# Rational Numbers: An Integration of Research

By Thomas A. Romberg; Elizabeth Fennema et al. | Go to book overview
 ings. The translation model has important implications for how learners might be assessed, and would have many of the characteristics mentioned. 6. Because teachers are the ones to implement curriculum change, understanding the relationship between teachers' content knowledge and the instructional decisions they make (i.e., what is taught, what questions are asked, what turn discussions will take, what representations are used, what materials are employed, etc.) is critical. Some research has examined teachers' mathematical and pedagogical knowledge. Future efforts should examine the relationship between such knowledge and actual teaching methods employed. Ultimately, improved knowledge and method should result in higher student achievement.

APPENDIX A PARTIAL SCOPE AND SEQUENCE FOR FRACTION CONCEPTS

(Suggested by Minneapolis Classroom Teachers 1989)

GRADE 4

Name and write fraction symbol when given a physical model: (circles, chips, paper folding). (M → WS)*

Model a fraction using physical materials or pictures (circles, chips, paper folding) when given the fraction symbol. (WS → M/P)

Explain what a fraction means when given a physical model or pictures (circles, chips, paper folding). (M/P → VS)

Represent a fraction with one type of physical material when given the fraction with another physical material (circles to chips; chips to circles; paper folding to chips; chips to paper folding). (M → M)

Explain the meaning of a fraction given in symbol form and give a real life "story" for the fraction. (WS → VS → RW)

Change improper fractions to mixed fractions using circles. (WS → M → WS)

Name a fraction using physical materials (circles, chips, paper folding) when the unit is varied. (M → VS)

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