# M. Kathleen HeidPennsylvania State University | Penn State · Department of Curriculum and Instruction

M. Kathleen Heid

Doctor of Philosophy

## About

65

Publications

3,937

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

1,346

Citations

Citations since 2017

Introduction

**Skills and Expertise**

## Publications

Publications (65)

Mathematics-specific digital technology has an ever-increasing presence in school mathematics learning, and qualitative research has shed light on the potential nature of that learning. Particularly for students at the critical early teen age (ages 10–14, or lower secondary school students), the incorporation of mathematics-specific digital technol...

Students with disabilities are increasingly taught in general education settings, including mathematics classes. Too often, math teachers confront challenging behaviors of students with disabilities in inclusive settings. The authors present five efficient tools effective teachers can add to their repertoire to combat problem behaviors during group...

One goal of school algebra is the development of students’ facility with algebraic structures. Essential to that development is a structural perspective, which we consider as having three interrelated components—(1) ability to recognize and look for elements of a given type, (2) awareness of structure, and (3) tendency to attend to and look for str...

Connections between Abstract Algebra courses and high school mathematics teaching commonly start with identification of abstract algebra topics in secondary school mathematics. We take an alternative path. We start in the daily practice of teaching school mathematics to determine how Abstract Algebra course experiences might be useful to teachers....

Available from Springer Open :
http://link.springer.com/book/10.1007%2F978-3-319-33666-4

This topical survey establishes an overview of the current state of the art in technology use in mathematics education from an international perspective, including both practice-oriented experiences and research-based evidence. Three themes are discussed: Evidence for effect; Digital assessment; Communication and collaboration. Exploiting the oppor...

SimCalc is an educational software and curriculum program designed to introduce students as young as middle school age to fundamental mathematical concepts—change and variation—that underpin the transition from algebra to calculus. The core underlying mathematical idea is the Fundamental Theorem of Calculus, and through activities involving change...

This study examines the relationship between mathematical knowledge—evidenced by a teacher’s engagement in mathematical processes and actions on the products of those processes—displayed by a beginning secondary mathematics teacher (Fiona) in her personal mathematical problem solving and in her classroom instruction. This process and action approac...

The importance of advancing the field of mathematics research is explored.

Computer Algebra Systems (CAS) are software systems with the capability of symbolic manipulation linked with graphical, numerical, and tabular utilities, and increasingly include interactive symbolic links to spreadsheets and dynamical geometry programs. School classrooms that incorporate CAS allow for new explorations of mathematical invariants, a...

Whereas it is essential that JRME manuscripts employ careful, systematic, wellargued, and appropriately documented approaches, such technical expertise is not enough to merit publication in JRME . The direction given on the JRME Web site advises reviewers to address these questions, “Does the research extend or deepen our understanding of important...

The Journal for Research in Mathematics Education has the reputation of being one of the top journals worldwide that publishes mathematics education research. The task of analyzing the viability of a manuscript as a potential JRME article naturally leads to the question: What is the purpose of publishing papers in a mathematics education research j...

Twenty-five years ago, a fast-food TV ad initiated a catchphrase, “Where's the beef?” The phrase, originally intended to point out the small amount of beef in fastfood hamburgers, evolved into a way to question the amount or substance of an idea or product. Adopted in popular culture, the phrase made its way into the 1984 vicepresidential debate, a...

The tempting answer at first glance is to make a decision about whether the piece should be published. That answer is too simple. Peer review of scholarly papers serves a much more important purpose. Reviews are a way for the field to monitor its progress and refine its products, and strong reviews are themselves scholarly work. In this editorial,...

I recently attended a meeting of research journal editors at which we shared some of our practices and procedures. The editors represented a range of educational fields. Impressed by the nature and number of reviews that the JRME editorial office requests and receives, one of the editors of a non-mathematics-education journal offered this explanati...

Investigating the teaching and learning of mathematics is an international enterprise, and the Journal for Research in Mathematics Education regularly benefits from the insightful contributions of reviewers and authors from every corner of the earth. JRME has long been considered one of the top international journals in mathematics education resear...

This issue of the Journal for Research in Mathematics Education is the first in which my name appears as editor, and this occasion leads me to reflect on what contributes to the success of a journal such as JRME . That reflection starts with thinking about what previous editors have done to make it a success, and there is no better place to start t...

This article discusses the challenge of improving the interrelationships between research and practice in mathematics education, and it outlines actions being taking to respond to that challenge. The need for improvement is bidirectional. The practice of classroom mathematics teaching needs to be better informed by an understanding of the implicati...

The NCTM's Research Committee has prepared this article as a means to raise the awareness about equity and issues surrounding equity from a research perspective as well as to support the NCTM's commitment to the Equity Principle. The committee discusses the concept of equity from three perspectives: as a subject of research, as a "critical lens" wi...

This article by the NCTM's Research Committee presents a call for an Agenda for Research Action in Mathematics Education. The committee reviews central cross-cutting issues for mathematics education research that address concerns from the political and practitioner communities regarding the coherence and utility of mathematics education research. I...

An international team of specialists had prepared this session to give state-of-the-art reviews as well as to let the participants experience and discuss “Creative Activities.” Gerald Goldin (New Jersey USA) and Norma C. Presmeg (Illinois USA) started with a survey including theoretical, psychological, social, and affective components. The emphasis...

Technology is giving us an opportunity to open new doors to mathematical understanding for our students, and we are failing to take advantage of that opportunity. Computer algebra systems (CASs)—and in particular, CAScapable calculators—provide ready classroom access to automated graphical, numerical, and symbolicmanipulation capabilities; and they...

Presents ways of using theories of knowing and learning to inform use of computer algebra systems (CAS) in school and early college mathematics. Describes the role of macroprocedures and microprocedures, process-object distinctions, and the movement towards more formal ways of expressing mathematical ideas. Discusses how these theories along with p...

Understanding students' understanding of mathematical ideas can inform mathematics teaching, and task-based interviews are one way in which teachers can learn more about their students' understandings. The CIME project was designed to empower mathematics teachers to use interviews to understand their students' mathematical understandings as well as...

Technology and technology-intensive mathematics curricula are catalysts for the mathematics education reform movement. Students can understand mathematics more deeply when they assume responsibility for their own learning as they engage in and reflect on authentic mathematical activity. Analyzing technology in mathematics classrooms as cognitive te...

The functional approach to the emergence of algebraic thinking described here suggests a study of algebra that centers on developing experiences with functions and families of functions through encounters with real world situations whose quantitative relationships can be described by those models. Computer-Intensive Algebra is a beginning algebra c...

As one reflects on the role of mathematical modeling in beginning algebra, an enriched image of algebraic thinking emerges with deeply rooted interactions between the ways in which students think about the real world and the ways in which they think about mathematical concepts. This commentary chapter, which draws on the contributions of the previo...

Computer-lntensive Algebra (CIA) focuses on the use of technology to help develop a rich understanding of fundamental algebraic concepts in real-world settings. CIA students learn about functions, variables, systems, equivalent expressions, and equivalent equations in the context of developing, critiquing, and exploring mathematical models of real-...

During each day that the secondary subgroup met, discussions were organized around a reaction to the keynote address of that day. Each of these reactions was specially prepared for the secondary group and was intended to address the concerns of secondary-level algebra.

As teachers begin to implement mathematics curricula that capitalize fully on computing technology and that are focused on concepts and applications instead of on execution of by-hand symbolic manipulation routines, their well-established routines of thinking about mathematics and its teaching no longer apply in seamless fashion. This case study, a...

The purpose of this series is to provide instructional ideas and materials that support implementation of the Curriculum and Evaluation Standards in local settings. This book addresses in a very practical way the content, pedagogy, and pupil assessment dimensions of reshaping school mathematics. Chapters include discussions and activities that proj...

The NCTM's Curriculum and Evaluation Standards for School Mathematics (Stan dards) (1989) designates four standards that apply to all students at all grade levels: mathematics as problem solving, mathematics as communication, mathematics as reasoning, and mathematical connections. These and NCTM's other standards are embedded in a vision of technol...

Computer programs are now available that perform most of the algebraic and numerical-manipulation procedures on which school mathematics now concentrates. The defining characteristic of these symbolic mathematical systems is that, unlike many of the popular computer languages, they can manipulate variables as well as numbers. They can perform ratio...

Mathematics competitions are a popular extracurricular activity for students at all grade levels. This booklet outlines some of the logistical and structural issues that competition organizers, administrators, coaches, and question writers face when they incorporate calculators into their competitions. Main topics included are: (1) "Decisions about...

Why calculators should be used for testing, as well as for instruction, is discussed. The focus of the curriculum would shift from computation to deeper development of concepts and to mathematical modeling. A broader curriculum would result. (MNS)

During the first 12 weeks of an applied calculus course, two classes of college students (n=39) studied calculus concepts using graphical and symbol-manipulation computer programs to perform routine manipulations. Only the last 3 weeks were spent on skill development. Class transcripts, student interviews, field notes, and test results were analyze...

During the first 12 weeks of an applied calculus course, two classes of college students ( n =39) studied calculus concepts using graphical and symbol-manipulation computer programs to perform routine manipulations. Only the last 3 weeks were spent on skill development. Class transcripts, student interviews, field notes, and test results were analy...

This analysis synthesizes the research on characteristics of the mathematically gifted and describes some ways in which programs can be designed to address those characteristics. (MNS)

The current study took place in the context of a mathematics-content course designed to engage prospective secondary mathematics teachers (PSMTs) in work with the concept of function. The data are derived from a task-based interview conducted with eight junior or senior PSMTs. In the interview, the Bottle Problem was selected to engage PSMT in grap...