The need for reforms in teaching mathematics in elementary schools poses a great challenge to the teachers. In this view, those teaching mathematics are called up to embrace and practice the required skills in order to deliver appropriate content of mathematics to elementary schools. This paper gives a description of some of the vital mathematics concepts in elementary schools and gives a reflection of the conceptual framework for mathematics.
The first one is the concept of real number properties. A real number implies a value which is a representative of a quantity within a number line. One of the properties of real numbers is that it can be ordered. Such properties only prove to be useful when working to solve equations, algebraic formulas and functions. Real number properties help in creation of various equations that are equivalent and allows for solving of various mathematical problems. In this essence, they help in explaining and justifying various solutions ( Natha and Koedinger, 2000) . For instance, in real world, a place value strategy is demonstrated as follows:
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“There are three aliens. Each has 27 teeth. How many teeth are there altogether? They are applying the distributive property of multiplication over addition. The student knows that 3 x 27 or 3 x (20 + 7) = 3 x 20 + 3 x 7 or a x (b + c) = (a x b) + (a x c).” ( Natha and Koedinger, 2000, p.176).
Another concept is patterns. Pattern is a mathematical property that helps in making mathematical prediction. For instance, one can be given the first 8 patterns and asked to predict what the 20th pattern will be. The concept of number pattern enables one to establish a relationship between various quantities. Patterns automatically lead to the concept of functions in mathematics. In the real world, the concept of pattern can be used as a skill for solving various problems. For instance, in whether forecasting, when the experts studies the patterns, they can easily predict what the pattern will be in future and help give various whether solutions ( Aljaberi, 2015) .
Mathematical operation is a concept that involves input of zero or more values which actually leads into an output value. Operations cover a wide scope of mathematics including binary and unary which lead to various functions like trigonometry and negation. In real world, operations can help to give vectors and directions in aeronautical and geospatial fields of engineering ( Aljaberi, 2015) .
Algebraic reasoning and problem solving is another mathematical concept. Algebra happens to be a general mathematic topic that covers most mathematical contexts. It involves the use of numbers and symbols to solve various equations, analyze mathematical functions and also determine various variables that involve relationships and expressions. It is important for the teachers to identify the pupils’ algebraic reasoning and problem solving skills in order to design a learning style that will develop their algebraic reasoning. This is the most suitable way of minimizing difficulties in learning algebra ( Blanton & Kaput, 2005) .
In order to make elementary mathematics more meaningful to students, the following two strategies can be appropriate. The first one is to create real life examples of the concepts that are being taught. This involves going beyond the theory and stories that are described in mathematics books and instead generating own real world examples that actually reflect of the concepts being learned. This helps students to grasp the concepts easily and get their meaning. The second strategy is to divide the students into smaller groups with presentations where the students get the opportunity to teach others. When the students are given the opportunity to teach, they actually learn better and conceptualize the entire idea as opposed to just seating and listening. Ideas that are well understood by few students can easily be shared amongst the entire class so that those who did not grasp the ideas well can have the opportunity to do so ( Anderson & Hoffmeister, 2007).
The understanding of real world mathematical teaching strategies gives insight to the personal philosophy of teaching as it makes teaching easy and manageable with minimal resistance from students. With such strategies, many students will positively embrace the lessons. Understanding of such strategies also minimizes the difficulties encountered when teaching mathematics in elementary schools. In addition, it makes teaching enjoyable and passionate ( Aljaberi, 2015) .
References
Aljaberi, N.M. (2015). University Pupils’ Learning Styles and Their Ability to Solve Mathematical Problems Int J. of Buss. and Soc. Sci. 6,152-65.
Anderson, C. R., & Hoffmeister, A. M. (2007). Knowing and teaching middle school mathematics: A professional development course for in-service teachers. School Science and Mathematics , 107 (5), 193–203.
Blanton, M. L., & Kaput, J. J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education, 36 (5), 412–446.
Natha, M. J. and Koedinger, K.R. (2000). Teachers’ and researchers’ beliefs about the development of algebraic reasoning J. Res. Math. Educ, 31, 168-90.
