Metacognition has long been viewed as an essential skill set for promoting student learning, knowledge transfer, self regulation and self efficacy. In his widely acclaimed work “Visible Learning,” John Hattie assigned an effect size of d=.69, equivalent to a 25 percentile point improvement (Marzano, 2009) to metacognitive instructional strategies (for a note on Hattie’s methodology see Shanahan, 2017). This finding suggests that metacognitive strategies yield significant growth in student achievement, sparking interest from both teachers and administrators. “Long-term effects of metacognitive strategy instruction on academic performance” a 2017 meta-analysis by de Boer, Donker, Kosntons and van der Werf reviewing 48 interventions in 36 studies exploring learning strategies with metacognitive components calculated an average effect size of g=.50 immediately following the intervention, and more interestingly, g=.63 in a follow up assessment. This evidence of durable improvement suggests that metacognition can be a cornerstone of effective instructional practice. 

 

Researchers Zemeria Mevarech and Brancha Kramarski have written extensively about the efficacy of metacognitive instruction in mathematics. In fact, their work was cited by researcher, scholar and teacher educator Dylan William in his work Embedded Formative Assessment. The IMPROVE model demonstrates significant growth over control groups in a variety of settings, including both “conventional test-like problems” (Mevarech and Kramarski, 1997) and “authentic tasks relating to everyday life” (Kramarski, Mevarech, & Arami, 2002). Mevarech and Kramarski also explored the sustainability of student growth highlighted by de Boer et al. in their 2003 piece entitled “The effects of metacognitive training versus worked out examples on students’ mathematical reasoning” (2003). This study also found that the effects of metacognitive training were more impactful on the growth of lower achieving students. 

 

IMPROVE is an instructional method comprising several steps represented by the letters of the acronym: 

Introducing the new concepts

Meta-cognitive questions

Practicing

Reviewing

Obtaining mastery

Verification 

Enrichment and remedial

 

The authors state “the teacher first introduces the new concepts, theorems, formula etc. to the whole class by modeling the meta-cognitive questioning technique” which includes “three kinds of self addressed questions: comprehension questions, connection questions and strategic questions and reflection questions” (Mevarech and Fridkin, 2006 p.87). They define their questions as follows: 

 

Comprehension questions orient students to articulate the main ideas in the problem (e.g., What is the problem all about?). Connection questions lead students to construct bridges between the given problem and problems solved in the past (e.g., What are the similarities and differences between the given problem and problems you have solved in the past, and why?). Strategic questions refer to strategies appropriate for solving the problem (e.g., What strategies are appropriate for solving the problem and why?). Finally, reflection questions guide students to look backward either during the solution process (e.g., Why am I stuck? What am I doing here?), or at the end (e.g., Does the solution make sense? Can I solve it differently?). 

 

The 2006 study “The effects of IMPROVE on mathematical knowledge, mathematical reasoning and meta-cognition” utilized an interesting experimental design to validate the intervention’s effects. The students in the study consisted of 81 pre-college students in Israel who had failed or performed poorly on college mathematics entrance exam ( p. 89). Most interestingly, the students in both the IMPROVE group (n=38) and control group (n=43) had the same instructor, eliminating teacher quality as a potential confounding variable. 

 

The following tables are taken directly from the article and demonstrate the significant comparative efficacy of the IMPROVE model over the control group on a math exam: 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

On General Metacognition: 

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​​And on Schraw and Dennison’s Metacognitive Awareness Inventory (Cronbach’s alpha= .87): 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Evidence from this study shows robust growth in both the mathematics achievement and the application of metacognitive principles. Given that metacognition has shown comparatively higher effects for lower performing students and students from lower socio-economic backgrounds (de Boer et al. 2017), the IMPROVE method and direct instruction in metacognitive strategies generally have the potential to drive significant growth in mathematics achievement.