Zhang, D., Indyk, A., & Greenstein, S. (2021). Effects of schematic chunking on enhancing geometry performance in students with math difficulties and students at risk of math failure . Learning Disability Quarterly , 44 (2), 82–95. https://doi.org/10.1177/0731948720902400

Journal Article

Zhang, D., Indyk, A., & Greenstein, S. (2021). Effects of schematic chunking on enhancing geometry performance in students with math difficulties and students at risk of math failure. Learning Disability Quarterly, 44(2), 82–95. https://doi.org/10.1177/0731948720902400


Advance online publication (2/7/20)


Attention problem; High school; K-12; Layout/organization of test items; Learning disabilities; Math; No disability; Speech/Language disability; Templates or organizers; U.S. context





A test format with colored representations and marks highlighting interactive elements of visual schematic chunking involved in problem solving were provided to students and compared to the students' performance on a test with black and white plain schematics (i.e., without this information). These visual elements were intended to focus student attention to important details. Additionally, randomly-selected students were provided with a reference guide with the theorems and postulates needed to solve the geometry test items.


Thirty-three (33) students in grade 9 in inclusive geometry classrooms at a suburban high school in the Northeast (U.S.) participated. Students were identified by teachers as having "having difficulty learning geometry." Participants were divided into two groups, students who had math difficulties (MD) (n=18) and students at risk of math failure but not meeting the criteria for the MD group (n=15). Students with MD included students who met one or more of the following: (a) received a grade of C or below in a high school geometry class [course grades served as a screening tool], and/or (b) eligible for special education services with a mathematics IEP goal, and/or (c) failed the state standardized test. Other demographic information was reported, such as gender, race, and socio-economic status.

Dependent Variable

A researcher-developed test was composed of 22 mathematics problems, addressing geometry content—such as calculation of parallel lines, description of spatial relations, application of theorems or postulates—and incorporating three different difficulty levels: simple one-step, difficult one-step, and multi-step. Participants were asked to explain how they solved the difficult and multi-step problems (i.e., show their work). The analysis of factors used a 3x2x2 design. There were two within subject variables—difficulty levels and with or without visual chunking—and one between-subjects variable—with or without reference guide.


The results showed that all students improved in performance with chunking representations. This was consistent with previous research on the integration of verbal interactive elements from math problem statements and color scheming and marking the visual interactive elements on a diagram. The research also extended the concept of "chunk" from just a physical shape to a schematic with meaning in relation to geometric properties, theorems, and postulates. Two possible moderating effects were reported, problem complexity and student knowledge of geometry. Problem complexity showed that the effects of chunking was not significant on one step problems but significant on more complex problems that required greater working memory load. Student knowledge of geometry was manipulated with the provision of a cheat sheet or not. Results showed that students with math difficulties showed significant improvement with chunking representation and cheat sheet while students at risk of failure did not. Chunking provided a first level of scaffolding helping with recognition while the cheat sheet provided a second level of scaffolding for retrieval from long term memory. These findings support the cognitive load theory and also suggests that different forms of scaffolding intervention or accommodations are useful for students with different levels of knowledge. Limitations of the study were reported, and future research possibilities and implications for practice were suggested.