Children’s gestures and the embodied knowledge of geometry

/ Reidar Mosvold / Leave a comment

Mijung Kim, Wolff-Michael Roth and Jennifer Thom have written an article that was recently published online in International Journal of Science and Mathematics Education. The article is entitled Children’s gestures and the embodied knowledge of geometry. Here is the abstract of their article:

There is mounting research evidence that contests the metaphysical perspective of knowing as mental process detached from the physical world. Yet education, especially in its teaching and learning practices, continues to treat knowledge as something that is necessarily and solely expressed in ideal verbal form. This study is part of a funded project that investigates the role of the body in knowing and learning mathematics. Based on a 3-week (15 1-h lessons) video study of 1-s grade mathematics classroom (N = 24), we identify 4 claims: (a) gestures support children’s thinking and knowing, (b) gestures co-emerge with peers’ gestures in interactive situations, (c) gestures cope with the abstractness of concepts, and (d) children’s bodies exhibit geometrical knowledge. We conclude that children think and learn through their bodies. Our study suggests to educators that conventional images of knowledge as being static and abstract in nature need to be rethought so that it not only takes into account verbal and written languages and text but also recognizes the necessary ways in which children’s knowledge is embodied in and expressed through their bodies.

Methods of instructional improvement in algebra

/ Reidar Mosvold / 1 Comment

Christopher R. Rakes, Jeffrey C. Valentine, Maggie B. McGatha and Robert N. Ronau have written a very interesting article where they provide a systematic review of research regarding improvement strategies in algebra instruction. Their article is entitled Methods of Instructional Improvement in Algebra: A Systematic Review and Meta-Analysis, and it was published in the latest issue of AERA journal Review of Educational Research. Algebra, they claim, is considered to be “the backbone of secondary mathematics education in the United States” (p. 372), but quite a low proportion of students pass their Algebra II exam. The National Mathematics Advisory Panel were therefore concerned that traditional algebra instruction was not as effective as it should be. In their article, Rakes and colleagues discuss what algebra is, what the main challenges for algebra instruction are, and they present a systematic review of literature based on the following questions:

  • What methods for improving algebra instruction have been studied?
  • How effective have these methods been at improving student achievement scores?
  • Which characteristics of teaching interventions in algebra are the most important for determining the effectiveness of the intervention on student achievement?

Their impressive review consisted of 82 studies that were selected from a time span of 40 years. The results of their study “indicate that a wide variety of reforms effectively improve student achievement in algebra. The degree to which these efforts focus on the development of conceptual understanding also influences the magnitude of effects” (p. 391). If you are interested in algebra instruction, you should definitely take the time to read this interesting 30 page article!

Here is the abstract of their article:

This systematic review of algebra instructional improvement strategies identified 82 relevant studies with 109 independent effect sizes representing a sample of 22,424 students. Five categories of improvement strategies emerged: technology curricula, nontechnology curricula, instructional strategies, manipulatives, and technology tools. All five of these strategies yielded positive, statistically significant results. Furthermore, the learning focus of these strategies moderated their effects on student achievement. Interventions focusing on the development of conceptual understanding produced an average effect size almost double that of interventions focusing on procedural understanding.

Reference

Rakes, C.R., Valentine, J.C., McGatha, M.B., & Ronau, R.N. (2010). Methods of Instructional Improvement in Algebra – A Systematic Review and Meta-Analysis. Review of Educational Research, 80(3), 372-400.