Abstract
The study aims to explore how pre-service mathematics teachers reveal their knowledge of infinity during the lesson planning process in the context of limit. Specifically, we adopted the dimensions of mathematics teachers’ specialized knowledge, which are related to mathematical knowledge and its relation with teaching. We conducted an exploratory case study design in a two-cycle lesson planning process with three senior pre-service mathematics teachers. The findings indicated that in the first planning process the participants did not use infinity as a way of thinking, rather they focused on paradoxes and potential infinity. After they taught their lesson plan, they started to think about the complexity of infinity not only in the context of limit but also in the concept itself during the lesson planning process. The findings did not cover the knowledge of infinity; rather, they yield important implications for lesson planning process to reveal teachers’ knowledge for teaching.
Highlights
Though the notion of infinity is not included in the elementary and secondary school curricula explicitly (e.g., MoNE, 2018; NCTM, 2000), it forms the base for many concepts including calculus concepts-limit, derivative and integral (Monaghan, 2001) and it is a concept that develops students’ mathematical thinking for many mathematical concepts
As part of a comprehensive study, which aimed to teach the concept of limit in a broad sense by focusing on the lesson planning, we focused to reveal how pre-service mathematics teachers reflect their mathematical knowledge in the concept of infinity in the context of the limit concept
The current study investigated the pre-service mathematics teachers’ mathematical knowledge about infinity within the lens of KoT and KPM and in the model of mathematics teachers’ specialized knowledge (MTSK) in the lesson planning phases aiming to teach the concept of limit in lesson study process
Summary
Though the notion of infinity is not included in the elementary and secondary school curricula explicitly (e.g., MoNE, 2018; NCTM, 2000), it forms the base for many concepts including calculus concepts-limit, derivative and integral (Monaghan, 2001) and it is a concept that develops students’ mathematical thinking for many mathematical concepts. What we know about pre-service mathematics teachers’ knowledge of infinity is largely based upon the studies that investigate how they conceptualize and understand the concept of infinity (e.g., Date-Huxtable et al, 2018; Kolar & Čadež, 2011; Wijeratne & Zazkis, 2016). Though these studies have investigated pre-service mathematics teachers’ mathematical knowledge of infinity in the eyes of conceptualization, they didn’t focus on instructional practices including thinking on students’ learning, planning a lesson, teaching the concept. This issue has not received as much attention as the studies on pre-service mathematics teachers’ knowledge (Montes & Carrillo, 2015)
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