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.

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).

Spotlight on the Principles/Standards: Building Mathematically Powerful Students through Connections

2002 ◽  
Vol 7 (9) ◽  
pp. 484-488
Author(s):  
Christine Thomas ◽  
Carmelita Santiago
Keyword(s):  
Mathematics Curriculum ◽  
School Mathematics ◽  
Mathematical Tasks ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Natural Inclination ◽  
Points Of View ◽  
Principles And Standards

Connections in mathematics can be implemented in ways that create excitement in the classroom, develop in students a love for doing mathematics, and foster students' natural inclination for pursuing mathematical tasks. According to the Curriculum and Evaluation Standards for School Mathematics, “If students are to become mathematically powerful, they must be flexible enough to approach situations in a variety of ways and recognize the relationships among different points of view” (NCTM 1989, p. 84). Principles and Standards for School Mathematics (NCTM 2000) further asserts that students develop a deeper and more lasting understanding of mathematics when they are able to connect mathematical ideas. The 1989 and 2000 Standards clearly delineate the power and importance of connections in the mathematics curriculum. This article examines and compares curricular recommendations for connections in the two documents.

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).

scholarly journals Procesos matemáticos en la práctica pedagógica: un comparativo entre Colombia y España

2020 ◽  
pp. 29-36 ◽  
Author(s):  
Raquel Fernandez-Cézar ◽  
Raúl Prada-Núñez ◽  
César Augusto Hernández-Suárez
Keyword(s):  
School Mathematics ◽  
National Council ◽  
Principles And Standards

Este trabajo buscaba determinar el nivel de empleo de los procesos matemáticos en la práctica docente en dos contextos de habla hispana, el de España y Colombia. Se consideró una muestra de 232 docentes que impartían matemáticas en los niveles medios de educación en diversas instituciones educativas de estos países. Se aplicó un instrumento que toma como referencia los cinco procesos matemáticos mencionados en el Principles and Standards for School Mathematics de la National Council of Teachers of Mathematics (NCTM), que totaliza 36 ítems. Se identificaron en ambos contextos debilidades en la práctica docente al respecto de la presencia de los procesos matemáticos tales como el razonamiento y prueba, la resolución de problemas y en especial, el establecimiento de conexiones de los conceptos matemáticos con otras áreas del currículo escolar. Se propone para contrarrestar esta situación adelantar una investigación complementaria de corte documental en la que se revisen los preparadores de clase y los textos guías utilizados por los docentes.

A Little-Used Art of Teaching: The Case of Storytelling

2006 ◽  
Vol 100 (1) ◽  
pp. 64-68
Author(s):  
David E. Meel ◽  
Deborah Gyurko ◽  
Michelle Gaspar
Keyword(s):  
Mathematical Understanding ◽  
School Mathematics ◽  
Teaching Mathematics ◽  
National Council ◽  
Working Through ◽  
New Concepts ◽  
Teaching Of Mathematics ◽  
Art Of Teaching ◽  
Principles And Standards ◽  
Math Teacher

How many students would agree with the statement “My math teacher fails in the area of creativity” when asked if their teachers try to enliven their classroom? So, where is the fun in our teaching of mathematics? In Principles and Standards for School Mathematics, the National Council of Teachers of Mathematics clearly recognizes the need for lively classrooms by stating, “Teaching mathematics well involves creating, enriching, maintaining, and adapting instruction to move toward mathematical goals, capture and sustain interest, and engage students in building mathematical understanding” (NCTM 2000, p. 18). We suggest incorporating storytelling as a means of introducing students to new concepts and working through the solution of several problems before the students even know they are investigating them.

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).

Activities for Students: Introducing Parametric Equations through Graphing Calculator Explorations

2006 ◽  
Vol 99 (9) ◽  
pp. 637-643
Author(s):  
Marlena Herman
Keyword(s):  
Mathematics Curriculum ◽  
Graphing Calculator ◽  
School Mathematics ◽  
Symbolic Representations ◽  
Principles And Standards ◽  
Over Time

The Algebra Standard of Principles and Standards for School Mathematics (NCTM 2000) suggests that the mathematics curriculum for grades 9–12 include the use of “a variety of symbolic representations, including recursive and parametric equations, for functions and relations” (p. 296). Parametric equations are very useful for representing graphs of curves that cannot otherwise be expressed as functions that define y in terms of x. The underlying idea of working with parametric equations is to express both x and y as functions of a third variable, called the parameter. The parametric equations are those functions assigned to x and y. The variable, typically t for time, makes parametric equations practical for modeling situations involving motion of an object along a given path by providing the coordinates of positions (x, y) of the object over time.

From Classroom Discussions to Group Discourse

2006 ◽  
Vol 99 (8) ◽  
pp. 544-551
Author(s):  
Azita Manouchehri ◽  
Dennis St. John
Keyword(s):  
Learning Communities ◽  
Ways Of Knowing ◽  
Mathematical Discourse ◽  
Teaching Mathematics ◽  
National Council ◽  
Classroom Discussions ◽  
Mathematics Classrooms ◽  
Principles And Standards ◽  
Current Movement ◽  
Human Inquiry

The vision to transform mathematics classrooms into learning communities in which students engage in mathematical discourse is a remarkable hallmark of the current movement, led by the National Council of Teachers of Mathematics, to reform mathematics education (NCTM 1991, 2000). According to NCTM, “the discourse of a classroom—the ways of representing, thinking, talking, agreeing and disagreeing—is central to what students learn about mathematics as a domain of human inquiry with characteristic ways of knowing” (NCTM 1991, p. 34). Indeed, both the Principles and Standards for School Mathematics (2000) and Professional Standards for Teaching Mathematics (1991) recommend that teachers of mathematics provide opportunities for children of all ages to participate in mathematical discourse.

A Virtual Spin on the Teaching of Probability

2007 ◽  
Vol 13 (9) ◽  
pp. 482-486
Author(s):  
Shari A. Beck ◽  
Vanessa E. Huse
Keyword(s):  
Mathematics Classroom ◽  
School Mathematics ◽  
Virtual Manipulatives ◽  
National Council ◽  
Integrating Technology ◽  
Concrete Manipulatives ◽  
Principles And Standards

The study of probability is part of one of the five major mathematics content strands as defined by Principles and Standards for School Mathematics (National Council of Teachers of Mathematics 2000). Traditionally, teaching the concepts of probability has required students to use concrete manipulatives, such as coins and number cubes, in order to perform various probability experiments. With the continued emphasis on integrating technology into the mathematics classroom, the teaching of probability has acquired a “virtual spin”—students now use various virtual manipulatives to perform probability experiments.

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