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

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

Enhancing functional thinking in grade 5–6 students through a dynamic mathematics intervention program

The aim of this study was to develop, implement, and evaluate an intervention program focusing on developing Grade 5 and 6 students’ functional thinking. The innovative aspect lies in addressing simultaneously various aspects of function—input–output, covariation, correspondence, and object— in terms of manipulating tasks that involve functional relationships. The program adopts promising design principles, including an inquiry-based approach, engaging students in embodied dynamic mathematics learning environments, and making connections to real-world situations. A sample of 104 students took part in the program. The results showed a significant improvement in students’ performance related to functional thinking between the pre- and post-tests. Grade 5 students’ mean value improved from 0.29 to 0.58 and Grade 6 students from 0.37 to 0.60, respectively. Analysis indicated that students with varying performance potential in developing functional thinking are likely to be significantly affected by the program. Regression analysis showed that students’ gender as well as mathematics- and functions-related self-concept and interest did not serve as predictive factors of students’ gain score magnitude. Students’ progression goes along with a significant shift in strategies used. While the dominant strategies in the pre-test relied on recursive and single variation, in the post-test, students moved to covariational and correspondence approaches. The findings indicate that upper primary school students are capable of grappling abstract facets of functions. This underscores the potential effectiveness of targeted interventions that adopt innovative design principles, particularly in light of the limitations of conventional curricula in adequately preparing students to explore functional relationships across diverse contexts

Classroom assessment tasks and learning trajectories

International audienceOne of the purposes of assessment is to inform the classroom teacher about students’ current understanding in order to improve the teaching and learning processes. Learning trajectories present a developmental progression towards increasing understanding of mathematical ideas and are commonly found in curriculum materials to assist teachers in planning instruction. Assessing students’ learning along the trajectory could serve as a mediator for adjusting the pacing and the selection of opportunities during the classroom enactment. We propose a framework for designing different types of assessment tasks to elicit evidence about how students respond to the mathematical ideas presented in the trajectory. We illustrate the application of the framework by drawing on a learning trajectory of fraction division for sixth grade students and discuss how the enactment of the trajectory in classroom could be adjusted to students’ current understanding

Classroom assessment tasks and learning trajectories

International audienceOne of the purposes of assessment is to inform the classroom teacher about students’ current understanding in order to improve the teaching and learning processes. Learning trajectories present a developmental progression towards increasing understanding of mathematical ideas and are commonly found in curriculum materials to assist teachers in planning instruction. Assessing students’ learning along the trajectory could serve as a mediator for adjusting the pacing and the selection of opportunities during the classroom enactment. We propose a framework for designing different types of assessment tasks to elicit evidence about how students respond to the mathematical ideas presented in the trajectory. We illustrate the application of the framework by drawing on a learning trajectory of fraction division for sixth grade students and discuss how the enactment of the trajectory in classroom could be adjusted to students’ current understanding

Pseudotumor Cerebri in a Child with Idiopathic Growth Hormone Insufficiency Two Months after Initiation of Recombinant Human Growth Hormone Treatment

Purpose. To report a rare case of pseudotumor cerebri (PTC) in a child two months after receiving treatment with recombinant human growth hormone (rhGH) and to emphasize the need of close collaboration between ophthalmologists and pediatric endocrinologists in monitoring children receiving rhGH. Methods. A 12-year-old boy with congenital hypothyroidism started treatment with rhGH on a dose of 1,5 mg/daily IM (4.5 IU daily). Eight weeks later, he was complaining of severe headache without any other accompanying symptoms. The child was further investigated with computed tomography scan and lumbar puncture. Results. Computed tomography scan showed normal ventricular size and lumbar puncture revealed an elevated opening pressure of 360 mm H2O. RhGH was discontinued and acetazolamide 250 mg per os twice daily was initiated. Eight weeks later, the papilledema was resolved. Conclusions. There appears to be a causal relationship between the initiation of treatment with rhGH and the development of PTC. All children receiving rhGH should have a complete ophthalmological examination if they report headache or visual disturbances shortly after the treatment. Discontinuation of rhGH and initiation of treatment with acetazolamide may be needed and regular follow-up examinations by an ophthalmologist should be recommended

Identification of first-grade students at risk of developing mathematical difficulties through online measures in arithmetic and pattern tasks: A study using error rates and response times

International audienceFor researchers and practitioners, it is important to identify students at risk of developing mathematical difficulties. The aim of this pilot study was to investigate whether it is possible to identify first-grade students who are at risk of developing mathematical difficulties (RMD) through online measures in arithmetic and pattern tasks. In our study, 54 first-grade students worked on 75 tasks in twelve sets on a computer screen. We also carried out a standardized mathematics test to identify students as RMD. We then investigated if error rates and response times as online measures allow to replicate the identification of students as RMD. Using a logistic regression model, we found that the error rates and response times allow identifying students as RMD with acceptable accuracy. We also found that tasks on symbolic number comparison, completing color patterns, and enumeration of small sets were particularly informative to identify students as RMD