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.

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.

Spotlight on the Principles/Standards: Problem Solving in the Middle Grades

2000 ◽  
Vol 6 (2) ◽  
pp. 105-108
Author(s):  
Carol E. Malloy ◽  
D. Bruce Guild
Keyword(s):  
Problem Solving ◽  
Mathematical Knowledge ◽  
Middle Grades ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Measurement Algebra ◽  
Principles And Standards ◽  
Mathematical Relationships

IN WHAT WAYS WOULD YOU LIKE YOUR middle-grades students to experience problem solving in the mathematics curriculum? Do you want the curriculum to capture the excitement of geometry and measurement, algebra, statistics, and number relationships? Do you want it to help students understand and build new mathematical knowledge and explore new mathematical relationships? Do you want the curriculum to be filled with opportunities for students to ponder, create, and critique arguments about mathematics? If this is your vision for your students, then you should be pleased with, and excited by, the Problem Solving Standard in Principles and Standards for School Mathematics (NCTM 2000).

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.

Implementation of the NCTM Curriculum Focal Points: Concept versus Content

2007 ◽  
Vol 13 (2) ◽  
pp. 78-80
Author(s):  
Jane F. Schielack ◽  
Cathy Seeley
Keyword(s):  
Mathematics Curriculum ◽  
School Mathematics ◽  
Focal Points ◽  
Major Step ◽  
Versus Content ◽  
P 16 ◽  
Principles And Standards ◽  
Coherent Curriculum ◽  
Grade 8

On September 12, 2006, the NCTM released a new lens through which to view the content presented in Principles and Standards for School Mathematics (NCTM 2000). In Principles and Standards, the Curriculum Principle calls for a mathematics curriculum to be coherent, focused on important mathematics, and well articulated across the grades. This means that an effective curriculum “gives teachers guidance regarding important ideas or major themes, which receive special attention at different points in time. It also gives guidance about the depth of study warranted at particular times and when closure is expected for particular skills or concepts” (NCTM 2000, p. 16). With the publication of Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence, NCTM has taken a major step toward defining the mathematics that every student should know and be able to do. Where the Principles and Standards presented content across multiple grade bands, this new publication applies the Curriculum Principle to create a specific example of a focused and coherent curriculum, prekindergarten through grade 8.

Proportional Reasoning: Lessons from Research in Data and Chance

2004 ◽  
Vol 10 (2) ◽  
pp. 104-109
Author(s):  
Jane Watson ◽  
J. Shaughnessy
Keyword(s):  
Middle School ◽  
Problem Solving ◽  
Mathematics Curriculum ◽  
Proportional Reasoning ◽  
School Mathematics ◽  
School Level ◽  
Principles And Standards ◽  
Middle School Level

PRINCIPLES AND STANDARDS FOR SCHOOL Mathematics (NCTM 2000) places proportionality among the major concepts connecting different topics in the mathematics curriculum at the middle school level (p. 217). What concerns us about many of the problems presented to students, however, is that they are often posed purely as a ratio or proportion from the start. Often the statement of a problem is a giveaway that a proportion is involved. For example, the question “If 15 students out of 20 get a problem correct, how many students in a class of 28 would we expect to get the problem correct?” does not tap the depth of proportional reasoning that is required for meaningful problem solving.

Shaping the Standards: Give Your Feedback on Basic Skills!

1998 ◽  
Vol 5 (3) ◽  
pp. 172-173
Keyword(s):  
Student Learning ◽  
Mathematics Curriculum ◽  
Basic Skills ◽  
School Mathematics ◽  
Nctm Standards ◽  
Writing Group ◽  
Teaching Assessment ◽  
Principles And Standards

In October 1998, the NCTM Standards 2000 Writing Group released a draft of Principles and Standards for School Mathematics, NCTM's updated Standards. As the title suggests, the draft includes a new section of principles, which are basic tenets about equity, mathematics curriculum, teachers and teaching, assessment, and technology, as well as standards for student learning that span preschool through grade 12.

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