[논문]교사의 수업 계획 및 실제 수업에서의 수학 교과서와 교사용지도서 활용 연구

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교사의 수업 계획 및 실제 수업에서의 수학 교과서와 교사용지도서 활용 연구
How Teachers Use Mathematics Curriculum Materials in Planning and Implementing Mathematics Lessons 원문보기

학교수학 = School Mathematics, v.13 no.3, 2011년, pp.485 - 500

초록
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수학 교사가 수업을 계획하고 계획한 수업을 실행할 때 교육과정 도서(교과서, 교사용지도서 등)를 어떻게 활용하는지에 대하여 시행된 연구가 많지 않은 실정이다. 이 논문은 미국의 초등 교사들이 초등 수학 교육과정의 프로그램 중의 하나인 Everyday Mathematics의 교육과정 도서를 어떻게 활용하는지, 또한 Everyday Mathematics가 가지는 교육과정 도서로써의 특징 요소들이 무엇인지 분석한다. 나아가 Stein & Kim(2009)의 연구에서 제안한 교육과정 도서를 규명하는 특징 요소들과 교사들의 교육과정 도서의 활용 간의 연관성을 추정한다. 수집된 자료는 미국 초등 교사의 수학수업 관찰노트와 관찰 전후에 실시한 인터뷰, 수업 시간에 사용한 모든 문서와 자료, 그리고 Everyday Mathematics의 교사용 지도서 등이다. 분석 결과, Everyday Mathematics는 높은 수준의 인지적 노력(cognitive demand)을 필요로 하는 수학과제들로 구성되어 있으며 (80 퍼센트), 교육과정 개발자들의 의도와 이유가 분명하게 드러나지는 않는 것으로 나타났다. 대부분의 교사들은 교사용 지도서를 참조하여 수업을 계획하고 실행하는데 있어서 지도서에서 제시한 문제나 활동을 변형하거나 부분적으로 선택하여 가르치는 것으로 나타났다. 이 과정에서 Everyday Mathematics 교육과정에서 제시한 인지적 노력 수준이 높은 수학 과제들의 27퍼센트만이 같은 수준에서 실행되는 것으로 나타났다. 교과서에서 실행 단계로 이동할 때 수학과제의 인지적 노력 수준이 감소하는 것은 교사용 지도서가 높은 인지적 노력수준의 수학 과제를 교사가 같은 수준에서 실행할 수 있도록 제대로 지원해 주지못하는 것에 기인하는 것으로 볼 수 있다.

Abstract ▼ AI-Helper

The purpose of this study is to investigate how elementary mathematics teachers use and implement a reform-oriented mathematics curriculum material, Everyday Mathematics, and to examine what features the curriculum material has. Eight elementary mathematics teachers in the United States participated in the study. Data sources consist of teacher classroom observation write-ups, interviews, and the curriculum material. The results from the analysis of the curriculum material suggest that 80 percent of the tasks are at the high-level in terms of cognitive demand and 26 percent of tasks are identified as transparent. The results also show that the teachers appeared to adapt the curriculum material and partially take suggestions or activities out of the curriculum material in enacting them in their mathematics classrooms. The analysis of enacted tasks suggests that the levels of cognitive demand were shifted from high-level to low-level; 27 percent of the high-level tasks in the curriculum material were maintained at the high-level as enacted in the mathematics classrooms. The level of cognitive demand shifted in many cases; shifts from high-level to low-level occurred. This contributes to the curriculum material not being transparent to teachers.

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문제 정의

In addition, by examining whether the curriculum material provides rationales or explanations of why and how certain activities or problems suggested in the material are necessary for a particular mathematical concept, idea, or topic in order to support teachers, this study attempt to identify the features of the curriculum material.
There are relatively few studies to examine and characterize curriculum materials in relation to teaching, teachers' design and construction, and enactment in their classrooms. Such efforts would offer insights on the relationship between curriculum materials and teaching.
The purpose of this study is to investigate the relationship between teacher and curriculum materials by examining how teachers use the Standards-based or reform-oriented mathematics curriculum material, Everyday Mathematics (University of Chicago School Mathematics Project, 2004), in planning lessons and enacting them in their mathematics classrooms. Relatively few research studies have been explored how teachers use and implement such Standards-based curriculum materials and furthermore, what features the curriculum material has.
This study investigates how mathematics teachers use and implement Standards-based elementary mathematics curriculum material, Everyday Mathematics, for their mathematics lessons and the features of the curriculum material such as transparency and the level of cognitive demand of mathematical tasks. Further, this study attempts to explore how the features of the curriculum material, by inference, affect the elementary mathematics teachers' use and enactment of the curriculum material.

제안 방법

In addition, all the 9 teachers were interviewed by the trained researchers before and after the successive classroom observations by semi-structured interview protocols; the interview protocols included such as "Describe how you’ve prepared for these lessons.
The research studies propose that mathematical tasks can be categorized as doing mathematics, procedures with connections to meaning, concepts, or understanding, procedures without connections to meaning, concepts, or understanding, and memorization according to the cognitive efforts required in accomplishing the tasks (see Task Analysis Guide, Stein, Smith, Henningsen & Silver, 2000, p. 16).
The task focuses first grade students' attention on the use of procedures of organizing data and making line plots for developing understanding of mathematical concept of median and mode.
Thus, the Teacher's Guide along with tasks for students was examined and analyzed for this study; in particular, the tasks on which mathematics lesson observed is based were analyzed in terms of the level of cognitive demands-doing mathematics, procedures with connections, procedures without connections, and memorization.

대상 데이터

Remillard (1999) suggested a model of teachers' curriculum enactment in mathematics teaching in which teachers play a role involving and selecting and redesigning curriculum plans as well as enacting such plans for their students in mathematics classrooms. In particular, the model consists of the design arena, the construction arena, and the mapping arena. In the design phase, teachers' role includes selecting and designing mathematical tasks for students by consulting and interacting with the curriculum materials explicitly.
However, the larger study began with nine teachers for the first semester of the study. This study investigates eight elementary mathematics teachers from four different elementary schools in one school district. The school district mandated Everyday Mathematics to improve mathematics teaching and student achievement in mathematics in elementary grades at the time of conducting this study.
It was the first year of the adoption of Everyday Mathematics when data for this study were collected. Two kindergarten, 4 first grade, and 2 second grade teachers participated in this study; all the teachers were female. The school district is located in an urban area and the population of students was dominantly composed of African-American and Hispanic students; about 90 percent of the students received free or reduced-price lunches and 10 percent of the students are English Language Learners.

성능/효과

Regarding the matter of the transparency of the curriculum material, the results showed that 73 percent (11 out of 15) were identified as not transparent; only 27 percent were judged as transparent.
For analysis in the study, lessons/sessions were randomly selected from each grade level in each curriculum and scrutinized in terms of the cognitive demand of mathematical tasks, transparency, and anticipation that are illustrated above. The study suggested that Everyday Mathematics is composed of more procedures with connections tasks (79 percent) than Investigations (11 percent); Investigations contain more doing mathematics task (89 percent) than Everyday Mathematics (12 percent). The study also revealed that 21 percent of Everyday Mathematics lessons were judged to be transparent.

후속연구

It is suggested to consider whether curriculum materials provide examples of students' actual work, thinking processes, or possible responses to help teachers implement them as intended (Ball & Cohen, 1996; Davis & Krajcik, 2005; Stein & Kim, 2009), which would develop teachers' pedagogical design capacity (Brown, 2009). Also, it is called for more research studies on mathematics curriculum materials such as how mathematical ideas and concepts are represented in the curriculum materials at the present time and should be represented in the future curriculum materials in order for mathematics teachers to enact the representation intended. Importantly, research studies on how Teacher's Guide ought to be designed and developed to support teachers who are in need for teaching for understanding and results from those studies would be valuable and meaningful in understanding of how teachers learn to teach for students' mathematical understanding (Collopy, 2003; Drake, 2010; Lloyd & Pitts Bannister, 2010).
Further study would need to examine what other features mathematics curriculum material possibly should be identified in order to explore the relationships between curriculum materials and teachers. It is suggested to consider whether curriculum materials provide examples of students' actual work, thinking processes, or possible responses to help teachers implement them as intended (Ball & Cohen, 1996; Davis & Krajcik, 2005; Stein & Kim, 2009), which would develop teachers' pedagogical design capacity (Brown, 2009).

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연합인증

교사의 수업 계획 및 실제 수업에서의 수학 교과서와 교사용지도서 활용 연구
How Teachers Use Mathematics Curriculum Materials in Planning and Implementing Mathematics Lessons 원문보기

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교사의 수업 계획 및 실제 수업에서의 수학 교과서와 교사용지도서 활용 연구 How Teachers Use Mathematics Curriculum Materials in Planning and Implementing Mathematics Lessons 원문보기

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교사의 수업 계획 및 실제 수업에서의 수학 교과서와 교사용지도서 활용 연구
How Teachers Use Mathematics Curriculum Materials in Planning and Implementing Mathematics Lessons 원문보기

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