Richard Lesh - Profile on Academia.edu (original) (raw)

Papers by Richard Lesh

These 14 research reports are grouped into three broad categories based on the Piagetian level co... more These 14 research reports are grouped into three broad categories based on the Piagetian level concerned. The articles, concerning preoperational concepts focus on problems such as: (1) finding an appropriate mathematical description of some of the primitive mathematical concepts; (2). the role of. '!activities" in early concept acquisition; (3) the similarities'anddifferences between Perceptual and conceptual processes; (4) the relation between memory improvement and improved operational ability; and (5) variables responsible for the large gap between visual-visual and haptic-visual discrimin ation. The articles concerning the transitional phases between-concrete and formal operations,focus on elementary transformation geometry concepts and emphasize the role that figurative content can play in influencing the difficulty of Piaget-type tasks. Tyo articles in this group focus on'affine transformations, similarities, or.projections. The articles-dealing with older subjects or formal operational concepts investigate topics such as: (1) the nature of specific mathematical concepts as they .relate to the cognitive structure of the learner; (2) understanding of frames of reference by preservice teacher education students as determined by Piagetian tasks; and (3). the bias for upright figures that students exhibit in forming concepts., (MP)

In this paper, a central claim will be that one of the most important influences that technology ... more In this paper, a central claim will be that one of the most important influences that technology should have on mathematics education is that many of the most important goals of mathematics instruction should consist of helping students develop powerful, sharable, and re-usable conceptual technologies for constructing (and making sense) of complex systems. A second claim will be that these new conceptual tools don't involve introducing completely new topics into the mathematics curriculum as much as they involve dealing with old topics in new ways that emphasize mathematicsas-communication (description, explanation) more than mathematics-as-rulesfor-symbol-manipulation. A third claim will be that, even though technologybased tools create the need to teach these new levels and types of understandings and abilities, in many cases, technology-based tools are not needed to teach them effectively. So, it is not necessary to have lots of classrooms full of educational technologies in order to provide learning experiences for students that are wise to the needs of a technology-based society. (Author) Reproductions supplied by EDRS are the best that can be made from the oinal document.

Educational Studies in Mathematics, Apr 22, 2008

This special issue of Educational Studies in Mathematics is dedicated to Jim Kaput, and it is a t... more This special issue of Educational Studies in Mathematics is dedicated to Jim Kaput, and it is a tribute to his continuing legacy in mathematics education. Kaput's is a legacy which has expanded, not contracted, since his death; and, it is a legacy that permeates the work of hundreds of people worldwide whose personal and professional lives were impacted in fundamental ways by this mentor supreme. Each of the authors were close colleagues of Jim, and each explores one or more themes that represented critical aspects of his work: Democratizing access to powerful ideas, The Infrastructural Nature of Technology, Representational Fluency, Bringing to Scale Curriculum Reforms Focusing on Foundations for the Future. These are themes that not only influenced a generation of junior researchers and developers, but that also had significant impacts on organizations ranging from the National Science Foundation and the Mathematics Association of America to businesses or countries that recognize the urgency to prepare their citizens for full participation in burgeoning knowledge economies. Kaput was a theory developer, a software developer, a curriculum developer, and a program developer. But, above all, he was a developer of people-who ranged from underprivileged junior researchers, to teachers, to graduate students, to colleagues throughout the world. In fact, even if we restrict attention to include only the worldwide community of mathematics educators, Jim changed the lives of enormous numbers of people who considered him to be at the hub of their own personal network of collaborators. Did anybody ever send Jim a message without getting a thoughtful reply within 48 hours? Did anybody ever fail to receive amazing amounts of insightful support when they sought his help on proposals, projects, publications, promotions, or job applications?

National Inst. of Education (DHEW) , Washington, D.C.

External Assessment in Mathematics Education

Springer eBooks, 2014

In this workshop, we will continue to reflect on a models and modeling perspective to understand ... more In this workshop, we will continue to reflect on a models and modeling perspective to understand how students and teachers learn and reason about real life situations encountered in a mathematics and science classroom. We will discuss the idea of a model as a conceptual system that is expressed by using external representational media, and that is used to construct, describe, or explain the behaviors of other systems. We will consider the types of models that students and teachers develop (explicitly) to construct, describe, or explain mathematically significant systems that they encounter in their everyday experiences, as these models are elicited through the use of model-eliciting activities (Lesh, Hoover, Hole, Kelly, & . During the workshop we will continue to explore these aspects of learning, teaching, and research by continuing our work in smaller groups focusing in: Student Development, Teacher Development, Assessment, Curriculum Development, Problem Solving, and an emphasis on Research Design. (Author)

Introduction to Part I Modeling: What Is It? Why Do It?

International perspectives on the teaching and learning of mathematical modelling, 2013

ABSTRACT At ICTMA-13, where the chapters in this book were first presented, a variety of views we... more ABSTRACT At ICTMA-13, where the chapters in this book were first presented, a variety of views were expressed about an appropriate definition of the term model – and about appropriate ways to think about the nature of modeling activities. So, it is not surprising that some participants would consider this lack of consensus to be a priority problem that should be solved by a research community that claims to be investigating models and modeling Key WordsAssessment–Cognitive dissonance–Competency/competencies–Concept/Conceptual–System–Constructivism–Curriculum–Materials–Design research–Developmental stage–Dewey–Embodiment–Emergent modeling–Engineering–Generative activities–ICTMA–Systems–K-–Learning environments–Mental model–Middle school–Model–Definition–Scientific–Model eliciting activity–Cycle–Theory–Pragmatism–Problem solving competency–Techno-mathematical literacy–Word problems–Workplace

Teachers' Evolving Conceptions of One-to-One Tutoring: A Three-Tiered Teaching Experiment

Journal for Research in Mathematics Education, Jul 1, 1997

This article describes a three-tiered teaching experiment in which teachers were studied over a p... more This article describes a three-tiered teaching experiment in which teachers were studied over a protracted period of time as they attempted to understand and improve their approaches to one-to-one tutoring. In a three-tiered teaching experiment model, emphasis is placed on (a) establishing a collaborative relationship between the research staff and the teachers, (b) careful choice of tasks for teachers and their students, (c) the development of “learning environments” for the study, and (d) the use of continuous and diverse dependent measures. The study documented the initial and revised strategies of teachers as they tutored children over a period of 10 weeks. Various indices of teacher change are reported, and some of the strengths and limitations of the methodology are discussed.

This paper focuses on some of the most important factors that appear to have strongly influenced ... more This paper focuses on some of the most important factors that appear to have strongly influenced the development of the dominant research designs used in mathematics education research. Factors discussed that have influenced research design in mathematics education include a concern about increasing the relevance of research to practice and the recognition of the complexity of all aspects of teaching and learning. Some relevant assumptions about student development, teacher development, and program development are also examined. (DDR) Reproductions supplied by EDRS are the best that can be made from the original document.

Collected Works -General (020) Guides -Non-Classroom Use (055) EDRS PRICE MFO1 /PC18 Plus Postage.

The impact of number type on the solution of multiplication and division problems: Further considerations

... Greaber, A., D. Tirosh. and R. Glover. 1989. Preservice teachers' misconception in solvi... more ... Greaber, A., D. Tirosh. and R. Glover. 1989. Preservice teachers' misconception in solving verbal problems in multiplication and division. Journal of Research in Mathematics Education 20: 95-102. Greer, B. 1985. Understanding of arithmetical operations as models of situations. ...

Proportionality and the development of pre-algebra understandings

Dienes revisited: Multiple embodiments in computer environments

Rational Number Project : Fraction Lessons for the Middle Grades, Level 1

Units of quantity: A conceptual basis common to additive and multiplicative structures

Units of Quantity: A Conceptual Basis Common to Additive and Multiplicative Structures Merlyn J. ... more Units of Quantity: A Conceptual Basis Common to Additive and Multiplicative Structures Merlyn J. Behr Guershon Harel Thomas Post Richard Lesh The issue of connections between and among mathematical knowledge structures is mentioned frequently in current writ-ing ...

Research-based observations about children’s learning of rational number concepts

Focus on learning problems in mathematics, 1986

This paper describes a variety of sharable multi-purpose research tools which have evolved from r... more This paper describes a variety of sharable multi-purpose research tools which have evolved from recent studies in which models & modeling perspectives (Lesh & Doerr, 2003) were used to investigate what it means for students to develop meaningful understandings of foundation-level concepts and abilities in an introductory statistics course. Such a course typically is intended to "cover" topics ranging from basic measures of probability, centrality, and spread, to more advanced topics such as analysis of variance, hypothesis testing, or regression and correlation. Although MMP studies have involved students from grade school through graduate school, as well as professionals in fields ranging from education to engineering, the students referred to in this paper were sophomore elementary education majors at Indiana University. This group is identified simply to give readers a frame of reference for observations made -not because it served as a treatment group or a control group of any kind… These students had sufficiently strong academic records to be admitted to a university program with high academic standards; but, compared with peers in other fields, none considered themselves to be outstanding in mathematics. The tools described here were designed mainly to investigate the following questions. (i) What are the most important "big ideas" that should be emphasized in a given mathematics topic area (e.g. statistics)? (ii) What does it mean to "understand" these ideas? (iii) How do these understandings develop? In fields like engineering, or in other "design sciences" which are more mature than mathematics education, researchers in leading research communities often devote significant portions of their time and efforts toward the development of tools and artifacts for their own use. Whereas, in mathematics education, our research community has spent relatively little time developing such tools and resources. One result of this neglect is that mathematics educators are unable to reliably observe, document, or measure either students' or teachers' levels of development for nearly any of the deeper or higher-order achievements that current theories hypothesize to be important. For this reason, this paper focuses on theory-based tools and tool development; and, to begin, main elements of MMP theoretical foundations are described in enough detail so that the tools will be useful to other researchers. Throughout this paper, bulleted questions or statements indicate issues about which a great deal is known -but that still should be investigated more thoroughly in order to more thoroughly understand their meanings and implications.

Journal of Research in Science Teaching, Mar 1, 1989

This study investigated the effects of two context variables, ratio type and problem setting, on ... more This study investigated the effects of two context variables, ratio type and problem setting, on the performance of seventh-grade students on a qualitative and numerical proportional reasoning test. Six forms of the qualitative and numerical-tests were designed, each form using a single context (one of two settings for each of three ratio types). Different ratio types appear to have a stronger impact on the difficulty of the qualitative and numerical proportional reasoning problems than small differences in problem setting. However, the familiarity of problem setting did show an increasingly large effect on qualitative reasoning as the difficulty of ratio type increased. We also investigated the nature of the relationships between rational number skills, qualitative reasoning about ratios, and numerical proportional reasoning. Qualitative reasoning appears to be sufficient, but not necessary for numerical proportional reasoning. The evidence for the requisite nature of rational number skills for proportional reasoning was equivocal. The implications of these findings for science education are discussed.

Representations and translations among representations in mathematics learning and problem solving