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.
Getting Ready (10 min. and 20 min.)
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.)
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.
'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
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:
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:
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--
"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)
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