scholarly journals The use of carefully planned board work to support the productive discussion of multiple student responses in a Japanese problem-solving lesson

2022 ◽  
Author(s):  
Fay Baldry ◽  
Jacqueline Mann ◽  
Rachael Horsman ◽  
Dai Koiwa ◽  
Colin Foster
Keyword(s):  
Problem Solving ◽  
Teaching Practice ◽  
Careful Planning ◽  
Student Responses ◽  
Research And Teaching ◽  
Mathematical Discussions ◽  
Solution Methods ◽  
Multiple Alternative ◽  
Productive Discussion ◽  
Alternative Solutions

AbstractIn this paper, we analyse a grade 8 (age 13–14) Japanese problem-solving lesson involving angles associated with parallel lines, taught by a highly regarded, expert Japanese mathematics teacher. The focus of our observation was on how the teacher used carefully planned board work to support a rich and extensive plenary discussion (neriage) in which he shifted the focus from individual mathematical solutions to generalised properties. By comparing the teacher’s detailed prior planning of the board work (bansho) with that which he produced during the lesson, we distinguish between aspects of the lesson that he considered essential and those he treated as contingent. Our analysis reveals how the careful planning of the board work enabled the teacher to be free to explore with the students the multiple alternative solution methods that they had produced, while at the same time having a clear overall purpose relating to how angle properties can be used to find additional solution methods. We outline how these findings from within the strong tradition of the Japanese problem-solving lesson might inform research and teaching practice outside of Japan, where a deep heritage of bansho and neriage is not present. In particular, we highlight three prominent features of this teacher’s practice: the detailed lesson planning in which particular solutions were prioritised for discussion; the considerable amount of time given over to student generation and comparison of alternative solutions; and the ways in which the teacher’s use of the board was seen to support the richness of the mathematical discussions.

Anticipating Student Responses to Improve Problem Solving

2007 ◽  
Vol 12 (9) ◽  
pp. 504-511
Author(s):  
Ann H. Wallace
Keyword(s):  
Problem Solving ◽  
Mathematics Teacher ◽  
Careful Planning ◽  
Actual Problem ◽  
Student Responses ◽  
The Difference ◽  
Problem Solve ◽  
Teaching Problem ◽  
Or Task ◽  
The Way

I have been a Mathematics Teacher and Educator throughout all four publications of the Standards documents (NCTM 1991, 1995, 1989, and 2000). Over the years, while concentrating on improving various aspects of my teaching, specifically, improving my students' ability to problem solve, I have been perplexed to see students pick numbers out of a problem and perform an operation with no regard for the context. To address this issue by teaching problem-solving lessons made me realize that I did not know the difference between students solving a problem and actual problem solving. A lesson beginning with a problem or task does not make it a problem-solving lesson, especially when students would inevitably solve it the way I had intended. Instead of problem solving, my students were trying to figure out what I was thinking. To prevent the temptation of leading students in this way of thinking required careful planning of problem-solving lessons.

Algorithmic Puzzles

2011 ◽  
Author(s):  
Anany Levitin ◽  
Maria Levitin
Keyword(s):  
Problem Solving ◽  
Computer Science ◽  
Algorithm Design ◽  
Divide And Conquer ◽  
Algorithmic Problem ◽  
Design Strategies ◽  
Job Interviews ◽  
Skill Levels ◽  
Problem Solving Skills ◽  
Solution Methods

While many think of algorithms as specific to computer science, at its core algorithmic thinking is defined by the use of analytical logic to solve problems. This logic extends far beyond the realm of computer science and into the wide and entertaining world of puzzles. In Algorithmic Puzzles, Anany and Maria Levitin use many classic brainteasers as well as newer examples from job interviews with major corporations to show readers how to apply analytical thinking to solve puzzles requiring well-defined procedures. The book's unique collection of puzzles is supplemented with carefully developed tutorials on algorithm design strategies and analysis techniques intended to walk the reader step-by-step through the various approaches to algorithmic problem solving. Mastery of these strategies--exhaustive search, backtracking, and divide-and-conquer, among others--will aid the reader in solving not only the puzzles contained in this book, but also others encountered in interviews, puzzle collections, and throughout everyday life. Each of the 150 puzzles contains hints and solutions, along with commentary on the puzzle's origins and solution methods. The only book of its kind, Algorithmic Puzzles houses puzzles for all skill levels. Readers with only middle school mathematics will develop their algorithmic problem-solving skills through puzzles at the elementary level, while seasoned puzzle solvers will enjoy the challenge of thinking through more difficult puzzles.

COLLABORATIVE RESEARCH, DELIBERATION, AND INNOVATION

Episteme ◽  
2014 ◽  
Vol 11 (3) ◽  
pp. 291-303 ◽  
Author(s):  
K. Brad Wray
Keyword(s):  
Problem Solving ◽  
Collaborative Research ◽  
Research Team ◽  
Team Work ◽  
Research Teams ◽  
Course Of Action ◽  
Wrong Direction ◽  
Group Members ◽  
Alternative Solutions

AbstractI evaluate the extent to which we could learn something about how we should be conducting collaborative research in science from the research on groupthink. I argue that Solomon has set us in the wrong direction, failing to recognize that the consensus in scientific specialties is not the result of deliberation. But the attention to the structure of problem-solving that has emerged in the groupthink research conducted by psychologists can help us see when deliberation could lead to problems for a research team. I argue that whenever we need to generate alternative solutions or proposals, groupthink is a genuine threat, and research teams would be wise to allow individuals opportunities to work alone. But the benefits of team work emerge when scientists seek to evaluate the various proposals generated, and determine a course of action. Then the group is less prone is groupthink, and the interaction of group members can be an epistemic asset.

scholarly journals Inconsistency Among Beliefs, Knowledge, and Teaching Practice in Mathematical Problem Solving: A Case Study of a Primary Teacher

2017 ◽  
Vol 7 (2) ◽  
pp. 27-40
Author(s):  
Tatag Yuli Eko Siswono ◽  
Ahmad Wachidul Kohar ◽  
Ika Kurniasari ◽  
Sugi Hartono
Keyword(s):  
Problem Solving ◽  
Teaching Practice ◽  
Mathematics Learning ◽  
Mathematical Problem ◽  
Primary Teacher ◽  
Mathematical Problem Solving ◽  
Mathematics Problems ◽  
And Mathematics ◽  
Teacher's Beliefs

This is a case study investigating a primary teacher’s beliefs, knowledge, and teaching practice in mathematical problem solving. Data was collected through interview of one primary teacher regarding his beliefs on the nature of mathematics, mathematics teaching, and mathematics learning as well as knowledge about content and pedagogy of problem solving. His teaching practice was also observed which focused on the way he helped his students solve several different mathematics problems in class based on Polya’s problemsolving process: understand the problem, devising a plan, carrying out the plan, and looking back. Findings of this study point out that while the teacher’s beliefs, which are closely related to his problem solving view, are consistent with his knowledge of problem solving, there is a gap between such beliefs and knowledge around his teaching practice. The gap appeared primarily around the directive teaching which corresponds to instrumental view he held in most of Polya’s process during his teaching practice, which is not consistent with beliefs and knowledge he professed during the interview. Some possible causes related to several associate factors such as immediate classroom situation and teaching practice experience are discussed to explain such inconsistency. The results of this study are encouraging, however, further studies still need to be conducted.

scholarly journals MEMBANGUN KARAKTER BANGSA MELALUI PEMBELAJARAN MATEMATIKA KURIKULUM 2013

2013 ◽  
Vol 14 (2) ◽  
pp. 73-80
Author(s):  
Wahyudin Wahyudin
Keyword(s):  
Problem Solving ◽  
Child Development ◽  
Character Education ◽  
Teaching Practice ◽  
Successful Implementation ◽  
Knowledge And Skills ◽  
The Core ◽  
Self Development ◽  
Points Of View ◽  
New Generation

The development of the character education still becomes the controversy among the educators, either from the theoretical or philosophical points of view. Actually, the core of the character education is not only viewed from philosophical difference, pedagogical ideology, or politics, but focused on the child development. Curriculum 2013 seeks to provide a problem-solving on the cultural matters and the national characters by integrating the characters / values /attitudes into the lessons, self-development, and the culture of the school. It is expected that a new generation of nation is developed in attitudes, knowledge, and skills. It has been clear that teachers thought, beliefs, and choices will influence their teaching practice. Therefore, it is necessary to build the views, beliefs, and positive selection within the teachers mind for the successful implementation of Curriculum 2013.   Perkembangan pendidikan karakter sampai sejauh ini masih penuh dengan kontroversi yang terutama berakar dalam berbagai perbedaan teoretis dan filosofis, meski sebenarnya inti dari pendidikan karakter tidak pada perbedaan filosofis, ideologi pedagogis, politik, dan sebagainya, melainkan tentang perkembangan anak. Kurikulum 2013 berupaya memberikan pemecahan persoalan budaya dan karakter bangsa dengan cara mengintegrasikan karakter/nilai/sikap ke dalam mata pelajaran, pengembangan diri, dan budaya sekolah, dengan harapan terbentuknya generasi baru bangsa yang utuh dalam sikap, pengetahuan, dan keterampilan. Dengan menyadari bahwa pandangan, keyakinan, dan pilihan para guru akan berpengaruh pada praktek pembelajaran, maka perlu dibangun pandangan, keyakinan, dan pilihan yang positif dalam diri para guru demi keberhasilan implementasi Kurikulum 2013.

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.

scholarly journals Teachers’ pedagogical content knowledge in teaching word problem solving strategies

ZDM ◽  
2019 ◽  
Vol 52 (1) ◽  
pp. 165-178 ◽  
Author(s):  
Csaba Csíkos ◽  
Judit Szitányi
Keyword(s):  
Problem Solving ◽  
Pedagogical Content Knowledge ◽  
Content Knowledge ◽  
Word Problem ◽  
Word Problems ◽  
Teaching Practice ◽  
Word Problem Solving ◽  
Pedagogical Content ◽  
Explicit Teaching ◽  
Problem Solving Strategies

AbstractThis research addressed Hungarian pre-service and in-service (both elementary and lower secondary) teachers’ pedagogical content knowledge concerning the teaching of word problem solving strategies. By means of a standardized interview protocol, participants (N = 30) were asked about their judgement on the difficulty of teaching word problems, the factors they find difficult, and their current teaching practice. Furthermore, based on a comparative analysis of Eastern European textbooks, we tested how teachers’ current beliefs and views relate to the word problem solving algorithm described in elementary textbooks. The results suggest that in the teachers’ opinion, explicit teaching of a step-by-step algorithm is feasible and desirable as early as in the 1st school grade. According to our results, two approaches (namely, paradigmatic- and narrative-oriented) concerning how to teach the process of word problems solving, originally revealed by Chapman, were found. Furthermore, teachers in general agreed with the approach taken in the textbooks on the subject of what kinds of word problems should be used, and that explicit teaching of word problem solving strategies should be introduced by using simple, routine word problems as examples.

“But I had it first!” Young children, possession, and social problem solving

2020 ◽  
Vol 24 (2) ◽  
pp. 21-25
Author(s):  
Julie Treweek ◽  
Janette Kelly-Ware
Keyword(s):  
New Zealand ◽  
Problem Solving ◽  
Young Children ◽  
Social Problem ◽  
Teaching Practice ◽  
Qualitative Case Study ◽  
Case Study Research ◽  
Social Problem Solving ◽  
Problem Solve

This qualitative case study research explored children’s social disputes in one New Zealand kindergarten. The disputes typically related to the possession of resources and space. “First possession” was found to be significant, hence the name of this article. The notion that children have to experience “possession” and “ownership” to learn about these fundamental concepts was reinforced. Young children’s problem solving during peer disputes was identified and teachers were seen “stepping back”, thus providing children with time and space to work through their disputes. Teachers reading this article will recognise the importance of having a shared philosophy that drives teaching practice. They will also be provoked to consider how they support children to problem solve and work through their disputes with others, and consider video as a reflective tool for improving their practice.

Investigations: Vehicles for Learning and Doing Mathematics

1996 ◽  
Vol 178 (2) ◽  
pp. 35-49 ◽  
Author(s):  
Carole Greenes
Keyword(s):  
Problem Solving ◽  
Teaching And Learning ◽  
Solution Method ◽  
Professional Organizations ◽  
Mathematical Concepts ◽  
Educational Benefits ◽  
Problem Situations ◽  
Mathematics Educators ◽  
Solution Methods ◽  
Problem Solving Strategies

Professional organizations of mathematics educators and mathematicians are calling for major reforms in the teaching and learning of mathematics. Among those reforms are a shift in emphasis in curriculum from mastery of lists of unrelated mathematical concepts and skills to exploration of rich mathematical topics and problem situations, and a shift in learning from memorizing and replicating algorithmic procedures to investigating and solving complex problems. To help students achieve proficiency in solving problems, the curriculum must focus on development of the major concepts of mathematics, the enhancement and enlargement of students' repertoires of problem-solving strategies and reasoning methods, and the refinement of communication and collaboration skills. Because they present intriguing problems whose solutions or solution methods are not immediately obvious, and require the application of concepts from different areas of mathematics, and, in some instances, knowledge from other content areas, investigations are powerful vehicles for helping students achieve expertise in solving problems. The nature of investigations and their educational benefits are described. Three types of investigations, whimsical, real, and mathematical, are defined and illustrated. For each investigation, the mathematical content and problem-solving strategies are identified, and a solution method is presented. The responsibilities of the teacher, before, during and after an investigation are described.

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