reformat paper

F_S/M_StrandNo_Initial_PaperIDinCMT

Current Issues and Trends in Mathematics Problem Solving – Meta Analysis

Liyana Nazurah Jaffar1, Norhayati Samuri2, Saidatul Akmal Awang Ali3, Syafi ‘Atikah Yusof4

Faculty of EducationUniversitiTeknologi Malaysia, Johor

AbstractProblem solving plays major role in mathematics education. It may differ from the past ten years to the recent. Several researchers and educators have focused on various perspectives. The purpose of this study is to analyze current trends and issues on problem solving in mathematics based on the research studies chosen. Meta-analysis was administered as a method to find the results. The results revealed similarity on the focused of the research regarding the focus area,methods used and level of the subjects. Among the aspects that worth being observed from the 30 papers that was chosen are technology, behaviour and words problem in problem solving.

Keywords: Problem solving in mathematics education, current trends and issues

IntroductionNowadays, problem solving becomes one of the major parts in our educational system. Every subject starts to integrate problem solving into the main content of knowledge because it gives lots of benefit to the students. According to Greiff et al. (2013), problem solving can be define as a process that had been taken when we want to get the desired goal from given situation. Problem solving is really relates to the thinking process because Carson (2007), said problem solving is only one type of thinking skills that we use to think in any situation. In the general statement, problem solving can be classified as a method that we use to find the best solution when we had any hesitation or problem.

Concept of problem solving is wider and multidimensional because its definition can change according to our own perspective. There are three components in the problem solving that always be highlighted by researcher which are problem solving as a process, instructional goal and instructional approach (Xenofontos, 2010; Hino, 2007). These three perspectives have their own reasons to belief problem solving is a main part that need to be master by students. Most of the researchers agree problem solving is a big issue that we must give an attention in educational system. Although the problem solving is really close to mathematics subject, it also had been used in another direction like engineering, financial, business, and science.

Programme for International Student Assessment (PISA) is one of the international assessments that emphasize problem solving. In PISA 2003, domain-specific and analytical problem solving had been included and for PISA 2012 it more focus on interactive problem solving (Greiff et al., 2013). Besides, the upcoming PISA on 2015 will be emphasizing about collaborative problem solving. It shows problem solving is not about working individually but also measures how we interact and communication with the others on solve any problems


that unfamiliar with us. Cai and Lester (2010), also said the learning environment of teaching problem solving must be on the natural setting and give freedom for students to present various solutions to their groups or class and learning through social interactions, meaning negotiation, and reaching shared understanding.

Greiff et al. (2013), said all life is problem solving which it is mean that problem solving is occur everywhere in our life. The hidden meaning that we can extract from this phrase actually problem solving has lots of advantages and importance in our daily life. One of the major goals emphasize problem solving in educational system is to encourage our students to be good problem solver. Problem solving also teach students to think out of box and always prepared to find the best solution although in unfamiliar situation. It shows the problem solving is really importance, but we also need to identify issues and challenges in understand and apply problem solving method in our life.

Mathematics known as a subject that related with problem solving. Although the problem solving is one of the important component in mathematics education, many students and teachers still do not know clearly about problem solving. So, lots of researchers take this opportunity to make a research or investigation about influence of mathematics problem solving into mathematics education. Major perspectives that always had been focused in mathematics problem solving are the research trends (Hino, 2007; Xenofontos, 2010), students and teachers’ beliefs, competences and practice (Pearce, 2013; Kuzle, 2013; Xenofontos, 2010; Hino, 2007), curricular importance and assessment. Through all of these researches, hopefully students and teachers can take the benefits and try to change their perception about problem solving in mathematics.

As we mentioned before, problem solving is really familiar in mathematics and lots of research had been done about it. However, the curriculum always change according to our modernization and needs in our daily life. As a general, most of the subtopics that had been highlighted before this is more focus on framework and models problem solving, strategies in problem solving, pedagogy in problem solving, assessment in problem solving, creative problem solving, collaborative problem solving, cooperative problem solving, problem based learning, visualization in problem solving and ICT in problem solving. However, we still did not know either all of these focus or subtopics are current trends and issues or not in mathematics problem solving. Hence, through this meta-analysis we will discuss and find the current trends and issues about mathematics problem solving in educational system.

Background of studyAccording to Schoenfeld (1992), problem solving in mathematics education is the process wherein students encounter a problem that is a question that they have no immediately clear resolution, nor an algorithm that they can directly apply to get an answer. Polya (1981), stated that problem solving is a process that starts from the minute students is faced with a problem until the end when the problem was solved. Problem solving identified as important skills in life that involves various processes including analysing, interpreting, reasoning, predicting, evaluating, and described (Anderson, 2009). Kolovou et al. (2009), interpret problem solving by referring to the higher cognitive abilities which direct solution is not necessary and mostly it require analysis and modelling of problem situations.

Problem solving in mathematics educationProblem solving is an important component of mathematics education because it is a vehicle for teaching and reinforcing mathematical knowledge and helping to meet everyday


challenges also a skill which can enhance logical reasoning (Taplin, 2006). National Council of Teachers of Mathematics (NCTM) has identified problem solving as one of the five basic standard mathematical processes. According to the NCTM, with problem solving in mathematics, students will acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations which can be exploited by them outside of mathematics classroom. In everyday life and in the workplace, good problem solver can lead to great advantage (NCTM, 2000).

In the context of problem solving in mathematics education, there are two categories which are routine and non-routine problem. Solving routine problem emphasize the use of set of known or determined (algorithms) procedures to solve problem while solving non routine problem emphasizing the use of heuristics and require little to no algorithm (Gilfeather & Scop, 1999). According to Yazgan (2013), routine problem can be solved by using a common method for students to replicate the methods learned in the past in the form of step-by-step, while non-routine problems are problems that cannot be predicted and no specified approach. Therefore, non-routine problems are considered more complicated and difficult than routine problems.

Current trends and issuesIn literature of mathematics education, numerous studies have been conducted in exploring the problem solving in mathematics curriculum until today. Most of the research is the study of attitudes or beliefs of students on solving problems (De Corte & Greer, 2000; Nicolaidou & Philippou, 2003; Sangcap, 2010), student learning styles in problem solving (Sirin, 2005; Carmo, 2006), skills and concepts in problem solving (Giganti, 2007; Bayat, 2010; Perveen et al., 2010), the process of problem solving (Polya, 1981; Schoenfeld, 1992; Tarzimah & Thamby Subahan, 2010) and the relationship between metacognition and problem solving (Muir & Beswick, 2005; Desoete, 2006; Eric, 2011). In addition, there are also some studies to find a more specific aspect in solving mathematical problems such as the problem posing (Kar et al.; 2010, Roslinda, 2013) and strategies used in problem solving (Anderson , 2009; Sulak, 2010).

Various models associated with mathematical problem solving process have been proposed in several previous studies. According to Schoenfeld (1992), a successful problem solver must combine various heuristic approaches when solving problems. The most heuristic plan supported by researchers is Polya model that composed of four levels which are understand the problem, devise a plan, carry out the plan and looking back (Muir & Beswick, 2005). By contrast, Garofalo and Lester (1985) have proposed metacognitive model for problem solving which consists of orientation, organization, implementation and verification as Polya model does not include metacognitive aspects.

Other than model, several studies also examined the important components in problem solving. There are also studies that explored the attitudes of students toward solving mathematical problems which, according to Fan et al. (2005), attitude is one of five core components, besides the concepts, skills, and metacognition process which will be emphasized in the students for them to be a good problem solver. The findings from the quantitative analysis and open response in the study of Eric (2011) showed that students


grade six were generally positive in problem solving, and found that students enjoyed the experience of solving mathematical problems because these activities create interest, involve cooperation, and provide a sense of challenge for themselves.

One of the most important goals in the learning of mathematics is to enhance the knowledge of mathematics including mathematical concepts and skills in problem solving (Bayat, 2010). Giganti (2007) states that if students know their mathematics skills and concepts well, but do not know how to put both together in a certain situation, then the student cannot do mathematics well. There are few studies that have been conducted to assess the importance of skills and mathematical concepts in problem solving. Among them is the study of Johari and Chung (2010) that related to the ability of form five students in solving problem and they found that the student ability of choice school is better than students in regular school as well as the ability of science students is better than art students. In experiments Perveen et al. (2010) found that students are not clear with the basic concepts of mathematics in which student’s lack of the ability and skills that can lead them into trouble in the next class.

Metacognitive aspect in solving mathematical problems also have a great interest for educators to conduct a relevant studies because they realize that the mathematical analysis of cognitive performance only is not enough to study the problem solving (Yin, 2005). Sek (2014) was aimed at identifying metacognitive behavior in problem solving among students grade five. Results showed that students use metacognitive behavior skills in solving mathematical problems at minimum level only, and found that the majority of students have trouble understanding the concept and understanding of the question. In the report of Zatur Junaida (2004), the use of metacognitive training can enhance students' ability to solve mathematical problems in elementary schools where the results showed that students in the experimental group achieved higher scores than students in the control group.

In literature, there are several studies where researchers focus on problem solving strategy (Muir & Beswick, 2005; Anderson, 2009). In order to apply problem solving steps, the strategies should be used during problem solving. According to Mabilangan (2012), problem solving strategy consists of the use of appropriate basic thinking skills and higher order thinking skills to solve the problem. Altun et al. (2004) found that the most prominent strategies used by students to solve mathematics problem is heuristic strategy consists of look for a pattern, make a systematic list, work backward, guess and check, draw a diagram, simplify the problem, make a table, eliminate the possibilities, reasoning and estimation. Research also found other strategies which is cognitive and metacognitive strategies. According to Montague and Applegate (2003), cognitive strategies and processes (i.e., specific problem-solving strategies) are read, paraphrase, visualize, hypothesize, estimate, compute, and check while metacognitive strategies and processes that develop awareness and regulation of the cognitive strategies include self-instruction, self-questioning, and self-monitoring.

Other than strategy, pedagogy is another one focus of mathematics education research and of professional learning. Research of Carpenter et al. (1988) shows that teacher is reflective and thoughtful individual while teaching is complex, cognitively demanding process involving problem solving and decision making. Teacher help students become


problem solvers if they choose suitable problems, set up their use, and evaluate student understanding and use of strategies (Othman, 2003). Interaction between teacher and student can be seen in the role of teacher in guiding student mathematical development by involving them in problems, facilitating the sharing of their solutions, observing and listening carefully to their ideas and explanations, and making wise and explicit mathematical ideas presented in the solutions (Suurtamm & Vézina, 2010).

From the point view of evaluation or assessment in mathematics problem solving, this can be seen in the TIMSS and PISA, where both are an international assessment studies to assessed worldwide students achievement especially in mathematics where problem solving is one of the key competences assessed in this assessment (Dossey et al., 2006). According to Szetala and Nicol (1992), effective assessment of mathematics problem solving require more than a look at the students answers, in other words, teacher need to look and analyse their processes and get students to communicate their thinking. They also stated that the difficulty of assessing complex processes required to solve problems is exacerbated by the failure of students to communicate clearly what they are doing or what they are thinking. Rather than scoring the solutions only, teachers analyse the response to the problems on the four basis categories which are answers, answer statements, strategy selection, and strategy implementation.

Another research done in mathematics problem solving is about the use of technology to solve mathematical problems. According to Mora and Rodríguez (2013), the use of technological tools offers new opportunities for students to discuss mathematical tasks from perspectives where visual and empirical approaches are widely enhanced and students can gain a deeper understanding of mathematical concepts. Li et al. (2009) state that by using computer software especially for Algebra topic like Mathematica, Maple and Derive, student can spend less time on doing algebraic manipulation, routine problem solving and sketching useless graphs and spend more time on understanding concepts, and applying them to solve more realistic and challenging problems. Meanwhile, Kuzle (2011) who conduct a research in dynamic geometry environment said that the use of dynamic geometry technology helps students engaging in meaningful mathematical activities and promotes deeper understanding of concepts.

To conclude this review on problem solving in mathematics education in sum, we can say that there are many issues that affect problem solving in mathematics teaching and learning process. However, these issues are still not known whether it was the current issues and trends or not in mathematics problem solving. Hence, through this meta-analysis, we attempted to find the current issues and trends in mathematic problem solving.

Method and procedureIn this meta-analysis, we only focus to describe the research studies in mathematics

problem solving which have been conducted from 2005 until present. There were 60 papers gathered at first, however, we only choose 30 papers to study deeply since another 30 papers did not fulfil our focus in conduct this meta-analysis. All of the papers that had been selected actually have their own focus on aspect of current trend and issues in mathematics problem solving which are technology in mathematics problem solving, behaviour of the samples


either they are teacher or students and lastly about word problem in mathematics problem solving that tells about the difficulties and strategy that had been use to implement problem solving in mathematics. Those papers were searched in commonly used electronic databases including Sage, Taylor and Francis, Jstor, ScienceDirect, SpringerLink, Scopus and Google Scholar via the following keywords like problem solving in mathematics, current trends and issues in mathematics problem solving, issues in problem solving and trends of problem solving in mathematics.

Results and discussionIn the synthesis and analysis, all the papers studies are summarized from the

international journal that had been selected. Most studies that have been conducted around 2005 to 2014 were qualitative research methods. From 60 papers that had been analysed, 28 papers from this journal were conducted in qualitative research which contains for interviewing, observations, document analysis while 21 papers were conducted in quantitative research that contains questionnaire, one group experiment, two groups experiment and ex-post facto. However, there also have papers that conducted in mixed method which are 11 papers.

According to the analysis all of papers, there are numerous studies on current issues and trends in mathematics problem solving which has been documented in a special journal published for mathematics education. There are nine issues that issuable from all the analysis which are patterns (1.7%), algebra and algebraic thinking (5%), theories of learning (10%), theories of strategies (10%), teacher education and professional development (11.7%), about affect, emotion, belief, ethics and attitudes (11.7%), technology (13.3%), behaviour (15%) and word problem (21.7%).

Only one paper discussed about patterns, three papers about algebra and algebraic thinking consist of pre algebraic problem solving strategies (Osta & Labban, 2007), assessing algebraic solving ability (Lim, 2006) and developing algebraic thinking (George & Will, 2010). Besides, six papers about theories of learning that contain papers of using manipulative (Catherine, 2006), dual processing theories of thinking (Ron, 2011), problem solving theory (Alan, 2013), inquiry-based teaching (Miller et al., 2014), building mathematical fluency (Hinton et al., 2014) and problem-based learning (Arzu & Yasemin, 2014). On the other hand, theories of strategies discussed papers of cognitive process (Yeo & Yeap, 2010), alternative solutions (Shin, 2011), the action map (Murad, 2008), conditional probability (Pedro, 2009), students’ problem solving strategies (Pimpaka et al., 2014), and effect of problem solving strategies (Sera, 2010).

Seven papers each tell issue about teacher education and professional development and affect, emotion, belief, ethics, and attitudes. Teacher education and development are consist of quadrilaterals as an ongoing task (Kerri et al., 2010), mathematical and didactical enrichment (Manon, 2011), developing problem solving experiences (Francois, 2013), problem solving instruction (Frank, 2013), beliefs about mathematical problem solving of the mathematics, science and elementary school pre-service teachers (Memnun et al., 2012), mathematical thinking in problem solving (Caneida et al., 2013) and transforming pedagogical practice (Suurtamm & Vezina, 2010). Affect, emotion, belief, ethics, and attitudes discussed papers of mathematical self-efficacy (Arizpe et al., 2009), problem solving in the primary school (Richard et al., 2013), problem solving and its element proof (Joanna & Martin, 2013), proof and problem solving at university level (Annie & John, 2013), affect in mathematics problem solving (Lorenzo et al., 2013), recognizing the ethical


dimension of problem solving (Elizabeth, 2008) and attitudes of elementary school students towards solving mathematics problem (Cigderm et al., 2014).

Technology issue consist of eight papers which are technological features while solving a mathematics problem (Lee et al., 2006), effect of web-based professional development (Alattin & Ahmed, 2012), primary school students’ strategies in early algebra problem solving supported by an online game (Marja et al., 2013), the use of video analysis and the knowledge quartet in mathematics teacher education programmes (Miriam, 2013), problem solving and problem posing in a dynamic geometry environment (Christou et al., 2005), interactive visualisation and affect in mathematical problem solving (Ines, 2013), solving mathematical problems within technological environment (Mora & Rodriguez, 2013) and the use of computational technology in problem solving (Trigo & Machin, 2013).

Nine papers come out with behaviour issues which are the role of teachers’ experience in solving the problem (Roza & Sally, 2005), an exploration of students’ problem solving behaviour (Muir et al., 2008), investigation of pre service teachers’ use of guess and check (Mary et al., 2012), effects of contemporary mathematics instruction for low performers on problem solving behaviour (Rudolf et al., 2007), approach to mathematical problem solving (Maria & Antoni, 2009), mathematical enculturation from the students’ perspective (Jacob & Ruurd, 2008), relationship of some psychological variables in predicting problem solving ability (Akinsola, 2008), conditions for promoting reasoning in problem solving (John & Carolyn, 2005), and patterns of meta cognitive behaviour during mathematics problem solving (Ana, 2013).

Thirteen papers from the whole analyse was studied about word problem. From the analysis, we found that issues about word problem were studied from both perspective which are students and teachers. All the papers consist of studied about role of visual representation type spatial ability and reading comprehension in word problem solving (Anton et al., 2014), effect of schema based instruction (Yan, 2008), visual representation in mathematical word problem solving (Azizah et al., 2010), problem representation and mathematical problem solving (Jennifer, 2012), comparison of two mathematics problem solving strategies (Yan et al., 2011), curriculum based measurement and standards based mathematics (Asha et al., 2014), mathematical reasoning in service courses (Kris & Allen, 2010), cooperative learning, mathematical problem solving and Latinos (Carlan et al., 2005), strategies for problem solving about speed (Chunlian et al., 2014), learning to solve addition and subtraction word problems in English (Debbie & Joanne, 2013), examining personalisation and achievement in mathematics word problems (Adeneye, 2014), effects of teaching precurrent behaviours on children’s solution of multiplication and division word problems (Heather et al., 2009) and student difficulties solving mathematical word problems (Daniel et al., 2013).

All the papers that had been analysed consist of lots of issues and different perspective. Issues that had mentioned in all papers was analysed to identify either there are current trend and issues or not in mathematics education field. From the discussion and analysis, we had found that some of issues are really current trend and issues in problem solving mathematics. Based on all the issues, the most three numbers of issues are technology, behaviour and word problem. This issues are still be the current trends and issues based on the years the paper was published.

Besides the issues, objects and phenomena of study also had been realized from this meta-analysis study. We had analysed all level education from elementary student that includes primary and secondary school to undergraduate university student and teachers from pre-service teacher to senior teacher was involved in the study that relate to problem solving in mathematics. In table 1, most of papers use primary school students as their subject for example students from 2nd grades until 6th grades. Secondary school students 6 papers and just


one paper using undergraduate students as their subject. The object of teachers just include of two part which are pre-service teacher, 4 papers and 5 papers using school teacher as their object and it is not matter of primary school teacher or secondary school teacher. Various issues have been studied by researchers including problem solving of word problems (by Carlan et al.. 2005; Awofala, 2014; Pearce et al., 2013), problem solving of topic or sub topic in mathematics (Lim et al., 2006; Iman et al., 2007; Miller et al., 2014) and technology in problem solving (Christou et al., 2005; Chacón, 2013; Mora & Rodríguez, 2013; Trigo et al., 2013). Table 1 consist 30 papers from the three most numbers of papers which are study about technology, behaviour and word problem issues.

Table 1 Number of research papers about technology, behaviour and word problems

As a result, all the three focus issues mentioned above can be specialised in numerous ways to particular topics, such as algebra, geometry, calculus, statistic, and so forth, as well as to specific educational levels and different types of research. Although the field of mathematics education has certainly moved, the issues posed today are still of the same kinds as the ones considered a decade ago.

ConclusionThe results of this meta-analysis show that word problem in mathematical problem solving which is one of the main issues and trends that had been focused from the past ten years. The difficulties faced by the students in solving word problem solving make the researcher focused more on the different strategies and skills. Besides, the issues also focused on behaviour towards mathematics problem solving. Mostly, the behaviours focused are on both parties which are the teacher and the students. Teachers’ experience in solving mathematical problem and students’ perspective also consisted. The changes and improvements by integrating technology into the education system make the researcher focused more into the usage of technology in mathematics problem solving. Therefore, technology become the issue occurred in the paper that has been analysed. It can be a continuous trend based on the needs of the educational system. Furthermore, there are also some issues identified in this analysis like patterns, algebra and algebraic thinking, theories of learning and strategies, teacher education and professional development and affect, emotion, belief, ethics and attitudes. The subjects for the research come from the teacher and the students. The students used at most as the subject matter because based on the finding, the studies directly focus on students’ participation, developing students’ experiences and the use of various techniques.

Level Number of paper(s)

TeacherPre-service teacher 4

School teacher 5

Student

Undergraduate student 1

Primary school student 12

Secondary school student 6

Both (teacher and student) 2


In future, there will be repetition on the issues occurred and deep focused. The situation maybe change if there are potential on new issues identified by educationalist. Moreover, since the exposedness given to the students is wide in range, there will be extra difficulties to the teacher to come out with new issues. That is why the same issues discussed in a decade.

References

Arizpe,O. Dewyer. J. and Stevens, T. (2009). Mathematical Self-Efficacy of Middle School Students Solving the Rubik Cube. International Journal for Mathematics Teaching and Learning. 1-11.

Awofala, A. O. A. (2014). Examining Personalisation of Instruction, Attitudes toward and Achievement in Mathematics Word Problems among Nigerian Senior Secondary School Students. International Journal of Education in Mathematics, Science and Technology, 2(4), 273-288.

Bayat, S., and Tarmizi, R.A. (2010). Assessing Cognitive and Metacognitive Strategies during Algebra Problem Solving Among University Students. Procedia Social and Behavioral Sciences, 8, 403–410.

Cai, J., and Lester, F. (2010). Why is Teaching With Problem Solving Important to Student Learning. National Council of Teachers of Mathematics.

Carlan, V. G., Rubin, R. and Morgan, B. M. (2005). Cooperative Learning, Mathematical Problem Solving, and Latinos. International Journal for Mathematics Teaching and Learning.

Carmo, L. and Gomes, A. (2006). Learning Styles And Problem Solving Strategies. 3rd E-Learning Conference. September 7-8. Coimbra, Portugal. 7-12.

Carson, J. (2007). A Problem With Problem Solving: Teaching Thinking Without Teaching Knowledge. Journal of Mathematics Educator, 17(2), 7-14.

Christou, C., Mousoulides, N., Pittalis, M. and Pantazi, D. P. (2005). Problem Solving and Problem Posing in a Dynamic Geometry Environment. The Montana Mathematics Enthusiast, 2(2), 125-143.

De Corte, L. V., and Greer, B. (2000). Connecting Mathematics Problem Solving to the Real World. International Conference on Mathematics for Living. 18-23November. Amman, Jordan.

Desoete, A. and Royers, H. (2006). Metacognitive Macroevaluations In Mathematical Problem Solving. Learning and Instruction, 16, 12-25.

Eric. C. C. M. (2011). Primary 6 Students’ Attitudes towards Mathematical Problem-Solving in a Problem-Based Learning Setting. The Mathematics Educator, 13( 1), 15-31.

Fan, L., Quek, K. S., Zhu, Y., Yeo, S. M., Pereira-Mendoza, L., & Lee, P. Y. (2005). Assessing Singapore students’ attitudes toward mathematics and mathematics learning: Findings from a survey of lower secondary students. Paper presented at the Third East Asia Regional Conference on Mathematics Education, Shanghai, China.

Francisco, J. M. & Maher, C. A. (2005). Conditions For Promoting Reasoning In Problem Solving: Insights From A Longitudinal Study. Journal of Mathematical Behavior . 24, 361–372.

Giganti, P. (2007). Parent Involvement and Awareness: Why Teach Problem Solving, Part I: The World Needs Good Problem Solvers!. CMC ComMuniCator. 31(4). 15-16.


Greiff, S., Holt, D. V., and Funke, J. (2013). Perspectives on Problem Solving in educational Assessment: Analytical, Interactive, and Collaborative Problem Solving. The Journal of Problem Solving, 5(2), 71-91.

Hino, K. (2007). Toward the Problem-Centered Classroom: Trends in mathematical problem solving in Japan. ZDM Mathematics Education Journal, 39(1), 503-514.

Hinton, V., Strozier, S. D. and Flores, M. M. (2014). Building Mathematical Fluency for Students with Disabilities or Students At-Risk for Mathematics Failure. International Journal of Education in Mathematics, Science and Technology. 2(4), 257-265.

Huerta, M. P. (2009). On Conditional Probability Problem Solving Research – Structures And Contexts. International Electronic Journal of Mathematics Education. 4(3), 1 -10.

Kar, T., Özdemir, E., Ipek, A. S., and Albayrak, M. (2010). The Relation between The Problem Posing And Problem Solving Skills Of Prospective Elementary Mathematics Teachers. Procedia Social and Behavioral Sciences 2 (2010). 1577–1583. Elsevier Ltd.

Kolovou, A., Van den Heuvel-Panhuizen, M., Bakker, A., and Elia, I. (2009). An ICT Environment To Assess And Support Students’ Mathematical Problem-Solving Performance In Non-Routine Puzzle-Like Word Problems. Paper presented at ICME11 [WWW document]. Retrieved November 02, 2014, from http://tsg.icme11.org/document/get/466.

Kuzle, A. (2011). Preservice Teachers’ Patterns Of Metacognitive Behavior During Mathematics Problem Solving In A Dynamic Geometry Environment. Doctor Of Philosophy, University of Georgia.

Kuzle, A. (2013). Patterns of Metacognitive BehaviorDuring Mathematics Problem-Solving in a Dynamic Geometry Environment. International Electronic Journal of Mathematics Education, 8(1), 20-40.

Lee, H. S. and Hollebrands, K. F. (2006). Students’ Use of Technological Features While Solving A Mathematics Problem. Journal of Mathematical Behavior, 25, 252–266.

Levingston, H. B., Neef, N. A. & Chon, T. M. (2009). The Effects Of Teaching Precurrent Behaviors On Children’s Solution Of Multiplication And Division Word Problems. Journal Of Applied Behavior Analysis. 42 (2), 361–367.

Lim, H. L. & Noraini Idris (2006). Assessing Algebraic Solving Ability Of Form Four Students. International Electronic Journal of Mathematics Education. 1(1), 55-76.

Mabilangan, R. A., Limjap, A. A., and Belecina, R. R. (2012). Problem Solving Strategies of High School Students on Non-Routine Problems: A Case Study. In Alipato (pp 23-46).

Miller, N. and Wakefield, N. (2014). A Mentoring Program for Inquiry-Based Teaching in a College Geometry Class. International Journal of Education in Mathematics, Science and Technology. 2(4).

Mora, F. B. and Rodríguez, A. R. (2013). Cognitive processes developed by students when solving mathematical problems within technological environments. The Mathematics Enthusiast, 10(1&2), 109-136.

Muir, T., and Beswick, K. (2005). Where Did I Go Wrong? Students’ Success at Various Stages of the Problem-Solving Process.

Muir, T., Beswick, K., and Williamson, J. (2008). “I’m not very good at solving problems”: An Exploration Of Students’ Problem Solving Behaviours. Journal of Mathematical Behavior, 27, 228–241.

Nicolaidou, M. & Philippou, G. (2003). Attitudes towards mathematics, self-efficacy and achievement in problem solving. European Research in Mathematics III.

http://tsg.icme11.org/document/get/466


Osta, I. and Labban, S. (2007). Seventh Graders' Pre Algebraic Problem Solving Strategies: Geometric, arithmetic, and algebraic interplay. International Journal for Mathematics Teaching and Learning.

Pearce, D. L., Bruun, F., Skinner, K., and Mohler, C. L. (2013). What Teachers Say About Student Difficulties Solving Mathematical Word Problems in Grades 2 5.International Electronic Journal of Mathematics Education, 8(1), 4-19.

Perveen, K. (2010).Effect Of The Problem-Solving Approach on Academic Achievement Of Students In Mathematics At The Secondary Level. Contemporary Issues In Education Research – March 2010. 3(3). 9-14.

Polya, G. (1981). Mathematical Discovery on Understanding Learning and Teaching Problem Solving.NewYork: John Wiley and sons

Roslinda, R., Goldsby, D., and Capraro, M. M. (2013). Assessing Students’ Mathematical Problem-Solving and Problem-Posing Skills. Asian Social Science. 9(16). 54-60. Canadian Center of Science and Education.

Sangcap, P. G. A., (2010). Mathematics-related Beliefs of Filipino College Students: Factors Affecting Mathematics and Problem Solving Performance. Procedia Social and Behavioral Sciences, 8, 465–475.

Schoenfeld, A. H. (1992). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making In Mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334-370). New York: Macmillan

Sek, Y. H. (2014). Tingkah Laku Metakognitif Dalam Penyelesaian Masalah Matematik. Master, Universiti Teknologi Malaysia, Skudai.

Sirin, A. and Guzel, A. (2005). The Relationship between Learning Styles and Problem Solving Skills Among College Students. E¤itim Dan›flmanl›¤› ve Araflt›rmalar› ‹letiflim Hizmetleri Tic. Ltd. fiti. (EDAM), 6(1), 255-264.

Sulak, S. (2010). Effect Of Problem Solving Strategies On Problem Solving Achievement In Primary School Mathematics. Procedia Social and Behavioral Sciences, 9, 468–472.

Suurtamm, C. and Vezina, N. (2010). Transforming pedagogical practice in mathematics: Moving from telling to listening. International Journal for Mathematics Teaching and Learning. 1-19.

Taplin, M. (2006). Mathematics through Problem Solving. Retrieved November 02, 2014, from http://www.mathgoodies.com/articles/problem_solving.htm

Tarzimah Tambychik and Thamby Subahan Mohd Meerah (2010). Students’ Difficulties in Mathematics Problem-Solving:What do they Say?. Procedia Social and Behavioral Sciences 8 (2010). 142–151. Elsevier Ltd.

Trigo, M. S. and Machín, M. C. (2013). Framing the Use Of Computational Technology In Problem Solving Approaches. The Montana Mathematics Enthusiast, 10(1&2), 279-302.

Xenofontos, C. (2010). International Comparative Research on Mathematical Problem Solving: Suggestions for New Reasearch Directions. Proceeding of CERME 6. 28 January- 1 February. France.

Yazgan, Y. (2013). Non-routine Mathematical Problem-Solving at High School Level and Its Relation With Success on University Entrance Exam. US-China Education Review A, 3(8), 571-579.

Yeo, J.B. W. and Yeap, B. H. (2010) Characterising the Cognitive Processes in Mathematical Investigation. International Journal for Mathematics Teaching and Learning. 1-10.

http://www.mathgoodies.com/articles/problem_solving.htm


Author(s):Liyana Nazurah Jafar1 ,Faculty of Education, UniversitiTeknologi Malaysia, JohorEmail: [email protected] Samuri2 ,Faculty of Education, UniversitiTeknologi Malaysia, JohorEmail: [email protected] Akmal Awang Ali3 ,Faculty of Education, UniversitiTeknologi Malaysia, JohorEmail: [email protected]’ Atikah Yusof 4 ,Faculty of Education, UniversitiTeknologi Malaysia, JohorEmail: s atikah22 @l ive . utm.my

mailto:[email protected]



reformat paper

Documents