Preservice Teachers’ Knowledge to Teach Functional Thinking

McAuliffe, Sharon; Vermeulen, Cornelis

doi:10.1007/978-3-319-68351-5_17

Cited by 3 publications

(1 citation statement)

References 23 publications

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“…In our research, we focused on the teachers' knowledge related to the development of functional thinking in the period when students are introduced to the concept of function, start to use formal function notation and work with the letter as a variable (students around [14][15]. Research that has addressed teachers' knowledge in the development of functional thinking has mostly focused on the earliest stages and is often linked to working with patterns (e.g., McAuliffe, Vermeulen, 2018;Wilkie, 2014). Other studies have addressed issues with specific concepts or properties from the topic of functions such as Zaslavsky et al (2002), Yoon, Thompson (2020, or with specific aspects of teaching, such as Ostermann et al (2018).…”

Section: Final Commentsmentioning

confidence: 99%

The specialized knowledge of middle school teachers concerning the concept of function

Slabý,

Semanišinová,

Climent

2022

AUPC

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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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Section: Final Commentsmentioning

confidence: 99%

The specialized knowledge of middle school teachers concerning the concept of function

Slabý,

Semanišinová,

Climent

2022

AUPC

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Development of prospective elementary teachers’ knowledge to teach early algebra through case discussions

Öztürk-Tavşan,

İşler-Baykal

2024

J Math Teacher Educ

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This study investigated the development of prospective elementary teachers (PETs)’ subject matter and pedagogical content knowledge for teaching early algebra through participation in case discussions. PETs attended five weeks of intervention as part of a method course, which included case discussions. During the intervention, the participants were presented with big ideas of equivalence and equations, generalized arithmetic, and functional thinking as the content of early algebra through text-based classroom cases. Data were collected through one-hour individual interviews before and after the early algebra lessons. The analysis of the pre-interviews indicated that prospective elementary teachers may not be ready to foster algebraic thinking in elementary grades in terms of the required knowledge for teaching. We found that PETs needed more development of required subject matter knowledge to guide algebraic thinking in elementary grades, such as the relational meaning of the equal sign, generalizing, representing, or justifying arithmetic or functional relationships, and reasoning with them. Likewise, PETs were found to lack in pedagogical content knowledge related to students’ conceptions and misconceptions and effective teaching strategies to promote early algebraic thinking. However, we found that specifically designed method courses could help develop PETs’ knowledge of teaching early algebra. Following early algebra lessons centered around case discussions, PETs showed progress in multiple aspects of knowledge across all big ideas, though their improvement in generalized arithmetic was somewhat less pronounced. This progress was observed in their subject matter and pedagogical content knowledge.

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An analysis of teacher knowledge for teaching functional thinking to elementary school students

Jeongsuk

Sunwoo²

2022

Asian Journal for Mathematics Education

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Given the significance of functional thinking at the elementary school level, there has been growing interest in teachers who play a major role in enhancing students’ functional thinking. This study surveyed 119 elementary school teachers in Korea to investigate their knowledge for teaching functional thinking. A written assessment was developed for this study regarding the knowledge of mathematical tasks, instructional strategies, and mathematical discourse to teach functional thinking. The results of this study showed that many teachers could design mathematical tasks corresponding to simple relationships of two quantities but some of them had difficulties in constructing the task for [Formula: see text]. Teachers could explain the affordances of key instructional strategies to foster functional thinking and identify students’ typical errors in recognizing or representing a functional relationship but some explanations included a superficial understanding of the core ideas of functional thinking. Based on these results this article closes with a discussion of several implications regarding the aspects needed for elementary school teachers to further promote students’ functional thinking.

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Preservice Teachers’ Knowledge to Teach Functional Thinking

Cited by 3 publications

References 23 publications

The specialized knowledge of middle school teachers concerning the concept of function

The specialized knowledge of middle school teachers concerning the concept of function

Development of prospective elementary teachers’ knowledge to teach early algebra through case discussions

An analysis of teacher knowledge for teaching functional thinking to elementary school students

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