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

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Hubeňáková V., Sproesser U., Semanišinová I.
Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
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2021
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vol. 13
115-125
EN
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.
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The specialized knowledge of middle school teachers concerning the concept of function

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Slabý M., Semanišinová I., Climent N.
Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
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2023
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vol. 14
81-101
EN
This study presents research focusing on in-service mathematics teachers and their approach to tasks aimed at developing of functional thinking. The analysis is based on the model of The Mathematics Teachers' Specialised Knowledge -- model MTSK by Carrillo et al. (2018). The research question is the following: What ``specialised knowledge'', in the sense of the MTSK framework, is revealed when a~middle school teachers solve and discuss the selected tasks? The research was conducted with 9 teachers, who voluntarily participated in the professional development. The teachers solved a~set of 30 tasks that were selected with a~focus on 4 aspects of the concept of function, different representations and transitions between them and different actions that learners engage in the task solving. In this study, we analysed the teachers' written solutions and the discussion with the teachers about a~particular task. Reflecting on their work as learners was very important in moving from dealing with the mathematics itself to shifting to developing their knowledge of mathematics teaching (KMT) and knowledge of features of learning mathematics (KFLM) in terms of the MTSK framework. The results helped us to identify gaps in teachers' specialised knowledge and consequently will help us to improve professional development courses for both in-service and pre-service teachers.
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