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Direct linkHackenberg, Amy J.; Creager, Mark; Eker, Ayfer – Mathematical Thinking and Learning: An International Journal, 2021
Three iterative, 18-episode design experiments were conducted after school with groups of 6-9 middle school students to understand how to differentiate mathematics instruction. Prior research on differentiating instruction (DI) and hypothetical learning trajectories guided the instruction. As the experiments proceeded, this definition of DI…
Descriptors: Mathematics Instruction, Teaching Methods, Individualized Instruction, Thinking Skills
Download full textHackenberg, Amy J.; Aydeniz, Fetiye; Matyska, Robert – North American Chapter of the International Group for the Psychology of Mathematics Education, 2019
A design experiment with 18 students in a regular seventh grade math class was conducted to investigate how to differentiate instruction for students' diverse ways of thinking during a 26-day unit on proportional reasoning. The class included students operating with three different multiplicative concepts that have been found to influence rational…
Descriptors: Grade 7, Mathematics Instruction, Individualized Instruction, Student Diversity
Hackenberg, Amy J.; Lee, Mi Yeon – Educational Studies in Mathematics, 2016
To understand relationships between students' quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. The study included six students with each of three different multiplicative concepts, which are based on how students create and coordinate composite…
Descriptors: Mathematics Instruction, Mathematical Logic, Fractions, Algebra
Hackenberg, Amy J. – Cognition and Instruction, 2010
In an 8-month teaching experiment, I investigated how 4 sixth-grade students reasoned with reversible multiplicative relationships. One type of problem involved a known quantity that was a whole number multiple of an unknown quantity, and students were asked to determine the value of the unknown quantity. To solve these problems, students needed…
Descriptors: Mathematics Instruction, Grade 6, Mathematics Achievement, Multiplication
Hackenberg, Amy J.; Lee, Mi Yeon – North American Chapter of the International Group for the Psychology of Mathematics Education, 2012
To understand relationships between students' quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. Six students with each of 3 different multiplicative concepts participated. This paper reports on the 6 students with the most basic multiplicative…
Descriptors: Middle School Students, Mathematics Instruction, Logical Thinking, Fractions
Hackenberg, Amy J.; Tillema, Erik S. – Journal of Mathematical Behavior, 2009
This article reports on the activity of two pairs of sixth grade students who participated in an 8-month teaching experiment that investigated the students' construction of fraction composition schemes. A fraction composition scheme consists of the operations and concepts used to determine, for example, the size of 1/3 of 1/5 of a whole in…
Descriptors: Numbers, Concept Formation, Grade 6, Mathematics Instruction
