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This study examined the prediction of academic success of Junior secondary school mathematics students using their cognitive style and problem solving technique. A descriptive survey of correlation type was adopted for this study. A purposive sampling procedure was used to select five Public Junior secondary schools in Ijebu-Ode local government area, Ogun state. For the purpose of this study, an arm of intact class JSSII students were selected from each selected school through a simple random sampling procedure. Three valid and reliable instruments were used to collect data for this study as Sigel's cognitive style test (SICOST), Problem solving technique test (PSTT) and Mathematics achievement test (MAT). Their content validity values were 0.79; 0.74 and 0.84 respectively using Lawshe method. The test-retest reliability value was 0.82 of SICOST, the coefficient of reliability values of PSCT and MAT were 0.79 and 0.87 respectively using Kuder-Richardson (K-R 20)'s formula. The results of the Pearson correlation and Multiple regression test show that: no significant relationship exists between the students' cognitive style and problem solving technique; the two predictor variables jointly significantly predicted academic success in mathematics; the relative effect of problem solving technique in mathematics is greater than that of cognitive style. It is recommended that problem solving intervention strategies should be used in handling the mathematical problems of students to enhance their academic success in other to serve as essential ingredients for achieving a holistic education.

This study aimed to describe the profile of secondary school students with high mathematics ability in solving shape and space problem in PISA (Program for International Student Assessment). It is a descriptive research with a qualitative approach, in which the subjects in this study were students of class VIII SMP N 1 Banda Aceh. The results show that in solving the problem PISA on shape and space, high mathematics ability students were able to identify the problem by making the information known from PISA issues related to the shape and space content.

This study aimed to describe the profile of secondary school students with high mathematics ability in solving shape and space problem in PISA (Program for International Student Assessment). It is a descriptive research with a qualitative approach, in which the subjects in this study were students of class VIII SMP N 1 Banda Aceh. The results show that in solving the problem PISA on shape and space, high mathematics ability students were able to identify the problem by making the information known from PISA issues related to the shape and space content.

This study aimed to describe the profile of secondary school students with high mathematics ability in solving shape and space problem in PISA (Program for International Student Assessment). It is a descriptive research with a qualitative approach, in which the subjects in this study were students of class VIII SMP N 1 Banda Aceh. The results show that in solving the problem PISA on shape and space, high mathematics ability students were able to identify the problem by making the information known from PISA issues related to the shape and space content.

Problem solving strategies of eight pre-service secondary school mathematics teachers (PSSMTs) were examined in this study. A case study research design was employed and clinical interview technique was used to collect the data. Materials collected for analysis consisted of audiotapes and videotapes of clinical interviews, subjects' notes and drawings, and researchers' notes during the interview. Strategies used by PSSMTs to solve a problem called "the fencing problem" were identified. Findings of the study suggest that the subjects used combinations of different strategies to solve problems. The implications of the finding were also discussed.

Mathematics word-problems continue to be an insurmountable challenge for many middle school students. Educators have used pictorial and schematic illustrations within the classroom to help students visualize these problems. However, the data shows that pictorial representations can be more harmful than helpful in that they only display objects or persons while neglecting the spatial relationships between those components (Hegarty & Kozhevnikov, p. 686). Research supports schematic diagrams that highlight spatial relationships and focus on related information within the problem (Hegarty & Kozhevnikov, 1999; van Garderen & Montague, 2003). In addition to these strategies, educators have used heuristics (systematic scripted procedures to solve word problems) as a way to provide structure and routine to a variety of word problems. This review of the literature found varying results for the use of some heuristics being implemented in present-day classrooms. On the other hand, both visual-spatial diagrams and heuristics have demonstrated value in middle school special education classrooms. These findings support the further use and research of visual-spatial representations and problem-solving heuristics in order to solve mathematics word problems.

Mathematics word-problems continue to be an insurmountable challenge for many middle school students. Educators have used pictorial and schematic illustrations within the classroom to help students visualize these problems. However, the data shows that pictorial representations can be more harmful than helpful in that they only display objects or persons while neglecting the spatial relationships between those components (Hegarty & Kozhevnikov, p. 686). Research supports schematic diagrams that highlight spatial relationships and focus on related information within the problem (Hegarty & Kozhevnikov, 1999; van Garderen & Montague, 2003). In addition to these strategies, educators have used heuristics (systematic scripted procedures to solve word problems) as a way to provide structure and routine to a variety of word problems. This review of the literature found varying results for the use of some heuristics being implemented in present-day classrooms. On the other hand, both visual-spatial diagrams and heuristics have demonstrated value in middle school special education classrooms. These findings support the further use and research of visual-spatial representations and problem-solving heuristics in order to solve mathematics word problems.

Problem solving continues to be a major focus of K-12 mathematics education reform. This case study shows how a teacher's middle school mathematics instruction evolved from teaching problem solving as computation exercises to teaching how to select and implement combinations of problem solving strategies. The teacher's thinking about problem solving instruction also evolved to encompass different understandings about what a problem is, what problem solving means, and what teachers' and students' roles are in teaching and learning problem solving. The result of this evolution was that the teacher's instruction became more closely aligned with reform goals for problem solving. This finding suggests that reform efforts should incorporate strategies and support for teachers to revise and refine their own instruction through reflection and dialogue with colleagues as they try out approaches and activities in their classrooms for teaching problem solving. (Contains 1 table.)

The results of the International Assessment of Educational Progress released in February 1992 indicate that in mathematics and science the United States ranks near the bottom, while South Korea and Taiwan rank at the top. This paper compares the nature of mathematical problem-solving instruction in Korean elementary schools to that in American elementary schools. Questionnaires that attempt to determine teachers' use of instructional strategies to promote problem solving, teachers' perceptions of the usefulness of specific problem-solving strategies, teachers' confidence in using those strategies, and beliefs concerning specific recommendations for problem-solving instruction were given to 164 Korean teachers from 7 urban public elementary schools (grade levels 1-6) in Seoul and 195 American teachers of grade levels 1-6 from 10 elementary schools from school districts in Phoenix, Arizona. Korean and American teachers reported similar amounts of time spent each week on mathematics instruction and problem solving; however the Korean school year is 44 days longer than the American school year. Korean teachers perceived textbooks as being more useful for problem-solving instruction, used less student grouping as an instructional technique, and used manipulatives less frequently. (MKR)

An overview of the Mathematical Problem Solving Project, MPSP, is given. The goals, organization, and history of the project are described and the progress toward those goals is discussed. The outcomes of the project are stated, a brief diary of activities given, and a listing of technical reports made. (MP)

The article begins with a brief overview of the situation throughout the world regarding problem solving. The activities of the ProMath group are then described, as the purpose of this international research group is to improve mathematics teaching in school. One mathematics teaching method that seems to be functioning in school is the use of open problems (i.e., problem fields). Next we discuss the objectives of the Finnish curriculum that are connected with problem solving. Some examples and research results are taken from a Finnish-Chilean research project that monitors the development of problem-solving skills in third grade pupils. Finally, some ideas on "teacher change" are put forward. It is not possible to change teachers, but only to provide hints for possible change routes: the teachers themselves should work out the ideas and their implementation.

This review of research generates principles for the design of instructional programs that foster critical-thinking dispositions. The dispositional aspect of critical thinking may be considered part of attitudinal memory, readily activated if sufficiently strong. We describe evidence suggesting that ill-structured problem-solving can provide middle schoolers with motivating activities that strengthen critical-thinking dispositions, thus fostering sensitivity to occasions for thinking critically and the inclination for engaging in such practices. The Jasper Series and Decision Making are reviewed as cases of programs for middle level mathematics learning that afford opportunities for ill-structured problem-solving activities that incorporate five important attitude-strengthening elements. Fazio (1995) identified these elements as direct experience, sensory experience, emotional reaction, freely chosen behavior, and attitude rehearsal. We describe how the design of the two mathematics programs incorporates attitude-strengthening elements that can potentially foster critical-thinking dispositions. Based on this review, we present a set of design principles to promote those dispositions. (Contains 2 figures.)

The present study examined the potential relationship between 1st and 5th year secondary school pre-service mathematics teachers' skills in understanding, method, modelling, verification, and extension dimensions of problem solving and their learning style characteristics. The data consisted of the skills pre-service teachers demonstrated in the solution process of open-ended problems. For this purpose, a graded scoring rubric was developed specific to each problem. Regarding the relationships between problem solving dimensions and the characteristics of McCarthy's learning styles, it was assumed that type 1 learners' skills were more dominant in the understanding dimension, type 2 learners' skills in the method and modelling dimensions, type 3 learners' skills in the verification dimension, and type 4 learners' skills in the extension dimension. On the basis of this assumption, problem-solving skills and learning style characteristics were associated and interpreted. The results obtained suggested that 5th year pre-service teachers were better in representing the skills pertaining to type 1 and type 2 learning styles, while 1st year pre-service teachers were better in representing the skills pertaining to type 1 learning style only. On the other hand, it was observed that a great majority of the pre-service teachers had a low level of the skills pertaining to type 3 and type 4 learning styles.

In this paper, we discuss our experiences with an after-school program in which we engaged middle-school students with low socioeconomic status from an urban community in mathematical problem solving. We document that these students participated in many aspects of problem solving, including the posing of problems, constructing justifications, developing and implementing problem-solving heuristics and strategies, and understanding and evaluating the solutions of others. We then delineate what aspects of our environment encouraged the students to take part in these activities, particularly emphasising the proactive role of the teacher, the tasks the students completed, and the social norms of our after-school sessions. Finally, we discuss the relationship between our study and the literature on equity research in mathematics education. (Contains 1 table and 4 footnotes.)

In this paper, we discuss our experiences with an after-school program in which we engaged middle-school students with low socioeconomic status from an urban community in mathematical problem solving. We document that these students participated in many aspects of problem solving, including the posing of problems, constructing justifications, developing and implementing problem-solving heuristics and strategies, and understanding and evaluating the solutions of others. We then delineate what aspects of our environment encouraged the students to take part in these activities, particularly emphasising the proactive role of the teacher, the tasks the students completed, and the social norms of our after-school sessions. Finally, we discuss the relationship between our study and the literature on equity research in mathematics education. (Contains 1 table and 4 footnotes.)

In this paper, we discuss our experiences with an after-school program in which we engaged middle-school students with low socioeconomic status from an urban community in mathematical problem solving. We document that these students participated in many aspects of problem solving, including the posing of problems, constructing justifications, developing and implementing problem-solving heuristics and strategies, and understanding and evaluating the solutions of others. We then delineate what aspects of our environment encouraged the students to take part in these activities, particularly emphasising the proactive role of the teacher, the tasks the students completed, and the social norms of our after-school sessions. Finally, we discuss the relationship between our study and the literature on equity research in mathematics education. (Contains 1 table and 4 footnotes.)

Several studies suggest that most students are not in the same level of development (Slavin, 2008). From concrete operation level to formal operation level, students experience lateness in the transition phase. Consequently, students feel difficulty in solving mathematics problems. Method research is a qualitatively descriptive-explorative research aimed at comprehending the process of mathematics problem solving based on students' thinking level. Formal subject described in a structured manner so that there is no information that eliminated in the calculation process. While in transition subject, information which is constructed is only based on empirical knowledge. And on a concrete subject, thinking process can directly determine the solution of a problem. Students in formal thinking level are able to plan a problem solving by relating an information that is obtained to an information which is logically asked. Transitional thinking level are able to visualise the problems logically when the context of the problems are closely related to the experience they have. And concrete thinking level is only able to plan problem solving when the problem can be immediately and easily analysed.

There are many factors that affect student engagement in science, technology, engineering and mathematics (STEM). Underlying this are the views of the broader community--and parents in particular--about the relevance of STEM, and the approach to the teaching and learning of STEM from the early years and continuing throughout schooling. Connected to this is the way industry articulates the importance of STEM related-skills that extend beyond traditional STEM occupations. University admissions policies also have a strong influence on student choices in the senior secondary years. The purpose of the strategy is to build on a range of reforms and activities already underway. It aims to better coordinate and target this effort and sharpen the focus on the key areas where collaborative action will deliver improvements to STEM education. The national strategy is focused on action that lifts foundational skills in STEM learning areas, develops mathematical, scientific and technological literacy, and promotes the development of the 21st century skills of problem solving, critical analysis and creative thinking. It recognises the importance of a focus on STEM in the early years and maintaining this focus throughout schooling. This document outlines two goals (ensure all students finish school with strong foundational knowledge in STEM and related skills; and ensure that students are inspired to take on more challenging STEM subjects), five areas for national action, and guiding principles for schools to support STEM education. [Cover title varies: "National STEM School Education Strategy, 2016-2026."]

The concept of mathematical problem solving is an important mathematical process in mathematics curricula of education systems worldwide. These math curricula demand that learners are exposed to authentic problems that foster successful problem solving. To attain this very important goal, there must be mathematics teachers well versed in content and the pedagogy of problem solving. This study investigated problem solving process of in-service secondary school teachers in a non-routine problem context. Teachers? written responses were examined based on Polya?s problem solving theory to elucidate their disposition in relation to the problem context. Findings suggest that the in-service teachers exhibit (1) greater lack of understanding of the non-routine problem, (2) insufficient capacity to select appropriate heuristic strategies, and (3) total failure to reach the final "look back" stage. This study recommends in-depth examination of the role of keywords, prior knowledge and experience in mathematical problems, and the importance of written testimonies in metacognition.

Improving problem solving abilities among students remain to be a challenge among teachers and students. This study aimed to identify problem solving ability of first year students as affected by cognitive development levels and teaching strategies of first year high school students in Mathematics I. The study utilized descriptive and experimental methods. A total of 150 students from three classes in a public secondary school in Central Luzon, Philippines were included. Tools were validated questionnaires to measure problem solving abilities and cognitive development levels. Data were analyzed using frequency, percentage, Mean, Standard Deviation, T-Test, ANOVA, and Regression Analysis. Results showed that the cognitive level of development of the students are satisfactory across all domains (X=2.81). Discovery, Exposition, and Traditional Methods of Teaching were found to significantly improve the problem solving ability of the students with a p-value of 0.000 in each group. All groups have no significant difference in performance which may imply that no teaching method is better than the other. Lastly, cognitive domains of the students in knowledge, comprehension, application and evaluation were found to be significant determinants of students' problem solving ability. The study results can be a springboard to improve problem solving abilities of high school students. Cognitive development could be considered as a basis for grouping high school students in all curriculum levels and can be evaluated by future researchers for effectiveness.

The performance of a group of grade 9 mathematics students trained to use a self-explanation procedure during study was compared with that of students who used their typical study procedures. The processing activities used by the students during the study session and those used in a subsequent problem-solving test were observed. The focus of analysis was on the knowledge access, knowledge generation, management, and elaboration activities used by students. The self-explanation group showed more frequent use of each type of activity and also obtained higher scores on the problem-solving test. The difference in posttest performance of the groups was greatest on a set of far transfer items. Of particular note was the carryover effect of self-explanation training on students' processing in a subsequent problem-solving session. The relationships among the processing activities, students' beliefs, prior knowledge, and posttest performance were examined using a partial least squares path analysis procedure. Use of the self-explanation method had an indirect effect on performance, this effect being mediated by associated knowledge access and knowledge generation activity. There was no direct effect of method on performance. The strongest predictor of performance was the level of knowledge generation activity. The students' prior knowledge measure had weak direct and indirect effects on performance. Appendixes include: code labels and descriptions of three major categories of events: an illustration of direct and indirect paths in written solutions of two students; and descriptions of manifest and latent variables used in path analysis. (Contains 31 references, 4 tables, and 2 figures.) (Author)

The performance of a group of grade 9 mathematics students trained to use a self-explanation procedure during study was compared with that of students who used their typical study procedures. The processing activities used by the students during the study session and those used in a subsequent problem-solving test were observed. The focus of analysis was on the knowledge access, knowledge generation, management, and elaboration activities used by students. The self-explanation group showed more frequent use of each type of activity and also obtained higher scores on the problem-solving test. The difference in posttest performance of the groups was greatest on a set of far transfer items. Of particular note was the carryover effect of self-explanation training on students' processing in a subsequent problem-solving session. The relationships among the processing activities, students' beliefs, prior knowledge, and posttest performance were examined using a partial least squares path analysis procedure. Use of the self-explanation method had an indirect effect on performance, this effect being mediated by associated knowledge access and knowledge generation activity. There was no direct effect of method on performance. The strongest predictor of performance was the level of knowledge generation activity. The students' prior knowledge measure had weak direct and indirect effects on performance. Appendixes include: code labels and descriptions of three major categories of events: an illustration of direct and indirect paths in written solutions of two students; and descriptions of manifest and latent variables used in path analysis. (Contains 31 references, 4 tables, and 2 figures.) (Author)

Purpose: This study aims to identify the problem solving abilities possessed by junior high school students. The type of research used is quantitative which uses a research design survey. The sample of this study is 98 students taken based on purposive sampling techniques. This study uses descriptive statistics to analyze the data generated. From the results of the analysis that has been done, it was found that there is a problem solving indicator by students in mathematics which is a indicated by the indicators of planning a solution which has a good category of a 56.1% (55 of 98) students, the indicator of problem solving has a good category of a 56.1% (55 out of 98) students, indicators of a problem solving planning had a good category of a 54.1% (53 of 98) students, and an indicator of understanding a problem had a good category of a 60.2% (59 of 98) students.

Mathematical problem solving was an crucial skill to be mastered by primary school student so that will help student to unravel their problems encountered in everyday life. By using the realistic mathematics approach, stundents learn mathematical concept based on reality or scope around students. This study aimed to develop an eligible learning materials and test the effectiveness of learning materials based on realistic mathematics education to enhance the problem solving skill of primary school students. This research and development study was conducted in Sawangan Subdistrict, Magelang Regency, Central Java, Indonesia. The testing subjects consisted of 12 students in the the preliminary field, there were 42 students in the main field, and 90 students in the operational field that divided into experiment dan control class. The data were collected by interviews, observation, and tests. The analyzing N-gain score and t-test with a significant level of 0.05 done to find out th effectiveness of the teaching materials. The developed of realistic mathematics eduation learning materials is feasible and effective in improving problem solving skill with significance value of 0.000 (p≤0.05). It can enhance the problem solving skills of 4 th grade elementary school.

Mathematical problem solving was an crucial skill to be mastered by primary school student so that will help student to unravel their problems encountered in everyday life. By using the realistic mathematics approach, stundents learn mathematical concept based on reality or scope around students. This study aimed to develop an eligible learning materials and test the effectiveness of learning materials based on realistic mathematics education to enhance the problem solving skill of primary school students. This research and development study was conducted in Sawangan Subdistrict, Magelang Regency, Central Java, Indonesia. The testing subjects consisted of 12 students in the the preliminary field, there were 42 students in the main field, and 90 students in the operational field that divided into experiment dan control class. The data were collected by interviews, observation, and tests. The analyzing N-gain score and t-test with a significant level of 0.05 done to find out th effectiveness of the teaching materials. The developed of realistic mathematics eduation learning materials is feasible and effective in improving problem solving skill with significance value of 0.000 (p≤0.05). It can enhance the problem solving skills of 4 th grade elementary school.