Zhang, D., & Rivera, F. (2021). Predetermined accommodations with a standardized testing protocol: Examining two accommodation supports for developing fraction thinking in students with mathematical difficulties . Journal of Mathematical Behavior , 62 (100861). https://doi.org/10.1016/j.jmathb.2021.100861

Journal Article

Zhang, D., & Rivera, F. (2021). Predetermined accommodations with a standardized testing protocol: Examining two accommodation supports for developing fraction thinking in students with mathematical difficulties. Journal of Mathematical Behavior, 62(100861). https://doi.org/10.1016/j.jmathb.2021.100861


Attention problem; Dictionary/glossary; Learning disabilities; Math; Middle school; Speech/Language disability; U.S. context





Performance on test-like tasks under three separate conditions was compared: (a) traditional test items without accommodations; (b) items with important words or phrases in bolded font, with additional explanatory information, which was termed "annotated" items; and (c) warm-up example items using whole numbers, prior to items testing fractions. The researchers emphasized that the explanatory information did not include explicit problem-solving steps, which they referred to as a "keyword strategy" (p. 7 of 21). The researchers further explained that each of these accommodations was intended "to help students with difficulties in mathematics (SDMs) engage in unit thinking, reasoning, and coordination and consequently improve their ability to process fraction tasks" (Abstract, p. 1 of 21).


Twenty-three (23) students with difficulties in mathematics attending grades 6–8 (middle school) participated. These participants were enrolled in a private school for students with learning disabilities in an unidentified state (U.S.). Five (5) participants each also had a diagnosis of attention-deficit hyperactivity disorder (ADHD) and four (4) students each had a speech/language impairment diagnosis or attended speech/language therapy. Inclusion criteria required that each participant had one or more of these criteria: (a) an identified learning disability, (b) significant difficulties in mathematics and a score below basic on standardized math assessment, (c) an IEP that included math goals. Demographic information, specifically race/ethnicity, was also reported.

Dependent Variable

Three researcher-created tests composed of five tasks each were used to assess student understanding and processes in solving mathematics problems with fractions. Some of the tasks were adapted or changed from a test developed by Maher and Yankelewitz (2017). Tasks included number line representations to story problems, concrete manipulative representations, and part-of-a-whole relationships, and were equivalent in difficulty across test versions.


The researchers reported that their qualitative inquiry of students' task problem-solving experiences yielded complex data. [Note: This summary emphasizes findings on the needs of students with disabilities pertaining to accommodations use.] The document included a substantial summary of studies on effects of accommodations on student performance. In the current study, students with math-related disabilities communicated various obstacles while completing tasks. A series of conclusions were reached: (a) Assessment performance data on response correctness or accuracy may not fully illuminate effects of accommodations, due to the individual differences in which students with math disabilities experience obstacles to problem-solving during testing. (b) A standard protocol of accommodations for all test-takers with math disabilities may not be sufficiently useful in addressing these individual differences in needs during problem-solving; instead, individualized accommodations could be needed. (c) Student participants' non-responses on the same items in different test conditions—with and without item annotations—require careful consideration of their meaning. The researchers suggested that students did not understand expectations despite simplified instructions; in other words, the annotations did not remove decoding-based obstacles. (d) Using whole number practice items prior to completing fraction items could support development of math reasoning capacity—that is, new learning. The issue of implementing accommodations broadly, in a standard protocol approach, in contrast with individualizing accommodations for each student's needs, was discussed. Future research possibilities were suggested.