“SEES” the Problem: A Critical Thinking Strategy for Solving Word Problems in Math

Author

Dr. Scott H. Demsky

Department of Mathematics

Broward College

Citation

Demsky, S. H. (2015). "SEES" the problem: A critical thinking strategy for solving word problems in math. Broward College.

Description

The “SEES” strategy is a step-by-step methodology that is intended to help undergraduate math students solve real-world application problems.  Real-world application problems in math, often called “word” problems, generally prove to be difficult for undergraduate students, requiring practice in a specific set of problem-solving skills.

The implementation of the “SEES” strategy which is outlined in this document is intended for use in Math for Liberal Arts I (MGF1106) at Broward College, a course for non-STEM (Science, Technology, Engineering and Mathematics) majors who are using this class to fulfill their 6-semester credit General Education requirement in mathematics.  Students are asked to use the “SEES” problem-solving template as part of 4 assignments which cover topics in the 4 content areas of the course:

  • Sets
  • Logic
  • Geometry
  • Probability and Statistics

However, it would be relatively straightforward to develop assignments which use the “SEES” template in other mathematics courses which require students to solve word problems.

DQP proficiencies addressed by this set of assignments

Specialized Knowledge
In order to successfully solve this set of problems, the student needs to understand and apply the following topics:

  • Set relationships and operations, and Venn diagrams
  • Logical and symbolic arguments, validity of arguments and truth tables
  • Similar triangles and proportions
  • Probability of an event

Intellectual Skills
The student needs to apply analytic and quantitative skills to solve the assigned problems. In addition, the student needs to utilize good communication skills to present their solutions in a step-by-step manner.

Broad and Integrative Knowledge
The last of the four assignments integrates knowledge and issues in the areas of mathematics, science, and safety. Clearly, mathematical knowledge is required to solve the probability problem. Although the given scenario is hypothetical in nature, it is very reminiscent of the 1986 Space Shuttle Challenger disaster and the findings which resulted from the subsequent inquiry. It was learned that the O-ring which failed and caused the disaster was known to have a very small, but positive, probability of failure. As demonstrated in the solution to this assignment, the mathematical nature of probability says that the probability of at least one failure increases as the number of launches increases. Thus, information about such potential failures must be communicated and must be adequately addressed in order to ensure the maximum safety of the participants.

Applied and Collaborative Learning
First, the student can apply the problem-solving strategy that they learn in these assignments to many other situations and disciplines beyond mathematics.  Second, the student will be capable of applying one or more of the specific outcomes learned to varied real-world problems, including:

  • Organizing and analyzing data
  • Constructing valid arguments
  • Using triangulation to measure large objects
  • Calculating the likelihood of events and, thus, being capable of making informed decisions to help ensure individual and public safety.

Civic and Global Learning
The last of the four assignments provides knowledge, thought processes, and insights that could better enable students to make informed safety decisions, resulting in a benefit to civic welfare.

Background and Context

In the Fall Semester of 2013, Broward College began implementation of its 5-year Quality Enhancement Plan (QEP).  One of the goals of the QEP is to enhance students’ critical thinking skills.  This goal is being addressed by enhancing assignments in selected courses using Broward College’s four Student Learning Outcomes (SLOs):

  • Explain questions, problems, and/or issues
  • Analyze and interpret relevant information
  • Evaluate information to determine potential conclusions
  • Generate a well-reasoned conclusion

In the academic year 2013-14, I created a template for solving word problems in College Algebra (MAC1105).  In 2014-15, I wanted to implement a similar strategy in Math for Liberal Arts I (MGF1106), a course in which a large percentage of the problems are word problems from the areas of Sets, Logic, Geometry, Probability and Statistics.  I adapted the SEE-I method of Paul, Elder and Nosich (of the Foundation for Critical Thinking) in conjunction with Broward College’s SLOs to create a step-by-step methodology for solving word problems that I call “SEES the Problem.”  “SEES” stands for State, Elaborate, Exemplify and Solve.  The four steps in the “SEES” process are:

  1. State the problem in your own words.
  2. Elaborate the problem:  discuss the purpose, assumptions, relevant information, questions.
  3. Exemplify and/or illustrate the problem:  describe the problem with an example, counterexample, picture, diagram, graph, etc.  This may help clarify your “point of view” and suggest potential conclusions.
  4. Solve the problem:  use mathematical concepts and reasoning to make inferences and draw a conclusion.  What are the implications and/or consequences of your conclusion?

The assignment file begins with a “SEES Overview” and “SEES Template” included with this submission.  The first file shows the relationship between the “SEES” process and Broward College’s SLOs.  The second is the template that I ask the students to complete when they use the “SEES” process to solve word problems.

Assignment

The 4 assignments can be found in the assignment file in the following order after the overview and template:

  1. “SEES – Sets Assignment.pptx”
  2. “SEES – Logic Assignment.pptx”
  3. “SEES – Geometry Assignment.pptx”
  4. “SEES – Probability Assignment.pptx”

In each of the above presentation files, the assignment is preceded by a similar example which is fully solved using the “SEES” methodology along with the relevant mathematics.  Here is a brief description of each assignment along with any notable differences between the example and the student assignment:

  1. Use a Venn diagram with 3 sets to analyze the given survey data.  The structure of the survey data given in the example is slightly different from that of the survey data given in the assignment, so the students will need to recognize this difference and alter their analysis as required.
  2. Convert a logical argument to symbolic form, and then create and analyze a truth table to determine if the argument is valid or invalid.
  3. Use similar triangles to determine the height of a tree. The format of the given information in the example is slightly different from that of the information given in the assignment, so the students will need to recognize this difference and alter their analysis as required.
  4. Use principles of probability to determine the likelihood that a repeatable event will happen at least once.

Rubric or Criteria

The Grading Rubric used for these four assignments can be found in the file “SEES Grading Rubric.pdf” included with this submission.  In this particular class implementation, the 4 assignments constituted 10% of the student’s course grade.

Alignment and Scaffolding

Each of the 4 assignments described here occurs at or near the end of its respective major class topic (Sets, Logic, Geometry, and Probability).  The students need to learn the content of the relevant section and to practice the associated skills through their homework assignments in order to be prepared to succeed on these particular assignments.  The “SEES” process gives them a structure for breaking down and solving these more advanced problems.  It is the hope that this process and the experience that the students gain using this process will help them to solve more complex problems in the future, whether or not it is in an educational environment and regardless of the specific discipline.

Reflections

As of the date of this submission, I have just completed the first implementation of these assignments in two sections of Math for Liberal Arts I (MGF1106).  In one section, the overall class average on these 4 assignments was just under 60% and in the other section it was just under 70%.  The last of these assignments will also be evaluated this summer by an independent team of graders using Broward College’s Critical Thinking Scoring Guide.

I believe that the students found these assignments challenging on two fronts:  i) the advanced nature of the mathematical content in comparison with the overall content of the entire chapter; and ii) following the step-by-step structure imposed by the “SEES” process.  Due to the rather large amount of content that is required by the course outline, I found it difficult to spend enough time teaching the students how to use the “SEES” process for solving more than just a few problems using critical thinking.  If more time could be focused on that activity, inside and/or outside of class, I think it could result in increased student success on these assignments as well as increased use of critical thinking by students in the future.


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