Understanding Students' Problem-Solving Knowledge through Their Writing

2007 ◽  
Vol 13 (2) ◽  
pp. 102-109
Author(s):  
Diana F. Steele
Keyword(s):  
Problem Solving ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Writing In Mathematics ◽  
Principles And Standards

The Curriculum and Evaluation Standards for School Mathematics, published in 1989 by NCTM, placed an emphasis on the importance of communication for learning and doing mathematics. Writing is one way to achieve this valuable communication in the classroom. In 2000, Principles and Standards for School Mathematics emphasized writing as being an important aspect of communication: “Writing in mathematics can also help students consolidate their thinking because it requires them to reflect on their work and clarify their thoughts about the ideas developed in the lesson' (NCTM 2000, p. 61). Several studies have also shown ways that writing can be an effective tool for improving students' learning of mathematics (Bell and Bell 1985; Pugalee 2001; Steele 2005). Pugalee (2001) found in his work with students that writing could potentially help students increase their problemsolving ability in mathematics.

Beyond the Golden Ratio: A Calculator-Based Investigation

2001 ◽  
Vol 94 (2) ◽  
pp. 138-144
Author(s):  
Peter L. Glidden
Keyword(s):  
Problem Solving ◽  
Mathematical Reasoning ◽  
Golden Ratio ◽  
School Mathematics ◽  
Opportunities To Learn ◽  
Mathematical Communication ◽  
Evaluation Standards ◽  
Mathematical Connections ◽  
Principles And Standards ◽  
Classroom Use

NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) calls for increased emphasis on problem solving, mathematical reasoning, mathematical communication, and mathematical connections. This call is reaffirmed in Principles and Standards for School Mathematics (NCTM 2000). A preferred way of achieving these goals is by having students perform mathematical investigations in which they explore mathematics, search for patterns, and use technology when appropriate. In short, students should be given opportunities to learn mathematics by doing mathematics. Of course, if students are to learn mathematics through investigations, teachers must have a ready supply of such investigations available for classroom use.

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).

Coordinate Geometry: A Powerful Tool for Solving Problems

1990 ◽  
Vol 83 (4) ◽  
pp. 264-268
Author(s):  
Stanley F. Taback
Keyword(s):  
Problem Solving ◽  
Teaching And Learning ◽  
Mathematical Problem ◽  
School Mathematics ◽  
Mathematical Problem Solving ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Mathematics Standards ◽  
Problem Situations ◽  
Coordinate Geometry

In calling for reform in the teaching and learning of mathematics, the Curriculum and Evaluation Standards for School Mathematics (Standards) developed by NCTM (1989) envisions mathematics study in which students reason and communicate about mathematical ideas that emerge from problem situations. A fundamental premise of the Standards, in fact, is the belief that “mathematical problem solving … is nearly synonymous with doing mathematics” (p. 137). And the ability to solve problems, we are told, is facilitated when students have opportunities to explore “connections” among different branches of mathematics.

Implementing the Standards: Uses of Technology in Prealgebra and Beginning Algebra

1990 ◽  
Vol 83 (3) ◽  
pp. 194-198
Author(s):  
M. Kathleen Heid
Keyword(s):  
Problem Solving ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematics Classrooms ◽  
Beginning Algebra ◽  
Grade Levels ◽  
Mathematical Connections

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 technologically rich school mathematics classrooms in which students and teachers have constant access to appropriate computing devices and in which students use computers and calculators as tools for the investigation and exploration of problems.

Felix Klein and the NCTM's Standards: A Mathematician Considers Mathematics Education

2000 ◽  
Vol 93 (8) ◽  
pp. 714-717
Author(s):  
Kim Krusen McComas
Keyword(s):  
Mathematics Education ◽  
School Mathematics ◽  
Rote Learning ◽  
German Mathematician ◽  
Evaluation Standards ◽  
10Th Anniversary ◽  
Felix Klein ◽  
Look Back ◽  
Principles And Standards ◽  
Year 2000

The year 1999 marked the 10th anniversary of the NCTM's Curriculum and Evaluation Standards for School Mathematics. It also marked the 150th anniversary of the birth of German mathematician Felix Klein, who lived from 1849 to 1925. Although the relation between these two anniversaries may not be obvious, the connection is that Klein, were he still alive today, would probably support the NCTM's Standards. As the year 2000 brings us NCTM's Principles and Standards for School Mathematics, let us look back to the year 1900 and find Felix Klein at the forefront of a movement to reform mathematics education from rote learning to more meaningful mathematical learning.

Problem Solving With Discrete Mathematics

1996 ◽  
Vol 2 (7) ◽  
pp. 426-431
Author(s):  
Louis M. friedler
Keyword(s):  
Problem Solving ◽  
School Mathematics ◽  
Discrete Mathematics ◽  
Evaluation Standards

The NCTM's Curriculum and Evaluation Standards for School Mathematics (1981) calls for an emphasis on problem solving at all levels and recommends introducing discrete mathematics topics. In fact, the first standard for grades K-4 states that “the study of mathematics should emphasize problem solving …” (p. 23).

Problem Solving: Is More Than Solving Problems

1998 ◽  
Vol 4 (1) ◽  
pp. 20-25
Author(s):  
Michael G. Mikusa
Keyword(s):  
Problem Solving ◽  
Correct Answer ◽  
Mathematical Problem ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Students First ◽  
Mathematics Class ◽  
General Goals ◽  
Problem Solvers

The curriculum and evaluation Standards for School Mathematics (NCTM 1989) states that one of its five general goals is for all students to become mathematical problem solvers. It recommends that “to develop such abilities, students need to work on problems that may take hours, days, and even weeks to solve” (p. 6). Clearly the authors have not taught my students! When my students first encountered a mathematical problem, they believed that it could be solved simply because it was given to them in our mathematics class. They also “knew” that the technique or process for finding the solution to many problems was to apply a skill or procedure that had been recently taught in class. The goal for most of my students was simply to get an answer. If they ended up with the correct answer, great; if not, they knew that it was “my job” to show them the “proper” way to go about solving the problem.

What Is in the Daily News? Problem-Solving Opportunities!

1999 ◽  
Vol 5 (7) ◽  
pp. 390-394
Author(s):  
Robyn Silbey
Keyword(s):  
Problem Solving ◽  
Real World ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Daily News ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
The Everyday ◽  
Everyday World ◽  
Real World Problems

In An Agenda for Action, the NCTM asserted that problem solving must be at the heart of school mathematics (1980). Almost ten years later, the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) stated that the development of each student's ability to solve problems is essential if he or she is to be a productive citizen. The Standards assumed that the mathematics curriculum would emphasize applications of mathematics. If mathematics is to be viewed as a practical, useful subject, students must understand that it can be applied to various real-world problems, since most mathematical ideas arise from the everyday world. Furthermore, the mathematics curriculum should include a broad range of content and an interrelation of that content.

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).

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