Publication Date
| In 2026 | 0 |
| Since 2025 | 0 |
| Since 2022 (last 5 years) | 1 |
| Since 2017 (last 10 years) | 3 |
| Since 2007 (last 20 years) | 9 |
Descriptor
| Multiplication | 9 |
| Middle School Students | 7 |
| Algebra | 6 |
| Mathematical Concepts | 6 |
| Mathematics Instruction | 6 |
| Fractions | 4 |
| Grade 7 | 4 |
| High School Students | 4 |
| Logical Thinking | 4 |
| Numbers | 4 |
| Concept Formation | 3 |
| More ▼ | |
Source
| Educational Studies in… | 2 |
| North American Chapter of the… | 2 |
| Cognition and Instruction | 1 |
| International Journal of… | 1 |
| Journal for Research in… | 1 |
| Journal of Mathematical… | 1 |
| Mathematical Thinking and… | 1 |
Author
| Hackenberg, Amy J. | 9 |
| Lee, Mi Yeon | 4 |
| Aydeniz, Fetiye | 1 |
| Creager, Mark | 1 |
| Eker, Ayfer | 1 |
| Matyska, Robert | 1 |
| Sevinc, Serife | 1 |
| Tillema, Erik S. | 1 |
Publication Type
| Reports - Research | 9 |
| Journal Articles | 7 |
| Speeches/Meeting Papers | 2 |
| Tests/Questionnaires | 1 |
Education Level
| Middle Schools | 7 |
| Junior High Schools | 6 |
| Secondary Education | 6 |
| Elementary Education | 3 |
| Grade 7 | 3 |
| High Schools | 3 |
| Grade 6 | 2 |
Audience
Location
Laws, Policies, & Programs
Assessments and Surveys
What Works Clearinghouse Rating
Peer reviewed
Direct linkHackenberg, Amy J.; Sevinc, Serife – Educational Studies in Mathematics, 2022
Students entering sixth grade operate with three different multiplicative concepts that influence their reasoning in many domains important for middle school. For example, students who are operating with the second multiplicative concept (MC2 students) can begin to construct fractions as lengths but do not construct improper fractions as numbers.…
Descriptors: Multiplication, Fractions, Grade 7, Middle School Students
Hackenberg, 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. – 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
