Unit 1 - A need for change
Unit Objectives
- When given a prompt, participants will be able to describe the need for problem based learning tasks.
- Participants will be able to reflect upon the impact of PBL in the mathematics classroom.
- Participants will be able to identify questions within mathematics texts that can be modified to be more problematic.
- When given varying problems, the participant will be able to compare and reflect upon the problematic nature of each.
Getting Ready
Introduction
You may have read a recent report titled “U.S. Teens Lag as China Soars on International Test;” the report read that 15-year-olds in the U.S. ranked 25th out of 34 other countries on a mathematics test (http://www.bloomberg.com/news/2010-12-07/teens-in-u-s-rank-25th-on-math-test-trail-in-science-reading.html). Why are we so low on this ranking? The top ranking school, in Shanghai China, was reported in the article to have reduced rote learning while offering more choice in curriculum at the local level (student/teacher). This was not the only suggestion offered to U.S. schools, but is the one suggestion that we can work towards in our own classroom. You may not have the ability to change the curriculum, but by offering students more choice in their knowledge construction we may be able to make changes. With problem-based approaches the teacher is able to offer a significant amount of choice to the learner, as well as promote knowledge construction, rather than rote-learning.
Reflection
Reflect upon the way in which you were taught mathematics in secondary school. What was the role of the teacher in the classroom? What was the nature of the tasks in the classroom? Was there any one particular teacher that made learning math exciting? If so, why do you think that was the case? Was there any one teacher that made learning math tedious or boring? If so, why do you think that was?
Lesson
What is Problem-based learning?
Problem-based learning can best be described as a student-centered activity that engages students in solving an authentic real-world problem. Consider the following example: “Jim is twice the age of his brother Bob, who is 2 years younger than their cousin Phil. Together the sum of their ages is 22. How old is each person?” Do you believe that this situation is authentic? Considering the fact that the last time I wanted to know someone’s age, I asked them for it, and they responded with a numerical, not algebraic, answer, we can conclude that this situation is far from authentic. Can you think of an example which might be authentic? Perhaps having students design a garden plan for a school courtyard would be both authentic and fit the curriculum needs. Most authentic situations leave students to have to figure out a large amount of information before delving into the problem. So, if in the above situation we told students the dimensions of the courtyard, the situation would not be as "problematic" for students, and would therefore require less thinking. The goal in problem-based learning is to encourage as much thinking as possible! Problem-based activities have no limit on length, they can be as short as a quick problem-of-the-day or as long as an entire unit of study. Keep this fact in mind as you go through the course.
Video
As you watch the video for this module, you will see examples of a specific approach to problem-based learning. Furthermore, you will see how highly structured mathematics problems (questions) can be transformed into authentic learning situations for students. Pay close attention to how Dan Meyer approaches these varying problems and try to relate the video to your own classroom. The video can be accessed using the following link: Math Class Needs a Makeover
Reflection
Reflect upon the following questions regarding the video for this unit.
- How can Dan Meyer's approach support a problem based learning environment?
- Can you offer any specific questions from the text that you use in your classroom that can be modified in the ways that Dan Meyer suggests?
- What are some of the problems that you see arising with such implementation?
- How can such an implementation positively effect students?
- What does assessment look like in such an implementation?
Put it into Practice
Can you make the following "problem" more problematic?
| A snack company decides they are going to increase the amount of potato chips in a standard size bag. They decide to increase the amount from 12 ounces to 16 ounces.
(a) What is the difference between the original size and the new size? (b) What is the percent increase from the original size to the new size? |
 |
Compare and Contrast
How does the following "problem" compare with the above problem? What makes this "problem" inherently more problematic? Is it an appropriate task for learners?
| Suppose the bag of chips pictured now contains 18 oz of chips. How much did the original bag contain? |  |
References and Resources
Dan Meyer. (May 2010). Math class needs a makeover [Video File]. Retrieved from http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html
Wiki Links
Move on to Unit 2 - Anatomy/Implementation of a Problem Based Lesson