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Using Mathematical Tasks To Provoke Intellectual Need Kien Lim University of Texas at El Paso kienlim@utep.edu Sep 9, 2010

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What Constitutes a Good Mathematical Task? What is Intellectual Need? Why is it Important? ObjectivesObjectives

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Sequence Of Activities 1.Find out what constitute a good mathematical task 2.Solve a few problems 3.Discuss

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What is “Mathematics”? Old-view Mathematics Collection of definitions, formulas, rules, and procedures The focus is on the “how” and the “answer” Students are taught the procedure and then practice it New-view Mathematics A subject that involves thinking and sense-making The focus includes the “why” and meaning Students engage in problem-solving, making connection, justifying, representing, and communicating

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Purpose of Classroom Tasks To engage learners in thinking, sense- making, reflecting, and abstracting To engender discussions among learners to learn “new” mathematical knowledge To provide learners an opportunity to practice what they have learned Thompson, Carlson, and Silverman (2007)

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Characteristics of a Good Task Mathematically driven Requires justifications and explanation Intrinsic to students Van de Walle (2003)

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Tasks that Motivate Students Extrinsically Motivating Something new (e.g., manipulatives) Fun and exciting (e.g., game) Intrinsically Motivating Intriguing

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What Leads to Mathematical Learning? “For students to learn what we intend to teach them, they must have a need for it, where by ‘need’ is meant intellectual need, not social or economic need.” (Harel, 2007)

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The line segment represents 1 2 / 3 km. Extend the line to represent 3 3 / 4 km. Be as accurate as you can without measuring the actual length of original line segment. Problem #1 for You 1 2 / 3 km

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What do you think is the math concept for which this task is trying to provoke? What key ideas are necessary for solving this problem? Follow-up Questions #1 1 2 / 3 km 1 km How? Cut into 5 pieces. 1 km 3 / 4 km Why 5? 1 2 / 3 = 5 / 3 Referent unit (1km) Mixed num. - improper fraction conversion

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Consider these 4 products of numbers: Problem #2 for You Without computing the actual value of each product, identify those products that have the same value. (i)2 5 2 6 11 12 (ii) 3 11 25 44 (iii) 5 12 2 55 (iv) 5 10 22 33

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What do you think is the math concept for which this task is trying to provoke? Follow-up Question #2 = 2 4 3 2 5 2 11 = 2 2 3 5 2 11 2 = 2 4 3 2 5 2 11 = 2 2 3 5 2 11 2 (i)2 5 2 6 11 12 (ii) 3 11 25 44 (iii) 5 12 2 55 (iv) 5 10 22 33

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How Does Intellectual-Need- Provoking Task Facilitate Learning? Students encounter a problematic situation due to the limitation of their existing knowledge They experience a desire to resolve the situation Their resolution of the situation may lead to construction of new knowledge or modification of existing knowledge

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In Selecting a Need-Provoking Task, What Questions Can We Ask Ourselves? What mathematical learning can the task potentially provoke? Is the task intrinsic to students? Do students experience a limitation of their existing knowledge and a need for the new math idea in order to solve the problem?

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Recapitulation What Problems Have We Worked On Today? 1. Extending 1 2 / 3 km Line Problem 2. Finding Equal Product Problem What Concept do these Problems Seek to Provoke? Ruferent Unit & Procedure for Converting Mixed # to Improper Fraction Prime Factorization

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As a Math Teacher, You Can … Avoid problem-free tasks Provide opportunities for your students to experience the intellectual need for the math concepts that you want them to learn Select tasks that requires thinking, sense- making, exploring, justifying, and explaining

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An Article Lim, K. H. (2009). Provoking intellectual need. Mathematics Teaching in the Middle School, 15(2), 92-99.

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Thank You

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