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This resource was developed by CSMC faculty with support from the National Science Foundation. The opinions and information provided are not necessarily supported by the NSF.

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Committees and Reports that have Influenced the Changing Mathematics Curriculum

This PP is one of a series of resources produced by the Center for the Study of Mathematics Curriculum. The CSMC is one of the Centers for Learning and Teaching supported by the National Science Foundation. These materials are provided to facilitate greater understanding of mathematics curriculum change and permission is granted for its educational educational use.

Committee on Essential Mathematics for Minimum Army Needs

http://www.mathcurriculumcenter.org

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Committee on Essential Mathematics for Minimum Army

Needs

Appointed 1943Final Report 1943

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Final Report of Committee on Essential Mathematics for Minimum Army NeedsU. S. Office of Education and The National Council of Teachers of MathematicsMathematics TeacherOctober 1943

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An emerging emergency---World War II

• “The enlisted man has certain minimum mathematical needs”

• “The typical inductee does not have the training in mathematics which he needs”

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Committee on Minimum Army Needs

• Virgil S. Mallory, Montclair (N.J.) State Teachers College (chair)

• Rolland R. Smith, Springfield, MA public schools• C. Louis Thiele, Detroit, MI public schools• F. Lynwood Wren, George Peabody College for Teachers• William A. Brownell, Duke University, consultant for the

Civilian Pre-Induction Training Branch, A .S. F.• John Lund, U. S. Office of Education• Giles M. Ruch, U. S. Office of Education

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Final report had 5 general sections

• Discussion on the Nature of the Essential Mathematics

• Outline for Essential Mathematics for Minimum Army Needs

• General Suggestions with Respect to Instruction

• Specific Suggestions with Respect to Instruction

• Setting Up the Instructional Program

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Nature of the Essential Mathematics

• What the list of essential mathematics is and what it is not:

1. “This list does not constitute a course in mathematics.”

2. The topics listed reflected the minimum basis for inductees.

3. “It is a fallacy to assume that enrollment in advanced high school courses in mathematics assures proficiency in the minimum essentials listed in this report.”

4. “The topics are appropriate objectives of instruction for all young men about to enter the Army.”

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The list continued…5. “This report does not sacrifice general education to the

particular needs of the Army.”6. This report is not to be oversimplified; the reader should

realize that more is called for than just computational competence.

7. Two aspects of mathematical learning were recognized as being neglected: understanding and experience in application.

8. Men about to enter the Army must be educated in “the ability to meet quantitative problems effectively, confidently, and sensibly.”

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Outline for Essential Mathematics for Minimum Army

Needs(as taken directly from the report)

A. Reading and Writing Arithmetical Symbols

B. Counting (by 1’s, 2’s, 5’s, and 10’s to 500)

C. Operations with Whole Numbers

D. Operations with Common Fractions

E.Operations with Decimal FractionsF.Part-Whole Relationships, with common

fractions, decimal fractions, and percents

G. Ratio and ProportionH. Powers and RootsI. Graphs and Maps

J. TablesK.Formulas and

equationsL.Positive and

Negative Numbers M. Measurement,

including understanding of basic units

N. Geometric ConceptsO. Drawing and

ConstructionP.Miscellaneous

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Examples illustrating military connections

• Graphs and Maps:• Interpreting maps and graphs. Used in discovering

the location of artillery, the command post, hostile forces; determining the height of points on a terrain (from a map showing contour lines); scouting and reconnaissance; radio and signal communication.

• Positive and Negative numbers: • Used for indicating direction of flow of both

alternating and direct current; machine gun firing tables; angle of sight instruments; calculating data for range cards on machine guns; determining direction’ designating storage battery terminals.

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General Suggestions with Respect to Teaching

• The committee recommended points of emphasis for instruction:

1. Remedial instruction2. New Concepts3. Applications4. Importance of meaning and understanding

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Specific Suggestions with Respect to Instruction

• Heavy emphasis on number sense in approximation and estimation as well as problem solving.

• Some examples of problems to give students:

Operations with Whole Numbers:Problem-solving:

o If only 37 men of a detail of 72 report on time, how many are late?

o If you can pack 8 shells in a box, how many boxes will be needed for 256 shells?

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Setting Up the Instructional Program

Part 1: Focusing on Students• Within this section of the report the

committee focused on several concerns, including:

– make sure mathematics majors had the necessary skills and ideas;

– provide students out of school with opportunities to make up mathematics deficiencies.

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Setting Up the Instructional Program

Part 2: Focusing on evaluation• Need for assessment instruments.• Importance of observation as an evaluation

tool.“Competence in observation is possible when the observer knows what he is looking for and what constitutes sound evidence.”

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Significance of the Report• Reinforced previous calls for mathematics to

be taught for and learned with understanding.• Provided a basis of mathematical instruction to

ensure that Army needs were met.• Recommended a course of action for inductees

who were already out of school.• Recommended the agencies promoting pre-

induction training be “encouraged and multiplied.”

• Emphasized the need for real world/military connections to theoretical mathematics.

• Emphasized the need for an assessment tool to ensure a minimum level of mathematics was learned.

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References

“Esssential Mathematics for Minimum Army Needs”. (1943). Mathematics Teacher, 36(6), 243-282.

Garrett, A. W. & Davis Jr., O. L. (2003). A time of uncertainty and change: School mathematics from World War II until the new math. In G. M. A. Stanic & J. Kilpatrick (Eds.), A history of school mathematics v.1 (pp. 493-520). Reston, VA: NCTM.

Reeve, W. D. (1942). The importance of mathematics in the war effort. Mathematics Teacher, 35(2), 88-89.