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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.; Lee, Mi Yeon – Journal for Research in Mathematics Education, 2015
To understand relationships between students' fractional knowledge and algebraic reasoning in the domain of equation writing, an interview study was conducted with 12 secondary school students, 6 students operating with each of 2 different multiplicative concepts. These concepts are based on how students coordinate composite units. Students…
Descriptors: Secondary School Mathematics, Equations (Mathematics), Mathematics Skills, Multiplication
Lee, Mi Yeon; Hackenberg, Amy J. – International Journal of Science and Mathematics Education, 2014
To investigate 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 students were interviewed twice, once to explore their quantitative reasoning with fractions and once to explore their solutions of problems…
Descriptors: Correlation, Logical Thinking, Thinking Skills, Mathematical Concepts
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
