Helpful Definitions:

Multiple Heuristics: Teaching students multiple procedures for solving problems.

 

Explicit Instruction: Directly explaining procedures and concepts to students.

 

Student Verbalization of their Reasons: Sometimes referred to as self talk. Students try to talk out their own ideas.

 

Cognitive Based Interventions: Includes meta-cognition strategies, schema instruction, self talk, and behavior management strategies. 

 

Sequence or Range of Examples: Giving students examples of how to solve an easy, normal, and hard version of a question. 

 

Multiple Content Domains Taught: Teaching multiple strands, such as teaching geometry, fractions, number sense, and not just one domain at a time. 

 

Fluency Instruction: Teaching number sense, and math facts, with the goal of increasing student speed and accuracy for arithmetic. 

 

Using Visual Representatives: Diagrams and manipulatives.

 

Formative Assessment, Coupled with Targeted Optional Additional Instruction: Offering students additional instruction, based on their assessed needs. 

 

Schema Based Instruction: Teaching students to methodologies to employ when facing challenging problems. This can include things like, teaching math vocabulary, and word problem procedures for analysis. IE: Ask yourself, what words do you recognize in the word problem, what is the word problem asking you, what don’t you know, what procedures might you use?

 

High Yield Strategies:  

Multiple heuristics, explicit instruction, student verbalization, cognitive based instruction, and scaffolding, all appear to be high yield strategies that teachers can implement into their instruction with ease. The effect size found here for direct instruction of math concepts to learning disabled students is much higher than the mean effect size of direct instruction found by John Hattie of .57 and might be a reflection of the fact that both math instruction and learning disabled students require more explicit instruction. 

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I had the opportunity to speak to Dr. Jon Star about the use of multiple heuristics and he had extensively researched this topic. He suggested that teachers can overwhelm students if they include too many procedures and recommended teachers instruct two procedures for each type of math problem. 

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Low Yield Strategies: 

Ability grouping, small group instruction, goal setting, alternate work environments, word problems and same age peer tutoring, formative assessment, all appeared to provide little to no benefit to students within the research. This does not mean that teachers should never use these strategies; however, it might suggest that these strategies might be harder to execute in such a way that consistently benefits students. Formative assessment for example, is necessary in my opinion for several instructional strategies that have been shown as high yield within the literature, including individualization and RTI. Personally, I think formative assessment is absolutely critical, as it allows us to make informed instructional choices. However, this is likely the true problem with the meta-analysis data on formative assessment, as that assessment data is only as valuable as the instruction that follows it. Similarly, I have found in class peer tutoring to be one of my most effective teaching tools; however, I couple that peer tutoring with individualization and classroom economy. In my personal opinion, the more specific interventions are to assessment criteria, the more useful they are. So for example small group instruction in an alternative classroom, that does not match the instruction being done in class or worse, is happening during regular math instruction, is unlikely to have a large benefit. With that in mind, I think teachers should consider, when using these low yield strategies, how they can avoid potential pitfalls and how they can increase the specificity of my intervention. 

 

Written by Nathaniel Hansford

Last Edited: 2022-03-27
 

References:

 

Myers. (2021). Mathematics Interventions for Adolescents with Mathematics Difficulties: A Meta‐Analysis. Learning Disabilities Research & Practice., 36(2), 145–166.

 

R, Getsen, Et al. (2009). A Meta-analysis of Mathematics Instructional Interventions for Students with Learning Disabilities:
 

J, Myers. (2022). A Meta-Analysis of Mathematics Word-Problem Solving Interventions for Elementary Students Who Evidence Mathematics Difficulties. The Review of Educational Research. Retrieved from <https://journals-sagepub-com.ezproxy.lakeheadu.ca/doi/full/10.3102/00346543211070049>. 

 

N, Hansford. (2022). Math Fluency. Pedagogy Non Grata. Retrieved from <https://www.pedagogynongrata.com/math-fluency>. 

 

N, Hansford. (2022). Differentiation. Pedagogy Non Grata. Retrieved from <https://www.pedagogynongrata.com/differentiation>. 

J, Hattie. (2022). Metax. Visible Learning. Retrieved from <https://www.visiblelearningmetax.com/Influences>.