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The Spirit Of Mathematical Modeling – A Philosophical Study On The Occasion Of 50 Years Of Mathematical Modeling Education, Peter Frejd, Pauline Vos
The Spirit Of Mathematical Modeling – A Philosophical Study On The Occasion Of 50 Years Of Mathematical Modeling Education, Peter Frejd, Pauline Vos
The Mathematics Enthusiast
We mark the 50th anniversary of mathematical modeling education by reviving the term the spirit of mathematical modeling (SoMM), which idealistically reflects core aspects of mathematical modeling. The basis of our analysis is the notion of bildung, which is an educational philosophy that strives for harmonizing heart, mind, social life and culture. We built SoMM on five descriptions of mathematical modeling: two research studies from the 1970s, two studies about the work of professional modelers, and one about an environmental school project. We captured SoMM as a collection of aspects at the micro, meso and macro level: at the micro …
Displaying Gifted Students’ Mathematical Reasoning During Problem Solving: Challenges And Possibilities, Attila Szabo, Ann-Sophie Tillnert, John Mattsson
Displaying Gifted Students’ Mathematical Reasoning During Problem Solving: Challenges And Possibilities, Attila Szabo, Ann-Sophie Tillnert, John Mattsson
The Mathematics Enthusiast
When solving problems, mathematically gifted individuals tend to internalize intuitive ideas and approaches, and to shorten their reasoning. Consequently, for teachers it is difficult to observe gifted students’ mathematical reasoning in the context of problem solving. In this paper we investigate nine gifted Swedish 9th grade students’ mathematical reasoning during problem solving in small groups at vertical whiteboards. The data consists of 5 filmed group-activities, that were analysed according to a framework of collaborative problem-solving (Roschelle & Teasley, 1995). The analysis shows that every group solved proposed problems successfully within different socially negotiated Joint Problem Spaces (JPS) and, importantly, that …
An Analysis Of Graduate Teaching Assistants’ Noticing Skills During Calculus And Physics Tutoring Scenarios, Lindsay Borger, M. J. Camarato, Molly H. Fisher
An Analysis Of Graduate Teaching Assistants’ Noticing Skills During Calculus And Physics Tutoring Scenarios, Lindsay Borger, M. J. Camarato, Molly H. Fisher
The Mathematics Enthusiast
Professional noticing of mathematical thinking, as defined by Jacobs, Lamb, and Philipp (2010) can be broken down into three components: attending to relevant cues, interpreting the mathematical understanding, and deciding the next best instructional steps. Most research on this topic has been conducted with elementary children. However, there is a gap in the research on professional noticing at more advanced levels, particularly college students. The purpose of this study was to take the concept of professional noticing and apply it to mathematics education at the post-secondary level. Specifically, the question we sought to answer in this study was: To what …