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...
... middle of paper ...
...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.
Poly, G. (1973). How to solve it: A new aspect of mathematical model. (2nd ed). Princeton, New Jersey: Princeton University Press.
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.
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.
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.
The Article "No Tears Here! Third Grade Problem-Solvers" by Kim Hartweg and Marlys Heisler focuses on a professional development project conducted in third grade classrooms. This project centered on integrating problem-solving into mathematics. Through this project the classes participating used open response problems. When solving these open response problems, the students thought about strategies they could use and would work on these problems on their own or with a partner. The students participated in productive struggle and after they completed the problem, the students would share their ideas and possible solutions. This presentation of ideas brought about a class discussion, which ended with the students summarizing the classes findings.
This essay will concentrate firstly on psychological aspects, as a part of internal factors and secondly on environmental and social aspects, as a part of external factors. Block 3, Open University.
One of the research-based intervention strategies that I gathered is the use of the Questions-Answer Relationships strategy, which is also known as QAR. Although QAR is typically used as a strategy for comprehension in literacy when given reading passages to answer questions on, it can also be applied to the Math content area when used appropriately in regards to analyzing math graphics, charts, and word problems. After several different studies were conducted, education experts concluded that a major area of need which students who struggle with Math have to overcome is that they need to be able to accurately interpret any provided Math graphics and break down word problems in order to produce an effective answer. The QAR strategy provides students with a structured process of examining the assessment questions in order to assist in finding the answer. By determining what the question is truly asking for, the students can avoid overlooking important details, identify irrelevant information, and find the answer or its evidence in the provided information (http://www.interventioncentral.org/,
One of Polya’s most noted problem solving techniques can be found in “How to Solve it”, 2nd ed., Princeton University Press, 1957.
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
...pter covered the problem statement,research questions, aim and sub objectives, scope, and contribution this study for student itself, teacher and community especially in education area.
Skemp, R (2002). Mathematics in the Primary School. 2nd ed. London: Taylor and Francis .
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.
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.
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.
...S. and Stepelman, J. (2010). Teaching Secondary Mathematics: Techniques and Enrichment Units. 8th Ed. Merrill Prentice Hall. Upper Saddle River, NJ.
A somewhat underused strategy for teaching mathematics is that of guided discovery. With this strategy, the student arrives at an understanding of a new mathematical concept on his or her own. An activity is given in which "students sequentially uncover layers of mathematical information one step at a time and learn new mathematics" (Gerver & Sgroi, 2003). This way, instead of simply being told the procedure for solving a problem, the student can develop the steps mainly on his own with only a little guidance from the teacher.
Many parents don’t realise how they can help their children at home. Things as simple as baking a cake with their children can help them with their education. Measuring out ingredients for a cake is a simple form of maths. Another example of helping young children with their maths is simply planning a birthday party. They have to decide how many people to invite, how many invitations they will need, how much the stamps will cost, how many prizes, lolly bags, cups, plates, and balloons need to be bought, and so on. Children often find that real life experiences help them to do their maths more easily.