The four levels of cognitive demands in mathematical tasks
Introduction
In this unit, we will explore the four levels of cognitive demand and analyze tasks based on the demands.
Consider this question as we explore this unit: Why is it important to consider these levels of demand?
Learning Targets
By the end of this unit, you will be able to...
🎯 Identify the 4 levels of cognitive demands
🎯 Analyze tasks based on the demands
Lesson 1: What are the 4 levels of Cognitive Demands?
Lesson Video:
Review this video:
Low-Level Cognitive Demand
Memorization Tasks are:
- Reproduction of facts
- Use Formulas/Rules
- No explanations are required
Procedures Without Connections:
- Require Algorithmic Thinking
- Focus is on producing the right answer
- No connection between concepts
- No explanations are required
High-Level Cognitive Demands
Procedures With Connections
- Tasks are focused on gaining an understanding of mathematical concepts
- Require some degree of cognitive effort
- Some explanations are required
Doing Mathematics Tasks
- Requires students to persevere through a problem rather than just follow a procedure and solve for an answer.
- Require Non-Algorithmic Thinking
- Requires an understanding of mathematical concepts and the ability to apply these concepts
- Explanations are required
How each level might manifest in error analysis:
Memorization: When analyzing errors at this level, the focus would be on basic factual recall, like identifying simple calculation mistakes or misremembering key definitions, which can be corrected by reviewing basic concepts.
Procedures without connections: Analyzing errors at this level would involve identifying mistakes in following a set algorithm or applying a procedure without understanding the underlying concepts, often resulting in consistent errors in similar types of problems.
Procedures with connections: When analyzing errors at this level, the focus would be on identifying misconceptions where a student might be applying a procedure correctly but misinterpreting the context or relationships between concepts, requiring a deeper analysis of their thought process.
Doing mathematics: At this level, error analysis would involve complex reasoning and critical thinking, where students might make errors due to a fundamental misunderstanding of mathematical principles, requiring a comprehensive analysis of their strategy and reasoning to identify the root cause.
Lesson 2: Analyzing tasks based on the demands
Analyze the questions that are related to each task and note: what are your noticings and wonders?
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Consider this:
