Search results for "mathematical reasoning"
showing 6 items of 6 documents
Friend Influence and Susceptibility to Influence: Changes in Mathematical Reasoning as a Function of Relative Peer Acceptance and Interest in Mathema…
2016
This study investigated friend influence over mathematics achievement in 202 same-sex friendship dyads (106 girl dyads). Participants were in the third grade (around age 9) at the outset. Each friend completed a questionnaire describing interest in mathematics and a standardized mathematical reasoning assessment. Peer nominations provided a measure of peer acceptance. The results revealed evidence that interest in mathematics moderates both the degree to which the higher-accepted friend was influential and the degree to which the lower-accepted friend was susceptible to influence. Specifically, the third-grade mathematical reasoning of the higher-accepted friend predicted an increase in the…
Networked Analysis of a Teaching Unit for Primary School Symmetries in the Form of an E-Book
2021
In mathematics education, technology offers many opportunities to enrich curricular contents. Plane symmetries is a topic often skipped by primary teachers. However, it is important and may be worked in attractive ways in dynamic geometry software environments. In any regular classroom there are students with different levels of mathematical attainment, some needing easy tasks while others, particularly mathematically-gifted students, need challenging problems. We present a teaching unit for plane symmetries, adequate for upper primary school grades, implemented in a fully interactive electronic book, with most activities solved in GeoGebra apps. The book allows student to choose which itin…
Reasoning with paper and pencil: The role of inscriptions in student learning of geometric series
2009
The purpose of this article is to analyse how students use inscriptions as tools for thinking and learning in mathematical problem-solving activities. The empirical context is that of learning about geometric series in a small group setting. What has been analysed is how students made use of inscriptions, self-made as well as those provided by text books and teachers, and the role these inscriptions played in the coordination of students’ learning/communication. Through the use of inscriptions (made on the chalkboard and with paper and pencil), the students externalised their thinking while engaging in mathematical reasoning on the topic of geometric series. The inscriptions were significan…
Automated Checking of Flexible Mathematical Reasoning in the Case of Systems of (In)Equations and the Absolute Value Operator
2021
We present an approach and a tool for automatically providing feedback on solutions that involve complicated reasoning patterns. Currently the tool supports linear systems of equations and inequations that may also contain the absolute value operator and a restricted form of rational functions. This suffices for designing problems that are laborious to solve with standard mechanical procedures, but much easier using short-cuts that students may find by creative thinking. Earlier research has found that struggling with important mathematics promotes conceptual development. Our goal is to encourage students to such struggling. A crucial feature is to give them great freedom to choose the path…
On Mathematical Thought, 1
2012
Taking into account some basic epistemological considerations on Psychoanalysis by Igna-cio Matte Blanco, it is possible to deduce some first simple remarks on certain logical as-pects of schizophrenic reasoning. Further remarks on mathematical thought are also made in the light of what established, taking into account the comparison with the extreme patho-logical schizophrenic paradigm.
Stable same-sex friendships with higher achieving partners promote mathematical reasoning in lower achieving primary school children
2015
This study is designed to investigate friend influence over mathematical reasoning in a sample of 374 children in 187 same-sex friend dyads (184 girls in 92 friendships; 190 boys in 95 friendships). Participants completed surveys that measured mathematical reasoning in the 3rd grade (approximately 9 years old) and one year later in the 4th grade (approximately 10 years old). Analyses designed for dyadic data (i.e., longitudinal Actor-Partner Interdependence Models) indicated that higher achieving friends influenced the mathematical reasoning of lower achieving friends, but not the reverse. Specifically, greater initial levels of mathematical reasoning among higher achieving partners in the …