Send-a-problem: Making the connection between data and models

Julie Smith, Lafayette College
Author Profile
This material is replicated on a number of sites as part of the SERC Pedagogic Service Project


Students in an upper division money and banking course practice analyzing economic data and incorporating the qualitative movements in data into a macroeconomic model (aggregate expenditure and output Phillips Curve models).

During the multiple rounds of problem solving facilitated by this send-a-problem, students identify how movements in macroeconomic data can be interpreted and applied to a theoretical macroeconomic model.

Learning Goals

Read and interpret graphs (Proficiency: interpreting existing knowledge)

Analyze data changes (Proficiency: interpreting and manipulating economic data)

Determine how qualitative data changes get included in theoretical models (Proficiency: applying existing knowledge)

Analyze the effects of changes in the variables in the Aggregate Expenditure-Output Phillips Curve model (Proficiency: applying existing knowledge)

Context for Use

Knowledge required: This exercise is intended to be administered after covering the aggregate expenditure-output Phillips curve model by the instructor. The aggregate expenditure model graphs the relationship between the policy rate chosen by the central bank and the level of real output; these variables have an inverse relationship. The output Phillips curve graphs the relationship between the level of real output and the inflation rate; these variables have a positive relationship. The connection between the two models is the level of real output. Here is a Sample graph (Microsoft Word 2007 (.docx) 12kB May31 12) that shows the aggregate expenditure-output Phillips curve model. (For more information see chapter 12 and chapter 13 of L. Ball Money, Banking and Financial Markets)

Class size: This exercise was originally designed for a class size of 20 to 24 students. A minimum class size of 9-12 students is suggested, but the exercise can easily be adapted for larger classes. (See teaching notes for additional explanation.)

Time required: It is designed to take approximately 35 minutes.

Description and Teaching Materials

Two handouts are provided to support this exercise. Handout for data/model send a problem (Microsoft Word 2007 (.docx) 246kB May31 12) includes each of the three exercises. Answer key send-a-problem economic data and models (Microsoft Word 2007 (.docx) 27kB May14 12) includes the answers for the three exercises.

Teaching Notes and Tips


This exercise was designed to extend the material covered in class. The textbook covers aggregate expenditure and output Phillips curve models but does not provide students the opportunity to analyze data and interpret how real-world data is incorporated into theoretical models.

Dividing the class into groups of 3-4 students determines the number of overall groups. The final number of groups should be divisible by 3 in order to fully allocate the three problems (each which asks the students to determine where and how the data will affect the model; the data presented are different and affect the model differently) during three rounds of the exercise. Following these parameters allows the exercise to be scaled up to any class size.

Each problem is affixed to a different envelope, with multiple envelopes for the same problem depending on the class size. For example, for a class size of 90, the instructor prepares 10 envelopes for each of 3 problems to be distributed to 30 groups of 3 students each. Clearly labeling each envelope with an identifier to indicate the different problem it represents (using largely written problem number indicators or different color envelopes) allows for ease of rotating envelopes at each round, ensuring that each group receives a different problem in each round.

This 35-minute exercise is comprised of the following stages: 10 minutes for the first problem-solving round, 7-8 minutes for the second problem solving round, 10 minutes for the final round critique round, and 7-8 minutes for reporting out.

The first round of the exercise takes a bit more time as it requires students to first identify important components of the Aggregate expenditure-output Phillips Curve model. The second round takes less time as they are more familiar with the problem-solving process which is congruent with the first round. Students should not be informed in advance that the final round is a critique of students generated examples in contrast to the problem-solving process of the first two rounds.

Student groups are provided their first problem and instructed that they have 10 minutes to formulate an answer to be placed in the envelope at the end of the round. After each team has had the opportunity to answer the first set of questions posed to their group and placed their answers in the attached envelope and envelopes are rotated around class in a manner that ensures that each group receives a new problem in the second round.

Teams answer a second (related but different) question, place their answer in the envelope when time is called and again pass the envelope in a manner which ensures that they receive yet another new problem.

When teams receive their third envelope they are asked (by the instructor) to read the associated questions, remove previous round answers from the attached envelope, and read these aloud to their team. Groups are asked to compile a final solution to the problem. They should use their peers answers and their own expertise to compile a final solution.

In order to use time most efficiently during each round, and reinforce positive interdependence, students can be assigned discussion roles which rotate at each round such as facilitator, reflector, and summarizer. It is important to provide an explicit description of each role as a component of the student handout so that they are indeed utilized.
  • facilitator
  • reflector
  • summarizer
During the problem solving stages of the exercise, it is imperative that the instructor move throughout the classroom checking in on students, monitoring progress and intervening when necessary. Although instructors may be tempted to directly answer student questions during this period of time, student learning is enhanced to a greater degree if the instructor guides struggling students by posing reflective questions back to them.
Further considerations:
Instructors may choose to alter the final stage of the send-a-problem in a variety of ways.
    • Students can be instructed to critique each answer included in the envelope, identifying components which are incomplete or inaccurate (as opposed to compiling a final solution to the problem).
    • Students can be instructed to read the provided question and identify the steps that facilitate the construction of a complete answer. Thereafter, they identify whether the results of each of these steps is revealed in the two solutions contained in the envelope.
Conclusion to the exercise:

Reporting back to the larger group can be facilitated by tossing a soft ball to a random group and asking them to share part of their answer. Thereafter, students toss the ball to another group to share a remaining part of the exercise. This process continues until all parts of the answer have been covered.

Alerting students in advance that some groups will be randomly called upon to explain their answers to the class at the close of the exercise helps to motivate students to work diligently on the task during class and - because the reporting out process occurs in this manner (via a somewhat random draw of students) - students are more engaged in the reporting out process.


Since students are receiving feedback regarding their understanding during each stage in the send-a-problem exercise, they are participating in formative assessment.

This send-a-problem exercise also has a formal summative assessment associated with it since students are asked to complete a similar question on their final exam.

References and Resources

Ball, Laurence. 2011. Money, Banking and Financial Markets (2nd edition). Worth.