In-Lecture Story Problems

These activities are flexible enough to be used in any number of courses at almost any level. We use the technique mostly in upper-division geoscience courses, but they could be used from middle-school math and science courses up to graduate-level science and engineering courses. Any course and topic that lends itself to challenging students with story problems and leveraging their prerequisite math skills to solve an applied problem.

For our implementation in an undergraduate Hydrology or Structural Geology course we have prerequisite courses of college-level Algebra or Trigonometry, respectively. But any instructor wishing to use the technique can consider what they expect students to already KNOW as well as what they want the students to gain. In some ways, this activity can be used as a way to put students within a class on more equal footing.

We use these activities throughout the course and in a few different ways. Nearly every lecture includes at least one story problem and some days we do up to three of them. They are addressed using the following options:
A stand-alone activity for no grade as a simple group activity and mechanism to spur discussion and faculty feedback on math practices.
An in-class assignment where the instructor collects the students work and evaluates their individual (or group) responses for a low-stakes assessment.
A review tool as a "road-check" for a given topic or for an upcoming exam.

Goals are completely dependent on the topic, grade-level, and instructor's priorities.
The single, general content goal is to increase students' mastery of critical reading to determine the appropriate approach to quantitative work in the sciences.

For our purposes, the higher-order goals are:
1. Ascertain students' current math competency and ability to critically evaluate a story problem to find the important information.
2. Connect students' current math competency to science concepts.
3. Increase active learning in classes, especially allowing for teacher/student interaction and immediate feedback.

Other skills/qualities students may gain include:
1. Improved confidence in accessing prior knowledge to solve problems.
2. Critical thinking and appreciation of quantitative scales and physical bases of data.
3. Working in groups and public speaking.

In-lecture story problems are a simple, flexible method for incorporating quantitative skill-building into your classes. They are based on installing a systematic approach to applied math problems where students divide up a story problem into "Given/Find/Solve" steps. It requires a critical reading of the problem, parsing at the single word scale, trying to absorb physical meaning from the description. Students explicitly write each of the "Given" variables, identify the "Find" variable, the intended result, and follow with "Solve," to select the appropriate equation and calculate the solution.
A single, one-off story problem can be a useful interjection of activity into a standard lecture. A more involved, scaffolded approach to walk students through a challenging, layered problem is an opportunity to guide students and provide feedback as you ask them to harness their basic math skills.
The basic design is to include a story problem within a lecture (or even a lab or discussion section) as a pause to have students critically evaluate a quantitative problem relevant to the science topic at hand.
For example, in Hydrology, we might be introducing watersheds and water balance. It is useful to have students calculate volumes of water and flow out of the system based on a rain event within the watershed area. This isn't necessarily intuitive for many students and can be frustrating because it SEEMS like it should be easy. But often, they aren't sure how to even begin to set up the problem.
Included in the supporting materials is a Power Point document that includes an explanation and two examples. The first example is from a sophomore- to junior-level Hydrology course. The topic is from later in the semester as we transition to Groundwater.
The second example is from a junior- to senior-level Structural Geology course. The students are posed a hypothetical field scenario and need to develop an accurate stratigraphic column from dipping strata.
Slide set w/ Examples (PowerPoint 2007 (.pptx) 93kB Jun2 21)

This activity is very flexible and can be as simple or complicated as an adopter would like. However, there are some tips that will make the activity run more smoothly and enhance your courses and improve students quantitative methods and skills.
1. Use the activities regularly. A one-off quantitative activity is minimally useful because most of the students will not engage and let a few students work through the problem and answer questions. The more you do it and the more active you make it (follow-up questions, individual student call-outs, think-pair-share, etc.) the more receptive students will be.
2. Have clear tie-in to content. The power of the activity is establishing the relevance of math to the scientific topic.
3. Use 1-3 problems in any one lecture. One or two is best, because it encourages time for follow-up discussion and possibly redoing the problem as a group.
4. Ask students to write down the words "Given," "Find," and "Solve." I even require it for homework problem sets and encourage them to use this approach on exams!
5. Give them enough time to work through the problem individually or in groups of 2-3. Ensure that students are each completing the calculations!
6. Model good practice by going through the problem this way yourself during a debrief and other classroom demonstrations of solutions. I upload my own hand-written solutions to problem sets after students have completed and submitted the homework. They can compare my solution to theirs after they've been graded and returned.

The three approaches we take with In-lecture Story Problems are (1) low-stakes concept introduction or practice problem, (2) low-stakes content review or targeted pre-exam review, and (3) graded in-class assignment.
Assessments of these approaches are as follows:
(1) Concept introduction or practice problems are not formally assessed, but followed up with a class discussion and question/answer session. Informal assessment includes polling the class for completion and correct answers. If students are getting incorrect answers, or report confusion, it is important to address it quickly and in a positive way. The goal is to improve their approach to and comfort level with math.
(2) Content or pre-exam review are assessed in much the same way as above. However, it is helpful to follow up with additional, alternative problems to ensure reinforcement. With a looming exam, it is critical to reduce student fears rather than increase them.
(3) In-class assignments are given as problems for students to work on briefly (less than 10 minutes) during lecture individually. They are collected and graded. Grading is done similarly to exams, with variable points based on correctness, completeness, organization, inclusion of units, significant figures, and reasonableness of answer (if incorrect), The grading encourages students to practice care in completing problems and pay attention to details. Grades are usually on a 5- to 8-point scale, with partial credit awarded on the aforementioned criteria. For example, a correct answer with all work shown may be worth the full value of an 8-point problem. An incorrect answer, but with the correct procedure but also missing the units may be worth 5 points.

POLYA, George. Mathematical discovery. On understanding, learning, and teaching problem solving. Combined Edition. New York, Chichester, Brisbane, Toronto: John Wiley & Sons, 1962.