Approaches to calculation

Approaches to calculation By I n figure 3 Barney has utilized switching in representation of the mathematical phenomenon. Code switching is a form of writing whereby a writer switches between two or more forms of writing or languages. The utilization of code switching in children occurs through important switches between standard, implicit and their very own symbols. Through the use of code switching, children can traverse between home mathematics which is rather casual and the more formal mathematics they learn in school. Through this they get a deeper understanding of the more complicated mathematic symbols and algorithms (Forrest, hunton & kellendonk, 2002, pp234- 279). The supplementation of mathematics learnt in school with their home based symbols can make kids have a deeper and better comprehension of what is taught in class.
In figure 3 Barney has used various symbols to communicate his idea. He has used beans, flowerpots, the hand, arrows, numerical (10, 1, 2, 3, 6, 4 and 5) and letters (t, I, s). Barley strives to represent mathematical expressions using symbols. He states that “ 10 t 1 is p” which means that 10 take away 1 gives 9. In this instance he uses the letter “ t” to represent the mathematical symbol of (–) which means minus. The letter “ p” stands for 9 in an inverted form. The whole representation is supposed to mean that 1 taken away from 10 gives 9 or in a mathematical symbol way it’s simply 10-1= 9. He also states that “ 2 t is 1” to mean 1 taken away from 2 gives 1. He uses another form in the second instance involving arrows and a flowerpot with beans in it. The arrows emerging from the pot are symbols that represent the act of taking away a bean the pot and the number of beans in the pots to the right of the arrow represents the number of beans that are left once the bean is takeaway from the pot. This whole representation stands for a standard mathematical symbol of 2-1= 1 and 8-1= 7 expressed in Barney’s own symbols. Code switching is evident here as he switches from using numerical and letters to drawings and arrows. He then switches to using numbers and arrows and “ is” which represent the equal sign in a standard mathematical representation. The arrows denote the minus or take away sign. Lastly he draws the hand with a numerical on it to denote that the number has been taken away from a set and ‘ is’ means the equals sign (Giangrasso & Shrimpton, 2013, pp112- 178). Barley’s recordings give a pictorial representation to the mathematical expression and appeals to the eyes of the reader and gives a better understanding of the expression. It is also clear that Barley strives to make the adult understand his intention through the use of various symbols to represent one thing.
Another form of jottings that may be used is the insertions of tags in a mathematical expression (Forrest, hunton & kellendonk, 2002, pp234- 279). There might be use of tags such as ‘ I mean’ or ‘ You know’. Children however strive to correctly write words or tags and there is normally non uniformity in the size of the letters and there maybe misspelling. For instance, as shown in figure 1 (a) below, a child may draw 4 grapes and 2 grapes and write the word 6 altogether misspelt as ‘ 6ooltogether’ between them. This is to mean that the two grapes added to the four grapes give a total of six grapes (Forrest, hunton & kellendonk, 2002, pp234- 279). Another form of representation is the use of the hand, grapes, a line and written numbers. The grapes are drawn at the end of the hand and a line drawn from the tip of fingers to cut between the grapes then the number of grapes to the left and right are written beside them and so is the total number (Giangrasso & Shrimpton, 2013, pp112- 178). This simply means the grapes on the left of the line and the right when added gives the total number. This is shown in figure 1 (b) below.
Figure 1 Code switching for a set of jottings
All the symbolic representations are never taught and just arise from the children’s own ways of thinking. The symbols and the code switching are great shows of unique mathematical thoughts and advancement towards the comprehension of intellectual symbolism.
Dosage calculations: a multi-method approach. Boston, Pearson. Giangrasso, A. P., & Shrimpton, D. M. (2013).
Forrest, a., hunton, j., & kellendonk, j. (2002). Topological invariants for projection method patterns. Providence, American Mathematical Society.