Criticial Thinking in Science & Math

As previously noted, the work of John C. Bean has guided much of our faculty resource development. Here’s Bean’s 10 strategies for designing critical thinking tasks (pp. 151 – 159)

  • Tasks linking course concepts to students’ personal experience or previous knowledge
    • Describe a time when…
    • Think of an example of personal experience with…
    • State what you know & what you wonder
    • Math prompt from Bean (p. 151)
  • Explanation of course concepts to new learners
    • Sample prompts  (from Bean, p. 152)
      • Explain to your mother why water stays in a pail when swung in a vertical circle around your head
      • Write a procedure for finding the number m modulo n that a fifth grader could understand
      • Using layperson’s language, explain to a new diabetic what is meant by the glycemic index of foods and why knowing about the glycemic index will help the diabetic maintain good blood sugar levels
  • Thesis support assignments–Give a thesis and ask for development of arguments both for and against the thesis
    • Sample prompts (from Bean, p. 153)
      • People suffering from schizophrenia or manic-depressive disorder should/should not be forced to take their medication
      • An electric dipole is place above an infinitely conducting plane.  The dipole does/does not feel a net force or a torque.  Explain.
  • Problem-posing assignments
    • Problems can be explored through thesis development/defense or with less formal exploratory writing
    • Sample prompts
      • From Bean (p. 153-154)
        • An hourglass is being weighed on a sensitive balance, first when sand is dropping in a steady stream from the upper to lower part and then again when the upper part in empty.  Are the two weights the same or not? Write an explanation supporting your answer to this question.  Write to a fellow student who is arguing for what you think is the wrong answer
        • Your thirteen-year-old-brother mailed you a cartoon showing a picture of Frank and Ernest taking a number from a dispenser at an ice-cream parlor. The number they draw is the square root of -1.   Ernest has a puzzled look on his face. Your brother is taking a pre-algebra class and is familiar with the idea of square roots such as the square root of 4 = 2. He also knows how to do arithmetic with positive and negative integers. However, he does not understand the cartoon and wants you to explain it to him.  Prepare a written explanation for your brother that builds on his current mathematics background
      • Suppose you have a younger sister who is taking biology in high school. She comes home angry about a question he has gotten wrong on a genetics test. “It’s not fair”, she says, “I know my answer is correct. We learned that when two heterozygotes are crossed, 25% of the offspring will be recessive. There was a true/false question on the test about a pair of orange tigers who had a total of 8 cubs together in the course of their lives. 7 were orange and 1 was albino. The question asked if it was true or false that the tiger parents were heterozygous. It has to be false because they didn’t get 25% of their offspring being albino. You can do a Punnett square to show what’s supposed to happen”. In complete sentences, explain to your sister why the tiger parents in this question do in fact have to be heterozygous and how these results may be explained.
  • Data-provided assignments—the flip side of a thesis-provided assignment with students deducing the thesis/argument that the data supports
  • Template assignments
    • See tip
    • An example from Bean (p. 155)
      • Based on yesterday’s discussion, our class hasn’t resolved the question of ______. Several of my classmates argued that __________. I agree with them that ________. However, they are mistaken when they _______.  In contrast, I argue that _____.
  • Assignments with role-playing or “what if” situations
    • What if an extinct animal was resurrected
    • What if life was found on another planet
    • What if your telomeres stopped shortening
    • A prompt from Bean (p. 156)
      • Assume that space scientists, working with sports clothing manufacturers, have developed a superflexible space suit that allows athletes to run and jump freely on extraterrestrial soil.  As an all-world sports-promoter, your uncle, Squeebly Rickets, decides to schedule an exhibition baseball game on the moon.  One of his first tasks is to provide instructions for laying out the baseball diamond and outfield fences.  But then he begins to wonder, How will the lack of atmosphere and the greatly reduced gravitational force affect the game? For help, he turns to you as an expert in physics.
  • Summaries or abstracts of articles or course lectures
    • 5 minute summaries at the end of every lecture help reinforce learning
    • A prompt from Bean (p. 157)
      • Write a four-sentence summary of the attached scientific paper, followed by four questions.  Your first four sentences make up a four-sentence summary of the scientific article—one sentence for each section of the paper.  Recall that the Introduction states the question addressed in the study and explains why the question is important.  Methods tells how the question was answered. Results shows the outcome of the experiment, and Discussion analyzes the results and suggest the impact of the new knowledge.  Your second four sentences are four questions raised in your mind by the article
  • Dialogues or argumentative scripts
    • What would the ______ say to the ____________
    • Write a short dialogue between Darwin and Lamarck
    • Think of a controversy in your field and ask students to write dialogues between characters with different points of view
  • Cases and simulations—consider creating short cases adapted from recent news stories, campus events, or developments in your field and require students to assume the role of someone inside the case

For more ideas, see: