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Contibutions of Curricula. A Historical Look at How We Teach Addition. Purpose of Project. Down with reform – Back to the basics! Wait! Didn’t we try that before? Learn more and start earlier! Focus on key concepts each year. - PowerPoint PPT Presentation
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A Historical Look at How We Teach Addition
Purpose of Project
• Down with reform – Back to the basics! Wait! Didn’t we try that before?
• Learn more and start earlier!Focus on key concepts each year.
• How much has curricula really changed over the years? In what ways? In what ways has it stayed the same throughout the reforms?
Methods
• Choose Focus
• Chart
• Categorize
1897 1918 1929 1937
1958 1964 1969 1974 2004
• Collect Textbooks
Textbook Philosophies
• Problem Solving "The problem material is drawn from the life in which children and their parents are living to-day. It is within their knowledge or experience, and presents real, rather than imaginary situations" (1918, p. iii).
1897 1958 1969 19741918 1929 1937 20041964
Textbook Philosophies
• Problem Solving
1897 1958 1969 19741918 1929 1937 20041964
• Drill and Memorization
“Rote counting and the learning of facts from flash cards, for example, are not acceptable procedures” (Stokes et al., 1958, p. 2).
Drill can “reinforce concepts that have been approached as part of the over-all structure of mathematics” (Eicholz et al., 1969, p. 5).
When once a child has sensed a number fact, he should be made to memorize it, and use it until its use becomes as automatic and unconscious as walking or talking” (1918, p. iv).
Textbook Philosophies
• Problem Solving
• Drill and Memorization
• Fun/Engaging vs. Social
1897 1958 1969 19741918 1929 1937 20041964
“No pupil should have to moan, “Aw! It’s the same old stuff,” when he flips through his math book. The pages…are varied. They’re lively. They look like fun” (1974, p. vi).
“The teaching program must revolve around social living. All plans, whether they pertain to study materials or to teaching methods, must have a social approach” (1958, p. 1).
Textbook Philosophies
• Problem Solving
• Drill and Memorization
• Role of Teacher
1897 1958 1969 19741918 1929 1937 20041964
• Fun/Engaging vs. Social
"Do not allow the notes to stifle your own effective teaching methods and creative efforts" (1969, p. 17).
"The teacher's position is unique in that she alone has sufficient insight into the backgrounds of her pupils to know how to make the subject meaningful to them” (1964, p. 1).
"The teacher should recognize differences in children, and give the stronger ones an opportunity to test their power” (1918, p. 3).
Textbook Philosophies
• Problem Solving
• Drill and Memorization
• Role of Teacher
• Role of Parent
1897 1958 1969 19741918 1929 1937 20041964
• Fun/Engaging vs. Social
“Because the parent is the first teacher, the text is so constructed that the parent can readily gain insight into the concepts presented on each page” (1964, p.1).
Addition Philosophies
• Scope
1897 1958 1969 19741918 1929 1937 20041964
OLD
"In many schools, particularly those that accept children six years of age in the first grade, it may be inadvisable to attempt any formal work with numbers; while other first-grade classes whose members are seven, eight, or more years of age may accomplish more work than is here indicated" (1918, p. 1).
NEW
“Everyday Mathematics begins with the premise that students can, and must, learn more mathematics than has been expected from them in the past” (2004, p. ii).
Addition Philosophies
• Scope
• Symbols
1897 1958 1969 19741918 1929 1937 20041964
• Meaning and words before symbols
+ means “and”, say “plus”
+ means “and”, say “and”
“The children use the terms and symbols plus (+) and minus (-) from the beginning” (1964, p. 18).
Addition Philosophies
• Scope
• Symbols
1897 1958 1969 19741918 1929 1937 20041964
• Physical Manipulation
"Every wide-awake primary teacher knows the value of dramatization, playing store, the game element, etc. and is quick to invent and adopt the proper device as needed" (1918, p. 1).
“You should allow them to use these concrete objects as long as necessary. However, to discourage the children’s dependence on these crutches, put the materials someplace where they can be readily used if needed, but do not pass them out to each child” (1969, p. 95).
Addition Philosophies
• Scope
• Symbols
• Creating Problems
1897 1958 1969 19741918 1929 1937 20041964
• Physical Manipulation
• Make own problems
• Describe methods
• Interesting gap
Addition Philosophies
• Scope
• Symbols
• Creating Problems
• Proof
1897 1958 1969 19741918 1929 1937 20041964
• Physical Manipulation
"Beginning at the top of the column, add the first two numbers, and to this sum add the third number…Now, to be sure you are right, begin at the bottom and add upward" (1929,p. 68-9).
Layout
1897 1958 1969 19741918 1929 1937 20041964
ToolsMessyNarrativeBlended Topics
Order: 1897
Order: 1918
Order: 1929
Order: 1937
Order: 1958
Order: 1964
Order: 1969
Order: 1974
Order: 2004
Order: Composite
Order: End LevelTotals to 9
Totals to 10
Totals to 19
2-Digit
Application to Reading
“It would be interesting to compare the order and duration of concepts taught over the year among the countries. I wonder if either of these factors influences how well children learn the various concepts.”
What about assessments? Have they changed as much as the curricula?
Articles on TIMSS and International Studies
Examples: Missing Addend1897
1918
1937
1958
1969
2004
1964
Examples: Combinations1897
1969
1974
1964
Examples: Combinations1958
1937
2004
Examples: Vertical
1897 1918
1929 1937
• Early
• No symbol
Examples: Vertical1958
• Both forms
Examples: Vertical
1964
“Once the children thoroughly understand addition and the idea of solving equations, vertical notation for addition problems is introduced” (1969, p. 86).
1969
1974
2004
Examples: Commutative1897
19581969
1974
1929
2004
Examples: Associative
1969
1974
1964
Examples: Identity
1969 1974
1929
1964
2004
Examples: Expanded Form
1897
1969
1964
Examples: Other Operations1958
1897
Strategies For Adding Two, Single-digit Numbers1897 1918 1929 1937 1958 1964 1969 1974 2004
Manipulatives X X X X X X X X
Counting Up X X
Number Line X XPractice (Dot Cards/Dominoes) X X X X
Ten Trays XBreak Apart/ Combinations X
1969
1897 1918 1929 1937 1958 1964 1969 1974 2004
Ovals/Parentheses X X XCross Out and Write Sum X
Add Downward X X
Pictures X
Dot Cards X X
Strategies For Adding Several One-Digit Numbers
1969
1897
1897 1918 1929 1937 1958 1964 1969 1974 2004
Ten Frames XBundles and Single Sticks
XBeads on Grid XPlace Value Chart XAddition Columns XBreak Apart/ Expanded Form
X
Strategies For Adding a Single-digit and Two-Digit Number
1964 19741929
1897 1918 1929 1937 1958 1964 1969 1974 2004
Place Value Chart XAddition Columns: + Ones Then Tens
XBase-10 Blocks X
Tens Frames XBreak Apart/ Expanded Form
X
Strategies For Adding Two, Two-Digit Numbers
1964
1929
2004
1974
Other Thoughts Related to Readings
• A few of the textbooks advocate explaining your answers or assert that math should be “social”, yet they do not express a philosophy toward discourse.
• How closely did teachers follow these curricula?
• If the pages for each topic from these books were combined, which would teachers use?
Resources
1897 1958 1969 19741918 1929 1937 20041964
Baird, S.W. (1897). Graded Work in Arithmetic: First Year Numbers From 1 to 20. New York: American Book Company.
Buswell, G.T., Brownell, W.A., & Dolch, M.P. (1937). Jolly Number Tales: Book One. Boston: Ginn and Company.
DeVault, M.V., Greenberg, H.J, Frehmeyer, H., & Bezuszka, S.J. (1974). SRA: Mathematics Learning System Text: Level 1. Chicago: Science Research Associates, Inc.
Eicholz, R.E. et al. (1969). Elementary School Mathematics (2nd Edition): Book 1. Ontario: Addison-Wesley (Canada) Limited.
Elwell, C.E., Stanislas, S.M., & Fitzgerald, J.F. (1964). Teacher's Edition of New Ways in Numbers: Book 1. Boston: D.C. Heath and Company.
Fowlkes, J.G. & Goff, T.T. (1929). The Modern Life Arithmetics: Six-Book Series, Book One. New York: The Macmillan Company.
Stokes, C.N., Adams, B., & Bauer, M.B. (1958). Arithmetic in My World: 1. Boston: Allyn and Bacon, Inc.
The University of Chicago School Mathematics Project. (2004). First Grade Everyday Mathematics: Teacher's Lesson Guide Volume 1 & 2. Chicago: Wright Group/McGraw-Hill.
Watson, B.M. (1918, 1922, 1924). Simplified Primary Arithmetic. Boston: D.C. Heath and Company.