Workshop 3

Uncovering Critical Thinking Skills

About the Workshop

Moving from hands-on to minds-on work can be quite a challenge for both students and teachers. Interpreting one's experiences in a mathematical or scientific way is neither an easy nor obvious process. This is an important part of critical thinking in math and science--using evidence to build answers to questions. This workshop will focus on strategies for making critical thinking an integral part of doing math and science.

The Great Bean Bag Adventure In our first experiment, we considered "the basics" of sprouting seeds. We wanted to find out if any of the following conditions alone will cause seeds to sprout--water, light, soil, or air. What we used: 5 plastic baggies 10 paper towels 12 dry lima beans 3 lima beans soaked overnight in water water dark drawer, cupboard, or closet potting soil petroleum jelly What we did: Folded and placed two paper towels in each baggie. Labeled and prepared the baggies as follows:  condition Seed only (control) Seed + water moistened paper towel; Seed + no light 3 dry beans; Seed + soil enough soil to lightly cover paper towel; Seed + no air preparation  3 dry beans 3 beans that had soaked overnight placed in the dark 3 dry beans 3 dry beans coated with petroleum jelly

Getting Ready (10 min. and 20 min.)

1. What are critical thinking skills? Work as a group to generate a list.
2. From the list of questions that you recorded for your homework, select three that seem like they would foster critical thinking in your students. On a chalkboard or chart paper, compile questions from the group. What do these questions have in common? Can you characterize a question that fosters critical thinking?

Site Conversation 1 (5 min.)

What techniques have you used to help students articulate their thought processes? How do these techniques vary according to children's developmental level?

Site Conversation 2 (5 min.)

Harolyn Bowden says that she knows her students are thinking critically when they are able to access knowledge from an earlier lesson and apply it to the topic at hand. How do you know when your students are using critical thinking skills? What do you consider to be evidence of critical thinking in math? In science? What do you look for and listen for?

Going Further (10 min. and 20 min.)

1. Elementary school curricula is often organized by "themes." How can different content areas (e.g., language arts, social studies, etc.) be used in a way that fosters critical thinking skills and math and/or science? Discuss as a group.
2. Think about a specific activity in math or science that you have planned for the upcoming week. In pairs or small groups, work with your colleagues to generate ways of infusing critical thinking skills into your activity.

Homework for Workshop 4

By this time, you should have at least one experiment underway as part of The Great Bean Bag Adventure. Record your data and observations on a data table, and bring it with you to Workshop 4.

TRY THIS!

'Round About pi

Suggested Grade Level: 4-5

Students approximate the value of pi by measuring and comparing the circumference and diameter of common circular objects.

What You Need

String
Tape measures or rulers

What To Do

Have students find circular objects around the classroom (such as garbage cans, coins, glue sticks, and water bottles) and measure both the circumference and the diameter of each object. (If you don't have access to tape measures or flexible rulers, students can measure circumference by wrapping a piece of string around the object, and then measuring the length of string using a ruler.)

Students should record their measurements in a table similar to the following:

After students have finished their measurements, ask students to label the fourth column of their table "Comparison."

Have students compare the circumference measurements to the diameter measurements and look for a pattern. Guide their investigations by asking them to create a ratio of circumference (C) to diameter (D). This value should be recorded in the fourth column of the table.

Help students think about the ratio they created by asking the following types of questions:

• Do you notice any patterns between the ratios you made?
• Do you think that the ratio is the same for all the circles in the world?

Students' ratios should all equal approximately 3. Explain to students that this ratio is the same for ALL circles. Mathematicians have found this ratio to equal approximately 3.14 and have given the ratio its own name, pi, and its own symbol, pi.

For Younger Students

Younger students can also begin to explore relationships among circles. Try the following activity:

1. Tape or tie a piece of string to a pencil or crayon.
2. Hold the free end of the string onto a piece of paper.
3. With the tip of the pencil on the paper, pull it around in a circle, keeping the string taut.

Students can try this activity with different lengths of string. Help them discover the relationship between the length of the string and the size of the circles.

One Connection to the Standards

Standard 9: Geometry and Spatial Sense

In grades K-4, the mathematics curriculum should include two- and three-dimensional geometry so that students can--

• describe, model, draw, and classify shapes;
• investigate and predict the results of combining, subdividing, and changing shapes;
• develop spatial sense;
• relate geometric ideas to number and measurement ideas;
• recognize and appreciate geometry in their world.

"Children are naturally interested in geometry and find it intriguing and motivating; their spatial capabilities frequently exceed their numerical skills, and tapping these strengths can foster an interest in mathematics and improve number understanding and skills."

National Council of Teachers of Mathematics, (NCTM). 1989. Curriculum and evaluation standards for school mathematics. Reston, VA: The National Council of Teachers of Mathematics. (pg. 48)