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Students' Reasoning Around The Functional Relationship, Michele Carney, Angela Crawford
Students' Reasoning Around The Functional Relationship, Michele Carney, Angela Crawford
Curriculum, Instruction, and Foundational Studies Faculty Publications and Presentations
Proportional reasoning is related to flexible use of the scalar and functional relationships that exist in proportional situations. More specifically, in regard to the functional relationship, students’ understanding of the multiplicative comparison that exists between two quantities in a ratio is a key concept. We conducted student interviews with 12 high performing students to examine their conception of the functional relationship. Analyses provided initial evidence that the majority of students did not conceive of the multiplicative comparison when solving problems designed to press the functional relationship, indicating students’ written work that makes use of the functional relationship should not imply …
Developing Multiplication Fact Fluency, Jonathan Brendefur, S. Strother, K. Thiede, S. Appleton
Developing Multiplication Fact Fluency, Jonathan Brendefur, S. Strother, K. Thiede, S. Appleton
Curriculum, Instruction, and Foundational Studies Faculty Publications and Presentations
Using specific components of three broad learning theories—cognitive, social-interactional, and behavioral—students in 3rd, 4th and 5th grade classrooms were given multiplication fact fluency instruction over a period of five weeks for 10-15 minutes each day. Two different approaches were utilized with two distinct groups of students for the purpose of comparing different approaches to fluency development. Results indicate that students using a strategy-based approach for fluency development by means of instructional tasks emphasizing social-interactional and cognitive theories (particularly Bruner’s theory of Modes of Representation) increased multiplication fact fluency, with a greater degree of consistency, than students …