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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 Presentation
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Using Mathematical Tasks To Provoke Intellectual Need
Kien LimUniversity of Texas at El Paso
Sep 9, 2010
• What Constitutes a Good Mathematical Task?
• What is Intellectual Need?Why is it Important?
Objectives
Sequence Of Activities
1. Find out what constitute a good mathematical task
2. Solve a few problems
3. Discuss
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
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)
Characteristics of a Good Task
• Mathematically driven
• Requires justifications and explanation
• Intrinsic to students
Van de Walle (2003)
Tasks that Motivate Students
• Extrinsically Motivating Something new (e.g., manipulatives)
Fun and exciting (e.g., game)
• Intrinsically Motivating Intriguing
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)
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
• 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
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
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
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
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?
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
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
An Article
Lim, K. H. (2009). Provoking intellectual need. Mathematics Teaching in the Middle School, 15(2), 92-99.
Thank You