Problem Solving as Theorizing (in process) (original) (raw)
The Place of Problem Solving and Mathematical Thinking in the Mathematical Teaching
2015
The purpose of this study is to investigate the effect of problem-solving subject given for the improvement of problem-solving skills and for teaching the problem-solving strategies on primary preservice mathematics teachers’ ability to use the problemsolving stages and on their mathematical thinking levels. The study is oriented to descriptive survey, which is one of the quantitative research methods. In the study that was conducted throughout 13 weeks (26 hours), the students were taught Polya’s (1945) problem-solving stages, which are formed of four steps, and they were also the problem-solving strategies in order to improve their problem-solving skills. In the study, two problems developed by Posamentier and Krulik (1998) was used as data collection tool, and “Mathematical Thinking Scale” developed by Ersoy (2012) was used to determine whether the problem-solving lesson has an effect on mathematical thinking. The findings obtained demonstrate that problem-solving subject has a p...
Problem Solving in Mathematics Education
Encyclopedia of Mathematics Education, 2014
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Problem Solving - Purpose and Means of Learning Mathematics in School
Procedia - Social and Behavioral Sciences, 2015
Of all school subjects, mathematics introduces and develops the "problem-solving" concept, as fundamental component of school learning with a strong formative effect on students. In mathematics, solving problems represents the most effective concept to contextualization and re-contextualization of concepts, to operational and basic mathematical knowledge transfer to ensure a sustainable and meaningful learning. The resolvent conduct of the student also involves, in addition to the cognitive factors, factors aiming the affectivity and the experience of the student. In this context, the study conducted on a significant group of students at the end of the secondary school aimed at knowing the importance given by students to solving problems, the preferred type of problems and the performance level achieved by the students in solving math problems. Taking into account the complex intellectual activity, the nature of difficulties which the student faces in solving problems is varied, ranging from perceptual difficulties to those concerning his cognitive self-regulation.
Teaching of Problem Solving in School Mathematics Classrooms
The Proceedings of the 12th International Congress on Mathematical Education, 2015
The 1980s saw a worldwide push for problem solving to be the central focus of the school mathematics curriculum since the publication of Polya's book about solving mathematics problems in 1954. However, attempts to teach problem solving typically emphasised the learning of heuristics and not the kind of mathematical thinking used by mathematicians. There appears to be a lack of success of any attempt to teach problem solving within school curriculum. Problem solving strategies learned at lower levels tended to be ignored instead of being applied in their mathematical engagements at the higher levels, possibly because of the routine nature of the high-stake national examinations. The era of mathematical problem solving, its research and teaching and learning in schools ended, ambivalent on research findings and imprecise on recommendations for its teaching in schools. Based on the teaching and research experience of the organising team, we think that problem solving should still be the direction for teaching mathematics in schools. As such, this discussion group is proposed to identify the practices in teaching problem solving in school mathematics classrooms across different parts of the world, and how these practices are linked to the success.
1991
One of the five goals proposed in the National Council of Teachers of Mathematics' (NCTM) "Curriculum and Evaluation Standards for School Mathematics" is for students to become "mathematical problem solvers." To achieve this goal, the NCTM proposes fundamental changes in both the content of mathematics curricula and the pedagogy of the mathematics classroom that outline a broad role for problem solving. Textbooks and other published curricula are believed to play a significant role in the classroom instruction of mathematical problem solving. Described and compared are the conceptions of problem solving found in one commonly used elementary mathematics textbook ("Addison-Wesley Mathematics") and three distinctive elementary mathematics curricula ("Real Math", "Comprehensive School Mathematics Program", and "Math in Stride"). Although in each, problem solving was professed to be of central importance to the development of mathematical understanding and competence, how problem solving is defined and taught varied amongst the four published curricula. The different ways that problem solving is defined, formulated, and taught are explored, and the pedagogical and epistemological assumptions that underlie these differences are also discussed. The four curr.cula are compared on various perspectives of problem solving, the levels at which it was incorporated into the curriculum and how the authors of each curriculum viewed "mathematics as problem solving." (14 references) (MDH)
Topic Study Group No. 19: Problem Solving in Mathematics Education
2017
Mathematical problem solving has been an important research and practice domain in mathematics education worldwide. It's agenda focuses not only on analysing the extent to which cognitive, social, and affective factors influence and shape learners' development of problem solving proficiency, but also on the role played as a medium for teaching and learning mathematics and the development of both teachers' and learners' problem solving proficiencies. TSG 19 on Problem Solving in Mathematics Education was dedicated to the furthering and sharing of knowledge on this important topic. To this end, the mathematics education community was invited to submit contributions that address the aforementioned themes relevant and related to Problem Solving in Mathematics Education. We received 56 submissions from 30 different countries on a wide range of problem solving related topics. From these 56 submissions 15 papers were accepted to be presented as part of our main TSG program (15 min presentation, 5 min discussion) as well as 27 papers to be presented as an oral communication (10 min presentation, 5 min discussion). Within the main TSG program the following 15 papers were presented:
CEPS Journal, 2022
Problem solving and problem posing are leading mathematical activities that stimulate mathematical thinking. From the theoretical point of view, these activities are very complex, partly due to the various issues that describe/define problem solving and problem posing and their role in the process of teaching and learning mathematics. Problem solving and problem posing are interrelated activities; we could say that they are in an interdependent relationship: we solve the problems we pose, we pose the problems in a way that we can solve them. However, the two processes are not equally present in every situation. Research into problem solving focuses mainly on the following areas: the basic characteristics of a mathematical problem; the nature (conceptual, procedural) and role of representation (interplay between internal and external) of a mathematical problem; mental schemas for problem solving; heuristics as principles, methods and (cognitive) tools for solving problems; types of generalisations and reasoning (abductive, narrative, naïve, arithmetic, algebraic); problem solving as a challenging activity for mathematically gifted students; and the role of the teacher in guiding problem solving as a way of implementing student problem solving in the classroom. Regarding problem posing, there are also some critical questions: How can the existing definitions of problem posing be categorised? How is problem posing conceived by the research community in relation to other mathematical constructs? What are the possible ways of implementing problem posing in research and teaching settings? Regarding problem solving, problem posing is formulated/used in research findings for generating (formulating, finding, creating) new problems; reformulating existing problems; creating and/or reformulating problems; raising questions and viewing old questions from a new angle; and an act of modelling. Research has demonstrated and frequently confirmed that (mathematical) problem posing and solving possess great potential for learners, but the reality in terms of teaching practice, external examinations, teaching material, and mathematics curricula seems out of alignment with the research findings. In this focus issue, we have considered two aspects of problem posing and problem solving: conceptualisation and implementation in the mathematics classroom. This issue contains five articles that address the issues of problem posing and problem-solving. The authors come from different backgrounds (Greece, Croatia, Hungary, Germany), which means that diverse perspectives and research
Introduction to International Perspectives on Problem Solving Research in Mathematics Education
The Mathematics Enthusiast, 2013
Any field of research and innovation must be exposed to revisions, criticisms and to an intense scrutiny not only to discuss the state of the art but, hopefully, to identify prospective changes and new areas of study and exploration as well.Problem Solving has been such an area, with a prominent place in mathematics education and whose contributions continuously appear in conference proceedings, handbooks, journals, books and, more recently, in digital endeavors. Problem Solving involves an approach that fosters reflection and delving into mathematical ideas to explain individuals' cognitive behaviors within social media. Here, we argue that ideas do not live by themselves isolated from the semantic networks that sustain the life of cognition: meaning. These networks constitute a key ingredient for developing understanding and structural perspective of concepts through problems. In the long term, (and maybe not that long) these networks provide integration of knowledge that lear...