Exploring Problem Based Learning

in MathematicsHeartland Convention 2012

Kaitlin TroostValorie Zonnefeld

The sage on the stage

Teacher-Centered

Guide on the Side, not the sage on the stage

A Danger of Social Constructivism

Student-Centered

Allows God’s absolute truth in mathematics to speak for itself

Uses many of the same pedagogies as student-centered

Content-Centered

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?

Logical Thinkers Problem Solvers

Problem-Based Learning

World

Any comments or questions? Reinforce the next day with a Frisbee and

tape measure

Pi Activity

Pattern Blocks

Given the three block patterns, identify how the pattern is growing from Case 1 to Case 3.

Represent this growth

How did you approach this?

Pattern Blocks

Memorization Procedures Without Connections Procedures With Connections Doing Mathematics

Stein, Smith, Henningsen, and Silver 2000, p. 16

Four Levels of Cognitive Demand

Reproducing a fact learned from memory Not ambiguous No connection to concepts or underlying

meaning

2 + 7 =Represent ¼ as a decimal and a fraction

Four Levels of Cognitive DemandMemorization

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 DemandProcedures without Connections

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 DemandProcedures WITH Connections

Complex thinking N0 path or recipe to follow Students need to access necessary

knowledge Cognitively demanding

In my bag of candy ½ 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 DemandDoing Math

MemorizationProcedures Without Connections

Procedures With ConnectionsDoing Mathematics

How would you categorize the pi activity? How about the pattern block activity

Four Levels of Cognitive Demand

MemorizationProcedures Without Connections

Procedures With ConnectionsDoing 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

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

Visit a creek Estimate depth Estimate water flow (Math’s Teacher, May 2012)

A bag of oranges Volume Peel it to find surface area (Math’s Teacher, Oct.

2011) Stack oranges for space

Ideas

Ideas

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

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

Design a mini-golf course Pull up Hy-Vee’s on-line add

Ideas

What’s 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

yummymath.com www.khanacademy.org blog.mrmeyer.com www.nctm.org www.coolmath.com

Online Resources

Activity Sheets

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=http://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-nh0QGEhOjmBw&zoom=1&iact=hc&vpx=270&vpy=190&dur=1465&hovh=275&hovw=183&tx=151&ty=123&sig=108937824454470224396&page=1&tbnh=122&tbnw=86&start=0&ndsp=21&ved=1t:429,r:15,s:0,i:101

Work force picture http://www.opttek.com/OptForce

Resources