Learning Of Mathematical Problem Solving Research Articles

A model for scaffolding mathematical problem-solving: From theory to practice

Devising a plan is an important phase in the teaching and learning of mathematical problem-solving in a mathematics classroom. In this paper, we propose devise a plan (DP) model for scaffolding students in devising a plan to engage them in mathematical problem-solving for classroom instruction and beyond. Although mathematics educators have proposed problem-solving scaffold, mainly building on Polya’s (1945) and Schoenfeld’s (1985) problem-solving models, for authentic problem-solving in the classroom, the phase on devising a plan was generally brief. We expand on the scaffolding of the intermediate stages of devising the plan for teachers to teach problem-solving, with a more ambitious goal of enabling students to engage in independent problem-solving beyond the classrooms. Features that are used in the planning stage of problem-solving are identified through a systematic literature review. Our proposed DP model includes the use of both metacognitive strategies and problem-solving heuristics. The application of our proposed model was exemplified by the solution of three non-routine problem on proportionality.

Peer tutoring models in collaborative learning of mathematical problem solving and their effect on group achievement

Peer tutoring models in collaborative learning of mathematical problem solving and their effect on group achievement

Mother Tongue versus English as a Second Language in Mathematical Word Problems: Implications to Language Policy Development in the Philippines

This study investigated the performance of 150 Tagalog and 131 Sinugbuanong Bisaya grade three pupils with regard to solving mathematical word problems written in their mother-tongue (L1) and in English as their second language (L2). The respondents were subjected to a validated teacher-made parallel tests based on the competencies stipulated in the first and second quarter mathematics curriculum guide of the Philippines. Results of which were compared and analyzed using two-tailed t-test. Findings show that the Tagalog pupils performed better in their mother-tongue over English as their second language. On the other hand, Sinugbuanong Bisaya pupils performed better in English as their second language over their mother-tongue. While results appear contradictory, contextual discussions offer valuable insights into the situation, allowing avenues for more exploration and investigations. As implication to language policy development, this study offers the use of translanguaging in content area instruction and assessment, specifically in the teaching and learning of mathematical problem solving

An Exploration of the Cognitive, Motivational, Emotional and Regulatory Behaviours of Elementary-School Novice and Expert Problem Solvers

Over the past two decades, the perennial low success rates of elementary students in mathematical problem solving and the difficulties experienced by teachers in meeting the various needs of their students with this type of task have become quite a hot topic. While there is a general consensus among education scholars about the crucial role played by cognitive, emotional and motivational self-regulatory processes in mathematical problem-solving learning and performance, so far, no study has looked simultaneously and finely at these three dimensions in specific profiles of students. That issue is the focus of this contribution. To gain fine-grained and complete understandings of the behaviours of “above average” and “below average” problem solvers, both research from educational psychology on emotion and motivation and the work done in mathematics education on the cognitive and metacognitive characteristics of these two learner profiles were called upon. This qualitative study conducted among 22 upper elementary students is based on a cross-analysis of their verbal and written output. The data revealed that inappropriate reading of the problem by “below average” learners masks a difficulty with taking all the relational calculations involved in the problem into account and a strong conception of the uselessness of the problem’s context. These behaviours do not improve during the solution process due to the absence of control and regulation strategies. Findings regarding “above-average” achievers make it possible to identify the most important cognitive, emotional, motivational and regulatory processes that go along with problem-solving expertise. Implications in terms of educational practices are also discussed.

Examining the Effects of Using Polya’s Problem- solving Model on Mathematical Academic Achievement and Analyzing Ability of the Fourth Grade Students

The study sought to investigate the effects of Polya’s Problem-Solving Model (PPSM) on learning achievement and analyzing ability in mathematics of fourth grade students. The sample of 32 students out of three sections was selected purposively as the subject of the study. Pretest and posttest one-group experimental design, achievement test and time series record were used to collect data. The collected data were analyzed using descriptive statistic and t-test. The t-test analysis revealed a statistical significant difference between the mean scores of in favor of posttest (M=13.78; SD=3.02) than the pretest (M=6.66; SD=2.44) at p=.00, indicating the improvement in the mathematical academic achievement using PPSM. Moreover, the time series record also showed that there was significant progression in the performances of the students after the inclusion of the PPSM. Thus, this study recommends the implementation of PPSM as an alternative method of instruction in teaching and learning of mathematical problem solving.

Model Pembelajaran Berbasis Masalah Untuk Meningkatkan Kemampuan Pemecahan Masalah Matematis dan Kemandirian Belajar Siswa

The view towards the difficult math learning comes after students get results that always lower than other subjects due to the lack of students ability in mathematics, interest, motivation, basic capabilities, and cognitive ability, educators and instructional model in teaching. Math learning objectives for students is so that students have the ability or skills in problem solving to hone a careful, logical reasoning, analytical, critical, ang creative. Implementation ofproblem based learning can enhance problem-solving capabilities and self-reliance of students in learningmathematics are expected to reduce the problem above. Learning,problem based learning,through the stages of scientific methods can improve the ability of mathematical learning students independence, indicated with a mean score of normal students gain higher than students who use direct learning instruction (conventional). Test result of statistical test showed the value of the sig (2-tailed) 0,006 < 0,05, which mean that the ability of mathematical problem solving learning and Problem Based learning is bettter than Direct Instruction Learning. Zhitung= 6,601 and the value of Asymp. Sig (2-tailed) = 0,00 < α = 0,05, which means that there is a difference that isof significance fo the classroom experiments after receiving treatment learning Problem Based Learning in the independenceof his studies for the better.

Chinese and Singaporean sixth-grade students’ strategies for solving problems about speed

This study examined 361 Chinese and 345 Singaporean sixth-grade students’ performance and problem-solving strategies for solving 14 problems about speed. By focusing on students from two distinct high-performing countries in East Asia, we provide a useful perspective on the differences that exist in the preparation and problem-solving strategies of these groups of students. The strategy analysis indicates that the Chinese sample used algebraic strategies more frequently and more successfully than the Singaporean sample, although the Chinese sample used a limited variety of strategies. The Singaporean sample’s use of model-drawing produced a performance advantage on one problem by converting multiplication/division of fractions into multiplication/division of whole numbers. Several suggestions regarding teaching and learning of mathematical problem solving, algebra, and problems about speed and its related concepts of ratio and proportion are made.

A Modeling Perspective on the Teaching and Learning of Mathematical Problem Solving

This study analyzed the processes used by students when engaged in modeling activities and examined how students' abilities to solve modeling problems changed over time. Two student populations, one experimental and one control group, participated in the study. To examine students' modeling processes, the experimental group participated in an intervention program consisting of a sequence of six modeling activities. To examine students' modeling abilities, the experimental and control groups completed a modeling abilities test on three occasions. Results showed that students' models improved as they worked through the sequence of problem activities and also revealed a number of factors, such as students' grade, experiences with modeling activities, and modeling abilities that influenced their modeling processes. The study proposes a three-dimensional theoretical model for examining students' modeling behavior, with ubsequent implications for the teaching and learning of mathematical problem solving.