Preservice teachers’ mathematical knowledge for teaching combinatorial thinking

International audienceIn the paper, we conceptualize Mathematical Knowledge for Teaching as introduced and elaborated by Ball et al. (2008) for the topic of combinatorics using Lockwood (2013) model of combinatorial thinking. We developed test consisting of three combinatorial problems and 6 connected tasks (for each problem) focused on the Common Content Knowledge (CCK), Specialized Content Knowledge (SCK), Knowledge of Content and Students (KCS) and Knowledge of Content and Teaching (KCT) to answer our research question: What are the differences in the combinatorial PCK between preservice teachers with regard to their combinatorial CK? We analyse and discuss data collected from 10 preservice teachers concerning one of the combinatorial problems and its connected tasks

Preservice teachers’ mathematical knowledge for teaching combinatorial thinking

International audienceIn the paper, we conceptualize Mathematical Knowledge for Teaching as introduced and elaborated by Ball et al. (2008) for the topic of combinatorics using Lockwood (2013) model of combinatorial thinking. We developed test consisting of three combinatorial problems and 6 connected tasks (for each problem) focused on the Common Content Knowledge (CCK), Specialized Content Knowledge (SCK), Knowledge of Content and Students (KCS) and Knowledge of Content and Teaching (KCT) to answer our research question: What are the differences in the combinatorial PCK between preservice teachers with regard to their combinatorial CK? We analyse and discuss data collected from 10 preservice teachers concerning one of the combinatorial problems and its connected tasks

Can a mathematics teacher learn how to provide good formative assessment?

summary:Formatívne hodnotenie je prínosom pre žiacke učenie. Preto má zmysel uvažovať o jeho kvalite ako takej a o kvalite formatívneho hodnotenia, ktoré poskytuje konkrétny učiteľ. V článku predstavujeme rubriky na meranie kvality formatívneho hodnotenia a krátky výskum zameraný na možnosti rastu učiteľov v tejto oblasti pomocou spomínaných rubrík. Tento výskum a jeho závery by mohli podnietiť učiteľov k sebareflexii nad formatívnym hodnotením, ktoré poskytujú svojim žiakom.summary:Formative assessment is beneficial for pupils’ learning. Therefore, it is reasonable to consider its quality in general and the quality of formative assessment provided by a particular teacher. In the paper, we present rubrics on the quality of formative assessment measurement and a short study focused on the teacher’s development in this area with using the above rubrics. The research and its findings could promote teachers’ self-reflection on their own practice of formative assessment

Questioning as formative assessment and its quality measurement

International audienceThis paper presents the tool for measuring the quality of questioning in mathematics classes. Its construction is based on video analysis and interviews with teachers. Actually, we identified five different categories within the constructs of questioning. These rubrics have potential to be used in research and in teacher education

Comparing German and Slovak teachers’ knowledge of content and students related to functions

A crucial aspect of learning about (linear) functions is being able to change between graph and equation. Common German and Slovak textbooks propose different procedures for these representational changes. Within a sample of 49 German and 56 Slovak teachers, we analyzed if these different procedures can also be observed in the teachers’ corresponding knowledge of content and students, i. e. if the teachers expected different student strategies and errors. The results confirm this assumption and emphasize the importance to consider this teacher's knowledge in a country-specific way and being careful when comparing such knowledge of teachers from different countries

Pre-service mathematics teachers: How to make them ready to be ready

International audienceThe changes concerning the final state examination, determined by the novelty of Slovak university law, stimulated us to make serious changes in the examination model of Didactics of Mathematics at our university. Moreover, we have observed significant gaps in pedagogical content knowledge (PCK) of our secondary pre-service teachers during the last years. These two stimuli led us to an improvement of the course of Didactics of Mathematics. In this paper, we present our new approach which was mainly focused on the assessment of the lesson plans presented by the pre-service teachers. The assessment was based on the rubrics which were developed through the course. After the application of the new approach, we have observed growth in PCK. We have partially confirmed reliability of the rubrics as well

Comparing German and Slovak teachers’ knowledge of content and students related to functions

A crucial aspect of learning about (linear) functions is being able to change between graph and equation. Common German and Slovak textbooks propose different procedures for these representational changes. Within a sample of 49 German and 56 Slovak teachers, we analyzed if these different procedures can also be observed in the teachers’ corresponding knowledge of content and students, i. e. if the teachers expected different student strategies and errors. The results confirm this assumption and emphasize the importance to consider this teacher's knowledge in a country-specific way and being careful when comparing such knowledge of teachers from different countries

Introduction to TWG20: mathematics teacher knowledge, beliefs, and identity

International audienc