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Anna Stokkey Podcast- Science of Math Studies and Resources 

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Anna Stokkey Podcast- Science of Math Studies and Resources 

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This is the resource page for Episode 20 of the Chalk & Talk podcast.

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We provide resources related to effective math instruction. Our goal is to ensure that all students, regardless of background or status, have equitable access to high-quality math instruction. To guide the Science of Math, we rely on well-researched instructional strategies and research about how students learn.

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Take a journey through the history of mathematics, from ancient times to the modern day. Discover the milestones that shaped this discipline.

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Explore some of the most fascinating facts about math that illustrate its beauty and complexity. Perfect for engaging students and sparking curiosity.

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In Education Next I criticized the proposed California Math Framework for basing recommendations on bad evidence. The State of California now seems to agree that using a particular assessment, going by the acronym of MARS (a collection of math tasks) to evaluate student achievement is unwarranted. In May, the California State Board of Education considered and rejected the test when issuing a List of Valid and Reliable Assessments required by California Education Code Section 47607.2.

The Education Next article singled out a study of a summer Youcubed math camp that claimed to increase student achievement by 2.8 years after 18 days of instruction. Jack Dieckmann of YouCubed offered a rebuttal to my criticism and I responded, with both statements published in Education Next. Two paragraphs from my response summarize the argument.
I focused on outcomes measured by how students performed on four tasks created by the Mathematical Assessment Research Service (MARS). Based on MARS data, Youcubed claims that students gained 2.8 years of math learning by attending its first 18-day summer camp in 2015. Dieckmann defends MARS as being "well-respected" and having a "rich legacy," but offers no psychometric data to support assessing students with the same four MARS tasks pre- and post-camp and converting gains into years of learning. Test-retest using the same instrument within such a short period of time is rarely good practice. And lacking a comparison or control group prevents the authors from making credible causal inferences from the scores." Is there evidence that MARS tasks should not be used to measure the camps' learning gains? Yes, quite a bit. The MARS website includes the following warning:"Note: please bear in mind that these materials are still in draft and unpolished form." Later that point is reiterated, "Note: please bear in mind that these prototype materials need some further trialing before inclusion in a high-stakes test." I searched the list of assessments covered in the latest edition of the Buros Center's Mental Measurements Yearbook, regarded as the encyclopedia of cognitive tests, and could find no entry for MARS. Finally, Evidence for ESSA and What Works Clearinghouse are the two main repositories for high quality program evaluations and studies of education interventions. I searched both sites and found no studies using MARS.
In the latest version of the framework, released near the end of June, references to the summer camps have been removed. But references to another Youcubed study using MARS data remain. The framework cites a 2021 study (Boaler and Foster, 2021) to endorse heterogeneous grouping in middle school, reproducing two figures (see Figs. 9.1 and 9.2) to document the claim that students in detracked, heterogeneously grouped middle schools out-performed students grouped by ability, asserting a gain "equivalent to 2.03 years of middle school growth."[i]

Since I published the Education Next article, additional evidence has emerged that calls into question using MARS tasks to evaluate achievement gains. On May 18, 2023 the California State Board of Education considered and rejected the assessment (also known as MAC/MARS from its use by the Silicon Valley Math Initiative) for assessing achievement in charter schools. Interestingly, the assessment review was conducted by WestEd, the same firm that edited the framework over the past year.

MAC/MARS failed the first step in the review, consideration of technical quality. The review considered four criteria, including validity and reliability (see page 17 of May Item 2 documentation). MARS did not meet state standards for technical quality.

Tomorrow, July 12, the Board will vote on the math framework. The Board is now in the strange position of voting on a framework that uses as supporting evidence results from an assessment that the board itself rejected in May.

[i] Mike Lawler (@mikeandallie on Twitter) has identified numerous flaws in the Boaler and Foster, 2021 study.

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More Evidence that the CA Math Framework Cites Flawed Research - Tom Loveless

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In Education Next I criticized the proposed California Math Framework for basing recommendations on bad evidence. The State of California now seems to agree that using a particular assessment, going by the acronym of MARS (a collection of math tasks) to evaluate student achievement is unwarranted.

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Intensive instruction was recently identified as a high-leverage practice in special education, and DBI is a research based approach to delivering intensive instruction across content areas (NCII, 2013). This course provides learners with an opportunity to extend their understanding of intensive instruction through in-depth exposure to DBI in mathematics, complete with exemplars from actual classroom teachers.

NCII, through a collaboration with the University of Connecticut and the National Center on Leadership in Intensive Intervention and with support from the CEEDAR Center, developed course content focused on enhancing educators' skills in intensive mathematics intervention. The course includes eight modules that can support faculty and professional development providers with instructing pre-service and in-service educators who are learning to implement intensive mathematics intervention through data-based individualization (DBI). The content in this course complements concepts covered in the Features of Explicit Instruction Course and so we suggest that users complete both courses.

Modules 1-8: Intensive Intervention in Mathematics

There are 8 modules within this course. Each course has an introduction, three parts, and a conclusion.

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Intensive Mathematics Intervention: Training Modules | NCII

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Explore eight in-depth training modules to help enhance educator skills on implementing intensive mathematics intervention through data-based individualization.

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WWC | Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades

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This practice guide provides evidence-based practices that can help teachers tailor their instructional approaches and/or their mathematics intervention programs to meet the needs of their students.

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Selecting what to teach by assessing learners' skill strengths and areas for improvement is only one of two steps for effective instructional planning. This initial step indicates which skills learners have mastered and not mastered. The second step of instructional planning is to align what to teach with how to teach it. The instructional hierarchy helps teachers connect instructional tactic to student need or stated another way, it gives teachers an evidence-based way to decide how to teach a particular skill (i.e., acquisition, fluency-building, or generalization instruction. 10,11,12

Citation: Advocates for the Science of Math (2021). How Teachers Can Make Learning Happen Based on The Science of Learning. Authors.

(1) Haring, N. G., & Eaton, M. D. (1978). Systematic instructional technology: An instructional hierarchy. In N. G. Haring, T. C. Lovitt, M. D. Eaton, & C. L. Hansen (Eds.), The fourth R: Research in the classroom (pp. 23-40). Merrill.

(2) Binder, C. (1996). Behavioral fluency: Evolution of a new paradigm. Behavior Analyst, 19, 163-197.

(3) VanDerHeyden, A. M., & Codding, R. S. (2020). Belief-Based Versus Evidence-Based Math Assessment and Instruction: What School Psychologists Need to Know to Improve Student Outcomes. Research-Based Practice; Communique, 48(5), p. 1, 20-25.

(4) VanDerHeyden, A. M., & Solomon, B. (2023). The limits of accuracy and why fluency is a superior metric. School Psychology, 38(3), 160-172. https://doi.org/10.1037/spq0000528

(5) Mayfield, K. H., & Chase, P. N. (2002). The effects of cumulative practice on mathematics problem solving. Journal of Applied Behavior Analysis, 35, 105-123. https://doi.org/10.1901/jaba.2002.35-105

(6) Burns, M. K., VanDerHeyden, A. M., & Jiban, C. (2006). Assessing the instructional level for mathematics: A comparison of methods. School Psychology Review, 35, 401-418. https://doi.org/10.1080/02796015.2006.12087975

(7) Powell, C. B., Simpson, J., Williamson, V. M., Dubrovskiy, A., Walker, D. R., Jang, B., ... & Mason, D. (2020). Impact of arithmetic automaticity on students' success in second-semester general chemistry. Chemistry Education Research and Practice, 21(4), 1028-1041. https://doi.org/10.1039/D0RP00006J

(8) Rohrer, D., Dedrick, R. F., Hartwig, M. K., & Cheung, C. N. (2019, May16). A randomized controlled trial of interleaved mathematics practice. Journal of Educational Psychology. Advance online publication. https://dx.doi.org/10.1037/edu0000367

(9) Burns, M. K., Codding, R. S., Boice, C. H., & Lukito, G. (2010). Meta-analysis of acquisition and fluency math interventions with instructional and frustration level skills: Evidence for a skill-by-treatment interaction. School Psychology Review, 39(1), 69-83. https://doi.org/10.1080/02796015.2010.12087791

(10) Codding, R. S., Shiyko, M., Russo, M., Birch, S., Fanning, E., & Jaspen, D. (2007). Comparing mathematics interventions: Does fluency predict intervention effectiveness? Journal of School Psychology, 45, 603-617.

(11) Maki, K. E., Zaslofsky, A. F., Knight, S., Ebbesmeyer, A. M., & Chelmo-Boatman, A. (2020). Intervening with Multiplication Fact Difficulties: Examining the Utility of the Instructional Hierarchy to Target Interventions. Journal of Behavioral Education, 30(1), 1-25.

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How Teachers Can Make Learning Happen - The Science of Math

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Selecting what to teach by assessing learners' skill strengths and areas for improvement is only one of two steps for effective instructional planning. This initial step indicates which skills learners have mastered and not mastered. The second step of instructional planning is to align what to teach with how to teach it.

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We provide resources related to effective math instruction. Our goal is to ensure that all students, regardless of background or status, have equitable access to high-quality math instruction. To guide the Science of Math, we rely on well-researched instructional strategies and research about how st