Children’s gestures and the embodied knowledge of geometry

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.

January issue of Science & Education

The January issue of Science & Education has been published. One of the articles contained in the issue is of relevance to mathematics education: A Pilot Study of a Cultural-Historical Approach to Teaching Geometry. The article is written by Stuart Rowlands from the University of Plymouth. Here is the abstract of his article:

There appears to be a widespread assumption that deductive geometry is inappropriate for most learners and that they are incapable of engaging with the abstract and rule-governed intellectual processes that became the world’s first fully developed and comprehensive formalised system of thought. This article discusses a curriculum initiative that aims to ‘bring to life’ the major transformative (primary) events in the history of Greek geometry, aims to encourage a meta-discourse that can develop a reflective consciousness and aims to provide an opportunity for the induction into the formalities of proof and to engage with the abstract. The results of a pilot study to see whether 14–15 year old ‘mixed ability’ and 15–16 year old ‘gifted and talented’ students can be meaningfully engaged with two such transformative events are discussed.

Students’ use of technological tools

Ioannis Papadopoulosa and Vassilios Dagdilelis have written an article that was published online in the Journal of Mathematical Behavior yesterday. The article is entitled Students’ use of technological tools for verification purposes in geometry problem solving. Here is a copy of the article abstract:

Despite its importance in mathematical problem solving, verification receives rather little attention by the students in classrooms, especially at the primary school level. Under the hypotheses that (a) non-standard tasks create a feeling of uncertainty that stimulates the students to proceed to verification processes and (b) computational environments – by providing more available tools compared to the traditional environment – might offer opportunities for more frequent usage of verification techniques, we posed to 5th and 6th graders non-routine problems dealing with area of plane irregular figures. The data collected gave us evidence that computational environments allow the development of verification processes in a wider variety compared to the traditional paper-and-pencil environment and at the same time we had the chance to propose a preliminary categorization of the students’ verification processes under certain conditions.

A cultural-historical approach to teaching geometry

Stuart Rowlands has recently written an article called A Pilot Study of a Cultural-Historical Approach to Teaching Geometry, which was published in Science & Education on Wednesday. Here is the abstract of the article:

There appears to be a widespread assumption that deductive geometry is inappropriate for most learners and that they are incapable of engaging with the abstract and rule-governed intellectual processes that became the world’s first fully developed and comprehensive formalised system of thought. This article discusses a curriculum initiative that aims to ‘bring to life’ the major transformative (primary) events in the history of Greek geometry, aims to encourage a meta-discourse that can develop a reflective consciousness and aims to provide an opportunity for the induction into the formalities of proof and to engage with the abstract. The results of a pilot study to see whether 14–15 year old ‘mixed ability’ and 15–16 year old ‘gifted and talented’ students can be meaningfully engaged with two such transformative events are discussed.

Pearson’s correlation between three variables

Pauline Vos has written an article called Pearson’s correlation between three variables; using students’ basic knowledge of geometry for an exercise in mathematical statistics. The article was recently published in International Journal of Mathematical Education in Science and Technology. Here is a copy of the article abstract:

When studying correlations, how do the three bivariate correlation coefficients between three variables relate? After transforming Pearson’s correlation coefficient r into a Euclidean distance, undergraduate students can tackle this problem using their secondary school knowledge of geometry (Pythagoras’ theorem and similarity of triangles). Through a geometric interpretation, we start from two correlation coefficients rAB and rBC and then estimate a range for the third correlation rAC. In the case of three records (n = 3), the third correlation rAC can only attain two possible values. Crossing borders between mathematical disciplines, such as statistics and geometry, can assist students in deepening their conceptual knowledge.

The decorative impulse

Swapna Mukhopadhyay has written an article entitled The decorative impulse: ethnomathematics and Tlingit basketry. The article was published online in ZDM earlier this week. Here is the article abstract:

Pattern is a key element in both the esthetics of design and mathematics, one definition of which is “the study of all possible patterns”. Thus, the geometric patterns that adorn cultural artifacts manifest mathematical thinking in the artisans who create them, albeit their lack of “formal” mathematics learning. In describing human constructions, Franz Boas affirmed that people, regardless of their economic conditions, always have been engaged in activities that reveal their deeply held esthetic sense. The Tlingit Indians from Sitka, Alaska, are known for their artistic endeavors. Art aficionados and museum collectors revere their baskets and other artifacts. Taking the approach of ethnomathematics, I report my analysis of the complex geometrical patterns in Tlingit basketry.