In-Lecture Story Problems
Dr. Kyle C. Fredrick, Department of Earth Sciences, California University of Pennsylvania (firstname.lastname@example.org)
Dr. Cailey B. Condit, Dept. of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology and Earth and Space Sciences Dept., University of Washington. (email@example.com; firstname.lastname@example.org)
Most science teachers recognize, and there is abundant research suggesting the aversion students have to math and the barriers it creates to their success in science majors. In order to support student success and overcome these barriers, instructors have developed many methods to buttress quantitative topics and build student skills. One way to improve students' quantitative skills is to establish a systematic approach to math problems to lessen their fear and resistance. George Polya (1962) published a method for solving physics problems. We have used his approach and modified it into a straightforward in-class activity.
Guided story problems in a lecture or large-group format can be a powerful tool to improve students' quantitative skills and allow instructors to give immediate feedback and follow-up reinforcement of student learning.
Skills and concepts that students must have mastered
How the activity is situated in the course
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.
Content/concepts goals for this activity
The single, general content goal is to increase students' mastery of critical reading to determine the appropriate approach to quantitative work in the sciences.
Higher order thinking skills goals for this activity
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 goals for this activity
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.
Description and Teaching Materials
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)
Teaching Notes and Tips
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.
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.