using mathematical tasks to provoke intellectual need
DESCRIPTION
Using Mathematical Tasks To Provoke Intellectual Need. Kien Lim University of Texas at El Paso [email protected] 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. - PowerPoint PPT PresentationTRANSCRIPT
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Using Mathematical Tasks To Provoke Intellectual Need
Kien LimUniversity of Texas at El Paso
Sep 9, 2010
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• What Constitutes a Good Mathematical Task?
• What is Intellectual Need?Why is it Important?
Objectives
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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 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)25261112 (ii) 3112544
(iii) 512255(iv) 5102233
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What do you think is the math concept for which this task is trying to provoke?
Follow-up Question #2
= 24 32 52 11 = 22 3 52 112
= 24 32 52 11 = 22 3 52 112
(i)25261112 (ii) 3112544
(iii) 512255(iv) 5102233
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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