Content Analysis of Tasks
Ashley Cottle, CI3030-417
When it comes to creating tasks, it is important to know the levels of cognitive demand and what those levels look like through examples. Below is an example from each level of cognitive demand with an explanation as to why the problems are listed at that level. While reviewing the examples, look alongside the Smith & Stein Levels of Cognitive Demand chart if further explanation is needed, and once you are done looking at the examples, take the Task Sorting Challenge here.
Memorization:
Manipulatives/Tools Available: None
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Listen to this number: 624. Say the number.
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Now listen to me say 624 as an addition problem: 600+ 20 + 4
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Your Turn: Say 624 as an addition problem.
(Repeat step 3 with 29, 406, 317, 871, 314)
This task is considered memorization because there is no procedure needed to solve for the answer, and it also is just simple repetition, so there is no cognitive challenge here.
Procedures without Connections:
Low Cognitive Demand
This task is considered procedures without connections because it does require a student to understand place value and how manipulatives like Base Ten blocks work; however, it does not require much cognitive effort because the student really only needs to know how to count and how to add, so the student is not analyzing a mathematical concept or truly applying themselves.
Doing Mathematics:
Procedures with Connections:
Manipulatives/Tools Available: None
Jamie wants to solve this problem:
1. We planted 18 daffodils. Then we planted another 15 daffodils. How many daffodils did we plant?
He writes the equation: 18+15=__
Jamie thinks: I can break apart the numbers.
18=10+8
15=10+5
10+10=20
8+ 5=13
20+13=33
We planted 33 daffodils.
Solve these two problems using Jamie’s method:
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Jill has 17 stuffed animals. Her friend, Taisha, has 22 stuffed animals. How many stuffed animals do they have altogether?
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Ms. Smith has a can of 24 pencils for students to use. She bought 36 more pencils. How many pencils does she have now?
This is considered to be a procedures with connections task because it is requiring the student to apply knowledge he or she may or may not already have by using a certain method displayed in the question. It asks the student to think more in-depth about a mathematical problem and may require the student to use manipulatives like Base Ten blocks or a HUndreds chart to produce an answer; however, the student does not have to analyze or explain their method.
High Cognitive Demand
This task is considered to be the highest level of cognitive demand in relation to mathematics because the student is required to analyze the ways in which the students in the word problem solved the equations. This promotes higher level thinking and makes the student call on his or her previous knowledge of how to solve the problem; it also does not ask for the student to solve the problem algorithmically, but rather, it asks the student to explore and understand how to solve the problem using the empty number line method.