### A review of guidance and structure in elementary school mathematics instruction

#### Abstract

Guidance and structure have both been linked to higher achievement, but the two terms are not clearly defined and, thus, are used interchangeably. This makes it difficult to determine the practical implications of interventions and how teachers should apply guidance and structure in their own classrooms. This paper defines and differentiates guidance and structure in elementary school mathematics research. Specifically, guidance involves interactive and responsive student-teacher interactions during teaching while structure refers to the explicitness of the lesson plan, curriculum, or materials. We make this distinction because guidance provided by teachers requires a higher level of expertise and preparation from the teacher. We found some support for the benefits of guidance, with the caveat that teachers should consider individual student factors, such as prior knowledge. Structure encompasses a wider variety of activities, including worked examples, ordering problems from easy to difficult, or providing formula sheets during problem solving.

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Alfieri, L., Brooks, P. J., Aldrich, N. J., & Tenenbaum, H. R. (2011). Does discovery-based instruction enhance learning? Journal of Educational Psychology, 103(1), 1-18.

Alloway, T. P., & Gathercole, S. E. (2008). Working memory and learning: a practical guide for teachers. Los Angeles, London: SAGE.

Baroody, A. J., Purpura, D. J., Eiland, M. D., & Reid, E. E. (2014). Fostering first graders’ fluency with basic subtraction and larger addition combinations via computer-assisted instruction. Cognition and Instruction, 32(2), 159-197.

Baroody, A. J., Purpura, D. J., Eiland, M. D., & Reid, E. E. (2015). The impact of highly and minimally guided discovery instruction on promoting the learning of reasoning strategies for basic add-1 and doubles combinations. Early Childhood Research Quarterly, 30(Part A), 93-105.

Bruner, J. S. (1960). The process of education: Cambridge: Harvard University Press.

Carbonneau, K., & Marley, S. (2015). Instructional guidance and realism of manipulatives influence preschool children’s mathematics learning. The Journal of Experimental Education, 83(4), 1-19.

Chen, O., Kalyuga, S., & Sweller, J. (2015). The worked example effect, the generation effect, and element interactivity. Journal of Educational Psychology, 107(3), 689-704.

Cobb, P. (1995). Cultural tools and mathematical learning: a case study. Journal for Research in Mathematics Education, 26(4), 362-385.

Fisher, K. R., Hirsh-Pasek, K., Newcombe, N., & Golinkoff, R. M. (2013). Taking shape: supporting preschoolers’ acquisition of geometric knowledge through guided play. Child Development, 84(6), 1872-1878.

Fyfe, E. R., & Rittle-Johnson, B. (2016). The benefits of computer-generated feedback for mathematics problem solving. Journal of Experimental Child Psychology, 147, 140-151.

Fyfe, E. R., Rittle-Johnson, B., & DeCaro, M. S. (2012). The effects of feedback during exploratory mathematics problem solving: prior knowledge matters. Journal of Educational Psychology, 104(4), 1094-1108.

Fyfe, E. R., DeCaro, M. S., & Rittle-Johnson, B. (2015). When feedback is cognitively-demanding: the importance of working memory capacity. Instructional Science, 43(1), 73-91.

Gerard, L., Matuk, C., McElhaney, K., & Linn, M. C. (2015). Automated, adaptive guidance for K-12 education. Educational Research Review, 15, 41-58.

Kaminski, J. A., & Sloutsky, V. M. (2013). Extraneous perceptual information interferes with children’s acquisition of mathematical knowledge. Journal of Educational Psychology, 105(2), 351-363.

Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: an analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41(2), 75-86.

Kroesbergen, E. H., & Van Luit, J. E. H. (2002). Teaching multiplication to low math performers: guided versus structured instruction. Instructional Science, 30(5), 361-378.

Kroesbergen, E. H., & Van Luit, J. E. H. (2005). Constructivist mathematics education for students with mild mental retardation. European Journal of Special Needs Education, 20(1), 107-116.

Mayer, R. E. (2004). Should there be a three-strikes rule against pure discovery learning? The case for guided methods of instruction. American Psychologist, 59(1), 14-19.

Miller, L. (1980). BYTES: implications for staff development. In C. Denham & A. Lieberman (Eds), Time to learn (pp. 159-172). Washington, D.C.: Department of Education.

Moreno, R., & Durán, R. (2004). Do multiple representations need explanations? The role of verbal guidance and individual differences in multimedia mathematics learning. Journal of Educational Psychology, 96(3), 492-503.

Piaget, J. (1977). Epistemology and psychology of functions. Dordrecht, Boston: D. Reidel Publishing Company.

Purpura, D. J., Baroody, A. J., Eiland, M. D., & Reid, E. E. (2016). Fostering first graders’ reasoning strategies with basic sums: the value of guided instruction. The Elementary School Journal, 117(1), 72-100.

Sengupta-Irving, T., & Enyedy, N. (2015). Why engaging in mathematical practices may explain stronger outcomes in affect and engagement: comparing student-driven with highly guided inquiry. Journal of the Learning Sciences, 24(4), 550-592.

Sidney, P. G., & Alibali, M. W. (2015). Making connections in math: activating a prior knowledge analogue matters for learning. Journal of Cognition and Development, 16(1), 160-185.

Terwel, J., van Oers, B., van Dijk, I., & van den Eeden, P. (2009). Are representations to be provided or generated in primary mathematics education? Effects on transfer. Educational Research and Evaluation, 15(1), 25-44.

Timmermans, R. E., Van Lieshout, E. C. D. M., & Verhoeven, L. (2007). Gender-related effects of contemporary math instruction for low performers on problem-solving behavior. Learning and Instruction, 17(1), 42-54.

Tournaki, N., Bae, Y. S., & Kerekes, J. (2008). Rekenrek: a manipulative used to teach addition and subtraction to students with learning disabilities. Learning Disabilities: A Contemporary Journal, 6(2), 41-59.

Tsang, J. M., Blair, K. P., Bofferding, L., & Schwartz, D. L. (2015). Learning to “see” less than nothing: putting perceptual skills to work for learning numerical structure. Cognition and Instruction, 33(2), 154-197.

Vygotsky, L. (1962). Thought and language. Cambridge, MA: Massachusetts Institute of Technology Press.

Vygotsky, L. S., & Cole, M. (1978). Mind in society: the development of higher psychological processes. Cambridge, MA: Harvard University Press.

DOI: https://doi.org/10.26220/rev.2889

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