
Approach
Subtraction: Usual Approach
11.
12.
13.
14.
15.
16.
Golden Beads: Dynamic Division
1
Dynamic Addition with the Stamp Game
1
Dynamic Multiplication with the Stamp Game
1
Dynamic Subtraction with the Stamp Game
1
The Dot Game
1
Addition Strip Board: Using the Booklet of
1
Combinations
4
#
17.
Addition Strip Board: Families of Numbers
Grade
Notes
1
The Doubles of Numbers
18.
19.
20.
21.
Cut Tables: The Whole Chart
1
Cut Tables: The Half Chart
1
Cut Tables: The Addition Bingo Game
1
Subtraction Strip Board: The Booklet of Subtraction
1
Facts
22.
Subtraction Strip Board: Decomposition of a Number
1
(Families of Numbers)
23.
24.
25.
26.
27.
NA
28.
29.
30.
31.
32.
Fifth Exercise: Halves of Numbers
1
Cut Tables: The Finger Charts
1
Finger Chart: The Bingo Game
1
Multiplication Board: The Booklet of Model Forms
1
Multiplication Game: Bead Bar Multiplication
1
Fraction Skittles
1
Fraction Circles
1
Addition of Fractions with Same Denominator
1
Small Bead Frame: Numeration According to Position
1
Small Bead Frame: The Composition of Numbers
1
Multiplication Games: Multiplication by Ten
1
Products to Factors
Commutative Law – Inverse Products
33.
34.
35.
36.
Insert additional Lessons
1
Addition Finger Chart: The Simplified Chart
2
The Addition Snake Game
2
Addition Games: The Commutative Property
2
Sums with Parentheses
Sums with Several Parentheses
Distributive Property
37.
38.
39.
The Special Cases for Addition
2
Subtraction Snake Game
2
The Special Cases for Subtraction
2
Optional
5
#
40.
Multiplication Board: Cut Tables or Equations
Grade
2
Multiplication Cut Tables: The Third Chart
41.
42.
43.
Fourth Exercise: The Half Chart
2
Fifth Exercise: The Multiplication Bingo Game
2
Both Multiplication Snake Games
2
Multiplication Games: Bead Bar Squaring
2
44.
45.
Multiplication Board Squaring
The Snake Game of Squares
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
The Special Cases for Multiplication
2
Division Board: Families of Dividends
2
Division: Cut Tables
2
Division: Cut Tables Families of Divisors
2
Division: The Division Bingo Game
2
The Special Cases for Division
2
Golden Beads: Division -Two-Digit Divisor
2
Stamp Game: Distributive Division
2
Stamp Game: Distributive Division -Two-Digit Divisor
2
Stamp Game: Group Division
2
Fractional Equivalence
2
Subtraction of Fractions with Like Denominators
Small Bead Frame: The Decomposition of Numbers
2
Small Bead Frame Addition (Vertical Method)
2
Small Bead Frame Subtraction
2
Small Bead Frame: Multiplication as Repeated
2
Addition
62.
Small Bead Frame: Multiplication with Mental
2
Calculation
63.
Small Bead Frame: Multiplication by 1s, 10s, 100s,
2
and 1000s
Advanced Multiplication
64.
The Geometric Representation of the Decimal
2
Hierarchies
Notes
6
#
65.
Checkerboard: Value According to Position
Grade
2
66.
Checkerboard: Long Multiplication – Holistic
2
Approach
67.
Checkerboard: Long Multiplication with Mental
3
Calculation
68.
Large Bead Frame: Numeration According to Position
3
Composition of Numbers
The Decomposition of Numbers
69.
Large Bead Frame: Addition with the Large Bead
3
Frame
Subtraction with the Large Bead Frame
70.
Large Bead Frame: Multiplication with the Large
3
Bead Frame
71.
72.
Large Bead Frame: Red Zero Game
3
Checkerboard Long Multiplication with Partial
3
Products
Long Multiplication with Mental Carrying
73.
Checkerboard: Multiplication with the Checker Board
3
and Related Drawing
74.
Golden Bead Frame Composition of Numbers
3
Multiplication with the Golden Bead Frame
75.
76.
Golden Bead Frame Multiplication (Advanced)
3
Bank Game: Multiplication with a One-Digit Multiplier
3
Multiplication with a Two-Digit Multiplier
77.
Bank Game: Multiplication with a Three-Digit
3
Multiplier and more
78.
79.
80.
Multiplication of a Fraction by a Whole Number
3
Division of a Fraction by a Whole Number:
3
First Multiplication of Binomials and Trinomials The
3
Analysis of the Square
Notes
7
#
81.
The Passage from a Square to a Successive Square
Grade
3
Passage from a Square to a Non-Successive Square
82.
83.
84.
85.
The Square of the Decanomial
3
The Square of the Decanomial (continued)
3
Test Tubes: Short Group Division
3
Odd Facts
Uncommon Multiplication
86.
87.
88.
89.
Test Tubes: Abstract Short Group Division Technique
3
Test Tubes: Long Group Division
Test Tubes: Abstract Long Group Division
3
Test Tubes: Abstract Long Group Division
(advanced)
90.
Yellow Board: Decimal Numeration
3
Formation and Reading of Quantities
91.
Yellow Board: Forming and Reading the Symbols
3
The Pinwheel
The Association of Quantity and Symbol Progressive
and Regressive Counting
92.
93.
94.
95.
96.
97.
98.
99.
100.
101.
102.
103.
104.
105.
Yellow Board: Decimal Addition
3
Second Exercise: Decimal Subtraction
3
The Hundredth Circle
3
3
3
3
3
3
The Multiples
4
The Multiple Charts
4
Tables A and B
4
Table C The first filling out
4
The Search for the Lowest Common Multiple: LCM
4
The Search for the Greatest Common Factor: GCF
4
Notes
8
#
106.
Towards Abstraction with GCF and LCM
Grade
Notes
4
Second Filling Out of Table C
107.
108.
Search for Prime Factors on the Pegboard
4
Divisibility by Two
4
Divisibility by Three
Divisibility by Four
Divisibility by Five
109.
Divisibility by Twenty-five
4
Divisibility by Nine
NA
Considering Nine as Ten Minus One
4
Considering Ten as Nine Plus One
110.
111.
112.
Casting Out Nines in Addition and Multiplication
4
Casting Out Nines in Subtraction and Division
4
The Board of Powers
4
Nomenclature of the Powers
113.
The Powers of One
4
The Powers of Ten
Expanded Notation
114.
Geometrical Representation of the Hierarchies
4
Last Filling in of Table C: Exponents
115.
116.
117.
Powers of Two
4
Powers of Three
4
Passage from the Numerical Decanomial to the
4
Algebraic Decanomial
118.
The Passage to the Algebraic Decanomial
4
Writing of the Booklet for the Algebraic Decanomial
Reduction of the Algebraic Decanomial
119.
120.
121.
122.
123.
124.
125.
Products of Binomials and Trinomials
4
From the Real Square to the Symbolic Square
4
Products of Binomials with Hierarchical Materials
4
Squaring the Binomial
4
Algebraic Square or Literal Notation
4
Products of Trinomials
4
Cross Multiplication Introduction
4
Optional
9
#
126.
127.
128.
129.
Grade
Cross Multiplication Second Level
4
Cross Multiplication Third Level — Mental Carrying
4
Cross Multiplication Without Materials
4
Addition of Fractions with Unlike Denominators: Level
4
Notes
2
130.
Subtraction of Fractions with Unlike Denominators:
4
Level 2
131.
Passage to Abstraction in Addition and Subtraction of
4
Fractions: Level 2
132.
133.
134.
Multiplication of a Whole Number by a Fraction
4
Division of a Whole Number by a Fraction
4
Addition of Fractions with Unlike Denominators:
5
Level 3
135.
5
Improper Problems
Add Three Fractions
136.
5
Using Rectangles
137.
Addition of Fractions with Unlike Denominators
5
Complete Abstraction
138.
Subtraction of Fractions with Unlike Denominators:
5
Level 3
139.
140.
141.
142.
Multiplication of a Fraction by a Fraction: Level 3
5
Division of a Fraction by a Fraction: Level 3
5
Group Division of Fraction by Fraction
5
The Problem of the Very Thirsty Man
5
Multiplication of a Decimal by 1,10, 100 and 1000
5
Multiplication of Decimal Numbers on the Yellow
Board
143.
144.
Whole Numbers Times Decimal Numbers
5
Introducing the Decimal Checkerboard
5
Imposing Number Labels
Optional
10
#
145.
Decimal Checkerboard Multiplication: Decimal
Grade
Notes
5
Number times Whole Number
146.
Decimal Checkerboard Multiplication: Whole number
5
multiplied by a decimal number
147.
148.
149.
150.
151.
152.
153.
154.
Level Three: Decimal Number x Decimal Number
5
Multiplication With Related Drawing
5
Decimal Division
5
First Level: A whole number ÷ whole number
5
Second Level: Decimal ÷ Whole Number
5
Level Three: Whole Number ÷ Decimal Number
5
Case Four: Decimal Number ÷ Decimal Number
5
Introduction to Square Root
5
Nomenclature of Square Root
155.
First Presentation
5
Second Presentation: The Chart of Squares
NA
Square Root Third Presentation: Optional
5
Presentation
156.
157.
Square Root with the Golden Beads
5
Beginning the Subtraction
5
Sensorial Square Root
158.
Square Root Repeated Subtraction
5
Counting the Subtractions
159.
Square Root Beginning Division
5
Comparing the Wings
160.
161.
Square Root: Three digit root
5
Square Root A Further Passage to Abstraction: A
5
Drawing
162.
163.
164.
165.
166.
5
5
5
5
5
Optional
11
#
167.
Changing Fractions to Decimals with the Hundredth
Grade
Notes
6
Circle
The Concept of Percentage
168.
Changing Decimals to Percentages and Percentages
6
to Decimals
169.
170.
Changing Fractions to Percentages
6
Changing Angles to Fractions, Decimals, and
6
Percentages
NA
NA
171.
Square Root of a Decimal Number
6
Optional
Square Root of a Common Fraction
6
Optional
The Study of Simple Interest
6
Calculation of Interest
172.
173.
174.
175.
Calculation of Principal
6
Calculation of Time
6
The Negative Snake Game
6
Nomenclature of Integers
6
Using Symbols with Integers
Greater Than and Less Than
176.
177.
178.
179.
Addition and Subtraction of Integers
6
Multiplication and Division of Integers
6
The Additive Inverse
6
From a Number to Its Square (Review)
6
From a Square to a Non-Successive Square (Review)
From a Square to its Cube (Review)
180.
181.
182.
183.
184.
Passage from a Cube to a Successive Cube
6
Passage from a Cube to a Non Successive Cube
6
The Cube of a Binomial
6
The Cube of a Trinomial
6
Binomial Cube to Trinomial Cube
6
Binomial and Trinomial Hierarchical Cubes
185.
186.
187.
188.
Introductory Cubing of the Hierarchical Cubes
6
Cubing the Hierarchical Binomial
6
Cubing the Hierarchical Trinomial
6
Algebraic Binomial Cube
6
12
#
189.
190.
Grade
Algebraic Trinomial Cube
6
Cube Root: One Digit Root
6
Two Digit Root : A First Passage
191.
192.
193.
194.
195.
196.
197.
198.
Two Digit Cube Root: Second Passage
6
Two Digit Cube Root : Third Passage
6
Two Digit Cube Root: Last Passage with Material
6
Three Digit Cube Root: Trinomial
6
Three Digit Cube Root: Last Passage for Trinomial
6
Three Digit Root: Abstraction For Trinomial
6
Review All Cubing and Cube Root
6
6
Notes
2004 Randolph Ave.
Mail # 4100
St. Paul, MN 55105
(651) 690-6001
FAX (651) 690-6039
Curriculum Plan for Geometry
Level
1
Chapter
Material
Sensorial exploration of
shapes
All material for the development of the
sense of sight regarding size
a. Solid
Small geometric solids for the development PK on
of the stereognostic sense
b. Plane
PK to 2nd
gr.
Geometry Classified Nomenclature
2nd through
3rd
Nomenclature of the Plane
Figures
Concepts of congruence, similarity
and equivalence
a. Presentation of concepts
3
4
5
6
PK on
Geometry cabinet
Constructive Triangles: Series One
Detailed knowledge of Geometric
Figures
2
Level/
Grade
Geometric Insets, Geometry Charts
4th grade
b. Concepts in Action
Constructive Triangles: Series Two
c. Concepts of Equivalence in
Relationship to the Nomenclature
of the Plane Figures
From Surface to Area of Any
Plane Figure
Insets of Equivalence
Yellow Area material
Handmade material
5th grade
From a Solid to its Volume
Material for Volume "Blue Material"
Handmade material
6th grade
Relationships and Theorems
All Preceding Material
Jr. High
and
beyond

Teach it All Workshop - American Montessori Society

Transcription

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