Cognitive Demand in Mathematics Learning
Added on 2020-03-16
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Running head: CASE STUDY: MAINTAINING THE COGNITIVE DEMAND OF A CRITICAL MATHEMATICS1Case Study: Maintaining the Cognitive Demand of a Critical Mathematics
CASE STUDY: MAINTAINING THE COGNITIVE DEMAND OF A CRITICAL MATHEMATICS2Whole numbers are simple to operate with and understand. Children do understand how to count and the principles of numbers upon which counting is based at an early age. Even for the children who start their education with the unusual limited facility to do the numbers an intensive instruction facility can be used to assist them to reach their peer's levels. Children experience with counting gives them a foundation to solve basic addition, multiplication, subtraction, and division. Despite having a lot to do in their time in school they do start their learning with a substantial knowledge which they then build from. In the class, the students were given whole numbers and asked to do various operations on them. The questions were: 12 +10, 15-3, 284 and 10/5.The objective of the class was to evaluate how the children develop proficiency with whole numbers. To observe the way, they move from solving simple equations based on simple modeling to evaluate more complex calculations with the whole numbers. The lesson was focused on computing whole numbers as the teaching of computations gives the children an avenue to operate through many number ideas and integrate mathematical proficiency strands [ CITATION Car96 \l 2057 ]. The children were of grade 6. The names of the children used in this document have been changed to conceal their identity.In the process of the student computation of the solutions, they could discuss amongstthemselves to assist gauge their understanding. The discussion was in a group of four. This was the conversation in one of the groups.James: ok to get 12+10 you add ten and ten to obtain 20Irene: that’s wrong where do you get the other 10 you are using?Kevin: the number 12 composed of a 10 and a two so the then is added to the other ten to get twenty, but then James where did you take the 2 which is also found in 12?
CASE STUDY: MAINTAINING THE COGNITIVE DEMAND OF A CRITICAL MATHEMATICS3Caroline: the correct answer should be 22 if you take 5 *4 = 20 +2 = 22James: but there is no 5 anywhere in the question.Caroline: the tens are made of 2 fives each that give a total of 4 fives so you multiply by 4 to get 20 then add the 2 which remains unused in the equation.Irene: the answer is correct but I cannot get your method all stick with Kevin’s solution.Kevin: it’s shorter than doing all those multiplication. You just add 2 tens and a two. James: ok then how do you compute 10/5?Caroline: that’s 2Irene: how?Caroline: suppose you have 10 pieces of biscuit and you are 5 people how many do each of you get?James: ooh, that’s simple now I think everybody will get two.Keven: that’s is true if each person gets two then everyone will have an equal amount. That means our answer will be 2.The student in their solutions of the whole number operations showed cognitive demand by the way they analyzed the situations and derived relationships in the numbers before making a conclusion in their final answers. In the case with the divisions, Caroline was even able to relate the question to an actual life activity to enable her easily to derive the possible solution. This was easily understood by her other group members and they could agree on the final solution [ CITATION Fos01 \l 2057 ].In the working with the students some of them gave very unrealistic answers for this purpose I allowed the group members to confirm if the answer given was satisfactory to
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