Math Task Framework:
Contributors:
Stephanie Casper
Marissa Minnick
Samantha Townsend
April Warren
A professional development guide.
Low Cognitive Task Adaptation
As mentioned on the Math Task Framework and Implications pages, tasks can change categorization with simple changes and differences in implementation. This page illustrates how to reconstruct a low cognitive task into a high cognitive demand task. Be sure to read the explanation section at the bottom of the page to see why this task changed categorization.
Original Low Cogntive Development Task:
Procedures without Connections: Have the students look at the problems A - D and their answers. Next, ask students to fill in the blanks on the remaining four problems, E - H.
A: 100 - 80= 20 B: 80 - 20= 60 C: 50 - 30= 20 D: 60 - 50= 10
E: 100 - 20= __ F: 80 - 60= __ G: 50 - 20= __ H: 60 - 10= __
Reconstructed into High Cognitive Development Task:
(Answers provided in orange. A full response is included with A, whereas solely the answer are provided for B - D, as students will create many ways to solve the problems.)
Procedure with Connection: Have the students fill in the blanks in the following problems, A - D. Ask students to brainstorm and explain at least two different ways to solve each problem.
A: 125 - 50 = 75 B: 95 - 35= 60 C: 75 - 40= 35 D: 155 - 65= 90
Student Explanation for A: First, I solved this problem with base 10 blocks. I made the number 125 with 12 long blocks and 5 ones blocks. Then I separated 75 out from the 125 with 7 long blocks and 5 ones blocks. Last, I counted how many were left over and I had 5 long blocks, which represents 50.
I also solved the problem by thinking about what number I could take away from 125 to get 75. I knew that 100 - 25 is 75. Since I was subtracting from 125, though, and not 100, I knew that I had to subract the "extra" 25 from 125. this means I'd be doing 125 - 25 to get 100, then 100 - 25 to get 75. Since I'm subtracting 25 twice, I added them together and got 50.
Explanation:
This task was first classified as a low cognitive procedure without connection task because it was algorithmic and allowed students to use the examples provided in A through D to solve problems E through H. The original task required limited cognitive demand and was not related to the underlying concept. Furthermore, the task focused on producing correct answers and did not require any explanations.
In the revision process, the examples were eliminated and the numbers were replaced with larger numbers, yet were still rooted in five and tens. The revised problem also requires students to approach the problem in multiple ways and explain their processes. This revised task is classified as a high cognitive procedure with connection because it asks for students to represent their work in multiple ways, requires some degree of cognitive effort, and focuses students on the use of a procedure, subtraction, to develop a deeper understanding of "fill in the blank" problems, which may later be represented with variables.