• 한국수학교육학회지시리즈D:수학교육연구
• /
• 제25권4호
• /
• pp.285-309
• /
• 2022

A large body of previous studies investigated mathematical tasks by analyzing the design process prior to lessons or textbooks. While researchers have revealed the significant roles of mathematical tasks within written curricular, there has been a call for studies about how mathematical tasks are implemented or what is experienced and learned by students as enacted curriculum. This article proposes a mathematical task analytic framework based on a holistic definition of tasks encompassing both written tasks and the process of task enactment. We synthesized the features of the mathematical tasks and developed a task analytic framework with multiple dimensions: breadth, depth, bridging, openness, and interaction. We also applied the scoring rubric to analyze three multiplication tasks to illustrate the framework by its five dimensions. We illustrate how a series of tasks are analyzed through the framework when students are engaged in multiplicative thinking. The framework can provide important information about the qualities of planned tasks for mathematics instruction (proactive) and the qualities of implemented tasks during instruction (reactive). This framework will be beneficial for curriculum designers to design rich tasks with more careful consideration of how each feature of the tasks would be attained and for teachers to transform mathematical tasks with the provision of meaningful learning activities into implementation.

• 한국수학교육학회지시리즈A:수학교육
• /
• 제44권2호
• /
• pp.215-228
• /
• 2005

The purpose of this study is to development the scoring framework for teacher knowledge of fractions. This framework is qualified in the content-validity by professional educators' evaluation and in the reliability by correlation coefficient. 2 math educators judged that this framework is composed of appropriate scoring category, scoring criterion, and scoring level. After 2 teachers scored the tasks, correlation coefficient was calculated between evaluators. The coefficient is evaluated high in that it is more than 0.80.

• 한국수학교육학회지시리즈D:수학교육연구
• /
• 제26권1호
• /
• pp.39-43
• /
• 2023

Choosing to See: A Framework for Equity in the Math Classroom is a book intended to be a practical tool for teachers to build empowering mathematics classrooms for their students from marginalized groups. Pamela Seda and Kyndall Brown provide concrete guidance using seven key principles, the ICUCARE (pronounced "I See You Care") Equity Framework, to provide a pathway for teachers for how to meaningfully make their classrooms a more equitable space for all students.

• 한국학교수학회논문집
• /
• 제23권3호
• /
• pp.299-321
• /
• 2020

OECD가 주관하는 PISA는, 변화하는 미래 사회를 대비하여 학생들에게 필요한 역량은 무엇이고 각 국가에서는 이를 어떻게 길러주어야 하는가에 대한 고민에서 시작되었다. 2000년에 첫 번째 본검사를 시작으로 3년 마다 시행된 PISA는 어느덧 여덟 번째 주기를 준비하고 있다. PISA 2022는 10년 만에 수학이 주 영역이 되는 주기로, OECD PISA 국제본부는 기존 주기의 수학 소양의 정의와 평가틀을 수정 보완하고, 이를 반영한 예시 문항을 공개하였다. 이에 본 연구에서는 PISA 수학 소양에 대한 정의와 평가틀의 변화 흐름을 살펴보고, PISA 2022 평가틀과 함께 소개된 예시 문항의 특징을 분석하였다. 이를 통해 역량 기반 교육과정을 표방하는 2015 개정 교육과정의 성공적인 실행과 수학 학습 평가에 관한 시사점을 도출하였다.

• 한국수학교육학회지시리즈A:수학교육
• /
• 제54권3호
• /
• pp.261-282
• /
• 2015

The purpose of this study was to provide insights on making Korean mathematics framework by analytical comparison of three major assessments such as the NAEP 2015, the TIMSS 2015 and the PISA 2015. This study focused on the key differences and common themes of mathematics frameworks among three major assessments. In order to achieve this purpose, mathematical frameworks of the NAEP 2015, the TIMSS 2015, and the PISA 2015 were analyzed and compared. The criteria of the comparison were content domain and cognitive domain. The comparing criteria of content domain were based on NCTM content standards and cognitive domain were used the three understanding levels of Jan de Lange's pyramid model. Based on these comparisons, researchers discussed that Korea mathematical framework was needed to have a set of content categories that reflect the range of underlying mathematical phenomena and a set of cognitive levels which contain the range of underlying fundamental mathematical capabilities including consideration of contexts.

• 한국수학교육학회지시리즈D:수학교육연구
• /
• 제26권4호
• /
• pp.291-310
• /
• 2023

In this paper, we propose a theoretical framework for Chinese high school mathematics teachers use new textbooks based on the work of Remillard (1999) and Chau (2014). Based on this framework, a multiple case approach was used to investigate how two high school mathematics teachers from Shanghai use new textbooks. The results suggest that in the curriculum mapping arena, both the novice teacher and the expert teacher often planned to appropriate the unit content, and sometimes planned to add supplemental content. When organizing the unit content, novice teacher always planned to follow the new textbook in sequence, while expert teacher often would follow the new textbook in sequence, but sometimes planned to rearrange the unit content. In the design arena, both the novice teacher and the expert teacher tended to appropriate the introduced tasks and definitions. The novice teacher often planned to appropriate the example problems and exercise problems, while the expert teacher often intended to flexibly use the example problems and exercise problems. In the construction arena, the novice teacher seldom adjusted the planned tasks; in contrast, the expert teacher adjusted the planned tasks more frequently. In the reflection arena, the novice teacher often thought she should improve the mathematics tasks, while the expert teacher almost always thought he needed to improve the mathematics tasks. The framework shown in this paper provides a tool to investigate how mathematics teachers use textbooks.

• 한국수학교육학회지시리즈D:수학교육연구
• /
• 제23권3호
• /
• pp.149-164
• /
• 2020

This study aimed to establish an observation protocol for mathematical modeling as an alternative way to examine instructional alignment to the Common Core State Standards for Mathematics. The instructional alignment observation protocol (IAOP) for mathematical modeling was established through careful reviews on the fidelity of implementation (FOI) framework and prior studies on mathematical modeling. I shared the initial version of the IAOP including 15 items across the structural and instructional critical components as the FOI framework suggested. Thus, the IAOP covers what teachers should do and know for practices of mathematical modeling in classrooms and what teachers and students are expected to do. Based on the findings in this study, validity and reliability of the IAOP should be evaluated in follow-up studies.

• 한국수학교육학회지시리즈A:수학교육
• /
• 제52권4호
• /
• pp.567-586
• /
• 2013

The purpose of this study was to introduce the Knowledge Quartet (KQ) framework by which we can analyze teacher knowledge revealed in teaching mathematics. Specifically, this paper addressed how the KQ framework has been developed and employed in the context of research on teacher knowledge. In order to make the framework accessible, this paper analyzed an elementary school teacher's knowledge in teaching her fifth grade students how to figure out the area of a trapezoid using the four dimensions of the KQ (i.e., foundation, transformation, connection, and contingency). This paper is expected to provide mathematics educators with a basis of understanding the nature of teacher knowledge in teaching mathematics and to induce further detailed analyses of teacher knowledge using some dimensions of the KQ framework.

• 대한수학교육학회지:학교수학
• /
• 제15권2호
• /
• pp.243-262
• /
• 2013

본 연구는 인지적 측면에서 수학 교사의 교수 양식을 분석하는 것을 목적으로 하고 있다. 이를 위해 먼저 문헌 연구를 통해 수학에서 서로 대비되는 유형으로 분류될 수 있는 인지적 사고 요소들을 탐색하고, 확인적 요인분석을 통해 이 요소들을 시각적 양식과 분석적 양식으로 범주화할 수 있다는 것을 검증하였다. 요인 분석 결과를 바탕으로 두 가지 양식과 두 가지 양식이 대등하게 나타나는 혼합적 양식을 수학 교수 양식으로 설정하고, 교사들의 양식을 분석할 수 있는 분석틀을 개발하였다. 또한, 수학 교수 양식 분석틀을 Flanders의 언어 상호작용 분석법(Amidon & Flanders, 1967)에 적용하여 교사들의 수학 수업을 통해서 교수 양식을 분석할 수 있는 방법을 설계하였다. 그리고 이를 활용해 수학 수업에서 교사들이 사용하는 수학적 언어를 분석한 결과, 실제로 시각적 양식, 분석적 양식, 혼합적 양식이 나타나는 것을 확인하였다.

• 한국수학교육학회지시리즈E:수학교육논문집
• /
• 제32권3호
• /
• pp.297-314
• /
• 2018

본 연구는 교사지식 중에서 예비교사의 학생에 대한 지식을 Shulman-Fischbein 개념틀을 이용하여 해석함으로써 우리의 교사교육의 현실에 시사점을 제공하고자 하였다. Shulman-Fischbein 개념틀은 수학의 알고리즘적 SMK, 수학의 형식적 SMK, 수학의 직관적 SMK, 수학의 알고리즘적 PCK, 수학의 형식적 PCK, 그리고 수학의 직관적 PCK의 여섯 가지 요소로 구성되어 있다. 이를 위해 일련의 평면도형 영역의 문제를 다루고 학생의 오개념을 포함한 지필과제를 5명의 예비교사에게 제시하고 그들이 제출한 답변을 분석하였다. 분석 결과 예비교사들은 상당히 강한 SMK를 지니고 있음을 보여주었고, 수학의 형식적 측면을 강조하는 경향을 보였다. 또한 학생들의 오개념 분석 시 학생들의 수준을 깊게 고려하지 않았고, 오개념을 고치기 위한 교수학적 방법을 제안할 때에 구체적이지 못하고 피상적인 답변만을 제시하는 특징을 보여주었다.