Saturday, February 4, 2012

How to Encourage Critical Thinking in Science and Math

Posted by David Wetzel

Critical Thinking

Critical Thinking

Encouraging students to use critical thinking is more than an extension activity in science and math lessons, it is the basis of true learning.

Teaching students how to think critically helps them move beyond basic comprehension and rote memorization. They shift to a new level of increased awareness when calculating, analyzing, problem solving, and evaluating.

Another way to view the power of critical thinking – as students learn how to apply and use higher order thinking skills, they learn how to question the accuracy of their solutions and findings.

Students wonder why they got the results they did and not another outcome. This in turn leads to internalization of concepts, along with all important point of making connections with related concepts.

Teaching Critical Thinking

Some students have the natural ability to ask higher cognitive questions. Specifically when evaluating experimental findings in science or solving math problems. However, many students do not have this innate skill and need to learn how to ask higher order questions.

An important point for encouraging students to use critical thinking is by modeling these skills for your students. Students will inherently follow their teacher’s lead; this is why it is important to practice what we preach.

The following are examples of questions to ask your students to encourage them to think critically (Richard Paul).

Probing

  • What additional information do you need to solve the problem?
  • How does the data relate to your findings?
  • How does the evidence support your conclusions?
  • What would you need to do to determine if the solution is true?
  • How can you compare this with other problems?


  • Are their alternative solutions to the problem? If so, what are they?
  • What else may be true if this is correct?
  • What effect would _______ have?
  • What do you mean by that statement?

Implication

  • How could you ask that question differently?
  • What did you learn from solving this problem?
  • Is this the most important question to ask when solving the problem?
  • What questions need to be answered before answering this question?
  • What does this presume?

These questions all have one purpose – keeping the train on the track by guiding students through the critical thinking process. When you ask these and similar questions, you are encouraging your students to move from passive to active learning.

Avoiding Questions Easily Answered on the Internet

Questions and problems easily answered through a quick query on the internet are not an effective strategy for teaching critical thinking. Students need questions which require them to create a product to show what they learned. The following examples are referred to “Google-Proofing” in some circles.

  • Construct a data table and graph to display a comparison of cost of three competing cell phone companies.
  • Design an investigation to determine the best materials for building a hurricane proof house.
  • Compare the organs in the human body with other mammals.
  • Create a board game based on geometric shapes.
  • Redesign an existing product to reduce its carbon footprint.

The goal is to help students learn how to develop higher level questions and make connections when solving math problems or analyzing experimental data.

Quality Thinking In order to support quality critical thinking, the frequency of questions is not as important as the quality of questions. Also, increasing wait-time between teacher-student-teacher is important to success with teaching quality thinking. According to Kathleen Cotton, the following are factors to consider when asking students questions.

  • The average level of questions asked by teachers are 60 percent lower cognitive, 20 percent procedural, and 20 percent higher cognitive.
  • Increasing the frequency of higher cognitive questions to the 50 percent level produces superior gains in middle and high school student achievement.
  • Asking higher cognitive questions does not reduce student achievement on lower cognitive questions.
  • With predominate use of lower cognitive questions; students tend toward lower achievement.

The use of higher cognitive questions tends to elicit longer student answers in complete sentences, quality inference and conjecture by students, and the forming of higher level questions. This in turn results in increased student use of critical thinking and classroom participation. There is never a wrong time to begin encouraging your students to use critical thinking skills, so why not start today.

Sources

Cotton, Kathleen, Classroom Questioning, North West Regional Educational Laboratory.

Paul, Richard, Critical Thinking: How to Prepare Students for a Rapidly Changing World, Foundation for Critical Thinking.

The Best Resources in Teaching & Learning Critical Thinking in the Classroom


More Discrepant Events in Science

Posted by David Wetzel

Science Discrepant Events

Science Discrepant Events

The following are discrepant events that does not turn out as expected.

These anomalies challenge students’ beliefs and makes them more receptive to learning what you want them to learn.

Alcohol and Water Miscibility: Discrepant Event

Miscibility means how completely two or more liquids dissolve in each other.

Materials Needed per Group: two 50 mL beakers, 0ne 100 mL beaker, 100 mL water, 100 mL ethanol

Students complete the following:

Add 50 mL of water to 50 mL of water. They

Add 50 mL of ethanol to 50 mL of ethanol, you get 100 mL of ethanol.

However, when 50 mL of water is added with 50 mL of ethanol?

They get a 96 mL solution.

Why?

The water and ethanol molecules are different sizes, with the ethanol molecules are smaller. Some of the ethanol fits in the spaces between the water molecules.

Think about two other materials: a liter of sand and a liter of pebbles. If you pour the sand into the pebbles, the total volume will be less than two liters, because some of the sand fills in the spaces between the pebbles.

Bernoulli’s Principle: Discrepant Event

Materials Needed per Group: two empty soda cans, 23 straws, one metric ruler

Students complete the following:

Place 22 straws side-by-side 1 cm apart.

Place the two empty soda cans on the straws 5 cm apart.

Two empty soft drink cans are placed on several drinking straws. Air pressure forces the cans to roll toward each other.

Using the remaining straw, blow between the cans.

The cans roll towards each other until they collide.

Why?

As the velocity of the air between the two cans increases (being blown away), the pressure the air it applies to the inner sides of the cans decreases.

This allows the air on the opposing sides of the cans to push the cans towards to the area of lower pressure.

Ensure students understand that the air pressure on the outer sides did not increase, rather it was the decrease in pressure between the cans that allowed the cans to roll towards each other.

The cans were not “sucked” together. They were pushed together.

Additional Resources

Teaching Science using Discrepant Events

Mysterious Floating Cork

May the Force Be With You

More Discrepant Event

Math Problem Solving Game

Posted by David Wetzel

Often there are times in class when students finish their work or test early. Instead of students twiddling their thumbs physically or mentally, give them a challenging math problem to solve. Problem solving in math promotes critical thinking and math reasoning skills, as students develop solutions to complex mathematical situations.

The Problem

A strategy game which takes advantage of the movements of a specific chess piece - the Knight.

Knights can only move 2 spaces forward and then 1 space to the right or left or 1 space forward and then 2 spaces right or left.

The Challenge

How can a knight in the lower left hand corner of a 5×5 grid visit each square exactly once?

The knight may not revisit a square.

The Procedures

Students can select anywhere to start on the 5 x 5 grid.

Place a 1 in the starting square.

Then place a 2 in the next square and so forth as the strategy game continues

One excellent characteristic of this game is that there are multitude of solutions. Here is one solution:

Extensions

Use different size grids, such as 8 x 8 or 6 x 6.

Additional Math Problem Solving Resources

12 Tips for Solving Word Problems

Math and Problem Solving Skills

Math Teaching Strategies that Challenge Students