Problem Solving and Problem Posing in a Dynamic Geometry Environment

In this study, we considered dynamic geometry software (DGS) as the tool that mediates students’ strategies in solving and posing problems. The purpose of the present study was twofold. First, to understand the way in which students can solve problems in the setting of a dynamic geometry environment, and second, to investigate how DGS provides opportunities for posing new problems. Two mathematical problems were presented to six pre-service teachers with prior experience in dynamic geometry. Each student participated in two interview sessions which were video recorded. The results of the study showed that DGS, as a mediation tool, encouraged students to use in problem solving and posing the processes of modeling, conjecturing, experimenting and generalizing. Furthermore, we found that DGS can play a significant role in engendering problem solving and posing by bringing about surprise and cognitive conflict as students use the dragging and measuring facilities of the software

How do first-grade students recognize patterns? An eye-tracking study

Recognizing patterns is an important skill in early mathematics learning. Yet only few studies have investigated how first-grade students recognize patterns. These studies mainly analyzed students’ expressions and drawings in individual interviews. The study presented in this paper used eye tracking in order to explore the processes of 22 first-grade students while they were trying to recognize repeating patterns. In our study, we used numerical and color pattern tasks with three different repeating patterns (i.e., repeating unit is AB, ABC, or AABB). For each repeating pattern task, students were asked to say the following object of the given pattern. For these patterns, we identified four different processes in recognizing repeating patterns. In addition, we report differences in the observed processes between the patterns used in the tasks.This project has received funding by the Erasmus+ grant program of the European Union under grant agreement No 2020-1-DE03-KA201-077597

Developing student spatial ability with 3D software applications

This paper reports on the design of a library of software applications for the teaching and learning of spatial geometry and visual thinking. The core objective of these applications is the development of a set of dynamic microworlds, which enables (i) students to construct, observe and manipulate configurations in space, (ii) students to study different solids and relates them to their corresponding nets, and (iii) students to promote their visualization skills through the process of constructing dynamic visual images. During the developmental process of software applications the key elements of spatial ability and visualization (mental images, external representations, processes, and abilities of visualization) are carefully taken into consideration

Welche Vorgehensweisen nutzen Erstklässler*innen bei Musterfolgeaufgaben? Eine Eye-Tracking-Untersuchung

Mathematik wird vielfach als eine Wissenschaft der Muster und Strukturen bezeichnet. Muster und Strukturen stellen schon in der frühen mathematischen Bildung einen bedeutsamen mathematischen Inhaltsbereich dar (KMK, 2005). Zu Beginn der Primarstufe gehört unter anderem das Fortsetzen von Mustern der Form ●●●●●● zu üblichen Tätigkeiten im Inhaltsbereich Muster und Strukturen (Benz et al., 2015). In der frühen mathematischen Bildung werden Musterfolgen unter anderem in Form von statischen Mustern behandelt (Lüken, 2012). Statische Muster bestehen aus einer Grundeinheit (z. B. ●●), die sich kontinuierlich wiederholt (z. B. ●●●●●●). Die Grundeinheit statischer Muster kann sich hinsichtlich ihrer Länge (●● vs. ●●●), ihrer Struktur (●●● vs. ●●●) oder der Art der Repräsentation (●● vs. 1 4) unterscheiden. Bislang existieren jedoch wenige Erkenntnisse über die Vorgehensweisen von Kindern beim Fortsetzen solcher Musterfolgeaufgaben (Baumanns et al., 2022; Lüken & Sauzet, 2021). Erkenntnisse hierzu sind jedoch notwendig, um Kinder beim Aufbau von Fähigkeiten im Inhaltsbereich Muster und Strukturen zu unterstützen. Die vorliegende Pilotstudie untersucht im Rahmen des Erasmus+-Projekts DIDUNAS die Vorgehensweisen von Erstklässler* innen mithilfe von Eye-Tracking. Eye-Tracking hat sich in der Vergangenheit als nützlich erwiesen, um Vorgehensweisen von Schüler*innen zu untersuchen (Schindler et al., 2020). Den folgenden Fragestellungen wird nachgegangen: Welche Vorgehensweisen verwenden Erstklässler*innen bei Musterfolgeaufgaben? Gibt es Unterschiede in der Verwendung von Vorgehensweisen bei Musterfolgeaufgaben zwischen verschiedenen Arten von Mustern

Stereometry activities with DALEST

This book reports on a project to devise and test a teaching programme in 3D geometry for middle school students based on the needs, knowledge and experiences of a range of countries within the European Union. The main objective of the project was the development (and testing) of a dynamic three-dimensional geometry microworld that enabled the students to construct, observe and manipulate geometrical figures in space and which their teachers used to help their students construct an understanding of stereometr

Connections between algebraic thinking and reasoning processes

International audienceThe aim of the present study is to investigate the relationship of algebraic thinking with different types of reasoning processes. Using regression analyses techniques to analyze data of 348 students between the ages of 10 to 13 years old, this study examined the associations between algebraic thinking and achievement in two tests, the Naglieri Non-Verbal Ability Test and a deductive reasoning test. The data provide support to the hypothesis that a corpus of reasoning processes, such as reasoning by analogy, serial reasoning, and deductive reasoning, significantly predict students' algebraic thinking

The effect of two intervention courses on students' early algebraic thinking

International audienceThe aim of this study is to investigate the nature and content of instruction that may facilitate the development of students' early algebraic thinking. 96 fifth-graders attended two different intervention courses. Both courses approached three basic content strands of algebra: generalized arithmetic, functional thinking, and modeling languages. The courses differed in respect to the characteristics of the tasks that were used. The first intervention included real life scenarios, and semi-structured tasks, with questions which were more exploratory in nature. The second intervention course involved mathematical investigations, and more structured tasks which were guided through supportive questions and scaffolding steps. The findings, yielded from the analysis of pre-test and post-test data, showed that the first course had better learning outcomes compared to the second, while controlling for preliminary differences regarding students' early algebraic thinking

Using GeoGebra to develop primary school students' understanding of reflection

This paper presents a sequence of instructional activities with GeoGebra for the teaching of reflection in primary school. The authors demonstrate a way in which GeoGebra can be used to design an instructional program based on the stages of the 5Es instructional model (engagement, exploration, explanation, elaboration, and evaluation)

The impact of a teaching intervention on sixth grade students' fraction understanding and their performance in seven abilities that constitute fraction understanding

International audienceIn a previous study, we found that students' abilities in fraction recognition, definitions and explanations, argumentations and justifications, relative magnitude of fractions, representations, connections and reflection constitute fraction understanding of sixth grade students. In the present study, we examine the impact of an intervention comprising of lessons for developing the seven abilities on students' fraction understanding and their performance in the seven abilities. The sample comprised of 343 sixth grade students. Repeated measures analysis showed that the students of the experimental group outperformed those of the control group in their level of fraction understanding and their ability in fraction recognition, definitions and explanations, argumentations and justifications, connections and reflection

TMME, vol3, no.2, p.194 Frames of Reference and Achievement in Elementary Arithmetic

Abstract: This paper considers the relationship between 8-11 years old students ’ numerical achievement and a possible disposition towards the construction of particular frames of reference. The paper uses the characteristics of a variety of kinds of images to focus upon frames of reference and explores a possible relationship between children’s verbal descriptions of concrete and abstract nouns and the different ways they respond to aspects of elementary arithmetic. It seeks to establish whether or not children towards the extremes of arithmetical achievement (low and high achievement) have a disposition towards different kinds of frames of reference. The analysis suggests that at one extreme these may be largely descriptive, associated with episodes or specific characteristics that are derived from efforts to concretise the stimuli. At the other, these descriptive qualities are complimented by more relational characteristics that are indicative of greater flexibility in mathematical behaviour. The conclusions suggest that such differences may influence the interpretation that some children may make of the objects and actions that are the foundations of their numerical development and, as a consequence, this may affect the quality of the child’s cognitive shift from concrete to abstract thought. Key words: Frames of reference, arithmetic, mental representation