Introduction
Human growth, personality development and problem solving skills are a vital aspect of societal development and well as academic attributes which an individual should not only possess but apply in al life challenges. Towards this, it is the responsibility of every parent as member of a society not only to take care of the children but also to know how to help the children pass early childhood stage in life smoothly. This will help the children to adopt desirable character traits which make them responsible citizen of a country. “Crisis analysis is a critical aspect in prevention and management of crisis in human life” (Soifer, 2009) and (Masters, 2003). It is prudent to note that human life is full of challenges that require amicable solutions. Towards this, it is important to for human being to analyze the challenges in life and offer solution to them. This will go along way in curbing the negative impact of crisis in the society.
Teaching mathematics is quite important and plays a pivotal role in knowledge development among the students. In this regard, to provide students with the right insight and channel of mathematics, a procedural vivid program of teaching and understanding is necessary. Towards this, the whole concept of studying mathematics boils down to three main components; conceptual understanding, procedural fluency and problem solving. In addition, the concept of mathematics is not only critical to problem solving in human life but also in everyday business. According to Soifer, (2009), “A well organized instructional programs should enable all students to build a new mathematical knowledge. The concept of mathematic in solving problem and decision making is crucial and should be learnt at early stages of life. This will give the students an easy time developing critical thinking at early stages of academic life.
In the process of mathematical problem solving there exist a number of methods which are used. These include, one step problem, multi-step problems and process problem. In most cases, student encounter multi-step problems or process problems and the workings and solution to these problems involves a collaborative and procedural knowledge. This paper takes a critical analysis and a presentation on NYS Math Standards on Problem solving and further looks into the impact and role of mathematical problem solving concept in knowledge development.
Pedagogical skills of problem solving
Mathematical topics and skills can be easily got from active participation among the students. This is because participation enhances their ability to conceptualize and carry out a logical problem analysis and solution. Participation among the student will go along way in preparing each one of them to the task of solving real life problem as they occur. In this regard, “participation in problem solving should be encouraged among the students”(Masters, 2003).In the task of problem solving, students normally employs several strategies and tools. Towards this, teachers have the responsibility of ensuring that students are not only taught several strategies in problem solving but also encouraged to use different strategies and compare the results.
Souviney, (2005) illustrates that, Show a 6th grader one-fourth of a real cake and then ask, ”If I eat this much pizza, and then one-third of another cake, how much will I have eaten altogether? Show a 6th grader one-third of a real cake, and then ask, ”If I already ate one-fourth of a cake, and now eat this much, how much will I have eater altogether?”
“Neither of the preceding problems is a “symbol-symbol” or “word-word’ problem. Instead, the situations in both problems include a real object for instance a piece of cake, and a spoken word (to represent a past or future situation” (Souviney, 2005). Souviney, (2005) state that, “Like many realistic problems in which mathematics is used, the situation in these two cakes problems is inherently multimodal and each of the problems is a cake word problem in which one of the student’s difficulties is to translate the two givens into a homogeneous representation mode so that combining is sensible.“Not only may problems of the preceding type occur naturally in a multimodal form but solution paths also often weave back and forth among several representational systems, each of which typically is well suited for representing some parts of the situation but is ill suited for representing others”(Masters,2003). For example, “a student may think about the static quantities in a concrete way perhaps using pictures but may switch to spoken language to carry out the dynamic combining actions” (Souviney, 2005).Efficient problem solvers normal employ different methods and strategies.This strategy helps in enhancing the accuracy and the authenticity of the answers or solution got.
It is prudent to not that mathematics is crucial to personal and interpersonal development I the society. Personality development is an integral part of human growth and therefore parents should guide their children during childhood life. This is because self-esteem is quit important in strong personality development. Good parental advice and life changing events normally shape people’s personality either positively or negatively and the same concept applies with problem solving skills. It is therefore upon us to choose what is good for our growth and development.
Problem solving example
Given the equation below as illustrated by Behr, Lesh, Post & Silver, (1983)
5(-3x – 2) – (x – 3) = -4(4x + 5) + 13
* multiply all the factors.
-15x – 10 – x + 3 = -16x – 20 +13
* Group like terms. Xc
-16x – 7 = -16x – 7
* Add 16x + 7 to both sides and write the equation as follows
0 = 0
source: Behr, Lesh, Post & Silver, (1983)
Comparison of Primary and Intermediate level
The concept of problem solving in both primary and intermediate level are the same in procedural steps taken so as to come up with a realistic solution. However, the difference occurs in the nature and level of ambiguity of the problem.
Conclusion
Mathematics plays a critical role in problem solving and remains one of the best
tools in critical thinking as well as knowledge development. In this regard, it
is the responsibility of the government and all the education stakeholders to
ensure that student are adequately prepared to face real life challenges through
an organized and well prepared mathematics curriculum.
References
Behr. M., Lesh, R., Post, T., & Silver, E. (1983). Rational number concepts. The acquisition of mathematical concepts and processes. New York: Academic Press.
Larson, L.C. (1990).Problem-solving through problems. Problem books in mathematics. New York: Springer.
Masters, M. (2003).Let’s Prepare for the Grade 4 Math Test.New York: Educational Series.
Soifer, A. (2009).Mathematics as problem solving. New York: Springer.
Souviney, R. J. (2005).Solving math problems kids care about. New York: Good Year Books.