Learning to Teach Mathematics: Focus on Student Thinking

Universal Journal of Educational Research, 2016

This study examined how one teacher used research-based knowledge of how adolescents think about proportions. Observations, interviews, document collection, and a workshop intervention were utilized. The design of the workshop was inspired by the cognitively guided instruction studies and its purpose was to explore the research findings on adolescents' thinking about proportions. An individual case study was created to describe the teacher's instruction related to proportion concepts, rationales for instructional decisions, beliefs, and changes in all of these areas after participating in the workshop intervention. The case presented here shows positive changes in the teacher's instruction and beliefs after the workshop.

International journal of psychology and educational studies, 2020

In an attempt to improve Technological Pedagogical Content Knowledge (TPACK), prospective mathematics teachers (N=52) were trained in creating technology-based mathematics teaching materials. They learned visual programming, worked in pairs and created mathematics stories, which are intended to improve fourth grade students' mathematics word problem solving. Six of the prospective teachers were willingly participated in this study and watched students completing the stories in actual classroom environments. The purpose was to show them the value of their work and provide advice with regard to improve their TPACK. They (n=6) were interviewed within a qualitative research framework. This study reveals the prospective teachers´ opinions and beliefs regarding various aspects of the projects, such as students´ interest, students´ performance, as well as the teachers´ professional, pedagogical and individual improvement. The prospective teachers are convinced that teaching by means of technology support students' learning and that technology use in the classrooms is valuable. As a result, it can be confirmed that the process helped them improve their TPACK.

E liciting, responding to, and advancing students' mathematical thinking all lie at the heart of great teaching (NCTM 2014). We describe a formative assessment approach that teachers can use to learn more about their students' mathematical thinking and inform their instructional decisions. This assessment approach draws on a widely known set of frameworks for children's thinking, Cognitively Guided Instruction (CGI) (Carpenter et al. 2014). It enables teachers to learn from students by giving them time to voice their understandings and confusions. By listening carefully, teachers convey to students that their experience matters.

Australian primary mathematics classroom, 2006

Mathematics Education Research Group of Australasia, 2016

A central premise of this project is that teachers learn from the act of teaching a lesson and that this learning is evident in the planning and teaching of a subsequent lesson. We are studying the knowledge construction of mathematics teachers utilising multi-camera research techniques during lesson planning, classroom interactions and reflection. This paper reports on the learning of two Year 7 teachers, one in Melbourne and one in Chicago, teaching the same initial lesson focusing on division, remainders and context. Both teachers claimed to have learned about their students’ mathematical thinking after teaching the initial lesson, but found planning a second lesson to accommodate this learning challenging.

Perspectives in Education, 2013

This article about the discourse of pedagogy as related to child cognition in mathematics addresses the issue of what constitutes the main disciplinary content and the pedagogical content knowledge (PCK) of foundation-phase teachers. I argue that, unless child cognition itself is the primary disciplinary content of foundation-phase teachers' knowledge, it is likely that they will couch their pedagogical knowledge in teaching methods and materials more than in knowledge of conceptual development of learners and how such knowledge relates to teaching. In this first of a series of case studies, workshop-generated conversational and interview data were analysed qualitatively for discourse. The topics for the workshops were mathematical cognition and training in standardised test administration. The analysis showed that the discourse of teachers' expressed knowledge about their practice was embedded in the language of policy, curriculum, teaching methods of mathematics, and the o...

Australasian Journal of Early Childhood

ACTA SCIENTIAE, 2021

Background: The term computational thinking offers a new approach in the field of cognitive science, through the premise of systematizing the steps of problem solving that it can be applied in Artificial Intelligence and to other sciences. Objectives: Offer to participants a continuous training in the context of computational thinking and evaluate the impact of understanding these teachers about their respective concepts and practices. Design: Of a qualitative nature, involving specific dynamics of action-research, the design of the teaching experience involves the elaboration of tasks, used as a teaching hypothesis, subject to reassessments and readjustments. Settings and participants: In remote context, through the Teams platform, with eleven primary and higher schoolteachers from Brazil, Portugal, Cape Verde and Angola. Data collection and Analysis: Data obtained through the recordings of the meetings and the proposals of the participants, analyzed according to the four phases of the reflexive spiral and the expansive cycle. Results: The contributions and involvement of the teachers were significant, and some proposals of activities conceived, two of them presented in this article. Conclusions: With the partial results obtained it is expected that the insertion of computational thinking in basic education develops skills of different abstraction, which helps children in solving problems in all areas of life, not only in the use of computers or for future computer scientists. The participants' proposals will be published and made available online, to contribute to teacher training in the context of computational thinking.

This paper describes the experiences of a team of kindergarten teachers as they came to grips with what ideas students could meaningfully explore, represent, and communicate. We share how teachers collaboratively planned a problem-solving lesson for their students and in the process explored the mathematics for themselves as well. We discuss students' work demonstrating their engagement in the mathematics of the lesson and teachers' reflections on the lesson, thoughts about the significance of students' thinking, and efforts to orchestrate communication. Often kindergarten teachers think they have little influence on the mathematics learning of their children because they do not see the significance of ideas with which children can work. This paper describes a three-year effort made by all kindergarten teachers in one school to understand and influence their students' thinking about mathematical ideas. We discuss a professional development program that had a major in...