Developing mental rotation ability through engagement in assignments that involve solids of revolution

Spatial ability is essential for succeeding in the STEM (Sciences, Technology, Engineering and Mathematics) disciplines, especially mental rotation. Research points out that spatial ability is malleable, and therefore calls for developing learners’ ability by engaging them in appropriate assignments, starting from kindergarten. Given this, our paper presents several assignments designed for mathematics prospective teachers with the aim of fostering their mental rotation skills. Specifically, these assignments deal with solids of revolution, three-dimensional shapes formed by revolving a planar shape about a given axis that lies on the same plane

Vkljucevanje otrok v matematicne aktivnosti, ki vkljucujejo razlicne reprezentacije: trikotniki, vzorci in stetje

This paper synthesises research from three separate studies, analysing how different representations of a mathematical concept may affect young children’s engagement with mathematical activities. Children between five and seven years old engaged in counting objects, identifying triangles and completing repeating patterns. The implementation of three counting principles were investigated: the one-to-one principle, the stable-order principle and the cardinal principal. Children’s reasoning when identifying triangles was analysed in terms of visual, critical and non-critical attribute reasoning. With regard to repeating patterns, we analyse children’s references to the minimal unit of repeat of the pattern. Results are discussed in terms of three functions of multiple external representations: to complement, to constrain and to construct. (DIPF/Orig.

Using Cases as a Means to Discuss Errors in Mathematics Teacher Education

Errors are a major component of the pedagogical content knowledge (PCK) needed for teaching mathematics. In this study, 25 prospective teachers (PTs) in high schools were invited to solve a trigonometric task that had been assigned to high-school students and, subsequently, to relate to an authentic solution containing mathematical errors, which was presented in a dialogue by a pair of students. While all PTs reached the final, correct solution, eight provided only one of the two results in one step of the solution. Almost all (23) PTs identified at least one of the students’ errors. The case raised issues regarding the steps that should be written in a solution and the role of drawings in mathematical problems. This article suggests that exposing PTs to authentic teaching cases provides opportunities to discuss subtle issues related to their own mathematical knowledge and to obstacles that their future students might encounter when solving such tasks

The effects of an intervention on adults' beliefs and self-efficacy for implementing numerical tasks with young children

International audienceThis paper describes a course attended by 30 graduate students in mathematics education, nonpreschool teachers, that aimed to promote participants' knowledge of young children's development of numerical competencies. Prior to the course, participants held high positive beliefs towards children's engagement with numerical activities, but their self-efficacy was low. Findings indicated that mastery experience, mostly by repeatedly analyzing videos, and repeatedly designing tasks, afforded participants a chance to see how they were progressing and increased their self-efficacy

Shedding light on preschool teachers’ self-efficacy for teaching patterning

International audienceAs teacher educators, we recognize the importance of considering teachers’ self-efficacy for teaching mathematics. In this study, we investigate preschool teachers’ self-efficacy for teaching repeating patterns, both before and after participating in a professional development program. Findings from questionnaires indicated that self-efficacy related to subject-matter knowledge changed little, while self-efficacy related to pedagogical-content knowledge, increased. Interviews with teachers shed light on these findings

Noticing aspects of example use in the classroom: Analysis of a case

International audienceThis paper investigates promoting knowledge of example use in mathematics education by way of analyzing a case using theoretical tools. Participants were both prospective and practicing teachers attending a university course. An event taken from a tenth grade geometry class was analyzed in terms of example use, and then discussed. Participants related to the type of example given, the timing of the example, agency, what the example was an example of, and the aim of giving the example

Shedding light on preschool teachers’ self-efficacy for teaching patterning

International audienceAs teacher educators, we recognize the importance of considering teachers’ self-efficacy for teaching mathematics. In this study, we investigate preschool teachers’ self-efficacy for teaching repeating patterns, both before and after participating in a professional development program. Findings from questionnaires indicated that self-efficacy related to subject-matter knowledge changed little, while self-efficacy related to pedagogical-content knowledge, increased. Interviews with teachers shed light on these findings

Unsolvable mathematical problems in kindergarten: Are they appropriate?

International audienceNot all mathematical problems have a solution. This paper describes a decomposition problem, set in a real-life context, for which no mathematical solution exists. It describes the strategies children use and how the rea-life context impacted on children’s solutions. Results indicated that young children accept the possibility that a problem may not have a solution and that some turn to the context in order to find a practical solution instead

Tvoření úloh a jejich implementace jako obousměrný proces: Případ učitelů mateřských škol

Článek ukazuje, jaký vliv může mít další vzdělávání učitelů zaměřené na tvorbu úloh na jejich znalosti a praxi. Jsou představeny konkrétní principy tvoření úloh pro mateřské školy a tyto principy jsou ilustrovány na příkladech. Učitelé si vybírali několik úloh, které použili s jednotlivými dětmi ve svých třídách mateřských škol; implementace úloh byla nahrávána na video a analyzována při společných setkáních. Také setkání byla nahrávána na video a proběhla jejich kvalitativní analýza. Výsledky ukazují, že učitelé v  mateřských školách pozorněji sledovali znalosti svých žáků i charakteristiky úloh. To jim umožnilo upravit úlohy tak, aby směřovaly ke konkrétním matematickým konceptům