Overview
There has been an increasing attention on the interrelationship between mathematical problem solving and mathematical learning. Mathematical problem solving has been recognized as a process of inquiry whereby calculating and deriving the correct answers is only one of several phases. Several studies in mathematics education have identified the use of strategies to be central to solving mathematical problems (Pape & Wang, 2003; Verschaffel et al., 1999). Cai (2003) found that when students use problem- solving strategies, they are more successful in solving a mathematical problem. These problem-solving strategies, or heuristics strategies, are procedures that students should take before reaching the calculation phase of problem solving. They are designed to help students understand and organize their responses to answer the problems. While there is evidence that heuristic strategies have enhanced learners’ responses to verbal mathematical problems, there should be more attention given to study of heuristic strategies in mathematical non-routine problem solving, especially among primary school children (Kaizer & Shore, 1995).
Problem solving in Singapore
Research in mathematics education in Singapore has a relatively short history (Foong, 2007). Given the decreasing trend of research on problem solving internationally, Foong suggested that the large number of local degree studies on problem solving could be due to the fact that problem solving has been the central theme of Singapore school mathematics curriculum since 1990. Developing students’ ability in problem solving only started to be one of the mathematics learning objectives in the curriculum in the 1970s (Fan, 2007). As part of processes, heuristics for pro...
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...ublished dissertation in partial fulfillment of the requirement for the Degree of Master of Education.
Teo, C.H. (1997). Ministerial statement at budget debate in Parliament, Singapore, July.
Pape, S.J., & Wang, C. (2003). Middle school children’s strategic behavior: classification and relation to academic achievement and mathematical problem solving. Instructional Science, 31, 419-449.
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Schoenfeld, A. H. (1985). Mathematical problem solving. Englewood Cliffs, New Jersey: Prentice Hall.
Verschaffel, L., de Corte, E., Lasure, S., Van Vaerenbergh, G., Bogaerts, H., & Ratinckx, E. (1999). Learning to solve mathematical application problems: A design experiment with fifth graders. Mathematical Thinking and Learning, 1, 195-229.
Kieren, T., Gordon-Calvert, L., Reid, D. & Simmt, E. (1995). An enactivist research approach to mathematical activity: Understanding, reasoning, and beliefs. Paper presented at the meeting of the Ame rican Educational Research Association, San Francisco.
The article “Tying It All Together” by Jennifer M. Suh examines several practices that help students to develop mathematical proficiency. It began with a mathematics teacher explaining that her students began the year struggling to understand basic mathematics concepts, but after implementing the following practices into the classroom throughout the year, the students began to enjoy mathematics and have a better understanding of math concepts.
On tasks measuring math computation skills, Deanna was asked to solve problems using addition, subtraction, multiplication, division, fractions and algebraic equations. Deanna scored in the average range, as she was able to correctly respond to questions involving addition, subtraction, multiplication and division. Deanna noticeably struggled when solving equations involving fractions. Whether adding, subtracting, multiplying or dividing fractions, Deanna constantly got these questions wrong. In addition to this, Deanna’s lack of exposure to algebraic equations involving logarithm and exponents were noticeable as those questions were often left
Pateman, Neil A., Ed, et al. Proceedings Of The 27Th International Group For The Psychology Of Mathematics Education Conference Held Jointly With The 25Th PME-NA Conference (Honolulu, Hawaii, July 13-18, 2003). Volume 3. n.p.: International Group for the Psychology of Mathematics Education, 2003. ERIC. Web. 23 Apr.
The curriculum implies that teachers will teach students the skills they need for the future. Valley View’s High School math department announces, “Students will learn how to use mathematics to analyze and respond to real-world issues and challenges, as they will be expected to do college and the workplace.” Also, the new integrates math class allows students to distinguish the relationship between algebra and geometry. Although students are not being instructed a mathematical issue in depth, they are rapidly going through all the different topics in an integrated math class. Nowadays, students are too worried to pass the course to acquire a problem-solving mind. Paul Lockhart proclaims the entire problem of high school students saying, “I do not see how it's doing society any good to have its members walking around with vague memories of algebraic formulas and geometric diagrams and dear memories of hating them.” A mathematics class should not be intended to make a student weep from complicated equations, but it should encourage them to seek the numbers surrounding
Van de Walle, J., , F., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics, teaching developmentally. (Seventh ed.). New York, NY: Allyn & Bacon.
Mathematics education has undergone many changes over the last several years. Some of these changes include the key concepts all students must master and how they are taught. According to Jacob Vigdor, the concerns about students’ math achievements have always been apparent. A few reasons that are negatively impacting the productivity of students’ math achievements are historical events that influenced mathematics, how math is being taught, and differentiation of curriculum.
Silver, E. A. (1998). Improving Mathematics in Middle School: Lessons from TIMSS and Related Research, US Government Printing Office, Superintendent of Documents, Mail Stop: SSOP, Washington, DC 20402-9328.
Using literacy strategies in the mathematics classroom leads to successful students. “The National Council of Teachers of Mathematics (NCTM, 1989) define mathematical literacy as an “individual's ability to explore, to conjecture, and to reason logically, as well as to use a variety of mathematical methods effectively to solve problems." Exploring, making conjectures, and being able to reason logically, all stem from the early roots of literacy. Authors Matthews and Rainer (2001) discusses how teachers have questioned the system of incorporating literacy with mathematics in the last couple of years. It started from the need to develop a specific framework, which combines both literacy and mathematics together. Research was conducted through
Sherley, B., Clark, M. & Higgins, J. (2008) School readiness: what do teachers expect of children in mathematics on school entry?, in Goos, M., Brown, R. & Makar, K. (eds.) Mathematics education research: navigating: proceedings of the 31st annual conference of the Mathematics Education Research Group of Australia, Brisbane, Qld: MERGA INC., pp.461-465.
What factors affect successful problem solving, and what problem-solving strategy might be effective to help students become better math problem solvers? Students with learning disabilities often struggle with problem solving. Many special needs students have difficulty with reading, and thus cannot understand the traditional word problem. Students with learning disabilities often have difficulty the logical reasoning as well. “It is also common that their mathematics education has focused primarily on operations and not on understanding the reasons for operations or even a thorough understanding of the numbers that are involved in operations”, (Sharon Vaughn, 2015, p. 387). The textbook gives several suggestions on effective problem-solving strategies, such as teaching the “big idea”. This means teaching students the big idea or principle, thus aiding the students in applying these big ideas or principles to subordinate concepts. One way that I try to teach the “big idea” in my classroom is to provide real-life examples for students to problem solve. Another teacher strategy that aids in students understand of problem solving is sameness analysis. “The idea is to connect math concepts so that students see the ways in which aspects of mathematical problem solving are the same”, (Sharon Vaughn, 2015, p. 387). Sameness analysis, is one of the strategies that I used often when I taught fourth grade. I always felt that students gained a better understanding word problems, when they could identify the type of word problem they were trying to
Taking this as the central idea, maths teacherswe???? designed class lessons that asked students to use their intuitional knowledge and comprehension about percentages and proportions to relevant problems. Real and conceivable settings were developed that we hoped would connect with students’ familiarity and would motivate them to be involved in problem-solving behaviours. Most significantly, we hoped that classroom dialogue (of both students and teachers) would demonstrate and support self-regulating
Skemp, R (2002). Mathematics in the Primary School. 2nd ed. London: Taylor and Francis .
...S. and Stepelman, J. (2010). Teaching Secondary Mathematics: Techniques and Enrichment Units. 8th Ed. Merrill Prentice Hall. Upper Saddle River, NJ.
The early acquisition of mathematical concepts in children is essential for their overall cognitive development. It is imperative that educators focus on theoretical views to guide and plan the development of mathematical concepts in the early years. Early math concepts involve learning skills such as matching, ordering, sorting, classifying, sequencing and patterning. The early environment offers the foundation for children to develop an interest in numbers and their concepts. Children develop and construct their own meaning of numbers through active learning rather than teacher directed instruction.