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Challenging Math Problems
January 2021


"What does the research say about how an instructional emphasis on conceptually challenging math problems and problem-based learning can affect students of color and students from economically disadvantaged backgrounds?

Ask A REL Response

Thank you for your request to our Regional Educational Laboratory (REL) Reference Desk. Ask A REL is a collaborative reference desk service provided by the 10 RELs that, by design, functions much in the same way as a technical reference library. Ask A REL provides references, referrals, and brief responses in the form of citations in response to questions about available education research.

Following an established REL Northwest research protocol, we conducted a search for evidence- based research. The sources included ERIC and other federally funded databases and organizations, research institutions, academic research databases, Google Scholar, and general Internet search engines. For more details, please see the methods section at the end of this document.

The research team has not evaluated the quality of the references and resources provided in this response; we offer them only for your reference. The search included the most commonly used research databases and search engines to produce the references presented here. References are listed in alphabetical order, not necessarily in order of relevance. The research references are not necessarily comprehensive and other relevant research references may exist. In addition to evidence-based, peer-reviewed research references, we have also included other resources that you may find useful. We provide only publicly available resources, unless there is a lack of such resources or an article is considered seminal in the topic area.


Boston, M. D., & Wilhelm, A. G. (2017). Middle school mathematics instruction in instructionally focused urban districts. Urban Education, 52(7), 829-861.

From the Abstract:
"Direct assessments of instructional practice (e.g., classroom observations) are necessary to identify and eliminate opportunity gaps in students’ learning of mathematics. This study examined 114 middle school mathematics classrooms in four instructionally focused urban districts. Results from the Instructional Quality Assessment identified high percentages of lessons featuring cognitively challenging tasks, but declines in cognitive challenge during implementation and discussions. Overall instructional quality exceeded results from studies with nationally representative samples and paralleled results of studies of instructionally focused urban middle schools. Significant differences existed between districts, favoring the district with veteran teachers, long-term use of Standards-based curricula, and professional development initiatives."

Morales, H., & DiNapoli, J. (2018). Latinx bilingual students' perseverance on a mathematical task: A rehumanizing perspective. REDIMAT-Journal of Research in Mathematics Education, 7(3), 226-250.

From the Abstract:
"We draw on a rehumanizing perspective that covets a student-centered viewpoint around the discipline of mathematics. For Latinx bilinguals, we posit that a translanguaging practice is a vital option by which collective perseverance during problem solving can be sustained and leveraged for meaningful learning. This study explores and examines the collaborative efforts of a group of Latinx twelfth-grade students persevering to make meaning of an exponential relationship. We employed a discursive thematic analysis of this groups' ongoing engagement with a challenging mathematical task, paying specific attention to the ways in which these bilingual students encountered and overcame mathematical obstacles and setbacks. Our findings suggest that Latinx bilingual students can spontaneously and dialogically leverage communicative resources to help persevere with in-the-moment obstacles and build mathematical understandings. We argue for the development of more explicit translanguaging support systems in mathematics classrooms to privilege the viewpoint and experiences of the student, and the ways in which they develop mathematical understandings."

Riegle-Crumb, C., Morton, K., Nguyen, U., & Dasgupta, N. (2019). Inquiry-based instruction in science and mathematics in middle school classrooms: Examining its association with students’ attitudes by gender and race/ethnicity. AERA Open, 5(3), 1-17.

From the Abstract:
"Utilizing a nationally representative sample of middle school students, this article focuses on whether students who report experiencing more inquiry-based instruction in science and mathematics classrooms have more positive attitudes toward these subjects. Results of multilevel, multivariate regression analyses revealed that, net of the inclusion of control variables for student, teacher, and school characteristics, a higher frequency of inquiry-based instruction is significantly associated with greater interest, perceptions of utility, and self-efficacy for science and mathematics. Furthermore, although there is some evidence indicating that compared with female students, male students' perceptions of science utility are higher in relation to more inquiry-based instruction, overall, the weight of evidence clearly leans toward the conclusion that the attitudes of students from different gender and racial/ethnic backgrounds are similarly associated with greater exposure to inquiry-based instruction in both their science and mathematics classrooms."

Warshauer, H. K. (2015). Productive struggle in middle school mathematics classrooms. Journal of Mathematics Teacher Education, 18(4), 375-400. Retrieved from

From the Abstract:
"Prior studies suggest that struggling to make sense of mathematics is a necessary component of learning mathematics with understanding. Little research exists, however, on what the struggles look like for middle school students and how they can be productive. This exploratory case study, which used episodes as units of analysis, examined 186 episodes of struggles in middle school students as they engaged in tasks focused on proportional reasoning. The study developed a classification structure for student struggles and teacher responses with descriptions of the kinds of student struggle and kinds of teacher responses that occurred. The study also identified and characterized ways in which teaching supported the struggles productively. Interaction resolutions were viewed through the lens of (a) how the cognitive demand of the task was maintained, (b) how student struggle was addressed and (c) how student thinking was supported. A Productive Struggle Framework was developed to capture the episodes of struggle episodes from initiation, to interaction and to resolution. Data included transcripts from 39 class session videotapes, teacher and student interviews and field notes. Participants were 327 6th- and 7th-grade students and their six teachers from three middle schools located in mid-size Texas cities. This study suggests the productive role student struggle can play in supporting "doing mathematics" and its implications on student learning with understanding. Teachers and instructional designers can use this framework as a tool to integrate student struggle into tasks and instructional practices rather than avoid or prevent struggle."

Zahner, W., Velazquez, G., Moschkovich, J., Vahey, P., & Lara-Meloy, T. (2012). Mathematics teaching practices with technology that support conceptual understanding for Latino/a students. The Journal of Mathematical Behavior, 31(4), 431-446.Retrieved from

From the Abstract:
"We analyze how three seventh grade mathematics teachers from a majority Latino/a, linguistically diverse region of Texas taught the same lesson on interpreting graphs of motion as part of the Scaling Up SimCalc study (Roschelle et al., 2010). The students of two of the teachers made strong learning gains as measured by a curriculum-aligned assessment, while the students of the third teacher were less successful. To investigate these different outcomes, we compare the teaching practices in each classroom, focusing on the teachers' use of class time and instructional format, their use of mathematical discourse practices in whole-class discussions, and their responses to student contributions. We show that the more successful teachers allowed time for students to use the curriculum and software and discuss it with peers, that they used formal mathematical discourse along with less formal language, and that they responded to student errors using higher-level moves. We conclude by discussing implications for teachers and mathematics educators, with special attention to issues related to the mathematics education of Latinos/as."

Zhu, P., Garcia, I., Boxer, K., Wadhera, S., & Alonzo, E. (2019). Using a growth mindset intervention to help ninth-graders: An independent evaluation of the National Study of Learning Mindsets. New York: MDRC.

From the Abstract:
"To test whether a growth mindset intervention could improve the academic performance of adolescents, the National Study of Learning Mindsets (NSLM) implemented a low-cost growth mindset intervention specifically designed for ninth-graders in a nationally representative sample of regular high schools during the 2015-2016 school year. The national study used a student-level randomized controlled trial design to gauge the impacts of this intervention on students' mindsets about intelligence, their own behaviors, and their academic achievements. With support from the Bill & Melinda Gates Foundation, MDRC reviewed the data from the NSLM and conducted an independent evaluation of this growth mindset intervention. This evaluation found the following: (1) The intervention changed students' self-reported mindset beliefs, their attitudes toward efforts and failure, and their views on academic challenges; (2) Immediately after the intervention, students were more likely to take on challenging academic tasks; (3) The intervention produced statistically significant impacts on students' average academic performance, improving their average grade point average (GPA) as well as their math GPA, and reducing the proportion of students with failing grades; and (4) Certain groups of students and schools might benefit more from the intervention than others. These groups include students with relatively low academic achievement before the intervention, schools in the midrange of the academic performance spectrum, and schools where students are more inclined to take on challenging tasks. These findings are substantively consistent with the results published by the NSLM research team."


Keywords and Search Strings: The following keywords, subject headings, and search strings were used to search reference databases and other sources: "Conceptually challenging", ("Math" OR "mathematics" OR "mathematical" OR "problem-based learning"), ("Low income" OR "students of color" OR "minority" OR "socioeconomic" OR "socio-economic OR "economically disadvantaged"), Challenging, Problems, Complex, Tasks, "Productive struggle"

Databases and Resources: We searched ERIC for relevant resources. ERIC is a free online library of more than 1.6 million citations of education research sponsored by the Institute of Education Sciences (IES). Additionally, we searched Google Scholar and EBSCO databases (Academic Search Premier, Education Research Complete, and Professional Development Collection).

Reference Search and Selection Criteria

When we were searching and reviewing resources, we considered the following criteria:

Date of publications: This search and review included references and resources published in the last 10 years.

Search priorities of reference sources: Search priority was given to study reports, briefs, and other documents that are published and/or reviewed by IES and other federal or federally funded organizations, as well as academic databases, including ERIC, EBSCO databases, and Google Scholar.

Methodology: The following methodological priorities/considerations were given in the review and selection of the references:

  • Study types: randomized control trials, quasi experiments, surveys, descriptive data analyses, literature reviews, and policy briefs, generally in this order
  • Target population and samples: representativeness of the target population, sample size, and whether participants volunteered or were randomly selected
  • Study duration
  • Limitations and generalizability of the findings and conclusions

This memorandum is one in a series of quick-turnaround responses to specific questions posed by stakeholders in Alaska, Idaho, Montana, Oregon, and Washington, which is served by the Regional Educational Laboratory (REL) Northwest. It was prepared under Contract ED-IES-17-C-0009 by REL Northwest, administered by Education Northwest. The content does not necessarily reflect the views or policies of IES or the U.S. Department of Education, nor does mention of trade names, commercial products, or organizations imply endorsement by the U.S. Government.