basic justification by children that what their teacher has said is true

 basic justification by children that what their teacher has said is true

Question 1.

It is important that children should be given the chance by their teachers to develop to skills that they can use in the presentation and to be able to critically appraise mathematical concepts, arguments and calculations (Lerman, 2001). Much emphasis has been placed on students communication and presenting mathematical arguments by the ministry of education. This has made many children not to learn proper right and wrong mathematics and doing column sums. Instead students have been made to memorize what their teachers are saying as the correct results without having the ability to reason out whether the result is correct or not (Hurfed, 2004).

In mathematics as a subject proper reasoning is significant from early age as a child. The reasoning aspect should be considered in the preparation of mathematics curriculum. And mathematics teachers should consider how they incorporate reasoning aspect in mathematics to ensure understanding. This paper will focus on mathematics aspect of reasoning that establishes why mathematical calculations yield results that are true. The need of justifying mathematical results to be true or false gives mathematics a special characteristic distinguishing it from other subjects. Mathematics knowledge is made up using logical deduction rules and the outcome which is the result can be proved which not the same from other subjects is. This aspect should be conveyed to children in school by teachers to enhance their understanding of mathematical aspects. This will make them to know when the result of a given mathematical calculation is true and why it is true. An example is the knowledge that adding even numbers to even number gives odd number; odd number added to odd number gives even number (Manouchehri, 2006). There is need of making children to understand the even and odd adding rules despite their use to children as an automatic check for addition and subtraction. There has been a basic justification by children that what their teacher has said is true and this makes children to believe these rules to be true but this justification limits children in terms of development of reasoning and the independence in mathematical thinking (Rojas, 2003).

Another way of justifying this rules is to make children do many calculations in order to prove the rules practically for example; 6+7=13, 4+8=12, 8+9=17, this will help children find the joy of proving by themselves what they were taught which they can also share will other people though just looking at these examples cannot prove mathematical truth.

Because of the disadvantages in the above justification ways children need to understand what odd and even numbers are. To children even numbers are numbers of objects that can be grouped into two while in odd numbers the pairs of object will leave one object without a group. This will prove why the odd-even adding is true. The numbers can be replaced with symbols to enhance understanding in children (Cobb, 2000). Teachers teaching young children should ensure the following when teaching even-odd rules; that young children can be engaged in mathematical reasoning and therefore reasoning should be included in all mathematical classes, in primary level reasoning should be enhanced by using models like blocks, teachers should monitor the progress in reasoning of young children and appreciating this by explaining why the result given prove mathematical concept or statement being true, teachers should prepare students by gathering evidence by for example measuring, teachers should give students task that will require to explain their mathematical reasoning and why what they have discovered can be true, teachers can also make children to know that mathematics as a subject requires reasoning rather than just giving numbers because this will help children to not focus  on memorizing  what the teacher says but also reason out the results obtained (Wood, 2006).

There is also need by teachers to make children understand and  know how to solve problem in mathematics  and this can be done better through statistical literacy which help in understanding the concepts and the mathematical content being studied which helps in reasoning in order to solve the problem. It is also proper that opportunities should be given to children to participate in inquiry and arguments since this provides a powerful tool of reasoning and giving justification that will enable children at all levels to be able to criticize, explain and be able to justify mathematical concepts and facts.

Question 2

An example of question that children would answer yes or no is are there children with black pen in this class? This can help students to work collectedly in identifying those students with black pen in class. From this question students can build statistical arguments, thinking and learning. This will help students to be able to explain to the class the ways that were used in data collection, listen to other children explanation and make sense from those explanations. From for example 60 children in class, the children can find that 30 children have black pens. To develop their reasoning skills they will be required to explain how they got the answer. The children can be asked whether they are agreeing or disagreeing with the answer and to give explanations and help them to know how productive it is in developing mathematical reasoning through agreeing or disagreeing while giving reasons (Manouchehri, 2006). This will make children to know that arguing when giving answers in mathematics is not bad if it is done in a good way and that they need to be free with another child’s explanation and be able to draw out an explanation to support that.

This graph can help in making children to learn the logic of number of items being higher or less than. For example in answering that the number of cows is higher than the number of horses, the number of goats is less than the number of sheep, the number of horses is higher than the number of sheep and goats and that the number of horses, goats and sheep is less than the number of cows. The assessment of the mathematical reasoning of children using graph is important because it offers pictures that children can easily view thus helping them to easily give reasons for the response that they are giving. An example of objects can also be used to help students to easily identify with the questions for example the graph above uses domestic animals which are all known by children therefore helping them to easily answer the questions and get knowledge about mathematical reasoning of less than or more than (Andriessen, 2006).

References

Andriessen, J. (2006). Arguing to learn. In K. Sawyer. (Ed). The Cambridge handbook of

the learning sciences. (pp. 443-459). Cambridge: Cambridge University Press.

(Andriessen, 2006) (Cobb, 2000)

Cobb, P. (2000). Conducting teaching experiments in collaboration with teachers. In A.

Kelly & R. Lesh (Eds), Handbook of research design in mathematics and science (pp.

307-333). Mahwah, NJ: Lawrence Erlbaum Associates Inc.

(Hurfed, 2004)

Huferd-Ackles, K., Fuson, K., & Sherin, M. (2004). Describing levels and components of a

Math-Talk learning community. Journal for Research in Mathematics Education, 35(2),

81-116.

Lerman, S. (2001). Cultural discursive psychology: A sociocultural approach to studying

the teaching and learning of mathematics. Educational Studies in Mathematics, 46, 87-

113.

Manouchehri, A., & St John, D. (2006). From classroom discussions to group discourse.

Mathematics Teacher, 99( 8), 544-552.