Richard Lesh

Richard Lesh
Indiana University Bloomington | IUB

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159
Publications
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Publications

Publications (159)
Article
Full-text available
This study investigated the middle school preservice mathematics teachers’ conceptualization of what it means for a problem to be mathematically rich and contextually realistic and how their conceptions evolved during a series of professional development activities. Fifteen middle school preservice mathematics teachers were involved in this design-...
Chapter
Full-text available
The chapters in this section represent noteworthy steps in a research agenda with implications far beyond traditional conceptions of models and modeling, addressing key questions such as: How does the K-12 mathematics curriculum need to adapt to prepare students for the rapidly changing nature of “mathematical thinking” outside of school? What does...
Chapter
The purpose of this chapter is to highlight how work focusing on student‐level modelling and idea development can also serve as a powerful context to investigate parallel and interacting modelling processes at the teacher level. We assert that expertise in teaching is partly reflected in how teachers interpret and respond to classroom situations—in...
Chapter
In diesem Kapitel wird verdeutlicht, wie Modellierungsprozesse von Lernenden für die Lehrerausbildung zum Lehren von mathematischer Modellierung als ein wirkungsvolles Instrument eingesetzt werden können. Wir behaupten, dass sich die Expertise des Unterrichtens zum Teil darin widerspiegelt, wie Lehrkräfte Unterrichtssituationen interpretieren und d...
Chapter
For today’s students to be successful tomorrow in the world beyond school, their mathematics education must go beyond assembling a fixed toolkit of skills and procedures. They will need to be able to adapt and apply the material they learn in school in subtle ways, in order to produce tactful and appropriate solutions to problems under constraints...
Chapter
Damit die Schüler durch den heutigen Unterricht auch in der Welt außerhalb der Schule erfolgreich sein können, muss ihre mathematische Ausbildung über einen festgelegten Satz an Fertigkeiten und Routinen hinausgehen. Stattdessen müssen sie in der Lage sein, den in der Schule erlernten Stoff auf subtile Weise anzupassen und anzuwenden, um mit Feinge...
Article
Full-text available
In this article, we address the challenge of supporting students in real-world problem solving as a vibrant part of their in-school experience of mathematics. On one hand, we describe the issues associated with using traditional schooling approaches to prepare students for success in a world that is increasingly characterized by complexity and rapi...
Chapter
For over 30 years, researchers have engaged in inquiry within the Models and Modelling Perspective (MMP), taking as a fundamental principle that learners’ ideas develop in coherent conceptual systems called models. Under appropriate conditions, such as in Model Eliciting Activities (MEAs), this research has shown how learners’ models can grow throu...
Article
Full-text available
For roughly 35 years, the NCTM Research Presession has been held 1 or 2 days prior to the NCTM Annual Conference—hence the word presession . Beginning with the 2014 meeting in New Orleans, the NCTM Research Presession will be rebranded as the NCTM Research Conference. This change of name is intended to emphasize the critical role that research shou...
Chapter
In this overview and critique of perspective II, we briefly focus on several ways that Models & Modeling Perspectives (MMP) can be used to provide a unifying theoretical framework for developing both: (a) a coherent summary of the kind of research reported in this book, and (b) a useful list of testable claims that appear to be priorities to invest...
Article
Research has shown that educational media, such as television series or interactive games, can promote significant learning. However, it is quite common for producers to create several interconnected media, such as a television show and an associated web site, under the assumption that multiple platforms elicit greater learning than a single medium...
Chapter
The term “mathematical model” or just “model” is interpreted differently by different people in current international discussions about mathematical modelling. For many, the term “model” is restricted to interpretation systems which are explicit objects of thought. In this paper we ask the question, if interpretation systems should be considered to...
Data
As we enter the 21st century, there is an urgent need for new approaches to mathematics education emphasizing its relevance in young learners' futures. Modeling Students' Mathematical Modeling Competencies explores the vital trend toward using real-world problems as a basis for teaching mathematics skills, competencies, and applications. Blending t...
Article
A framework for a problem-driven mathematics curriculum is proposed, grounded in the assumption that students learn mathematics while engaged in complex problem-solving activity. The framework is envisioned as a dynamic technologicallydriven multi-dimensional representation that can highlight the nature of the curriculum (e.g., revealing the relati...
Article
Background Modeling abilities play an important role in engineering. The creation and use of representations is a central aspect of modeling, and students who are learning to model often use a variety of representations to express, test, revise, and communicate their own thinking. Consequently, model development often depends on representational fl...
Article
Full-text available
This article focuses on problem solving activities in a first grade classroom in a typical small community and school in Indiana. But, the teacher and the activities in this class were not at all typical of what goes on in most comparable classrooms; and, the issues that will be addressed are relevant and important for students from kindergarten th...
Chapter
Full-text available
In modern societies in the 21st century, significant changes have been occurring in the kinds of “mathematical thinking” that are needed outside of school. Even in the case of primary school children (grades K-2), children not only encounter situations where numbers refer to sets of discrete objects that can be counted. Numbers also are used to des...
Book
As we enter the 21st century, there is an urgent need for new approaches to mathematics education emphasizing its relevance in young learners’ futures. Modeling Students’ Mathematical Modeling Competencies explores the vital trend toward using real-world problems as a basis for teaching mathematics skills, competencies, and applications. Blending t...
Chapter
Much past research based on model eliciting activities (MEAs) has shown that it is possible to directly observe processes that enable students to develop progressively more productive ways of thinking about problem situations. In this paper, we introduce a class of MEAs that are designed to explicitly focus on the parallel and interacting developme...
Article
— Children’s interaction with educational computer games reflects not only their game-playing expertise but also their knowledge and skills about embedded educational content. Recent pilot data, drawn from an ongoing evaluation of children’s learning from educational media, illustrate that, much like earlier research on formal classroom mathematics...
Article
Research has shown that educational media, such as television series or interactive games, can promote significant learning. However, it is quite common for producers to create several interconnected media, such as a television show and an associated web site, under the assumption that multiple platforms elicit greater learning than a single medium...
Conference Paper
Educational media projects often span several platforms (e.g., games, TV, hands-on materials), under the assumption that multiple platforms elicit greater learning than a single medium. To test this assumption, 672 fourth graders were assigned to use different combinations of math-based Cyberchase media for eight weeks: DVD Only, Web Only, DVD + We...
Chapter
Research based on models and modelling perspectives (MMP) has shown that, in order for mathematical concepts and abilities to be useful beyond school, new levels and types of understandings are needed beyond those that have been emphasized in even the most innovative and future-oriented statements of curriculum standards. Similarly, teacher-level k...
Chapter
Full-text available
In this chapter we propose re-conceptualizing the field of mathematics education research as that of a design science akin to engineering and other emerging interdisciplinary fields which involve the interaction of “subjects”, conceptual systems and technology influenced by social constraints and affordances. Numerous examples from the history and...
Chapter
Hurford’s article is a useful introduction to the topic of complex systems and their potential significance in mathematics education. He focuses on two categories of issues. The first concerns the possibility of treating complex systems as an important topic to be included in any mathematics curriculum that claims to be preparing students for full...
Chapter
The first half of this book focused on research investigating what it means for students to "understand" modeling processes and models that are important in order for students to be able to use mathematics in real life situations beyond school. This second half shifts attention toward investigations about what is needed for modeling activities to b...
Chapter
Full-text available
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 shou...
Article
The ABET criteria for engineering programs include that students should have "an ability to apply mathematics, science and engineering", "an ability to design a system, component, or process to meet desired needs", "an ability to identify, formulate and solve engineering problems", and "an ability to communicate effectively", and "a knowledge of co...
Article
Editor's Note: This month's cover story describes how designers and policy makers alike developed a voting system that is useful, useable, and---above all else---fair. We are pleased to offer not only the following article by Jessica Friedman Hewitt, ...
Article
This chapter describes a model for evaluating complex organizations or systems. The design assessment model the authors propose is a response to current notions of assessment. There are assumptions we make about learning and the functioning of complex systems such as academic programs that do not match assumptions that are inherent in traditional f...
Chapter
This chapter describes a model for evaluating complex organizations or systems. The design assessment model the authors propose is a response to current notions of assessment. There are assumptions we make about learning and the functioning of complex systems such as academic programs that do not match assumptions that are inherent in traditional f...
Article
In this information age, the capacity to perceive structure in data, model that structure, and make decisions regarding its implications is rapidly becoming the most important of the quantitative literacy skills. We build on Kaput’s belief in a Science of Need to motivate and direct the development of tasks and tools for engaging students in reason...
Article
Full-text available
This article introduces Model-Eliciting Activities (MEAs) as a form of case study team problem-solving. MEA design focuses on eliciting from students conceptual models that they iteratively revise in problem-solving. Though developed by mathematics education researchers to study the evolution of mathematical problem-solving expertise in middle scho...
Article
Full-text available
Since the 1960s, numerous studies on problem solving have revealed the complexity of the domain and the difficulty in translating research findings into practice. The literature suggests that the impact of problem solving research on the mathematics curriculum has been limited. Furthermore, our accumulation of knowledge on the teaching of problem s...
Article
Full-text available
This paper is the second in a pair that Lesh, English, and Fennewald will be presenting at ICME TSG 19 on Problem Solving in Mathematics Education. The first paper describes three shortcomings of past research on mathematical problem solving. The first shortcoming can be seen in the fact that knowledge has not accumulated – in fact it has atrophied...
Article
The goal of this paper is to demonstrate the infrastructural nature of many modern conceptual technologies. The focus of this paper is on conceptual tools associated with elementary types of data modeling. We intend to show a variety of ways in which these conceptual tools not only express thinking, but also mold and shape thinking. And those ways...
Article
Mathematical modeling is about the development of powerful, and reusable interpretation systems that are used for designing or making sense of other systems. They can be used to describe systems that already exists, or may be used to create new systems that do not occur naturally. Mathematical systems only become models when they are used to model...
Conference Paper
Full-text available
The 13th International Conference on Artificial Intelligence in Education (AIED-2007) is being held July 9--13, 2007, in Los Angeles, California. AIED Conferences are organized by the International AIED Society on a biennial basis. The goal of the International ...
Chapter
What is the nature of typical problem-solving situations where elementary-but-powerful mathematical constructs and conceptual systems are needed for success beyond school in a technology-based age of information? What kind of “mathematical thinking” is emphasized in these situations? What does it mean to “understand” the most important ideas and ab...
Article
The name of Zoltan P. Dienes (1916–) stands with those of Jean Piaget, Jerome Bruner, Edward Begle, and Robert Davis as a legendary figure whose work left a lasting impression on the field of mathematics education. Dienes’ name is synonymous with the multibase blocks that he invented for the teaching of place value. Among numerous other things, he...
Chapter
Full-text available
This chapter describes a set of research and learning tools that are designed to benefit both investigators and participants who are working individually or in groups on modeling-eliciting activities (MEAs) or associated activities. We refer to them as Reflection Tools (or RTs) because, following a problem solving activity, RTs help students briefl...
Conference Paper
Full-text available
The symposium has two main goals: First, it would allow the contributors to the recent JLS special issue on complex systems in education to provide an overview of the issues raised in their respective papers as well as to discuss updated research of relevance. Second, it is hoped that this symposium will provide a forum for discussing the potential...
Article
Full-text available
The previous issue of ZDM raised several fundamental issues on the role of modeling in the school curricula at micro and macro levels. In this paper we complement the approaches described there by discussing some of the issues and the barriers to the implementation of mathematical modeling in school curricula raised there from the perspective of th...
Article
The word Tao usually is translated as way or path, but it refers to the deep structure of patterns and regularities beneath surface-level experiences. Similarly, Taoists use the terms naming or telling to refer to nearly any formal statement, proposition, or rule. So, for our purposes here, a particularization of Lao Tsu's famous saying might be: T...
Article
Full-text available
In this paper we briefly outline the models and modelling (M&M) perspective of mathematical thinking and learning relevant for the 21st century. Models and modeling (M&M) research often investigates the nature of understandings and abilities that are needed in order for students to be able to use what they have (presumably) learned in the classroom...
Article
Full-text available
We propose re-conceptualizing the field of mathematics education research as that of a design science akin to engineering and other emerging interdisciplinary fields which involve the interaction of “subjects”, conceptual systems and technology influenced by social constraints and affordances. Numerous examples from the history and philosophy of sc...
Article
If a curriculum developer's goal is to create a single linear sequence of tasks that lead to the development of some important mathematical concept, then some researchers have suggested that these sequences should follow progressions similar to stages of development that have been identified in Piaget-like research on the relevant concept(s). These...
Article
The kinds of mathematical processes, understandings, and abilities that are used in modeling are seldom emphasized in traditional mathematics textbooks, tests, and teaching. In a class of problems that 1 call model-eliciting activities, students engage in activities that are recognized and valued in the world outside the classroom. These activities...
Chapter
Full-text available
Lehrer and Lesh review research in the psychology of mathematical learning and mathematics education through a genetic, developmental framework that reflects both cognitive and sociocultural perspectives on learning. The authors examine individual cognitive processes and sociocultural contexts that underscore mathematical thinking. Origins of mathe...
Article
Full-text available
The research reported here describes similarities and differences between (a) mod-eling cycles that students typically go through during 60–90 min solutions to a class of problems thast we refer to as model-eliciting activities, and (b) stages of development that students typically go through during the "natural" development of constructs (conceptu...
Article
Previews this special issue of "Mathematical Thinking and Learning," which describes models and modeling perspective toward mathematics problem solving, learning, and teaching. Discusses its characteristics and foundations and provides an example of a model-eliciting activity. (KHR)
Article
This paper describes a proportional reasoning problem set within a real-life context and a complete analysis of one small group discussion of this problem over the course of a 90-minute block. The seventh-grade students' discourse is described to provide insights into typical mathematical interpretations of this problem, as well as some generalizat...
Article
Full-text available
This chapter provides an illustration of how the models and modeling perspective can be used in collegiate mathematics education research and instruction. The models and modeling approach (chapter 1) provides instructional designers with a well-defined structure for creating curriculum. The curricular activities for this approach, referred to as mo...
Article
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The problem solving process in most twenty-first century contexts involves teams working on problem situations. It involves partitioning a complex situation into parts that can be addressed by specialists. It involves communicating information in forms that are meaningful for other specialists and suitable for their tools. It involves planning, mon...
Article
In this final chapter, we consider some of the many research issues that need attention in the advancement of our discipline. Specifically, we have identified the following questions as worthy of consideration: 1. What role can research play in illuminating the multidisciplinary debates on the powerful mathematical ideas required for the 21st cent...
Article
Purdue University’s Center for Twenty-first Century Conceptual Tools (TCCT) was set up to investigate the types of problems students need to be able to solve in order to succeed in a technology-based age of information and the abilities and understandings that success requires. This paper describes the rationale behind the foundation of the TCCT, i...
Article
Over the last century, the repertoire and range of research approaches in education have changed dramatically. During the Thorndike era, and well beyond, a wave of enthusiasm for experimentation dominated the field (Campbell & Stanley, 1963; Kilpatrick, 1992; Romberg, 1992).
Article
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...
Article
This chapter overviews trends and shifts in research methods in mathematics and science education. It summarizes shifts in some basic assumptions about the role of research in mathematics and science education, background factors that support the proclivities of the researchers represented in the book, foreground factors that the researchers in the...