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).

Focused Strategies for Middle-Grades Mathematics Vocabulary Development

2007 ◽  
Vol 13 (4) ◽  
pp. 200-207
Author(s):  
Rheta N. Rubenstein
Keyword(s):  
Mathematics Education ◽  
Middle Grades ◽  
Mathematical Thinking ◽  
Vocabulary Development ◽  
School Mathematics ◽  
One Dimension ◽  
Mathematical Language ◽  
Mathematics Vocabulary ◽  
Principles And Standards

Principles and Standards for School Mathematics reminds us that communication is central to a broad range of goals in mathematics education (NCTM 2000). These goals include students' being able to (1) organize and consolidate mathematical thinking; (2) communicate coherently with teachers, peers, and others; (3) analyze and evaluate others' strategies; and (4) use language to express mathematics precisely. One part of communication is acquiring mathematical language and using it fluently. This article addresses learning vocabulary as one dimension of mathematics communication.

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.

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).

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.

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).

scholarly journals PENGARUH PEMBELAJARAN CAI-KONTEKSTUAL TERHADAP KEMAMPUAN BERPIKIR MATEMATIK DAN KARAKTER MAHASISWA

2017 ◽  
Vol 9 (1) ◽  
pp. 45
Author(s):  
Nanang Nanang
Keyword(s):  
Student Teacher ◽  
Mathematical Thinking ◽  
Thinking Skills ◽  
Contextual Learning ◽  
Test Method ◽  
Mathematics Students ◽  
Data Value ◽  
Academic Year ◽  
Initial Knowledge ◽  
Selection Of

The purpose of this study to determine the effect of CAI-Contextual learning of the ability to think mathematically and character of the student teacher participants of the course Capita Selecta Mathematical SMA. The population in this study is the fourth semester students of Mathematics Education STKIP Garut academic year 2015/2016. Selection of the sample by means of random sampling, the students obtained grade B as an experimental class and class A as the control class. Experimental class taught by CAI-Contextual learning, whereas the control class was taught by conventional learning. Retrieval of data obtained by the test method to get the data value of the initial knowledge of mathematics students and Mathematical Thinking Skills as well as the method of questionnaire to measure student character, and then analyzed with the average difference. The results showed that there are differences in the ability to think mathematically and character class students experiment with the control class. Since the average mathematical thinking skills and character students experimental class is bigger than the control class, it can be concluded that the CAI-Contextual learning positively affects the ability to think mathematically and character of the student teacher participants of the course Capita Selecta Mathematical SMA.

scholarly journals Piloting a problem solving module for undergraduate mathematics students

2019 ◽  
Vol 17 (2) ◽  
pp. 46
Author(s):  
David McConnell
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Thinking Skills ◽  
Mathematical Work ◽  
Assessment Practices ◽  
Traditional Teaching ◽  
Mathematics Students ◽  
Undergraduate Mathematics ◽  
Students First ◽  
Academic Year

We report on a new problem solving module for second-year undergraduate mathematics students first piloted during the 2016-17 academic year at Cardiff University.  This module was introduced in response to the concern that for many students, traditional teaching and assessment practices do not offer sufficient opportunities for developing problem-solving and mathematical thinking skills, and more generally, to address the recognised need to incorporate transferrable skills into our undergraduate programmes.  We discuss the pedagogic and practical considerations involved in the design and delivery of this module, and in particular, the question of how to construct open-ended problems and assessment activities that promote mathematical thinking, and reward genuinely original and independent mathematical work.  

Sign in / Sign up

Export Citation Format

Share Document