Victoria Bryant, Krista Dancy, Kaitlyn Higgins, Sarah Isenhour, Kristen Pruitt
CI 3030-416
Appalachian State University
What are LCD and HCD?
Low Cognitive Demand
Low Cognitive Demand (LCD) tasks are problems that do not require the student to have a conceptual understanding of why they are doing a problem in a certain way.
Memorization
- Involve either reproducing previously learned facts, rules, formulas, or definitions or committing these to memory.
- Cannot be solved using procedures because a procedure does not exist or because the time frame in which the task is being completed is too short to use a procedure.
- Is not ambiguous. Such tasks involve the exact reproduction of previously seen material, and what is to be reproduced is clearly and directly stated.
- Have no connection to the concepts or meaning that underline the faces, rules, formulas, or definitions being learned to reproduced.
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Example: If there are 25 students at recess and 13 students in music class. How many students are at recess and how many students are in music class?
Procedures without connections
- Algorithmic. Use of the procedure either is specifically called for or is evident from prior instruction or experience.
- Require limited cognitive demand for successful completion. Little ambiguity exists about what needs to be done and how to do it.
- Have no connection to the concepts or meaning that underline the procedure being used.
- Is focused on producing correct answers.
- Require no explanations or explanations that focus solely on describing the procedure that was used.
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Example: Solve. 354-56
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(Stein, Smith, Henningsen, & Silver, 2000).
High Cognitive Demand
High Cognitive Demands (HCD) are tasks that are given to students that require them to use a deeper understanding of why they are doing a problem in a certain way.
Procedures with Connections
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-Focuses on students' attention on the use of procedures for the purpose of developing deeper understanding of mathematical concepts and ideas.
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-Suggest explicit or implicit pathways to follow that involve the use of broad general procedures that have close connections to underlying conceptual ideas as opposed to narrow algorithms that are opaque with respect to underlying concepts.
- Usually are represented in multiple ways, such as with visual diagrams, manipulatives, symbols and problem situations. Making connections among multiple representations helps develop meaning.
- Require some degree of cognitive effort. Although general procedures may be followed, they cannot be followed mindlessly. Students are engaged in conceptual ideas that underlie the procedures to complete the task successfully and that develop understanding.
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Example: Think of a real-life situation that describes the following problem.
52-17=
Write the problem and then solve it.
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(Stein, Smith, Henningsen, & Silver, 2000).
Doing Mathematics
- Require complex and nonalgorithmic thinking- a predictable, well-rehearsed approach or pathway is not explicitly suggested by the task, task instructions, or a worked out example.
- Require students to explore and understand the nature of mathematical concepts, processes, or relationships.
- Demand self-monitoring or self-regulation of one’s own cognitive processes.
- Require students to access relevant knowledge and experiences and make appropriate use of them in working through the tasks.
- Require students to analyze the task as well s constraints that may limit possible solution strategies or solutions
- Require considerable cognitive effort and may cause some level of anxiety for the student as they are working through the problem due to the unpredictable nature of the solution process required.
Example: Lydia has a jar full of 103 gumballs. She gave 27 of the gumballs to her friend Steven. How many marbles does Lydia have left? Solve the problem two ways.
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(Stein, Smith, Henningsen, & Silver, 2000).