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).

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.

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.

Implementing The Standards: Students' Microcomputer-Aided Exploration in Geometry

1990 ◽  
Vol 83 (8) ◽  
pp. 628-635
Author(s):  
Daniel Chazan
Keyword(s):  
High School ◽  
Problem Solving ◽  
Mathematical Structure ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematics Standards ◽  
Mathematical Connections ◽  
Teachers And Students ◽  
K 12

Four important themes presented in the K–12 Curriculum and Evaluation Standards for School Mathematics (Standards) (NCTM 1989) are mathematics as problem solving, mathematics as communication, mathematics as reasoning, and mathematical connections. The high school component also stresses mathematical structure. Furthermore, the Standards calls for new roles for teachers and students and suggests that microcomputer technology can help support teachers and students in taking on these new roles.

On My Mind: Not All Manipulatives and Models Are Created Equal

2007 ◽  
Vol 13 (1) ◽  
pp. 6-9
Author(s):  
Sally K. Roberts
Keyword(s):  
Mathematics Instruction ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Mathematical Ideas ◽  
Mathematics Knowledge ◽  
Proof Techniques ◽  
Reasoning And Proof ◽  
Principles And Standards

The vision of the mathematics curriculum articulated in Principles and Standards for School Mathematics (NCTM 2000) calls for students to construct their own understanding of mathematical ideas by making, refining, and exploring conjectures based on evidence and use of a variety of reasoning and proof techniques (p. 3). For many of us who struggled to learn mathematics through a chalk-and-talk, do-it-my-way approach to mathematics instruction, the notion of using models and manipulatives to help the learner construct mathematics knowledge is both refreshing and exciting.

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?

Using Concept Maps to Link Mathematical Ideas

2000 ◽  
Vol 5 (9) ◽  
pp. 604-609
Author(s):  
Arthur J. Baroody ◽  
Bobbye H. Bartels
Keyword(s):  
Concept Maps ◽  
School Mathematics ◽  
National Council ◽  
Important Research ◽  
Mathematical Ideas ◽  
Standards Documents

The National Council of Teachers of Mathematics's standards documents (1989, 1991, 1995) emphasize making and assessing connections. Why are connections so important? Research suggests that understanding can be viewed as a connection between two pieces of information (Ginsburg 1977), and an understanding of elementary concepts is essential for mathematical power, for example, applying school mathematics to everyday tasks, inventing mathematical procedures, understanding and solving genuine problems, and comprehending more advanced mathematical ideas. The degree of a student's understanding is determined by the number, accuracy, and strength of connections (Hiebert and Carpenter 1992; Resnick and Ford 1981). A concept is well understood if it has many links to other aspects of knowledge that are accurate and strong.

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.

Evaluation of Empowerment in a High School Geometry Class

1997 ◽  
Vol 90 (9) ◽  
pp. 738-741
Author(s):  
Carolyn Ridgway ◽  
Christopher Healy
Keyword(s):  
High School ◽  
School Mathematics ◽  
National Council ◽  
Mathematical Ideas ◽  
High School Geometry ◽  
School Geometry ◽  
Geometry Class

Since the publication of the Curriculum and Eualuation Standards for School Mathematics in 1989, the National Council of Teachers of Mathematics has been encouraging teachers to give more responsibility and choice to students. Students become mathematically empowered as they solve problems together in a community oflearners, communicate with one another concerning mathematical ideas, and use reason and logic to defend their work. To teach in accordance with these standards has required teachers to sruft the ways in which they view and manage their classrooms (Frye 1991).

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