Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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Workshop 1

About the Workshop

When teachers elicit students' ideas at the beginning of a unit or an activity, making the transition from these ideas to student-centered investigations is often a challenge. How can students' ideas lead to productive hands-on, minds-on, and meaningful investigations? During this workshop, we'll consider how teachers can move students' thinking from exploring what they already know, to asking a question about what they want to know. We'll also consider how the ideas that emerge during an open-ended exploration or a brainstorming session might be "finessed" toward the learning goals intended by the teacher.

The Great Bean Bag Adventure

What does a seed need to sprout? We begin the Adventure by focusing on an old favorite—the bean—and we invite you and your colleagues to join us in the Adventure.

Getting Ready (15 min. each)

  1. What is your metaphor for teaching? Do you think of yourself as a midwife? A tour guide? A baker? Or maybe your metaphor is not a person, but an object, like a mirror, or a teleprompter, or a tape recorder. Take a few minutes to think about your metaphor, and then, as a group, share your metaphors and discuss the following:

    What is your role in your metaphor? What is the role of your students? How does your metaphor shape your approach to teaching and learning? How does it shape the expectations of your students?

  2. Working in pairs, answer the following: What does a seed need to sprout? Record your answers in a list. Then discuss with your partner how you could use these ideas as the basis for further investigation in science and/or math.

Site Conversation 1 (5 min.)

Students often enter into a new lesson with a wide range of knowledge about the particular math or science concept, and their understandings are often revealed by comments they make during open-ended explorations and class discussions. How have you dealt with the wide range of knowledge and understandings in your classroom?

Site Conversation 2 (5 min.)

When teachers give students freedom to develop their own questions for investigation, students' ideas do not always coincide with the intended learning goals, methods, and/or materials. What do you think is the appropriate balance between student ideas and teachers' goals? How do you maintain that balance?

Going Further (15 min. each)

  1. Think about a specific math or science activity that you have planned for the upcoming week. The activity should be one in which you can elicit students' ideas prior to the activity, and their ideas can be used as a starting point for further investigation. What strategies can you use to help your students find a question to investigate? Share your "next move" with your colleagues, and ask for their feedback and suggestions.
  2. As a group, discuss how you will to participate in The Great Bean Bag Adventure. Will you work on your own? In pairs? As a site? What experiment(s) do you want to conduct? What conditions will you consider? What will your variables be?

Homework for Workshop 2

What are your colleagues' metaphors for teaching? Conduct your own "teacher-on-the-street" interviews by asking several teachers at your school about their teaching metaphors. Keep track of what they tell you, and bring your results with you to Workshop 2. (If you have access to the Web, you can enter the metaphors on our Web site, and your data will be used in an upcoming article about teaching metaphors!)



Pattern Puzzles

Suggested Grade Level: K-3
Students explore part-whole understanding by using pattern blocks to fill in a pre-determined shape.


What You Need

The green triangles, blue rhombuses, red trapezoids, and yellow hexagons from a Pattern Block set.

For each pair (or small group) of students, create an activity sheet like the following:

The dimensions for the "big shape" are:

width=7.5 cm
height=4.5 cm
width of side 1=7.5 cm
width of side 2=2.5 cm

What To Do

  1. Provide each pair (or small group) of students with a Pattern Block activity sheet.
  2. Explain that they are to find a way to completely fill in the big shape on their activity sheet by using any combination of the green triangle, blue rhombus, red trapezoid, and yellow hexagon Pattern Blocks.
  3. After they have filled in their big shape, have students complete the first column of their chart with the number of each type of block they used.
  4. Students should then remove the Pattern Blocks from the big shape and find a different way to fill in the same shape. Have them record their new combination in the next column. This can be repeated many times.
  5. After students have found several different ways to make the exact same shape, engage them in a class discussion about the number of different combinations they have found.
  6. Try this activity again using a different big shape.

What Next

Try a similar activity, but have students record their answers in an equation rather than in a chart. Students may decide to write out their equations with pictures, words, or colors of the different shapes. For example:

For Older Students

1. You can challenge older students to figure out the maximum number of each type of Pattern Block that will fit into the big shape. Then, using fractions, they can determine the exact number of Pattern Blocks that will fit.

To figure out exactly how many HEXAGONS will fit into the shape, for example, students will give the hexagon a value of 1. If the hexagon is equal to 1, then the trapezoid is equal to 1/2, the rhombus is equal to 1/3, and the triangle is equal to 1/6.

Students can then use these fractional equivalencies to write equations from the data on their activity sheets (above), and their answers—all the same—will represent the number of hexagons that fit into the big shape. For example:

= 3(1/6) + 1(1/3) + 3(1/2) = 2 1/3 hexagons
= 2(1) + 2(1/6) = 2 1/3 hexagons
= 1(1) + 1(1/2) + 5(1/6) = 2(1/3) hexagons

You can repeat this exercise three more times, giving the trapezoid, the rhombus, and the diamond each a value of 1.

2. Another related activity you can do with older students is to have them solve problems like the following:

One Connection to the Standards Standard 13: Patterns and Relationships

In grades K-4, the mathematics curriculum should include the study of patterns and relationships so that students can —

  • recognize, describe, extend, and create a wide variety of patterns;
  • represent and describe mathematical relationships;
  • explore the use of variables and open sentences to express relationships.

"Physical materials and pictorial displays should be used to help children recognize and create patterns and relationships. . . . The use of letters and other symbols in generalizing descriptions of these properties prepares children to use variables in the future. This experience builds readiness for a generalized view of mathematics and the later study of algebra."

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. 60)


Series Overview
Workshop Synopses
About the Contributors
Workshop Components
More Workshop Components
Helpful Hints for Successful Site Investigations
The Great Bean Bag Adventure
Invitation to Interact
Featured Teachers:
–  Classroom Clips
–  Conversations
Workshop 1
Workshop 2
Workshop 3
Workshop 4
Workshop 5
Workshop 6
Workshop 7
Workshop 8
Suggested Teaching Resources


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