Let's Do It: Punchy Mathematics

1983 ◽  
Vol 31 (2) ◽  
pp. 10-14
Author(s):  
Jean M. Shaw
Keyword(s):  
Teaching And Learning ◽  
Primary Grades ◽  
Approaches To Teaching ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics

Let's Do It—activity approaches to teaching and learning mathematics in the primary grades, with extensions through grade six.

Let's Do It: Promoting Mathematical Thinking

1985 ◽  
Vol 32 (6) ◽  
pp. 7-13
Author(s):  
John Van de Walle ◽  
Charles S. Thompson
Keyword(s):  
Teaching And Learning ◽  
Mathematical Thinking ◽  
Primary Grades ◽  
Approaches To Teaching ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics

Let's Do It—activity approaches to teaching and learning mathematics in the primary grades, with extensions through grade six.

Connecting Research to Teaching: Probability and Statistics

1993 ◽  
Vol 86 (3) ◽  
pp. 244-248
Author(s):  
J. Michael Shaughnessy
Keyword(s):  
Teaching And Learning ◽  
Teaching Mathematics ◽  
Classroom Communication ◽  
Approaches To Teaching ◽  
Evaluation Standards ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Present Information ◽  
Probability And Statistics ◽  
The Many

This issue introduces a new department to the Mathematics Teacher, “Connecting Research to Teaching.” Articles will focus on mathematical and pedagogical ideas related to the NCTM's Curriculum and Evaluation Standards (1989) and the Professional Standards for Teaching Mathematics (1991). Authors will strive to present information to help teachers (1) understand students' conceptions or misconceptions of important ideas, (2) consider various approaches to teaching, and (3) offer activities that probe students' understanding. Although research offers no one correct answer to the many perplexing problems surrounding teaching and learning mathematics, the suggestions and perspectives may help teachers pursue their work with new insights. It is hoped that the department will also stimulate researchers to reflect on connecting research to the classroom. Communication and collaboration between teachers and researchers will benefit both groups and help each grow in appreciation of the other's tasks.

Mathematical Insight: Changing Perspective

2003 ◽  
Vol 96 (4) ◽  
pp. 238-242
Author(s):  
Cliff W. Sloyer
Keyword(s):  
Teaching And Learning ◽  
Higher Order ◽  
Approaches To Teaching ◽  
One Dimensional ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Mathematical Exploration ◽  
Problems And Solutions ◽  
Big Picture

Many great ideas in mathematics have resulted from examining problems and solutions from different perspectives or directions, but one-dimensional thinking in solving a problem is all too familiar. A number of approaches to teaching and learning mathematics, especially those involving algorithms of some form, lend themselves to a reinforcement of one direction in solving problems. Mathematical insight gained by changing perspective is occasionally suggested in specific problems, but the “big picture” of mathematical exploration, conjecture, and proof requires a deeper commitment to this process. This article focuses on problems that can benefit from a change in perspective by looking forward and backward. In particular, the transition from basic mathematical manipulations to higher-order levels of reasoning requires an awareness of such processes.

scholarly journals Problematizing teaching and learning mathematics as “given” in STEM education

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Yeping Li ◽  
Alan H. Schoenfeld
Keyword(s):  
Mathematics Education ◽  
Stem Education ◽  
Teaching And Learning ◽  
Science Technology ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Alternative Approach ◽  
And Mathematics ◽  
Scientific Engineering

AbstractMathematics is fundamental for many professions, especially science, technology, and engineering. Yet, mathematics is often perceived as difficult and many students leave disciplines in science, technology, engineering, and mathematics (STEM) as a result, closing doors to scientific, engineering, and technological careers. In this editorial, we argue that how mathematics is traditionally viewed as “given” or “fixed” for students’ expected acquisition alienates many students and needs to be problematized. We propose an alternative approach to changes in mathematics education and show how the alternative also applies to STEM education.

Teaching and Learning Mathematics

1987 ◽  
Vol 71 (458) ◽  
pp. 314
Author(s):  
Paul Ernest ◽  
Peter G. Dean
Keyword(s):  
Teaching And Learning ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics

scholarly journals A Study of Errors and Misconceptions in the Learning of Addition and Subtraction of Directed Numbers in Grade 8

SAGE Open ◽  
2016 ◽  
Vol 6 (4) ◽  
pp. 215824401667137 ◽  
Author(s):  
Judah Paul Makonye ◽  
Josiah Fakude
Keyword(s):  
Conceptual Understanding ◽  
Teaching And Learning ◽  
Study Data ◽  
Negative Numbers ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Number Lines ◽  
Addition And Subtraction ◽  
Logical Errors ◽  
Grade 8

The study focused on the errors and misconceptions that learners manifest in the addition and subtraction of directed numbers. Skemp’s notions of relational and instrumental understanding of mathematics and Sfard’s participation and acquisition metaphors of learning mathematics informed the study. Data were collected from 35 Grade 8 learners’ exercise book responses to directed numbers tasks as well as through interviews. Content analysis was based on Kilpatrick et al.’s strands of mathematical proficiency. The findings were as follows: 83.3% of learners have misconceptions, 16.7% have procedural errors, 67% have strategic errors, and 28.6% have logical errors on addition and subtraction of directed numbers. The sources of the errors seemed to be lack of reference to mediating artifacts such as number lines or other real contextual situations when learning to deal with directed numbers. Learners seemed obsessed with positive numbers and addition operation frames—the first number ideas they encountered in school. They could not easily accommodate negative numbers or the subtraction operation involving negative integers. Another stumbling block seemed to be poor proficiency in English, which is the language of teaching and learning mathematics. The study recommends that building conceptual understanding on directed numbers and operations on them must be encouraged through use of multirepresentations and other contexts meaningful to learners. For that reason, we urge delayed use of calculators.

Mogućnosti primene istraživački zasnovane nastave (IN) u početnom matematičkom obrazovanju

2021 ◽  
Author(s):  
Dragana Glogovac ◽  
◽  
Marina Milošević ◽  
Bojan Lazić ◽  
Keyword(s):  
Teaching And Learning ◽  
Teaching Practice ◽  
Teaching Mathematics ◽  
Teaching Process ◽  
Inquiry Based Learning ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Key Competencies ◽  
Insight Into

Modern primary education, especially mathematics, requires constant innovation of teaching practice in order to modernize, rationalize, and efficiently the teaching process. Teaching mathematics should be experienced as a process that promotes learning with understanding, stimulates motivation, active learning, research, critical thinking, analysis, problem solving, drawing conclusions, exchange of experiences. The tendency to improve the quality of mathematics education has resulted in many studies pointing to the benefits of research-based mathematics (IN) teaching, known as inquiry-based learning (IBL), recognized as an essential way of organizing the teaching process to develop key competencies, abilities and skills in 21st century. Тhe aim of this paper is to see, based on a comprehensive theoretical analysis and the results of previous research. The created model of teaching mathematics based on research represents a useful framework for improving the quality of the process of teaching and learning mathematics, and empowers teachers in its application and affirmation, gaining insight into the way of organizing research learning.

scholarly journals Student teachers’ perceptions of democracy in the mathematics classroom: Freedom, equality and dialogue

Pythagoras ◽  
2012 ◽  
Vol 33 (2) ◽  
Author(s):  
Wajeeh Daher
Keyword(s):  
Teacher Education ◽  
Student Teachers ◽  
Teaching And Learning ◽  
Mathematics Classroom ◽  
Mathematics Teacher Education ◽  
Comparison Method ◽  
Teachers Perceptions ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Two Stages

This article studies student teachers’ perceptions of the pedagogic and didactic aspects of teaching and learning mathematics in a democratic classroom. It is concerned primarily with issues of democracy in the mathematics classroom, specifically freedom, equality and dialogue. The research was conducted in two mathematics teacher education classes, where students were in their third year of study to major in mathematics. To find these students’ perceptions of democracy in the mathematics classroom the first two stages of the constant comparison method were followed to arrive at categories of democratic and undemocratic acts. The participants in the research emphasised that instructors should refrain from giving some students more time or opportunities to express themselves or act in the mathematics classroom than other students, because this would make them feel unequal and possibly make them unwilling to participate further in the mathematics classroom. The participants also emphasised that instructors should not exert their power to stop the flow of students’ actions in the mathematics classroom, because this would trouble them and make them lose control of their actions. Further, the participants mentioned that instructors would do better to connect to students’ ways of doing mathematics, especially of defining mathematical terms, so that students appreciate the correct ways of doing mathematics and defining its terms.

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