In the nineteenth and twentieth centuries, mathematics was the driving force behind virtually all technical and scientific advancements.
It has a substantial impact on our professional and social daily lives (Maasz and Schloeglmann, 2006). Education is vital for the success of students and the development of a nation. Mathematics education has traditionally been considered an essential component of both general education and science education. It is believed that a teaching approach is needed for any development endeavor to be effective (Lessani, Yunus, & Abu Bakar, 2017).
These differences in views and values regarding mathematics education result in distinct educational systems for mathematics. Teachers are responsible for facilitating students' thinking and learning; hence, they should endeavor to urge students to study. To be aware of teachers' teaching practice activities, we must have sufficient knowledge of learning and teaching approaches. In educational systems around the globe, diverse teaching strategies such as conventional (depends on the behaviorism learning theory), problem-solving, and discovery learning have been implemented. (Lessani, Yunus, & Abu Bakar, 2017)
Problem solving is an important component of mathematics education. The cognitivism learning theory underpins this strategy. Indeed, problem solving in mathematics helps students build a wide range of complicated mathematical structures as well as the capacity to solve a number of real-world situations (Tarmizi & Bayat, 2012). Furthermore, the National Council of Teachers of Mathematics (NCTM) has stated that mathematics teachers should emphasize problem solving throughout their lessons since it "encompasses skills and functions that are an important component of everyday life." Additionally, issue solving assists people in adapting to changes and unanticipated problems in their employment and other aspects of their lives. Problem solving extends beyond mathematical instructional dimensions, allowing students to see the impact of mathematics on the world around them (Taplin, 2011).
In regards to the discovery learning, the constructivist pedagogical philosophy underpins this strategy, which places the learner at the center of the learning process and places an emphasis on students actively constructing their knowledge and understanding under the tutelage of the instructor. Teachers using this strategy shouldn't try to force knowledge down students' throats. Instead, under the teacher's watchful eye and with substantial direction, children should be encouraged to explore their environment, learn new things, reflect, and think critically (Eby, Herrel & Jordan, 2005). Many thinkers and educational reform movements—from William James and John Dewey to Jean Piaget, Maria Montessori, and Lev Vygotsky—contributed to the development of the constructivist approach to learning (Gagnon & Collay, 2001).
According to the study of Lessani, Yunus, and Abu Bakar (2017), due to time constraints and classroom sizes, many mathematics educators now favor the problem-solving approach when instructing their students. Problem solving method helps students to develop creativity and deal with life challenges.
Eby, J. W., Herrell, A. L., & Jordan, M. L. (2005). Teaching K-12 Schools: A Reflective Action Approach. Englewood Cliffs, NJ: Prentice Hall
Lessani, A., Yunus, A.S., & Abu Bakar, A.B. (2017). Comparison of new mathematics teaching methods with traditional method. International Journal of Social Sciences, 3(2), 1285-1297
Maasz, J., & Schloeglmann, W. (2006). New Mathematics Education Research and Practice. Rotterdam: Sense Publishers.
Taplin, M. (2011). Mathematics through Problem Solving. Math Goodies. Retrieved from http://www.mathgoodies.com/articles/problem_solving.html
Tarmizi, R. A., & Bayat, S. (2012). Collaborative problem-based learning in mathematics: A cognitive load perspective. Procedia-Social and Behavioral Sciences, 32: 344- 350. https://doi.org/10.1016/j.sbspro.2012.01.051