Cognitive Demand Defined Participant Handouts

[Pages:84]Cognitive Demand Defined

Participant Handouts

Elementary Mathematics

Los Angeles Unified School District

Paint the Building

? On Monday, a painter had to paint a building that was shaped like a cube. When she read the label on the can of paint, she realized one can of paint would cover one face of the building. She had to paint all four sides and the roof of the building.

? On Tuesday, she had to paint the building next door. It was the size of two of the first buildings put together.

? On Wednesday, she had to paint the third building on the block. It was the size of three of the cubic buildings put together.

? On Thursday, she had to paint yet another building that was, of course, like four of the cubic buildings put together.

Your job is to figure out how many gallons of paint she would need each day. Continue this pattern up to ten cubic units put together? Use the T chart to help you. Create a formula to help you figure out how many gallons of paint it would take to paint a building 23 cubic units long.

The formula is__________________. It would take __________ gallons of paint to cover a building 23 cubic units long.

HO # 1

HO # 2

HO # 3

HO # 3b

Identifying Cognitive Demand: Task Analysis Guide

Lower-Level Cognitive Demands

Memorization Tasks

Procedures Without

Connections Tasks

Higher Level Cognitive Demands

Procedures With

Doing Mathematics Tasks

Connections Tasks

? Involves either producing ? Are algorithmic. Use of ? Focus students' attention on the use ? Requires complex and non-

previously learned facts,

the procedure is either

of procedures for the purpose of

algorithmic thinking (i.e., there is not

rules, formulae, or

specifically called for or

developing deeper levels of

a predictable, well-rehearsed

definitions OR committing

its use is evident based

understanding of mathematical

approach or pathway explicitly

facts, rules, formulae, or

on prior instruction,

concepts and ideas.

suggested by the task, task

definitions to memory.

experience, or placement ? Suggest pathways to follow

instructions, or a worked-out

? Cannot be solved using

of the task.

(explicitly or implicitly) that are

example).

procedures because a

? Require limited cognitive broad general procedures that have ? Requires students to explore and to

procedure does not exist or

demand for successful

close connections to underlying

understand the nature of

because the time frame in

completion. There is

conceptual ideas as opposed to

mathematical concepts, processes, or

which the task is being

little ambiguity about

narrow algorithms that are opaque

relationships.

completed is too short to

what needs to be done

with respect to underlying concepts. ? Demands self-monitoring or self-

use a procedure.

and how to do it.

? Usually are represented in multiple

regulation of one's own cognitive

? Are not ambiguous ? such ? Have no connection to

ways (e.g., visual diagrams,

processes.

tasks involve exact

the concepts or meaning

manipulatives, symbols, problem ? Requires students to access relevant

reproduction of previously

that underlie the

situations). Making connections

knowledge and experiences and

seen material and what is

procedure being used.

among multiple representations

make appropriate use of them in

to be reproduced is clearly ? Are focused on

helps to develop meaning.

working through the task.

and directly stated.

producing correct

? Require some degree of cognitive ? Requires students to analyze the task

? Have no connection to the

answers rather than

effort. Although general procedures and actively examine task constraints

concepts or meaning that

developing mathematical

may be followed, they cannot be

that may limit possible solution

underlie the facts, rules,

understanding.

followed mindlessly. Students need strategies and solutions.

formulae, or definitions

? Require no explanations,

to engage with the conceptual ideas ? Requires considerable cognitive

being learned or

or explanations that focus that underlie the procedures in order effort and may involve some level of

reproduced.

solely on describing the

to successfully complete the task

anxiety for the student due to the

procedure that was used.

and develop understanding.

unpredictable nature of the solution

process required.

? 2001 University of Pittsburgh

HO # 4

Thinking Through a Lesson Protocol

Considering and Addressing Student Misconceptions and Errors

Los Angeles Unified School District Elementary Mathematics Participant Handouts Fourth Grade 2007-2008

HO # 1

Overview of Activities

? Examine Thinking Through a Lesson Protocol (TTLP) ? Engage in Fourth Grade Lesson considering components of

the TTLP that the facilitator demonstrates ? Debrief the lesson with the TTLP as a frame for discussion ? Anticipate student misconceptions ? Review concept lesson and consider how student

misconceptions are addressed

HO # 2

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