Journal fur Mathematik-Didaktik最新文献

Language is a crucial aspect of mathematical thinking and learning, and it is therefore essential for teachers to be equipped with the skills required for linguistically responsive teaching. This includes the ability to identify potential linguistic challenges in expository texts. In the present study, we investigated the ability of pre-service teachers (N = 115) to identify potential linguistic challenges in a mathematical expository text for ninth graders. Participants identified about 12% of the potential linguistic challenges that were previously identified by a reference expert group. They identified challenges more frequently that were on the word level and considered to be mathematics-specific by the experts. Subjective judgements of disciplinarity of the challenges differed between participants, and between participants and experts. No differences in the ability to identify potential linguistic challenges were found between participants who studied language arts (German or English) or mathematics as a subject. Our results indicate that pre-service teachers may not be adequately prepared to identify and respond to linguistic challenges in mathematical expository texts.

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.

Students struggle with planning suitable solution methods in equation solving. Planning suitable solution methods is key to flexibility, a desired skill for equation solving. Comparing solution methods has been shown to foster flexibility. To support the learning benefits of the comparisons, productive classroom talk, which includes the discussion of different solution methods, is recommended. This study examines whether discussions that compare multiple methods include more planning processes than discussions that do not compare multiple solution methods or that are just about one solution method. The content analysis is based on utterances from 172 lessons from 43 classrooms in grades 9 and 10. The hypothesis is tested both across classes using binary logistic regression models and at the class level using paired samples t‑tests. The results show that planning processes are addressed about twice as often when comparing multiple solution methods. Additionally, the study finds that enacting solution methods is the most frequent topic in classroom talk about solving equations.

Good adaptive support by educational professionals is crucial for pre-school children's mathematical learning. Thus there is a need for appropriate instruments to evaluate the quality of the planning, implementation, and reflection process for mathematical learning opportunities in kindergarten. Existing instruments tend to focus on micro-adaptive learning support (MI-ALS), which considers the interaction between the professionals and the children. The quality of macro-adaptive learning support (MA-ALS), the teachers' planning of and reflection on learning opportunities, has yet to be comprehensively investigated. MA-ALS is important for the acquisition of subject-related (mathematical) competence, an aspect of kindergarten education that is gaining in importance in the pre-school curricula of many countries.The quality of mathematical learning support in kindergarten is conceptualized by differentiating between the quality of MA-ALS and MI-ALS. MI-ALS is also divided into general support (group management, emotional warmth) and subject-related support (learning stimulation, subject-specific language). A rating tool for analyzing the quality of mathematical learning support is presented and its psychometric quality is assessed. The tool is then used to analyze the teaching quality in two guided play situations (recorded) and two interviews each with 145 education professionals in Germany and Switzerland. A confirmatory factor analysis (CFA) confirms the validity of the distinction between group management, emotional warmth and subject-related support. The relationship between the level of MI-ALS and MA-ALS, the training of the teachers (academic vs non-academic), and the educational context (Germany vs Switzerland) is examined. The results corroborate the importance of including planning and reflection as a dimension of learning support quality.