Teaching Beginning Courses: Flower Power: Creating an Engaging Modeling Problem to Motivate Mathematics Students at an Alternative School

2003 ◽  
Vol 96 (6) ◽  
pp. 430-433
Author(s):  
Karen Koellner-Clark ◽  
Janice Newton
Keyword(s):  
Problem Solving ◽  
Alternative School ◽  
Mathematics Learning ◽  
School Mathematics ◽  
Mathematics Students ◽  
Modeling Problem ◽  
Principles And Standards

Using rich problem activities that require modeling can be engaging for students who struggle to understand the content in entrylevel courses. Further, they provide students with a forum in which communication and problem solving are expected. According to Principles and Standards for School Mathematics, “Interacting with others offers opportunities for exchanging and reflecting on ideas; hence, communication is a fundamental element of mathematics learning” (NCTM 2000, p. 348).

Principles for Principals: Facilitating Change

1989 ◽  
Vol 36 (6) ◽  
pp. 60-61
Author(s):  
Miriam A. Leiva
Keyword(s):  
Problem Solving ◽  
Teaching And Learning ◽  
School Mathematics ◽  
Instructional Leaders ◽  
Mathematics Students

Changes are taking place in the teaching and learning of mathematics—students are actively involved in doing mathematics with manipulatives and models; they are discussing problems among themelves with their teacher's guidance; they are exploring alternate ways to solve problems; and they are posing questions and examining solu tions (Dossey et al. 1988). This student-oriented, problem-solving approach is advocated by NCTM's Curriculum and Evaluw ion Standards for School Mathematics (Commission on Standards for School Mathematics of the NCTM 1987) and supported by the finding of the 1986 National As essment of Educa tional Progress. Principals, the instructional leaders in the schools. can be facilitator of change, and their support of innovative programs and activitie is crucial to reforming school mathematics.

IDEAS

1992 ◽  
Vol 39 (6) ◽  
pp. 32-39
Author(s):  
Lisa M. Passarello ◽  
Francis (Skip) Fennell
Keyword(s):  
Problem Solving ◽  
Number Sense ◽  
Mathematics Learning ◽  
School Mathematics ◽  
Grade Levels ◽  
Or Groups ◽  
And Mathematics ◽  
Parent Child ◽  
At Home ◽  
A Performance

This month's IDEAS emphasizes connections between science and mathematics by using a performance-, or authentic-, asessment format. The month of February is close to the heart of many students and teachers. The activity sheets and the extensions offer a different approach to the valentine month. Students have the opportunity to explore applications involving their own personal valentine—the heart. The activities involve number sense, problem solving, measurement, and statistics. Additionally, this month's IDEAS involves a variety of important mathematics concepts and ideas in a performance-based setting. The activity sheets are designed to be used in multiple grade levels. The activity sheets can be completed by individual students or groups of students. The at-home-activity sheet is designed to connect school-mathematics learning with the home. Encourage students to complete this activity sheet as a parent-child experiment.

Fostering Mathematical Thinking through Multiple Solutions

2000 ◽  
Vol 5 (8) ◽  
pp. 534-539
Author(s):  
Jinfa Cai ◽  
Patricia Ann Kenney
Keyword(s):  
Problem Solving ◽  
Multiple Solutions ◽  
Mathematical Thinking ◽  
School Mathematics ◽  
Reform Movement ◽  
Mathematics Students ◽  
Mathematical Concepts ◽  
Teachers And Students

The reform movement in school mathematics advocates communication as a necessary component for learning, doing, and understanding mathematics (Elliott and Kenney 1996). Communication in mathematics means that one is able not only to use its vocabulary, notation, and structure to express ideas and relationships but also to think and reason mathematically. In fact, communication is considered the means by which teachers and students can share the processes of learning, doing, and understanding mathematics. Students should express their thinking and problem-solving processes in both written and oral formats. The clarity and completeness of students' communication can indicate how well they understand the related mathematical concepts.

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).

Mathematical Modeling and the Presidential Election

1992 ◽  
Vol 85 (7) ◽  
pp. 520-521
Author(s):  
Joseph C. Witkowski
Keyword(s):  
Mathematical Modeling ◽  
Problem Solving ◽  
Secondary Schools ◽  
Presidential Election ◽  
Presidential Elections ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Modeling Problem ◽  
Mathematical Sciences ◽  
K 12

In recent years, interest in problem solving and mathematical modeling has increased. In 1975, the Conference Board of the Mathematical Sciences issued its Overview and Analysis of School Mathematics K-12, which recommended the incorporation of mathematical applications and modeling into secondary schools. More recently the Curriculum and Evaluation Standards for School Mathematics (1989) formulated by the NCTM stressed the importance of mathematical modeling as a facet of problem solving. The purpose of this article is to look at an interesting mathematical-modeling problem regarding presidential elections.

Teacher to Teacher: Playing around with Mono-pi-ly

2006 ◽  
Vol 11 (6) ◽  
pp. 294-297
Author(s):  
Cindy Kroon
Keyword(s):  
South Dakota ◽  
Three Dimensional ◽  
Department Of Education ◽  
School Mathematics ◽  
Mathematics Students ◽  
Measurement Standard ◽  
Three Dimensional Objects ◽  
Principles And Standards

According to the geometry standard in Principles and Standards for School Mathematics, “In grades 6–8, all students should precisely describe, classify, and understand relationships among types of two- and three- dimensional objects” (NCTM 2000, p. 232). The Measurement Standard goes on to state, “In grades 6–8, all students should develop and use formulas to determine the circumference of circles” (NCTM 2000, p. 240). In addition, South Dakota's Measurement Standard for Grade 7 delineates what mathematics students should know, such as “Given the formulas, find the circumference, perimeter, and area of circles” (South Dakota Department of Education 2004).

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?

Mythmatics

2005 ◽  
Vol 12 (3) ◽  
pp. 136-143
Author(s):  
Larry E. Buschman
Keyword(s):  
Problem Solving ◽  
Mathematics Instruction ◽  
Solution Method ◽  
Computational Algorithm ◽  
School Mathematics ◽  
Story Problems ◽  
Mathematical Question ◽  
Principles And Standards ◽  
Genuine Problem ◽  
Answering Questions

Principles and Standards for School Mathematics (NCTM 2000) recommends that classroom mathematics instruction be more problem- centered—children need to be given the opportunity to engage in genuine problem solving by answering questions to which the answer is not apparent or the solution method is not known in advance (Charles and Lester 1982; NCTM 2000). Traditionally, problem solving has been associated with routine word, or story, problems. However, almost any mathematical question can be a problem; even computational exercises can be problematic if the answer is not apparent and children have not been taught a solution method, such as a computational algorithm.

Writing Samples to Understand Mathematical Thinking

2002 ◽  
Vol 7 (9) ◽  
pp. 517-520
Author(s):  
Dianne S. Goldsby ◽  
Barbara Cozza
Keyword(s):  
Mathematical Thinking ◽  
School Mathematics ◽  
Mathematics Students ◽  
Principles And Standards

NCTM's Principles and Standards for School Mathematics emphasizes the need for all students to organize and consolidate their mathematical thinking through communication and to communicate their mathematical thinking coherently to others (NCTM 2000). Writing helps students focus on their own understandings of mathematics: “Students gain insights into their thinking when they present their methods for solving problems, when they justify their reasoning to a classmate or teacher, or when they formulate a question about something that is puzzling them” (NCTM 2000, pp. 60–61).

Geometric Conjectures: The Importance of Counterexamples

2003 ◽  
Vol 9 (4) ◽  
pp. 210-215
Author(s):  
Jeffery J. Boats ◽  
Nancy K. Dwyer ◽  
Sharon Laing ◽  
Mark P. Fratella
Keyword(s):  
Middle School ◽  
Pattern Recognition ◽  
Middle School Mathematics ◽  
School Mathematics ◽  
Mathematics Students ◽  
Reasoning Skills ◽  
Principles And Standards

TO DEVELOP STUDENTS' REASONING SKILLS, the NCTM's Principles and Standards for School Mathematics (2000) recommends that students make generalizations and evaluate conjectures. In particular, middle school mathematics students should be engaged in activities involving pattern recognition as a means of formulating such conjectures.

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