# How to Teach with Context-Rich Problems

There are three key steps to teaching with context-rich problems: selecting a problem, implementing the problem and assessing what the students have done. Instructors can negotiate through this process by asking themselves a series of questions.

## Selecting a problem

**What are the concepts you want students to apply?**

Any core concept for your class is appropriate to be explored with a context-rich problem. However, context-rich problems are even more effective in developing expert-like thinking if they also require students to use concepts beyond those most recently taught.

Context-rich problems can ask students to recall and select from concepts taught earlier in the course. Repeated practice not only keeps those concepts fresh in the students' minds, but also helps to develop expert-like thinking in which solutions are never selected because they are in the currently assigned chapter.

**What is the appropriate level of difficulty or complexity for your students?**

The level of difficulty depends not only the complexity of the concept(s) incorporated into the context-rich problem, but also on the selection of the components of the context-rich problem you include.

The level of difficulty or complexity of the problem needs to be consistent with your goals for the students and where they are in the learning process. Set a learning goal for the context-rich problem. You may want to use Bloom's taxonomy as a guide for developing your learning goal. (Do you want students working on knowledge, comprehension, application, analysis, synthesis or evaluation?) Alternatively, your discipline may have developed specific categories of learning goals such as Hansen proficiencies in economics. Pedagogies such as just-in-time teaching or classroom assessment techniques can help to determine where your students are in the learning process. For example, are they ready to apply a particular concept, or are they having difficulty comprehending the concept?The level of difficulty or complexity of the problem can be adjusted. Examples of traits that increase the difficulty of a problem include (UMPERD):

- The unknown quantity is not explicity specified in the problem statement
More information is given in the problem statement than is required to solve the problems

Unusual assumptions are necessary to solve the problem

The problem requires more than one core concept for a solution

The context is very unfamiliar

Not enough information is given and reasonable assumptions need to be made

**Where do I find existing context-rich problems?**

Examples using a variety of concepts and with varying degrees of difficulty are available to use in your courses.

**How do I write my own context-rich problems?**

You can create your own context-rich problems by setting a learning goal, starting with a common prompt to set the context of the problem and choosing among a variety of components that change the difficulty of the problem.

## Implementing the problem

When and where will the students be working on the problem?

Instructors have used context-rich problems in a variety of formats: low-stakes homework for students to demonstrate preparedness for class; graded homework; in class or out of class group work; and exam questions.

- If context-rich problems are used for high-stakes testing, it is important to offer students practice in advance so they are familiar with the steps involved in solving these problems.
- If small groups are assigned context-rich problems, pay careful attention to group size, group composition, individual tasks within the group, and individual accountability for the group's work. Information about cooperative learning can help guide you in these decisions.
- If the students will be working in groups, more complex and difficult problems are appropriate.
- If the problems will be on exams, less complex problems are required to fit within the time constraints.

**How can I help students be comfortable with context-rich problems?**

Students that are accustomed to working on traditional problems may struggle with the new format of context-rich problems.

Novices in many disciplines want clear-cut, right or wrong answer problems requiring cookie-cutter application of formulas or ideas. As you introduce context-rich problems into your courses, it will help to follow an apprenticeship approach. Brown, Collins and Duguid (1989) outline three stages of the apprenticeship approach.Model- Show students explicitly the problem solving processCoach- Instructors provide students feedback as they try it themselves. Feedback can also be from peers.Fade- Students practice on their ownBefore you give students their first context-rich problem to work on, model one for them. A more difficult or complex problem is appropriate to use when you model the problem solving process. A good way to start the students working on their own complex-rich problems is to have them work in-class in small groups on the problem. In this set up, students can help to coach each other through solving the problem, but you should expect that students will also need assistance from you. As students get more practice working with context-rich problems, their need for coaching will lessen.

**How can I use context-rich problems with other innovative pedagogies?**

Context-rich problems work well with several other innovative pedagogies such as just-in-time teaching and cooperative learning. Learn more about using context-rich problems.

## Assessing the problem

**What is the purpose of the assessment?**

Context-rich problems can be used to assess individual understanding of course content, or to assess the understanding of the class as a whole. If you would like to assess individual understanding, the problem can be assigned as a homework problem or on an exam. In this case, you may want to add prompts to indicate the desired length and format. It is also helpful to give general instructions to students on information you want included such as appropriate terms or graphs.

If you would like to assess the understanding of the class as a whole, the problem can be assigned in class. It's often helpful to have the students work on the problems in groups. In particular a think-pair-share exercise is very useful. You can follow up with a class discussion to see what gaps in understanding remain.

**How do I evaluate the context-rich problem?**

In comparison with traditional "one right answer" problems, grading context-rich problem answers may be more time-consuming and complex as answers may vary greatly and at times be unexpected.

The feedback you give may be very different depending on your goals for the assignment. If your goal is to help students develop their thinking (formative assessment) a simple scoring rubric may be sufficient. Sample student answers can be analyzed in class, or in small groups. It may be helpful to have groups of students compare two or more different solutions.

For summative assessments, it is helpful to give students a rubric in advance so they understand what is expected in their answers. Such guidelines will also help to evaluate unexpected solutions as sometimes occur with context-rich problems. For these higher-stakes assignments, it is important to specify the length of the answer, its format and its intended audience. Context-rich problems often provide writing prompts that guide students on these matters. (To whom is the answer written? Should it involve diagrams or graphs? Which concepts need to be explained?)

An example of a generic coding rubric used in physics for context-rich problems can be found on this UMPERD web site.

Some of the examples include grading rubrics developed by the author of the example.

If you would like more information about assessment strategies, visit the assessment module.