Case Study: Cognitive Demand in Mathematics

This case study examines how sixth-grade students engage with whole numbers and develop mathematical proficiency through collaborative discussions. It highlights the importance of cognitive demand in mathematics education, showcasing various teaching strategies that encourage student participation and understanding. The study emphasizes the need for teachers to be aware of students' prior knowledge and learning styles to enhance their mathematical comprehension.

Running head: CASE STUDY: MAINTAINING THE COGNITIVE DEMAND OF A CRITICAL MATHEMATICS
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Case Study: Maintaining the Cognitive Demand of a Critical Mathematics

CASE STUDY: MAINTAINING THE COGNITIVE DEMAND OF A CRITICAL MATHEMATICS
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Whole 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 (Carpenter, 1996). 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 amongst
themselves 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 20
Irene: 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 MATHEMATICS
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Caroline: the correct answer should be 22 if you take 5 *4 = 20 +2 = 22
James: 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 2
Irene: 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 (Fosnot, 2001).
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

CASE STUDY: MAINTAINING THE COGNITIVE DEMAND OF A CRITICAL MATHEMATICS
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them. This way they corrected each other and in the process developed analysis skill. Where
the members of a group were not able to agree one of them would make her/ his answer
known to the whole classroom and thereupon a student would be chosen at random to give
her view on the answer. He would, therefore, go forward to explain how he came up with the
solution concluded. The random choosing of students was to ensure all of them are attentive
to what’s going on in the classroom as well as give even the normally shy student a chance to
practice public presentation of their ideas. Most of the student in their views would first make
the context of the mathematics to be related to their daily life activities before concluding in
their answers. This tends to work for another student as most of the student who used this
approach could convince their counterpart to agree with their final solution with ease.
It was evident that students took pride in presenting their answers, the joy was
amazing when the others agreed that the solution given was correct. This was evident by the
vigor the students have in contributing to the subsequent questions. Those who were
corrected by others despite feeling annoyed I could assure them and they seemed determined
to prove their understanding in the following question. In the group discussions, some of the
students were too shy to make any contribution. For that purpose, I need further information
of how to motivate the students to freely air their view (Ball, 2008).
In the learning of mathematics, the student gained more when they have a variety of
ways to understand a concept. Using the children’s individual strength and style of learning
makes the mathematics curriculum and instructions very effective. Some of the children
embraced the use of visual concepts in their explanations. The confidence of the children and
even their competence and interest whenever the new experience acquired showed a
relationship with their past knowledge of the matter (Boston, 2011). When the concept is not
explicit then the children fail to make use of their prior knowledge and connect the current
situation to the mathematics taught in school. it's therefore essential to have knowledge of

CASE STUDY: MAINTAINING THE COGNITIVE DEMAND OF A CRITICAL MATHEMATICS
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what the children know and then go ahead to make them view the concepts mathematically.
The learning of maths should be based on children’s development knowledge and learn
within all the related fields. To make the children understanding much easier teachers should,
therefore, be knowledgeable on the children’s social, emotional as well as motor development
as this affects the development of mathematical understanding in children (National Council
of Teachers of Mathematics, 2017)

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References
Ball, D. L. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher
Education, 389–407.
Boston, M. &. (2011). A ‘task-centric approach’ to professional development: the cognitive demands
of instructional tasks used in teachers’ classrooms. Journal for Research in Mathematics
Education, 119–156.
Carpenter, T. F. (1996). Cognitively guided instruction: A knowledge base for reform in primary
mathematics instruction. Elementary School Journal, 5-15.
Fosnot, C. T. (2001). The Young Mathematician at Work. Portsmouth: NH: Heinemann.
National Council of Teachers of Mathematics. (2017, October 7). National Association for the
Education of Young Children. Retrieved from Early Childhood Mathematics: Promoting Good
Beginnings: https://oldweb.naeyc.org/about/positions/psmath.asp