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한국수학교육학회> D-수학교육연구> Problem Posing in the Instruction of Proof: Bridging Everyday Lesson and Proof

KCI후보

Problem Posing in the Instruction of Proof: Bridging Everyday Lesson and Proof

Hangil Kim
  • : 한국수학교육학회
  • : D-수학교육연구 24권3호
  • : 연속간행물
  • : 2021년 09월
  • : 255-278(24pages)
D-수학교육연구

DOI


목차

Ⅰ. INTRODUCTION
Ⅱ. LITERATURE REVIEW
Ⅲ. RESEARCH METHODLOGY
Ⅳ. RESULTS AND DISCUSIONS
Ⅴ. DISCUSSIONS AND IMPLICATIONS
REFERENCES

키워드 보기


초록 보기

Proof serves a critical role in mathematical practices as well as in fostering student’s mathematical understanding. However, the research literature accumulates results that there are not many opportunities available for students to engage with proving-related activities and that students’ understanding about proof is not promising. This unpromising state of instruction of proof calls for a novel approach to address the aforementioned issues. This study investigated an instruction of proof to explore a pedagogy to teach how to prove. The teacher utilized the way of problem posing to make proving a routine part of everyday lesson and changed the classroom culture to support student proving. The study identified the teacher’s support for student proving, the key pedagogical changes that embraced proving as part of everyday lesson, and what changes the teacher made to cultivate the classroom culture to be better suited for establishing a supportive community for student proving. The results indicate that problem posing has a potential to embrace proof into everyday lesson.

UCI(KEPA)

간행물정보

  • : 사회과학분야  > 교육
  • : KCI후보
  • :
  • : 계간
  • : 1226-6191
  • : 2287-9943
  • : 학술지
  • : 연속간행물
  • : 1997-2021
  • : 394


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6Problem Posing in the Instruction of Proof: Bridging Everyday Lesson and Proof

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발행기관 : 한국수학교육학회 간행물 : D-수학교육연구 24권 3호 발행 연도 : 2021 페이지 : pp. 255-278 (24 pages)

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(기관인증 필요)

초록보기

Proof serves a critical role in mathematical practices as well as in fostering student's mathematical understanding. However, the research literature accumulates results that there are not many opportunities available for students to engage with proving-related activities and that students' understanding about proof is not promising. This unpromising state of instruction of proof calls for a novel approach to address the aforementioned issues. This study investigated an instruction of proof to explore a pedagogy to teach how to prove. The teacher utilized the way of problem posing to make proving a routine part of everyday lesson and changed the classroom culture to support student proving. The study identified the teacher's support for student proving, the key pedagogical changes that embraced proving as part of everyday lesson, and what changes the teacher made to cultivate the classroom culture to be better suited for establishing a supportive community for student proving. The results indicate that problem posing has a potential to embrace proof into everyday lesson.

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Research and national standards, such as the Next Generation Science Standards (NGSS) in the United States, promote the development and implementation of K-12 interdisciplinary curricula integrating the disciplines of science, technology, engineering, mathematics, and computer science (STEM+CS). However, little research has explored how teachers provide epistemic support in interdisciplinary contexts or the factors that inform teachers' epistemic support in STEM+CS activities. The goal of this paper is to articulate how interdisciplinary instruction complicates epistemic knowledge and resources needed for teachers' instructional decision-making. Toward these ends, this paper builds upon existing models of teachers' instructional decision-making in individual STEM+CS disciplines to highlight specific challenges and opportunities of interdisciplinary approaches on classroom epistemic supports. First, we offer considerations as to how teachers can provide epistemic support for students to engage in disciplinary practices across mathematics, science, engineering, and computer science. We then support these considerations using examples from our studies in elementary classrooms using integrated STEM+CS curriculum materials. We focus on an elementary school context, as elementary teachers necessarily integrate disciplines as part of their teaching practice when enacting NGSS-aligned curricula. Further, we argue that as STEM+CS interdisciplinary curricula in the form of NGSS-aligned, project-based units become more prevalent in elementary settings, careful attention and support needs to be given to help teachers not only engage their students in disciplinary practices across STEM+CS disciplines, but also to understand why and how these disciplinary practices should be used. Implications include recommendations for the design of professional learning experiences and curriculum materials.

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다운로드

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초록보기

The Science Writing Heuristic (SWH) approach is described as an immersive argument-based science inquiry focusing particularly on learning through epistemic practices. In the literature, several previous studies indicate how academic achievement is positively influenced by the SWH. In addition to these previous studies, several meta-syntheses of qualitative data have been conducted on this particular topic. With these literatures in mind, a quantitative meta-analysis was conducted with ten studies (N = 724) to examine the effectiveness of the SWH on student achievement in Turkey. To present a thoroughly detailed report, this study also examined the following moderators: grade level, subject area, school location, intervention length, and report source. Overall, this study found that in Turkey, the SWH classrooms performed better in academic achievement tests than traditional lecture-based classrooms. Additionally, the SWH is more likely to be effective regardless of grade levels, subject areas, and school locations.

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4Utilizing Teacher Noticing within a Representation of an Elementary Engineering Lesson to Support Responsive Teaching in the Classroom

저자 : Anne Estapa , Kristina M. Tank , Michael Dupont

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다운로드

(기관인증 필요)

초록보기

Teacher noticing has been termed consequential to teaching because what you see and do not see impacts decisions made within the classroom. Further, how a teacher responds to student thinking depends on what a teacher sees in student thinking. Within this study we sought to understand what teachers noticed within an engineering lesson and the decisions made as a result of that noticing. Findings indicate that student teachers and cooperating teachers drew on their pedagogical knowledge for decisions, rather than taking up the integrated content of student thinking and understanding. These findings serve as a guide for the experiences needed to engage in the complex work of teaching or, more specifically, implementing engineering into instruction through a responsive teaching frame.

KCI후보

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저자 : Byungeun Pak

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다운로드

(기관인증 필요)

초록보기

Students' participation in epistemic practices, which are related to knowledge construction on the part of students, is becoming a crucial part of learning (Goizueta, 2019). Research on epistemic practices in science education draws attention to teachers' support of students to engage in epistemic practices in mathematics instruction. The research highlights a need for incorporating epistemic goals, along with conceptual and social goals, into instruction to promote students' epistemic practices. In this paper, I investigate how teachers interact with students to integrate epistemic goals. I examined 24 interaction excerpts that I identified from six interview transcripts of two beginning teachers' mathematics instruction. Each excerpt was related to the teachers' talk about their specific interaction(s) in a small group. I explored how each teacher's discursive moves and goals were conceptual, social, and epistemic-related as they intervened in small groups. I found that both teachers used conceptual, social, and epistemic discursive move but their discursive moves were related only to social and social goals. This paper suggests supporting teachers to develop epistemic goals in mathematics instruction, particularly in relation to small groups.

KCI후보

6Problem Posing in the Instruction of Proof: Bridging Everyday Lesson and Proof

저자 : Hangil Kim

발행기관 : 한국수학교육학회 간행물 : D-수학교육연구 24권 3호 발행 연도 : 2021 페이지 : pp. 255-278 (24 pages)

다운로드

(기관인증 필요)

초록보기

Proof serves a critical role in mathematical practices as well as in fostering student's mathematical understanding. However, the research literature accumulates results that there are not many opportunities available for students to engage with proving-related activities and that students' understanding about proof is not promising. This unpromising state of instruction of proof calls for a novel approach to address the aforementioned issues. This study investigated an instruction of proof to explore a pedagogy to teach how to prove. The teacher utilized the way of problem posing to make proving a routine part of everyday lesson and changed the classroom culture to support student proving. The study identified the teacher's support for student proving, the key pedagogical changes that embraced proving as part of everyday lesson, and what changes the teacher made to cultivate the classroom culture to be better suited for establishing a supportive community for student proving. The results indicate that problem posing has a potential to embrace proof into everyday lesson.

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