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To assess individual students’ abilities and misconceptions in mathematics, teachers need diagnostic competencies. Although research has addressed the quality of teachers’ diagnostic competencies in recent years, it is not very clear how to foster these competencies effectively in the course of prospective teachers’ university education. Research suggests that simulations with instructional support are promising tools for fostering complex competencies. We have developed a simulation that aims at measuring and fostering prospective primary school teachers’ competencies to assess students’ mathematical abilities and misconceptions based on their written task solutions. In this study, we analysed data from prospective primary school mathematics teachers who used one of three different versions of the simulation. Two versions contained a specific type of scaffolding, while the third version did not contain scaffolding. Specifically, the two scaffolding types were content-related scaffolding that emphasized the use of specific pedagogical content knowledge, and strategic scaffolding that emphasized diagnostic activities. The results suggest that integrating scaffolding into the simulation did not substantially influence participants’ overall perception of the simulation regarding presence, authenticity, or perceived cognitive load. Compared to participants in a control group without intervention, participants who used the simulation with scaffolding had higher diagnostic accuracy regarding overall assessment of students’ competence level. However, only content-related scaffolding but not strategic scaffolding or no scaffolding tended to improve participants’ competence in identifying students’ specific misconceptions. The results provide a first empirical basis for further development of the simulation.
Mathematics teachers’ motivational and emotional orientations regarding digital tools in mathematics classrooms are key aspects influencing whether and how technology is used to teach mathematics—making the support of those characteristics one central goal for teacher education. In this article we investigated if and how a workshop-based in-service teacher training can foster teachers’ perceived value of digital media in mathematics education, their self-efficacy, and their anxiety towards teaching mathematics with digital tools. In an intervention study with N = 83 in-service teachers with varying teaching experience, we used cluster analysis based on their experience, value, self-efficacy, and anxiety before the intervention to determine three different teacher orientations regarding teaching mathematics with digital tools. Paired sample t-tests with pretest and posttest data revealed that for two of three clusters these beliefs, motivation, and emotions changed in a positive way during the intervention while for the third no change was found. Our study sheds light on the role of motivational and emotional orientations for the implementation of digital tools in mathematics education: it shows that these orientations can be utilized to cluster teachers on this topic and illustrates that these orientations can be successfully fostered—while individual differences may exist in the effect and success of interventions.
The term evidence-based practice has gained importance in teacher education as well as in everyday school life. Calls from policymakers, academics, and society have become increasingly apparent that teachers’ professional actions should not exclusively be based on subjective experiential knowledge but also on empirical evidence from research studies. However, the use of evidence comes along with several challenges for teachers such as often lacking applicability of available sources or limited time resources. This case study explores how teachers at secondary schools think about the relevance and usage of evidence-based information in practice as well as the barriers associated with it. As we see a particular need for evidence-based teaching in STEM disciplines, we focus on these subjects. A thematic analysis of the data indicates that the teachers generally rate relevance highly, for instance seeing opportunities for support and guidance. However, the actual use of evidence-based information in the classroom is rather low. The teachers most frequently mentioned the feasibility of implementation in class as a quality indicator of evidence-based information. Based on the data, we discuss possible conclusions to promote evidence-based practice at schools. Furthermore, the study opens up directions for further research studies with representative teacher samples in various disciplines.
Tasks in which learners are asked to compare two data sets using box plots and decide which distribution contains more observations above a given threshold have already been investigated in research. There are indications that these tasks are solved schema-based and that different (correct and erroneous) schemas are used depending on the arrangement of the quartiles around the threshold. Erroneous schemas can cause systematic errors and are often based on typical misconceptions. For example, if learners did not complete the conceptual change and assume that in box plots – like in most other statistical representations (e.g., bar or circle diagrams) - more (box) area also represents more observations, they decide the task according to which box plot shows more box area above the threshold. However, this can lead to incorrect answers, as the box area does not represent frequency but the range of the middle half of the data (interquartile range) and thus a measure of variability. So far, these schema-based reasoning processes have mainly been investigated via differences in solution rates of congruent and incongruent items. The present study investigates whether eye-tracking data can help to better understand which information is processed in the different schemas. Our research interest is based on hypotheses specifying which box plot components are significantly involved in the different schemas. We assume that the gaze patterns of learners using different schemas differ both regarding the number and duration of fixations on the relevant box plot components (areas of interest) and in terms of the number of transitions between them. We asked N = 14 participants to solve congruent and incongruent items and simultaneously collected eye movement data. In the analysis, we first used the solution rates to assign the schemas most likely used. Subsequently, the eye-tracking data were analyzed regarding differences in line with our hypotheses. We found hypothesis-compliant effects in all schemas regarding the number of fixations and transitions, but not regarding fixation duration. These results not only validate the schemas identified in previous studies, but also indicate that the schemas differ primarily in terms of which quartile is focused.
Fostering student motivation is an important educational goal. However, motivation in the classrooms is rather heterogeneous, particularly in mathematics and physics. This study examines the potential of (textbook) tasks to promote student motivation. Based on self-determination theory (SDT) and theory of interest , a low-inference coding scheme was developed and validated by applying the framework of item response theory (IRT) to assess the motivational potential of tasks. Current ninth grade mathematics and physics tasks ( N = 254 task units) were analyzed using the categories differentiated instruction, real-life context, autonomy support, competence support , and support for relatedness . Additionally, differences between mathematics and physics tasks were examined. Results indicate the coding scheme’s high interrater reliabilities and empirical validity. Furthermore, we found only a low occurrence of motivational features in mathematics and physics tasks, with few subject-specific differences in favor of mathematics. The coding scheme can contribute to optimizing motivation-supportive instructional designs.
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.
Abstract
The selection of tasks based on the evaluation of task features can be considered a core practice of teaching and a relevant component of teaching quality. This is typically part of teachers’ preparation for their classroom teaching, which prompts the following question: What are the characteristics of the tasks that teachers use when selecting tasks for differentiated teaching? To answer this question, we analyzed systematic differences in the focus of 78 in-service high school and lower secondary school teachers during the evaluation of task features. The teachers had to select eight tasks about the practice of fractions with respect to their differentiation potential—operationalizing their adaptive teaching competence from a mathematics educational perspective. To analyze the differences, we performed a cluster analysis of the task features that the teachers drew upon. Three groups of teachers could be identified with variations in their focus on directly or indirectly relevant, domain-specific or domain-general task features. Taking into account such variations may explain differences in teaching quality and student outcomes and may be relevant when designing teacher professional development programs.
Abstract
The integration of dynamic visualisations, feedback formats and digital tools is characteristic of state-of-the-art digital mathematics textbooks. Although there already is evidence that students can benefit from these technology-based features in their learning, the direct comparison between the use of a comparable digital and printed resource has not yet been sufficiently investigated. We address this research gap by contrasting the use of an enriched digital textbook that includes these features and comparable printed materials without them. To do so, we investigate the achievement of 314 students in a pretest-posttest control group design in a five-hour series of lessons on conditional probability. Using the Rasch model and mixed ANOVA, the results indicate that students can benefit from digital textbook features, especially compared to the use of comparable printed materials. In line with other studies on mathematical achievement and the use of digital resources, our study also shows differences between boys and girls. It seems that particularly girls benefit from the use of the digital textbook, whereas, for the boys, it does not seem to make a difference what kind of resources they use. The group and gender differences are discussed against the background of other studies considering that, especially in Bayesian situations, the way statistical situations are visualised can be decisive for a student’s performance.
Abstract
To explain successful subject matter learning with digital tools, the specification of mediating cognitive processes is crucial for any empirical investigation. We introduce a cognitive process framework for the mechanisms of learning with digital tools (CoDiL) that combines core ideas from the psychology of instruction (utilization-of-learning-opportunity framework), cognitive psychology (knowledge-learning-instruction framework), and domain-specific research on learning and instruction. This synthesizing framework can be used to theoretically ground, firstly, the design of digital tools for learning, and secondly, the empirical analysis of students’ learning activities in digitally enriched educational settings via the analysis of specific student-tool interactions.
Research on fraction comparison shows that students often follow biased comparison strategies, in particular
such strategies that build on their knowledge of natural numbers. On the other hand they also apply successful
comparison strategies such as benchmarking or fraction magnitude processing. Which strategies are applied or
even combined depends on the students’ knowledge and on the task type. To investigate these complex relationships, we developed a balanced 2 × 2-dimensional itemset (congruent vs. incongruent items; benchmarking
vs. non-benchmarking items) and a Bayesian classification of individual students’ performance (solution patters,
response time, and individual distance effect), which we applied to an assessment of N = 350 sixth graders. We
could show that the classification of the students with respect to possible solution strategies matched our hypotheses: We could replicate existing patterns and found additional composite strategies such as ‘benchmarking
or bias‘ with a bias only in solution rates of non-benchmark items. In further analyses we found ‘benchmarking or
suppressed bias-strategies (i.e., a bias in problem solving time of non-benchmarking items). Our study extends
previous knowledge on individual strategies in fraction comparison and proposes a new person-centered
approach to classify individual student profiles even with small profile sizes.