Adam Mills, Teacher Assumption College Catholic High School
adam_mills@wecdsb.on.ca

As discussed in Part 1 of this series of articles, one of the major goals within my Physics courses is to expose my students to problem solving. In order to complete this I have my students engage in context rich problems through a cooperative group problem solving (CGPS) setting. Please refer to the previous article to see the initial setup I use in order to get my students ready to appropriately participate in these types of problem solving opportunities.

I have my students engage within their groups in solving context rich problems at least once a week if not more. Below I have shown an example of a context rich problem that I have the students complete immediately after they have been introduced to the concept of the constant acceleration equations.

You have just received your G2 and are so excited to drive on your own. While driving down the road one day at a leisurely 60 km/h you notice a mother goose walk out onto the road about 30 m ahead of you. From the time you see the goose to the time it takes your foot to start pressing on the brake is about 1.2 s (reaction time), as you slam on the brakes your car slows at a constant rate of 6.0 m/s2.  Does mother goose live?

Having your students use class time to work through problems like the one above will likely provide better insight into their understanding than having them complete standard textbook problems. Many textbook problems are such that novice problem solving strategies, like pattern matching and plug and chug, can successfully be applied without the students actually thinking about the physics behind the situation. Let’s take a look at some of the features of the above style of problem that differentiate it from a standard textbook question.

1. Limited use physics terminology.
By limiting the use of standard physics terms like constant acceleration or begins at rest, the students are required to apply their physics knowledge and make assumptions based on the context of the physical situation.

2. A direct physics question is not asked
In the above question instead of telling the students to find the displacement of the car, they are instead asked if mother goose lives. It is up to them to infer what physics quantity they need to determine in order to answer the question. It is important that while applying their problem solving strategy they explicitly write down what physical quantity they are trying to determine. Furthermore, there are some values stated, like the fact that the goose is 30 m away, that the students need to be careful in using.

3. Difficult if not impossible to use one equation in order to solve the problem
Many end of the section problems in our textbooks allow the students to be successful with the plug and chug strategy without ever engaging the problem. They typically look for values given, match them to physical quantities from a formula, complete some algebraic manipulation and obtain an answer. If this answer matches the back of the book, success! If it does not try a different equation. I find the above situation to be especially true when I ask students to solve constant acceleration problems. However, the example problem above does not allow a single equation to be used. The students are forced to fall back onto a problem solving strategy and work through the steps in order to obtain a solution.

Furthermore, I have seen students both strong and weak not even really use ‘equations’ to solve this problem but rather the area under a velocity time graph, which they had to draw in the Physical representation of their problem solving template.

4. Difficult to find a pattern matching solution to get an answer
By creating a realistic situation, as well as avoiding common physics cues, the students have a very difficult time matching the problem to a previous problem completed in class. Again this demands that the students fall back on their problem solving strategy.

5. Difficult to solve the problem without analyzing the situation
Finally by making the problem wordy and not providing any visuals, the students are required to really think about the physical situation they are presented with first before ever attempting to choose an equation. The method of representing the situation pictorially allows the students to analyze the problem, state the known and unknown variables and begin to get a feeling for how to approach the problem.

The major problem for us is making up these context rich problems for the students to complete in collaborative groups. Luckily, Heller and Heller have already created a vast library of such problems organized by topic.

The way that I apply these context rich problems in my classroom is two-fold. The weekly problems are used for assessment as learning opportunities. On these days the students are given the problem at the beginning of class with a limited number of formulas on the board at the front of the room. They must work together with their whiteboards using our problem solving strategy to develop their solution. This work period lasts for about 45 minutes. For the remainder of class the students move around the classroom looking at other group’s solutions including myself. During the last 10 minutes of class I highlight areas from various groups that were very well done and I provide a sample solution on my course website.

At the end of each unit I also have the students complete one of these problems and it is an assessment of learning opportunity. The format is very similar to the one described above; however, I usually try to create a problem that involves the students actually testing their solutions in the laboratory. I have found these days to be some of the most successful classes of the semester, as the students become very involved in achieving the results their solutions provided.

Here is an example of one of the assessments I use for my Grade 11 Physics class at the end of the Dynamics unit.

Mission Impossible
You are designing a stunt for a new action movie, in which a car is traveling along a road in a straight line with a constant speed. A package attached to a pulley system will be dropped once the car passes the laser sensor and must land directly in the car as it passes underneath the drop point. Your job is to determine the mass of the package that is required for it to land in the car as it passes by. The ‘stunt’ parameters have been set up in the back of the laboratory so that you can determine your constraints.  

With 10 minutes remaining in class you must have your package filled with the correct mass for testing. NO PRE-TESTING IS ALLOWED! You may only use the back setup to determine your constraints.

For this problem the students are provided with a visual of what is required since the system is setup at the back of the classroom.  The basic configuration is shown in the diagram below.



As I am sure you can deduce there is a lot of information that the students need to determine, such as the speed of their constant velocity car, the friction that exists in the sliding mass, the distance the package will drop etc. Very often when presented with context rich problems like the one above the students spend the majority of their time assessing the physical situation. There is no jumping to formulas right away since there is too much information for them to process before hand. Finally the testing phase usually engages the students on another level. Towards the end of class they eagerly await to see if their car will indeed catch the package.

References

1. Heller, Pat and Heller Ken, ‘Cooperative Group Problem Solving’, University of Minnesota, http://groups.physics.umn.edu/physed/Research/CGPS/CGPSintro.htm.
2. Heller and Heller — Context Rich Problems — http://groups.physics.umn.edu/physed/Research/CRP/on-lineArchive/ola.html

Tags: Pedagogy