Frank Lester | Indiana University (original) (raw)
Books by Frank Lester
[Abstract] Research suggests a strong relationship between what teachers believe about mathematic... more [Abstract] Research suggests a strong relationship between what teachers believe about mathematics
and teaching mathematics and the way they teach. However, we know very little about the relationship
between teachers’ beliefs and what they know about mathematics and how to teach it. For the past two
years, we have been conducting research concerning the mathematics beliefs and conceptions of
preservice elementary teachers. In this chapter, we describe how we have been doing this research and
report some preliminary results of this on-going study.
Papers by Frank Lester
The Arithmetic Teacher
An ice cream cone can be bought for 60 cents, and you have a quarter, a dime, and two pennies. Ho... more An ice cream cone can be bought for 60 cents, and you have a quarter, a dime, and two pennies. How much more money do you need to buy the cone?
Journal for Research in Mathematics Education
Within the past 25 years or so a new discipline has evolved from the confluence of research in su... more Within the past 25 years or so a new discipline has evolved from the confluence of research in such disparate disciplines as computer science, linguistics, neuroscience, philosophy, and psychology.
The Mathematics Teacher
Teaching according to the vision of the NCTM's Curriculum and Evaluation Standards will invol... more Teaching according to the vision of the NCTM's Curriculum and Evaluation Standards will involve numerous changes in the content and instruction of the school mathematics program. Moreover, this vision will also require a change in testing procedures and methods for evaluating the effectiveness of instructional practices (Clarke, Clarke, and Lovitt 1990; EQUALS and California Mathematics Council 1989; NAEP 1987; NCTM 1989). As is pointed out in NCTM's curriculum standards, an evaluation program that is properly aligned with the proposed curriculum standards can no longer use only written tests. Calculators, computers, and manipulatives must be included in the evaluation process.
The Journal of Experimental Education
Journal For Research in Mathematics Education, 1985
Journal For Research in Mathematics Education, 2013
National Council of Teachers of Mathematics Yearbook, 1976
This project was designed zo: (1) assess 7th-graders' metacognitive beliefs and processes and inv... more This project was designed zo: (1) assess 7th-graders' metacognitive beliefs and processes and investigate how they affect problem-solving behaviors; and (2) explore the extent to which these students can be taught to be more strategic and aware of their own problem-solving behaviors. The primary assessment was conducted by analyzing video tapes of 1. ividual students and pairs of students working 3n multi-step problems and non-standard problems, and subsequently being interviewed about their performance. The interview probed the students' mathematical knowledge, strategies, decisacns, beliefs, and affects. A variety of ''ritten protocol data, including pre-and post-tests, homework assignments, and In-class assignments were collected. The instruction was presented by onc of the investigators to a regular-level and an advanced-level 7th-grade class about 3 days per week for a period of 12 weeks. Among the four ca-.egories of the cognitive-metacognitive framework, which included orientation, organization, execution, and verification, the orientation category had the most important effect on students' problem-solving. Finally, it appeared that instruction was most likely to be effective when it occurs over a prolonged period of time and within the context of regular day-today mathematics instruction.
Hoosier Science Teacher, May 1, 1983
National Council of Teachers of Mathematics, Mar 25, 2004
Abstract. The authors discuss the purposes of mathematics education research, pointing out that d... more Abstract. The authors discuss the purposes of mathematics education research, pointing out that different researchers have different views. They propose a way to think about mathematics education research that can serve to move the research community toward ...
Mathematical Problem Solving and New Information Technologies, 1992
Research on mathematical problem solving has provided little specific infonnation about problem-s... more Research on mathematical problem solving has provided little specific infonnation about problem-solving instruction. There appear to be four reasons for this unfortunate state of affairs: (1) relatively little attention has been given to the role of the teacher in instruction; (2) there has been little concern for what happens in real classrooms; (3) there has been a focus on individuals rather than small groups or whole classes; and (4) much of the research has been largely atheoretical in nature. This paper discusses each of these reasons and presents a framework for designing research on mathematics problem-solving instruction. Four major components of the framework are discussed: extra-instruction considerations, teacher planning, classroom processes, and instructional outcomes. Special attention is given to factors that may be particularly fruitful as the focal points of future research.
Mathematics Education as a Research Domain: A Search for Identity, 1998
... Dorfler, W.: 1993,'Quality Criteria for Journals in the Field of Didactics of Mathem... more ... Dorfler, W.: 1993,'Quality Criteria for Journals in the Field of Didactics of Mathematics', in G. Nissen & M. Blomh0j (eds.). Criteria for Scientific Quality and Relevance in the Didactics of Mathematics. Danish Research Council for the Humanities, Roskilde, Denmark, 75-87. ...
[Abstract] Research suggests a strong relationship between what teachers believe about mathematic... more [Abstract] Research suggests a strong relationship between what teachers believe about mathematics
and teaching mathematics and the way they teach. However, we know very little about the relationship
between teachers’ beliefs and what they know about mathematics and how to teach it. For the past two
years, we have been conducting research concerning the mathematics beliefs and conceptions of
preservice elementary teachers. In this chapter, we describe how we have been doing this research and
report some preliminary results of this on-going study.
The Arithmetic Teacher
An ice cream cone can be bought for 60 cents, and you have a quarter, a dime, and two pennies. Ho... more An ice cream cone can be bought for 60 cents, and you have a quarter, a dime, and two pennies. How much more money do you need to buy the cone?
Journal for Research in Mathematics Education
Within the past 25 years or so a new discipline has evolved from the confluence of research in su... more Within the past 25 years or so a new discipline has evolved from the confluence of research in such disparate disciplines as computer science, linguistics, neuroscience, philosophy, and psychology.
The Mathematics Teacher
Teaching according to the vision of the NCTM's Curriculum and Evaluation Standards will invol... more Teaching according to the vision of the NCTM's Curriculum and Evaluation Standards will involve numerous changes in the content and instruction of the school mathematics program. Moreover, this vision will also require a change in testing procedures and methods for evaluating the effectiveness of instructional practices (Clarke, Clarke, and Lovitt 1990; EQUALS and California Mathematics Council 1989; NAEP 1987; NCTM 1989). As is pointed out in NCTM's curriculum standards, an evaluation program that is properly aligned with the proposed curriculum standards can no longer use only written tests. Calculators, computers, and manipulatives must be included in the evaluation process.
The Journal of Experimental Education
Journal For Research in Mathematics Education, 1985
Journal For Research in Mathematics Education, 2013
National Council of Teachers of Mathematics Yearbook, 1976
This project was designed zo: (1) assess 7th-graders' metacognitive beliefs and processes and inv... more This project was designed zo: (1) assess 7th-graders' metacognitive beliefs and processes and investigate how they affect problem-solving behaviors; and (2) explore the extent to which these students can be taught to be more strategic and aware of their own problem-solving behaviors. The primary assessment was conducted by analyzing video tapes of 1. ividual students and pairs of students working 3n multi-step problems and non-standard problems, and subsequently being interviewed about their performance. The interview probed the students' mathematical knowledge, strategies, decisacns, beliefs, and affects. A variety of ''ritten protocol data, including pre-and post-tests, homework assignments, and In-class assignments were collected. The instruction was presented by onc of the investigators to a regular-level and an advanced-level 7th-grade class about 3 days per week for a period of 12 weeks. Among the four ca-.egories of the cognitive-metacognitive framework, which included orientation, organization, execution, and verification, the orientation category had the most important effect on students' problem-solving. Finally, it appeared that instruction was most likely to be effective when it occurs over a prolonged period of time and within the context of regular day-today mathematics instruction.
Hoosier Science Teacher, May 1, 1983
National Council of Teachers of Mathematics, Mar 25, 2004
Abstract. The authors discuss the purposes of mathematics education research, pointing out that d... more Abstract. The authors discuss the purposes of mathematics education research, pointing out that different researchers have different views. They propose a way to think about mathematics education research that can serve to move the research community toward ...
Mathematical Problem Solving and New Information Technologies, 1992
Research on mathematical problem solving has provided little specific infonnation about problem-s... more Research on mathematical problem solving has provided little specific infonnation about problem-solving instruction. There appear to be four reasons for this unfortunate state of affairs: (1) relatively little attention has been given to the role of the teacher in instruction; (2) there has been little concern for what happens in real classrooms; (3) there has been a focus on individuals rather than small groups or whole classes; and (4) much of the research has been largely atheoretical in nature. This paper discusses each of these reasons and presents a framework for designing research on mathematics problem-solving instruction. Four major components of the framework are discussed: extra-instruction considerations, teacher planning, classroom processes, and instructional outcomes. Special attention is given to factors that may be particularly fruitful as the focal points of future research.
Mathematics Education as a Research Domain: A Search for Identity, 1998
... Dorfler, W.: 1993,'Quality Criteria for Journals in the Field of Didactics of Mathem... more ... Dorfler, W.: 1993,'Quality Criteria for Journals in the Field of Didactics of Mathematics', in G. Nissen & M. Blomh0j (eds.). Criteria for Scientific Quality and Relevance in the Didactics of Mathematics. Danish Research Council for the Humanities, Roskilde, Denmark, 75-87. ...
International Journal of Educational Research, 2011
Curricular effect on the teaching and learning of mathematics: Findings from two longitudinal stu... more Curricular effect on the teaching and learning of mathematics: Findings from two longitudinal studies in China and the United States ''What really works?'' has been one of the most frequently asked questions in the current debate about the mathematics education reform movement in general and about recent curricular innovations in particular. This Special Issue presents data from two longitudinal research projects in China and the United States of America to explore this question. Although China 1 and the United States have quite different cultural traditions, in both countries changing the curriculum has been viewed and used as an effective way to change classroom practice and to influence student learning to meet the needs of the everchanging world. The first project, conducted in China, compared the effects of a new, reform elementary mathematics curriculum to that of the conventional curriculum on classroom practice and student learning outcomes. The second project-the LieCal Project (Longitudinal Investigation of the Effect of Curriculum on Algebra Learning)-was conducted in the US. This project was designed to investigate not only the ways under which a reform curriculum can or cannot enhance student learning in algebra, but also the characteristics of the curricula that lead to student achievement gains. Both projects looked into changes in classroom practice by examining the nature of classroom instruction, analyzing cognitive features of the instructional tasks implemented in different classrooms and the characteristics of classroom interactions and changes in student learning outcomes. The China Project and the LieCal Project share similarities in their designs and data analyses. In particular, both projects address common and critical issues about teaching and learning in using reform curricula, including: (1) Does the use of a reform curriculum affect the quality and nature of classroom teaching? (2) Do students gain more in solving problems, as the developers of the reform curricula claim? (3) Do students sacrifice basic mathematical skills with the reform curriculum? (4) To what extent does the use of the reform curriculum improve learning for all students? This special issue includes six articles. The first article presents theoretical and methodological considerations about longitudinally investigating curricular effects on the teaching and learning of mathematics in a cultural context. Articles 2-5 focus on curricular effects on classroom instruction ('implemented curriculum') and on student learning outcomes ('achieved curriculum'). In particular, the second article reports findings about the impact of curriculum reform on teaching practice in primary mathematics in China. In a parallel form, the third article provides evidence about the kinds of instruction that transpires in classrooms using Standards-based and traditional mathematics curricula in the United States. Article four is a report of a study of the curriculum effects on student mathematics achievement in China. The fifth article is an investigation of curriculum effects on US middle school students' learning of algebra using various outcome measures. In the final article, we synthesize the results from the two projects and discuss several lessons learned about investigating and understanding curricular effects on the teaching and learning of mathematics. It is expected that this special issue will contribute to the field in several ways. Empirically, it is unique in that the two projects provide not only scientific evidence about the impact of curricular innovations on students' learning, but also venues to test fundamental hypotheses about curriculum and teaching variables linked to student learning outcomes in two distinctively different locations. Methodologically, the design and data analyses in the two projects inform researchers about ways to longitudinally investigate and understand the effects of curriculum reform efforts. Practically, the findings inform administrators, teachers, and curriculum developers about how to sustain the desirable changes in classroom practices and student outcomes through reform efforts.