An Interesting Probability Problem

1982 ◽  
Vol 75 (9) ◽  
pp. 765-768
Author(s):  
Ernest Woodward ◽  
Jim R. Ridenhour
Keyword(s):  
Problem Solving ◽  
Mathematics Teachers ◽  
School Mathematics ◽  
Mathematics Textbook ◽  
Probability Problem

In An Agenda for Action: Recommendations for School Mathematics of the 1980s, NCTM (1980) recommends that “problem solving be the focus of school mathematics in the 1980s." Unfortunately, present day mathematics textbook problems can often be classified and categorized, and so they are not really problems at all but actually computational exercises. As a result, mathematics teachers need to be continually searching for interesting, challenging problems. Recently we found such a problem (Gardner 1961).

scholarly journals The Effect of Problem Solving Course on Pre-Service Teachers’ Beliefs about Problem Solving in School Mathematics and Themselves as Problem Solvers

2018 ◽  
Vol 12 (2) ◽  
pp. 141-159
Author(s):  
Ljerka Jukić Matić
Keyword(s):  
Problem Solving ◽  
Mathematics Teachers ◽  
Teaching Practice ◽  
School Mathematics ◽  
Small Scale ◽  
Heuristic Strategies ◽  
Teachers Beliefs ◽  
Before And After ◽  
Problem Solvers ◽  
Positive Effect

Problem solving in schools begins with mathematics teachers. The degree to which mathematics teachers are prepared to teach for, about and through problem solving influences on their implementation of problem solving in school. We conducted a small scale study where we examined the effect of implementation of heuristic strategies and Polya’s steps in mathematics method course. We assessed pre-service teachers’ knowledge and attitudes about them as problem solvers before and after the course. Moreover we assessed their beliefs of problem solving in school mathematics. Those beliefs were assessed in two occasions: right after the course and after finished teaching practice. Although students’ knowledge on problem solving was improved, the results of students’ beliefs show that it is important that pre-service teachers, and consequently in-service teachers, are constantly reminded on the positive effect of constructivist and inquiry-based approach on teaching mathematics.

Investigating Problem-Solving Perseverance Using Lesson Study

2017 ◽  
Vol 111 (3) ◽  
pp. 207-212 ◽  
Author(s):  
Kristen N. Bieda ◽  
Craig Huhn
Keyword(s):  
High School ◽  
Problem Solving ◽  
Mathematics Teachers ◽  
Lesson Study ◽  
School Mathematics ◽  
High School Mathematics ◽  
High School Mathematics Teachers

Middle and high school mathematics teachers share what they learned about supporting students by conducting a series of three lesson studies.

Exploring Nonroutine Functions Algebraically and Graphically

2011 ◽  
Vol 104 (7) ◽  
pp. 508-513
Author(s):  
Christine P. Trinter ◽  
Joe Garofalo
Keyword(s):  
High School ◽  
Problem Solving ◽  
Mathematics Teachers ◽  
Multiple Representations ◽  
School Mathematics ◽  
High School Mathematics ◽  
Mathematics Tasks ◽  
Preservice Mathematics Teachers

Nonroutine function tasks are more challenging than most typical high school mathematics tasks. In our classes of precalculus students and preservice mathematics teachers, we have found that nonroutine tasks encourage our students to expand their thinking about functions and their approaches to problem solving. As a result, they gain greater appreciation for the power of multiple representations and a richer understanding of functions.

Some Interesting and Thought-Provoking Geometric Fallacies

2007 ◽  
Vol 101 (2) ◽  
pp. 114-119
Author(s):  
Alan Sultan
Keyword(s):  
High School ◽  
Problem Solving ◽  
Mathematics Teachers ◽  
School Mathematics ◽  
High School Mathematics ◽  
High School Mathematics Teachers

Some interesting geometric fallacies that were used in a problem-solving course for preservice high school mathematics teachers. Errors in logic and false assumptions lead to misleading conclusions. The authors demonstrate that incorrect sketches lead us to wrong conclusions. The use of Geometers Sketchpad is one strategy that will benefits students.

Piano Tuners and Problem Solving

1989 ◽  
Vol 82 (4) ◽  
pp. 248-249
Author(s):  
Randolph A. Philipp
Keyword(s):  
Problem Solving ◽  
Mathematics Teachers ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Central Focus

The draft of the NCTM Standards document states that problem solving should be the central focus of the mathematics curriculum (Commission on Standards for School Mathematics of the NCTM 1987). Now, more than ever, problem solving is being defined as a process. Akers (1984, 34) defined problem solving as “what you do when you don't know what to do,” and Schoenfeld (1988) wrote, “Indeed, ‘figuring it out’ is what mathematics is all about” (p. 8). Mathematics teachers, left with the task of determining how problemsolving skills should be taught, have the potential to play a key role in developing and sharing problems that interest students. I will share a certain type of problem that I think might be of some interest at the secondary and college levels.

scholarly journals INVESTIGATION OF USE CASES OF MATHEMATICS TEXTBOOKS IN THE TEACHING PROCESS FROM A DEVELOPMENTAL PERSPECTIVE

2021 ◽  
Vol 79 (6) ◽  
pp. 880-893
Author(s):  
Nurullah Yazici
Keyword(s):  
Primary School ◽  
Mathematics Teachers ◽  
Undergraduate Education ◽  
School Mathematics ◽  
Professional Life ◽  
Developmental Perspective ◽  
Classroom Teaching ◽  
Mathematics Textbook ◽  
Teaching Process ◽  
Primary School Mathematics

It is important to determine the behaviors of primary school pre-service teachers, who have successfully completed the "Mathematics Textbook Review" course during their undergraduate education, regarding the use of textbooks in their professional life. Therefore, it is important to determine the approaches of pre-service teachers who have positive ideas about using the mathematics textbook in their undergraduate education and the reasons for these approaches in the process after starting the profession. This research was designed with a developmental perspective from qualitative research approaches and was conducted with two different study groups in Turkey. The first study group consists of 162 primary school mathematics pre-service teachers. The second group consists of 43 primary school mathematics teachers who worked for at least two years in their professional life. As a result of the research, more than half of the pre-service teachers (n=132) stated that they would use textbooks as a basic resource in the in-class teaching process. Pre-service teachers' reasons for using the course book in the classroom teaching process were grouped under four categories: "it is a guide for teaching, homework, affordability, and opportunity for repetition". When the data obtained from the mathematics teachers were examined, it was determined that most of the teachers did not use the textbook as the main source in the classroom teaching process. When the obtained data are examined holistically, it is concluded that even though the rate of pre-service teachers thinking of using the textbook is high, this rate will decrease in professional life. Keywords: Pre-service teachers, mathematics teacher, mathematics textbook, developmental perspective

scholarly journals An Evaluation of the Primary Fourth-Grade Mathematics Textbook in Jordan in the Light of NCTM Standards: تقويم كتاب الرّياضيّات للصف الرّابع الأساسيّ في الأردن في ضوء معايير (NCTM)

2021 ◽  
Vol 5 (3) ◽  
Author(s):  
Nadia Hamlan Matouq, Habis Saad Alzboon
Keyword(s):  
Problem Solving ◽  
Mathematics Teachers ◽  
Fourth Grade ◽  
National Standards ◽  
Mathematical Representation ◽  
Mathematical Operation ◽  
Mathematical Communication ◽  
Nctm Standards ◽  
Mathematics Textbook ◽  
Reasoning And Proof

This study aimed at evaluating the content of the Jordanian mathematics textbook for the elementary fourth-grade in order to find out the extent that the fourth-grade mathematics textbook includes the standards of the American national for Council mathematics teachers (NCTM-2000), which concerned with mathematical operations (problem-solving, reasoning and proof, mathematical communication, Connections mathematical, mathematical representation) from the point of view of mathematical Connections teachers in Ma'an Governorate, thus, to find out the reasons for the low achievement of students in mathematics international tests. In order to fulfill these objectives, the descriptive analytical approach was used, that is a list of (NCTM) standards was prepared and changed into a questionnaire which was applied on a sample consisted of (119) male and female mathematics teachers for the primary fourth grade representing the study community. The results of the study showed that the extent to which the basic (NCTM) standards are included in the mathematics book for the fourth grade was at a moderate percentage on average about (2.76), the mathematical connection standard had the highest availability at (3.10), followed by the mathematical communication standard (3.08), the representation of mathematical operation at (2.99) respectively, and the problem solving standard at (2.51), whereas the reasoning and proof standard had the least representation. The findings also indicated there were statistically significant differences with regard to the experience variable and for the favor of (11-and more) category. Regarding the social gender, it did not have an effect. The study sets out several recommendations such as, developing the mathematics curriculum in the light of national standards, increasing the percentage of (NCTM) standards in the fourth-grade mathematics textbook, and the necessity to focus on issues connected with proof and reasoning, and problem solving.

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