Die Bedeutung und Funktion des Schreibens im Mathematikheft

Im Mathematikunterricht gibt es unterschiedliche Schreibaktivitäten im Schulheft. Sie reichen vom schriftlichen Aufgabenlösen über freie Notizen bis hin zu komplexeren Schreibaktivitäten wie Hefteinträgen und Lerntagebüchern. Diese Schreibaktivitäten erfüllen im Wesentlichen zwei verschiedene Funktionen (Peverly & Wolf, 2019): Erstens ist das eine Produktfunktion (auch Speicherfunktion), die bedeutet, dass Informationen schriftlich im Heft fixiert werden, um für eine spätere Verwendung verfügbar zu sein. Zweitens erfüllt Schreiben eine Prozessfunktion (auch Enkodierungsfunktion). Dieser Funktion liegt die Erkenntnis zu Grunde, dass Schreiben ein intensiver kognitiver und metakognitiver Prozess ist, durch den Wissen verarbeitet, strukturiert, selektiert und generiert wird (Galbraith, 1999; Hayes & Flower, 1980; Keys, 1999). Sie umfasst insbesondere Lerneffekte, die während des Schreibens auftreten. Sowohl aus der Produkt- als auch aus der Prozessfunktion des Schreibens lässt sich die Rechtfertigung ableiten, dass Schüler*innen im Mathematikunterricht mit einem Schulheft arbeiten. Durch verschiede Formen der konkreten Umsetzung dieser Schreibaktivitäten können dabei unterschiedliche Ziele verfolgt werden

Socioeconomic status and word problem solving in PISA: the role of mathematical content areas

Mathematics performance and socioeconomic status (SES) are positively related, but the reasons are not well understood. Moreover, the strength of the relationship in large-scale assessments like PISA differs between countries, for example, between Finland and Germany. In the PISA studies, mathematical word problems are used, which cover four mathematical content areas. In the present study, we reanalyzed data from PISA 2003 to 2018 to investigate whether word problems in these content areas were related differently to SES across the two countries. The results suggest that the relationship can be attributed to different content areas in both countries. This emphasizes the importance of considering item characteristics when addressing the relationship between SES and mathematical word problem solving

“I added the numbers, it’s math!”: how sense-making in “age of the captain” problems differs between a mathematics classroom and a language classroom

Students’ solution process of mathematical word problems depends on the situational context, e.g. the school subject (Dewolf, Van Dooren & Verschaffel, 2011). We analysed approaches to “age of the captain problems” (ACP; Verschaffel, Greer & De Corte, 2000) that present a situation that makes no sense, but are nonetheless frequently “solved” by a majority of primary school students. 48 primary school students (age M = 9.4, 54% female) in a mathematics or a language classroom were given five ACP. Afterwards, classroom interviews were conducted in both groups. Quantitative analyses show a non-significant tendency that students in the mathematics class were more likely to provide an arithmetic response to ACP. Interviews revealed that students in both groups experienced a cognitive dissonance regarding the expectation to provide an arithmetic solution, but differed in their approach to resolve it. This suggests that sense-making in ACP is influenced by the classroom context

How to combine collaboration scripts and heuristic worked examples to foster mathematical argumentation – when working memory matters

Mathematical argumentation skills (MAS) are considered an important outcome of mathematics learning, particularly in secondary and tertiary education. As MAS are complex, an effective way of supporting their acquisition may require combining different scaffolds. However, how to combine different scaffolds is a delicate issue, as providing learners with more than one scaffold may be overwhelming, especially when these scaffolds are presented at the same time in the learning process and when learners’ individual learning prerequisites are suboptimal. The present study therefore investigated the effects of the presentation sequence of introducing two scaffolds (collaboration script first vs. heuristic worked examples first) and the fading of the primarily presented scaffold (fading vs. no fading) on the acquisition of dialogic and dialectic MAS of participants of a preparatory mathematics course at university. In addition, we explored how prior knowledge and working memory capacity moderated the effects. Overall, 108 university freshmen worked in dyads on mathematical proof tasks in four treatment sessions. Results showed no effects of the presentation sequence of the collaboration script and heuristic worked examples on dialogic and dialectic MAS. Yet, fading of the initially introduced scaffold had a positive main effect on dialogic MAS. Concerning dialectic MAS, fading the collaboration script when it was presented first was most effective for learners with low working memory capacity. The collaboration script might be appropriate to initially support dialectic MAS, but might be overwhelming for learners with lower working memory capacity when combined with heuristic worked examples later on

Eye-tracking methodology in mathematics education research: A systematic literature review

Eye tracking is an increasingly popular method in mathematics education. While the technology has greatly evolved in recent years, there is a debate about the specific benefits that eye tracking offers and about the kinds of insights it may allow. The aim of this review is to contribute to this discussion by providing a comprehensive overview of the use of eye tracking in mathematics education research. We reviewed 161 eye-tracking studies published between 1921 and 2018 to assess what domains and topics were addressed, how the method was used, and how eye movements were related to mathematical thinking and learning. The results show that most studies were in the domain of numbers and arithmetic, but that a large variety of other areas of mathematics education research was investigated as well. We identify a need to report more methodological details in eye-tracking studies and to be more critical about how to gather, analyze, and interpret eye-tracking data. In conclusion, eye tracking seemed particularly beneficial for studying processes rather than outcomes, for revealing mental representations, and for assessing subconscious aspects of mathematical thinking

Different complex word problems require different combinations of cognitive skills

Abstract Mathematical word problem solving is influenced by various characteristics of the task and the person solving it. Yet, previous research has rarely related these characteristics to holistically answer which word problem requires which set of individual cognitive skills. In the present study, we conducted a secondary data analysis on a dataset of N = 1282 undergraduate students solving six mathematical word problems from the Programme for International Student Assessment (PISA). Previous results had indicated substantial variability in the contribution of individual cognitive skills to the correct solution of the different tasks. Here, we exploratively reanalyzed the data to investigate which task characteristics may account for this variability, considering verbal, arithmetic, spatial, and general reasoning skills simultaneously. Results indicate that verbal skills were the most consistent predictor of successful word problem solving in these tasks, arithmetic skills only predicted the correct solution of word problems containing calculations, spatial skills predicted solution rates in the presence of a visual representation, and general reasoning skills were more relevant in simpler problems that could be easily solved using heuristics. We discuss possible implications, emphasizing how word problems may differ with regard to the cognitive skills required to solve them correctly

Different complex word problems require different combinations of cognitive skills

Mathematical word problem solving is influenced by various characteristics of the task and the person solving it. Yet, previous research has rarely related these characteristics to holistically answer which word problem requires which set of individual cognitive skills. In the present study, we conducted a secondary data analysis on a dataset of N = 1282 undergraduate students solving six mathematical word problems from the Programme for International Student Assessment (PISA). Previous results had indicated substantial variability in the contribution of individual cognitive skills to the correct solution of the different tasks. Here, we exploratively reanalyzed the data to investigate which task characteristics may account for this variability, considering verbal, arithmetic, spatial, and general reasoning skills simultaneously. Results indicate that verbal skills were the most consistent predictor of successful word problem solving in these tasks, arithmetic skills only predicted the correct solution of word problems containing calculations, spatial skills predicted solution rates in the presence of a visual representation, and general reasoning skills were more relevant in simpler problems that could be easily solved using heuristics. We discuss possible implications, emphasizing how word problems may differ with regard to the cognitive skills required to solve them correctly.ISSN:0013-1954ISSN:1573-081