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Using Mathematical Tasks To Provoke Intellectual Need

Using Mathematical Tasks To Provoke Intellectual Need. Kien Lim University of Texas at El Paso kienlim@utep.edu Sep 9, 2010. O b j e c t i v e s. What Constitutes a Good Mathematical Task? What is Intellectual Need ? Why is it Important?. S e q u e n c e O f A c ti v i t i e s.

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Using Mathematical Tasks To Provoke Intellectual Need

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  1. Using Mathematical Tasks To Provoke Intellectual Need Kien LimUniversity of Texas at El Pasokienlim@utep.edu Sep 9, 2010

  2. Objectives • What Constitutes a Good Mathematical Task? • What is Intellectual Need?Why is it Important?

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

  4. 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

  5. Purpose of Classroom Tasks Thompson, Carlson, and Silverman (2007) • 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

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

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

  8. 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)

  9. Problem #1 for You 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. 1 2/3 km

  10. Follow-up Questions #1 • 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? Referent unit (1km) Mixed num. - improper fraction conversion How? Cut into 5 pieces. 1 2/3 km Why 5? 1 2/3 = 5/3 3/4 km 1 km 1 km 1 km

  11. Problem #2 for You Consider these 4 products of numbers: (i) 25261112 (ii) 3112544 (iii) 512255(iv) 5102233 Without computing the actual value of each product, identify those products that have the same value.

  12. Follow-up Question #2 (i) 25261112 (ii) 3112544 (iii) 512255(iv) 5102233 = 24 32 52 11 = 22 352  112 = 24 32 52 11 = 22 352  112 What do you think is the math concept for which this task is trying to provoke?

  13. 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

  14. 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?

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

  16. 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

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

  18. Thank You

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