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Mathematics 320: Project 23

Introduction. Each group will analyze the mathematical content of a given sample text. An Explanation
of how the analysis should be conducted is given below. Projects that are insightful, clearly articulated, and
mathematically accurate will be awarded the most points.
Background. The Mathematics Learning Study Committee of the National Research Council has put
forth a model of mathematical understanding called mathematical proficiency [1]. Mathematical proficiency
consists of the five following strands:

• conceptual understanding - comprehension of mathematical concepts , operations , and relations
• procedural fluency - skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
• strategic competence - ability to formulate , represent, and solve mathematical problems
• adaptive reasoning- capacity for logical thought , reflection, explanation, and justification
productive disposition - habitual inclination to see mathematics as sensible, useful, and worthwhile,
coupled with a belief in diligence and one’s own efficacy.

You should keep in mind that these strands are interdependent, and it is argued that for students to become
mathematical proficient , instructional programs must address each strand .

Figure 1. The intertwined strands of mathematical proficiency.

Directions. Your project should consist of the following in the form of a written or typed paper less than
two pages .

• A brief description of the mathematical concept(s) the given investigation covers. In other words,
what should your students get from this lesson in a nutshell.

• Determine which of the five strands of mathematical proficiency, given above, are covered in your
sample lesson. Give an explicit example of the content for each strand that you have determined to
be in the lesson.

• If you find that some strands were not covered in the lesson, then modify the sample lesson so that
it incorporates the missing strands.


Group Project
A1 Moving Between Fractions and Decimals
A2 Moving Between Fractions and Decimals
B1 From Fractions to Decimals
B2 From Fractions to Decimals
C1 Cooking with Fractions
C2 Cooking with Fractions
D1 Comparing Fractions
D2 Comparing Fractions
E1 Fund-Raising Fractions
E2 Fund-Raising Fractions


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