Exploring Problem Based Learning in Mathematics Heartland
Convention 2012 Kaitlin Troost Valorie Zonnefeld
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The sage on the stage Teacher-Centered
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Guide on the Side, not the sage on the stage A Danger of Social
Constructivism Student-Centered
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Allows Gods absolute truth in mathematics to speak for itself
Uses many of the same pedagogies as student- centered
Content-Centered
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The next classroom observation, have someone draw arrows on
your seating chart for all discourse that occurs. Are all questions
directed to you? Do you repeat student questions? What is the
center of your classroom?
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Logical Thinkers Problem Solvers
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Problem-Based Learning World
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Any comments or questions? Reinforce the next day with a
Frisbee and tape measure Pi Activity
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Pattern Blocks Given the three block patterns, identify how the
pattern is growing from Case 1 to Case 3. Represent this
growth
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How did you approach this? Pattern Blocks
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Memorization Procedures Without Connections Procedures With
Connections Doing Mathematics Stein, Smith, Henningsen, and Silver
2000, p. 16 Four Levels of Cognitive Demand
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Reproducing a fact learned from memory Not ambiguous No
connection to concepts or underlying meaning 2 + 7 = Represent as a
decimal and a fraction Four Levels of Cognitive Demand
Memorization
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A recipe to follow Low cognitive demand Little ambiguity
Focused on the answer, not the process Davis wants to tile his
rectangular room which is 8 feet by 10 feet. How many square feet
of tile will he need to purchase? Four Levels of Cognitive Demand
Procedures without Connections
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Focus on the procedure to create deeper understanding A path to
follow may be suggested Often multiple representations are used
Requires mental effort Using base-ten blocks, show that.17 is less
than.2 Four Levels of Cognitive Demand Procedures WITH
Connections
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Complex thinking N0 path or recipe to follow Students need to
access necessary knowledge Cognitively demanding In my bag of candy
of the pieces are red, 1/3 are blue, the remaining 21 are white.
How many pieces are in the bag? Four Levels of Cognitive Demand
Doing Math
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Memorization Procedures Without Connections Procedures With
Connections Doing Mathematics How would you categorize the pi
activity? How about the pattern block activity Four Levels of
Cognitive Demand
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Memorization Procedures Without Connections Procedures With
Connections Doing Mathematics Can Differentiate Instruction based
on the question Students who perform best on project-based problem
solving were in classrooms in which tasks were implemented at high
levels of cognitive demand Leutzinger, L. ICTM Journal, 2010 Good
teaching demands a blend of all four levels Four Levels of
Cognitive Demand
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What could you do with newspapers Work with place value Find
Purchase car Give students a large amount of frequent flier miles
to plan a trip around Europe with. What topics could you cover with
this? What can you do with census data? Kristin Kanaskie 2011 Fall
ICTM Journal p. 4 Ideas
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Visit a creek Estimate depth Estimate water flow (Maths
Teacher, May 2012) A bag of oranges Volume Peel it to find surface
area (Maths Teacher, Oct. 2011) Stack oranges for space Ideas
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Turning everyday living activities into math Have students
record, survey, analyze, and collect data: number of texts
send/received a day hours of sleep hours of T.V. hours of favorite
activity... Students can collect data in a journal and expand using
graphs and calculations Ideas
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How much water do you use in the shower? How long does it takes
to fill up a gallon Average amount of time spent in the shower (Dan
Meyer) Exploring surface area using cheese blocks of same volume
but different surface areas Which takes longest to melt in the
microwave (Dan Meyer) Using a bike to look at speed, gears for
ratio and proportion. Using plastic cups... how many cups will you
have to stack to be the height of your teacher (Dan Meyer) Three
doors with a prize, stay with your same choice or switch? The Monty
Hall problem Ideas
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Design a mini-golf course Pull up Hy-Vees on-line add
Ideas
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Whats Math Got to Do With It? By Joe Boaler Fostering Geometric
thinking: A guide for teaching by Mark Driscoll Applications of
Secondary School Mathematics: Readings from the Mathematics Teacher
by the NCTM Problem-Based Learning for Math and Science: Integrated
Inquiry and the Internet by Diane L. Ronis The Essentials of
Mathematics, Grades 7-12 by Kathy Checkley Book Resources
Make Learning Real Make Learning Real God wrote creation in the
language of mathematics PBL allows concepts to be taught in context
- an avenue for integration of faith Dan Meyer Presentation is
posted at Bored student photo
http://www.google.com/imgres?q=bored+student&um=1&hl=en&safe=active&client=safari&sa=N&rls=en&biw=1191&bih=604&tbm=isch&tbnid=8umVDWkckUyetM:&imgrefurl=h
ttp://ecodesignproject4th.blogspot.com/2011/11/lethargic-students.html&docid=-
MNFWsymC6V7mM&imgurl=http://1.bp.blogspot.com/_dR2248KTLUs/TKX6gG7ZJII/AAAAAAAABCE/bFbK8cCNaI4/s1600/bored%252Bstudent.jpg&w=283&h=424&ei=Y4-VT8W7F-
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dsp=21&ved=1t:429,r:15,s:0,i:101 Work force picture
http://www.opttek.com/OptForce Resources
