Math Education 6125

research & summaries writing question and need the explanation and answer to help me learn.

Required Readings:
 Stein & Smith (1998)
 Smith (2004)

Task 1:
 Read Stein and Smith’s (1998) article about the cognitive demand of math tasks.
Pay particular attention to the four levels of cognitive demand: memorization,
procedures without connections, procedures with connections, and doing
mathematics.
 Complete the Task Sorting Activity. Based on how you understand the four
categories presented in the above article, sort Tasks A-P in Appendix C, High
School into the four categories. Appendix C starts on p. 68 (or 24 of 28), but the
first page is the answer key. Please SKIP the answer key and go to the next page
and start sorting.
 After sorting the activities, please check the agreement between you and the
answer key. Select three tasks that your classification disagreed with that of Stein,
Smith, and colleagues OR that you found particularly hard to classify even if your
final classification did agree with the authors’. Provide a short discussion (2-3
sentences) about why you think each of the three tasks you chose was difficult for
you to classify.
 Finally, answer the following question: Is there a difference between “level of
cognitive demand” and “difficulty”? In what ways are they similar? In what ways
are they different?

Task 2:
 Selecting worthwhile tasks (usually of high cognitive demand) is only the first
step. The execution of the tasks, in other words, how to orchestrate classroom
discourse through worthwhile tasks, is also extremely important.
 Read Smith (2004) and then respond to the following questions:
o How would you rank the prom dress task and the gumball task according
to Smith & Stein’s four levels of cognitive demand? Provide a brief
justification.
o What are some of the key differences in terms of the ways Mrs. Jones and
Mrs. Hamada carried out/implemented the tasks?
Keep your answer to EACH of the above within one-page, single-spaced. However, your
answer to EACH should not be significantly shorter than a full paragraph (5-6 sentences)

Task 3 Math Challenge (bonus: extra 10 points, will be added to your final score):
 Solve Task A on the sorting activity for high school (Appendix C).
 Fully justify your solution. Simply providing a number, regardless of correctness,
will receive 0 credit
Requirements: 2 pages
Levels of DemandsLower-level demands(memorization):•reproducing previously learned facts, rules, formulas, definitions or committing them to memory•Cannot be solved with a procedure•Have no connection to concepts or meaning that underlie the facts rules, formulas, or definitionsHigher-level demands(procedures with connections):•use procedure for deeper understanding of concepts•broad procedures connected to ideas instead narrow algorithms•usually represented in different ways•require some degree of cognitive effort; procedures may be used but not mindlesslyLower-level demands (procedures without connections):•are algorithmic•require limited cognitive demand•have no connection to the concepts or meaning that underlie the procedure•focus on producing correct answers instead of understanding•require no explanationsHigher-level demands(doing mathematics):•require complex non-algorithmic thinking•require students to explore and understand the mathematics•demand self-monitoring of one’s cognitive process•require considerable cognitive effort and may involve some level of anxiety b/csolution path isn’t clearLeinwand, S., D. Brahier, and D. Huinker. Principles to Action. Reston, VA:National Council of Teachers of Mathematics, 2014 (pg 18)
Strategies for Modifying Tasks Increasing the cognitive demands of tasks. • Ask students to create real-world stories for “naked number” problems. • Include a prompt that asks students to represent the information another way (with a picture, in a table, a graph, an equation, with a context). • Use a task “out of sequence” before students have memorized a rule or have practiced a procedure that can be routinely applied. • Eliminate components of the task that confine student thinking or provide too much scaffolding. • Create opportunities for repeated reasoning or pattern finding • Create a prompt that asks students to write about the meaning of the mathematics concept. • Add a prompt that asks students to make note of a pattern or to make a mathematical conjecture and to test their conjecture. • Include a prompt that requires students to make a generalization. • Include a prompt that requires students to compare solution paths or mathematical relationships and write about the relationship between strategies or concepts. • Select numbers carefully so students are more inclined to note relationships between quantities (e.g., two tables can be used to think about the solutions to the four, six, or eight tables).

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