Contibutions of Curricula

1. Contibutions of Curricula A Historical Look at How We Teach Addition

2. 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?

3. 1918 1929 1937 1897 1958 1964 1969 1974 2004 Methods • Collect Textbooks • Choose Focus • Chart • Categorize

4. 1897 1918 1929 1937 1958 1964 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). 1974 1969 2004

5. Textbook Philosophies • Problem Solving • Drill and Memorization 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). “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). 1897 1974 1918 1929 1937 1958 1969 1964 2004

6. Textbook Philosophies “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). • Problem Solving • Drill and Memorization • Fun/Engaging vs. Social “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). 1897 1974 1918 1929 1937 1958 1969 1964 2004

7. Textbook Philosophies "Do not allow the notes to stifle your own effective teaching methods and creative efforts" (1969, p. 17). • Problem Solving • Drill and Memorization "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). • Fun/Engaging vs. Social • Role of Teacher "The teacher should recognize differences in children, and give the stronger ones an opportunity to test their power” (1918, p. 3). 1897 1974 1918 1929 1937 1958 1969 1964 2004

8. Textbook Philosophies • Problem Solving “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). • Drill and Memorization • Fun/Engaging vs. Social • Role of Teacher • Role of Parent 1897 1974 1918 1929 1937 1958 1969 1964 2004

9. Addition Philosophies • Scope 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). 1897 1974 1918 1929 1937 1958 1969 1964 2004

10. Addition Philosophies • Scope • Meaning and words before symbols • + means “and”, say “plus” • + means “and”, say “and” • Symbols “The children use the terms and symbols plus (+) and minus (-) from the beginning” (1964, p. 18). 1897 1974 1918 1929 1937 1958 1969 1964 2004

11. Addition Philosophies • Scope “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). • Symbols • 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). 1897 1974 1918 1929 1937 1958 1969 1964 2004

12. Addition Philosophies • Scope • Make own problems • Describe methods • Interesting gap • Symbols • Physical Manipulation • Creating Problems 1897 1974 1918 1929 1937 1958 1969 1964 2004

13. Addition Philosophies • Scope "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). • Symbols • Physical Manipulation • Creating Problems • Proof 1897 1974 1918 1929 1937 1958 1969 1964 2004

14. Layout Blended Narrative Topics Messy Tools 1897 1974 1918 1929 1937 1958 1969 1964 2004

15. Order: 1897

16. Order: 1918

17. Order: 1929

18. Order: 1937

19. Order: 1958

20. Order: 1964

21. Order: 1969

22. Order: 1974

23. Order: 2004

24. Order: Composite

25. Totals to 9 Totals to 10 Order: End Level Totals to 19 2-Digit

26. Application to Reading Articles on TIMSS and International Studies “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?

27. Examples: Missing Addend 1897 1918 1937 1958 2004 1969 1964

28. Examples: Combinations 1897 1964 1969 1974

29. Examples: Combinations 1958 1937 2004

30. Examples: Vertical • Early • No symbol 1897 1918 1929 1937

31. Examples: Vertical 1958 • Both forms

32. Examples: Vertical 1969 “Once the children thoroughly understand addition and the idea of solving equations, vertical notation for addition problems is introduced” (1969, p. 86). 1974 2004 1964

33. Examples: Commutative 1897 1929 1958 1969 2004 1974

34. Examples: Associative 1964 1969 1974

35. 1929 Examples: Identity 1964 2004 1969 1974

36. Examples: Expanded Form 1964 1897 1969

37. Examples: Other Operations 1958 1897

38. 1969 Strategies For Adding Two, Single-digit Numbers

39. 1969 1897 Strategies For Adding Several One-Digit Numbers

40. 1964 1974 1929 Strategies For Adding a Single-digit and Two-Digit Number

41. 1929 1974 1964 2004 Strategies For Adding Two, Two-Digit Numbers

42. 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?

43. Resources 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. 1897 1974 1918 1929 1937 1958 1969 1964 2004