A Problem-Posing Approach to Specializing, Generalizing, and Extending Problems with Interactive Geometry Software

2003 ◽  
Vol 96 (4) ◽  
pp. 270-276
Author(s):  
José N. Contreras
Keyword(s):  
School Mathematics ◽  
Problem Posing ◽  
Mathematical Activity ◽  
National Council ◽  
Mathematics Problems ◽  
Mathematics Educators ◽  
Principles And Standards ◽  
And Mathematics

Mathematicians and mathematics educators (e.g., Brown and Walter [1990]; Freudenthal [1973]; Halmos [1980]; Kilpatrick [1987]; Moses, Bjork, and Goldenberg [1990]; Pólya [1954]; and Silver [1994]) consider problem posing to be an important mathematical activity and therefore believe that students should have experiences posing problems. For instance, Kilpatrick argues that the experience of “creating one's own mathematics problems ought to be part of every student's education” (1987, p. 123). In the same vein, reform documents of the National Council of Teachers of Mathematics strongly support the inclusion of problem posing both as a curricular activity and as a means of instruction (NCTM 1989, 1991, 2000). For example, Principles and Standards for School Mathematics states that teachers should “regularly ask students to formulate interesting problems based on a wide variety of situations, both within and outside mathematics” (NCTM 2000, p. 258).

Radical Constructivism and Mathematics Education

1994 ◽  
Vol 25 (6) ◽  
pp. 711-733 ◽  
Author(s):  
Leslie P. Steffe ◽  
Thomas Kieren
Keyword(s):  
Education Research ◽  
Mathematics Education ◽  
Cognitive Development ◽  
Mathematics Education Research ◽  
School Mathematics ◽  
Reform Movement ◽  
Radical Constructivism ◽  
Mathematics Educators ◽  
And Mathematics ◽  
Research In Mathematics Education

Our intention in this article is to provide an interpretation of the influence of constructivist thought on mathematics educators starting around 1960 and proceeding on up to the present time. First, we indicate how the initial influence of constructivist thought stemmed mainly from Piaget's cognitive-development psychology rather than from his epistemology. In this, we point to what in retrospect appears to be inevitable distortions in the interpretations of Piaget 's psychology due primarily to its interpretation in the framework of Cartesian epistemology. Second, we identify a preconstructivist revolution in research in mathematics education beginning in 1970 and proceeding on up to 1980. There were two subperiods in this decade separated by Ernst von Glasersfeld's presentation of radical constructivism to the Jean Piaget Society in Philadelphia in 1975. Third, we mark the beginning of the constructivist revolution in mathematics education research by the publication of two important papers in the JRME (Richards & von Glasersfeld, 1980; von Glasersfeld, 1981). Fourth, we indicate how the constructivist revolution in mathematics education research served as a period of preparation for the reform movement that is currently underway in school mathematics.

Effective and Efficient Use of Math Writing Tasks

2018 ◽  
Vol 112 (2) ◽  
pp. 143-146 ◽  
Author(s):  
Matt M. Bixby
Keyword(s):  
School Mathematics ◽  
Clear Picture ◽  
Student Writing ◽  
National Council ◽  
Writing In Mathematics ◽  
Mathematics Class ◽  
Principles And Standards ◽  
The Many

Almost twenty years ago, the National Council of Teachers of Mathematics (NCTM) published Principles and Standards for School Mathematics (2000), which recommended that teachers should incorporate more writing into their math lessons, claiming that writing helps students “consolidate their thinking” (p. 402) by causing them to reflect on their work. In recent years, various studies point to the many benefits that can be gained by writing in mathematics class (e.g., O'Connell et al. 2005; Goldsby and Cozza 2002). Much research suggests that writing activities, if implemented effectively, can help students enjoy class more (Burns 2005) and can also help them deepen their understanding of the content (Baxter et al. 2002). In addition to benefiting students, student writing benefits teachers as well by providing a clear picture of what their students understand and even deepening understanding of the content for teachers themselves (Burns 2005; Pugalee 1997).

Technology Tips: When Is a Good Fit Not a Good Fit? Dynamic Regression with the TI-Nspire Graphing Calculator

2008 ◽  
Vol 102 (4) ◽  
pp. 300-305
Author(s):  
Michael Edwards ◽  
Michael Meagher ◽  
S. Asli Özgün-Koca
Keyword(s):  
Graphing Calculator ◽  
School Mathematics ◽  
Mathematical Education ◽  
National Council ◽  
Mathematics Textbooks ◽  
Multiple Points ◽  
Complex Concept ◽  
Mathematics Classrooms ◽  
Points Of View ◽  
Principles And Standards

In Principles and Standards for School Mathematics, the National Council of Teachers of Mathematics (NCTM) acknowledges the importance of exploring mathematical ideas from multiple points of view: “Different representations often illuminate different aspects of a complex concept or relationship…. The importance of using multiple representations should be emphasized throughout students' mathematical education” (2000, p. 68). In particular, NCTM notes that the introduction of technology in school mathematics classrooms provides new ways for teachers and their students to explore connections among representations: “Computers and calculators change what students can do with conventional representations and expand the set of representations with which they can work” (2000, p. 68). In this article, we discuss an interesting finding that our students made as they explored linear regression with a teacher-constructed TI-Nspire calculator document. The calculator's capability to link variables across two or more pages in the same document led students to findings that are important yet rarely discussed in school mathematics textbooks.

The Wonder and Creativity in “Looking Back” at Problem Solutions

1988 ◽  
Vol 81 (6) ◽  
pp. 429-434
Author(s):  
Stanley F. Taback
Keyword(s):  
Problem Solving ◽  
Mathematics Instruction ◽  
Position Paper ◽  
School Mathematics ◽  
National Council ◽  
Mathematical Competence ◽  
Mathematics Educators ◽  
Looking Back

Mathematics educators have always viewed problem solving as a preferential objective of mathematics instruction. It was not, however, until the National Council of Teachers of Mathematics published its position paper An Agenda for Action: Recommendations for School Mathematics of the 1980s that problem solving truly came of age. As its very first recommendation, the Council (1980) directed that “problem solving be the focus of school mathematics in the 1980s” and proclaimed that “performance in problem solving will measure the effectiveness of our personal and national possession of mathematical competence.”

Some number concepts of disadvantaged children

1965 ◽  
Vol 12 (5) ◽  
pp. 359-361
Author(s):  
M. E. Dunkley
Keyword(s):  
Curriculum Development ◽  
Difficult Problem ◽  
School Mathematics ◽  
Study Group ◽  
Number Concepts ◽  
Disadvantaged Children ◽  
The Past ◽  
Mathematics Educators ◽  
Average Students ◽  
And Mathematics

In the past decade efforts to improve school mathematics in this country have been devoted primarily to programs for average and above average students. The more difficult problem of curricula for below average achievers in mathematics has always been with us, and now we seem to have made enough progress and gained enough experience to tackle this problem. The School Mathematics Study Group held a conference in April, 1964, to acquaint a representative group of mathematicians and mathematics educators who bad worked on curriculum projects with some of the problems associated with below average acbievement.2 The conference made several recommendations for experimentation and curriculum development.

Guiding Young Children in Successful Problem Solving

1982 ◽  
Vol 29 (5) ◽  
pp. 15-17
Author(s):  
Kil S. Lee
Keyword(s):  
Problem Solving ◽  
Young Children ◽  
Conference Report ◽  
School Mathematics ◽  
National Council ◽  
Mathematical Skills ◽  
The Past ◽  
Mathematics Educators ◽  
Mathematics Curricula

In the past twenty years, problem solving has received much attention from mathematics educators. Inclusion of imaginative problems in school mathematics curricula was recommended in the 1963 Cambridge Conference report. Problem solving was the first of the ten basic mathematical skills identified by the National Council of Supervisors of Mathematics in 1976 and the position of the NCSM was endorsed by the National Council of Teachers of Mathematics in 1978. “That problem solving be the focus of school mathematics in the 1980s” is the first of eight recommendations expressed in An Agenda for Action: Recommendations for School Mathematics of the 1980s published by the NCTM.

The Portrayal of Parents in the School Mathematics Reform Literature: Locating the Context for Parental Involvement

1998 ◽  
Vol 29 (5) ◽  
pp. 555-582
Author(s):  
Dominic D. Peressini
Keyword(s):  
Mathematics Education ◽  
Parental Involvement ◽  
Education Reform ◽  
Research Agenda ◽  
School Mathematics ◽  
Mathematics Reform ◽  
Mathematics Educators ◽  
And Mathematics

In this article, using reform recommendations that call for parental involvement as a springboard, I provide an analysis of the positioning of parents in the school mathematics reform literature. Employing Foucault's (1980) conception of “regimes of truth,” I demonstrate how the literature has created the accepted discourse for mathematics education reform. I then argue that the professionalization of teachers has distanced parents from schools and led to conflict between parents and mathematics educators and that to reconcile this conflict, ways in which parents can be included in mathematics education must be considered. It is essential first, however, to understand issues central to involving parents in mathematics education. A research agenda for parental involvement in mathematics education is presented.

The Forum: The Computer in Secondary Mathematics: The Computer-a Facilitator in Management and Instruction

1973 ◽  
Vol 66 (1) ◽  
pp. 6-83
Author(s):  
E. Glenadine Gibb ◽  
William F. Atchison
Keyword(s):  
Secondary School ◽  
Secondary Mathematics ◽  
Computer Assisted Instruction ◽  
Computer Assisted ◽  
National Council ◽  
Mathematics Educators ◽  
And Mathematics ◽  
Assisted Instruction ◽  
Computer Development

In the midst of the rapidly changing field of computer development, one of the problems facing mathematics teachers in secondary schools and mathematics educators in colleges and universities is the optimal role of the computer in secondary school mathematics classes and the accompanying needs in teacher education to prepare teachers to use the computer in their classes. In 1965 the National Council of Teachers of Mathematics Committee on Computer Oriented Mathematics outlined available options. Since that time, others (including Gleason 1968; Zoet 1969; Alpert and Bitzer 1970; Hansen 1970; Travers 1971; and Jerman 1972) have dealt with the persistent question “How should we use the computer in our schools?” Two general directions seem to have emerged: (1) instructional individ-ualization through computer-managed in-struction (CMI) and computer-assisted instruction (CAI) and (2) the use of the computer as a computational device and as a means of simulating concepts within the present curriculum.

Writing About the Problem Solving Process to Improve Problem Solving Performance

2003 ◽  
Vol 96 (3) ◽  
pp. 185-187 ◽  
Author(s):  
Kenneth M. Williams
Keyword(s):  
Problem Solving ◽  
Mathematical Knowledge ◽  
Mathematical Problem ◽  
School Mathematics ◽  
Mathematical Problem Solving ◽  
National Council ◽  
Instructional Programs ◽  
Principles And Standards ◽  
Problem Solving Process ◽  
Problem Solvers

Problem solving is generally recognized as one of the most important components of mathematics. In Principles and Standards for School Mathematics, the National Council of Teachers of Mathematics emphasized that instructional programs should enable all students in all grades to “build new mathematical knowledge through problem solving, solve problems that arise in mathematics and in other contexts, apply and adapt a variety of appropriate strategies to solve problems, and monitor and reflect on the process of mathematical problem solving” (NCTM 2000, p. 52). But how do students become competent and confident mathematical problem solvers?

Delving Deeper: New Life for an Old Topic: Completing the Square Using Technology

2010 ◽  
Vol 104 (3) ◽  
pp. 230-236
Author(s):  
Steve Phelps ◽  
Michael Todd Edwards
Keyword(s):  
Mathematics Teaching ◽  
Mathematical Structure ◽  
School Mathematics ◽  
National Council ◽  
Mathematical Ideas ◽  
Use Of Technology ◽  
Teachers And Students ◽  
Principles And Standards

Mathematics teaching has always been a curious blend of the old and the new. As the use of technology becomes more commonplace in school classrooms, this blend becomes even more pronounced. When teachers and students revisit traditional topics using technology, they are afforded opportunities to connect mathematical ideas in powerful, previously unimagined ways. The National Council of Teachers of Mathematics (NCTM) captures the importance of connections clearly in its Principles and Standards for School Mathematics (2000): “The notion that mathematical ideas are connected should permeate the school Technologymathematics experience at all levels. As students progress through their school mathematics experience, their ability to see the same mathematical structure in seemingly different settings should increase” (p. 64).

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