Writing and/or Development of Integrated Problem-Solving Curriculum Units

The sample activity "Straw Houses," described below, shows how thinking skills, collaborative skills, academic content, real-life problem solving, and performance assessment can be incorporated into a single lesson. The lesson design was used as a Problem Solving and Critical Thinking in Mathematics (PSCTM) teacher-training tool to facilitate the application of integrative instruction in K-8 classrooms. After integrative classroom applications became part of the teaching repertoire, teachers were encouraged to adapt or abbreviate lesson planning.

The lesson is divided into three major sections:

• Pre-Teaching Decisions (used before teaching) includes both an academic focus--mathematical content and thinking processes--and a collaborative focus. It provides a means of monitoring and evaluating student success in relationship to those focuses.

• Directions for Teaching the Lesson (used during teaching) provides instructions for facilitating:
  • whole group understanding of the problem through open-ended questioning.

  • small group planning, carrying out the plan, and looking back on the problem through open-ended "pocket questions"--questions posed to small cooperative groups only when necessary to refocus the group or facilitate more thoughtful or thorough use of the problem-solving thinking phases--and through a worksheet containing evaluation information used during or after small group problem solving.

  • whole group debriefing through open-ended questioning of small group experiences, of possible connections among groups and to other problems/situations, and of the academic focus of the problem.

• Teacher Reflection After the Lesson (used after teaching) focuses on student learning and on teaching.

By design, students actively engage in inquiry and problem solving during both whole group and small cooperative group experiences. By design, the teacher acts as facilitator and reflective practitioner. The teacher makes decisions before, during, and after teaching; uses open-ended questioning throughout teaching; and incorporates both teacher and student evaluations.

Grade level: 2-8 (can be adapted for primary)

Length of lesson: 60 minutes

I. Pre-Teaching Decisions

A. Problem
1. Type: Open-ended real-life cooperative group lesson

2. Title: "Straw Houses"

3. Sources for problem idea: Museum of Science and Industry's "Architeacher" pamphlet for content information, and PSCTM project for the lesson design

B. Purpose of lesson

1. Content topic: 3D-2D geometry exploration

2. Critical-thinking and problem-solving processes: Structured use of all thinking phases

3. Social and collaborative skills: Reaching consensus, contributing ideas, and encouraging each other to do the same

C. Materials needed

1. Teacher materials: Teacher-designed transparency of the problem, the rules of play, and group roles

2. Small group materials: 100 straws and one roll of masking tape; a worksheet containing directions, recording information, and evaluation information; teacher-designed rating scale measuring sturdiness and attractiveness of the house; and role/job cards (optional)

D. Monitoring and evaluating

1. Academic focus: Thorough consideration of each of the thinking phases (understanding, planning, carrying out the plan, and looking back)

2. Criteria for success: At least half the time spent in understanding and planning

3. Social and collaborative focus: Reaching consensus and contributing ideas

4. Criteria for success: Group consensus on open-ended questions, and high ratings on rating scale measuring sturdiness and attractiveness of the house

5. Teacher monitoring tool: Teacher annotations

6. Small group and individual student tool: Written feedback by cooperative groups and rating scale measuring sturdiness and attractiveness of the house

II. Directions for Teaching the Lesson

(whole group)

A. Statement of purpose: You are to use straws and masking tape to build a house that is sturdy and attractive. You will use your social skills of coming to consensus in each thinking phase.

B. Problem or activity: The teacher can display a transparency that provides background information for the Straw Houses activity.

C. Questioning for UNDERSTANDING:

1. The teacher reads the transparency title and asks the following questions:
* What does the title of our problem tell you about what we might be doing today?

* What would be an example of architecture having both design and function?

2. The teacher reads the first paragraph on the transparency ("When an object is created...") and asks the following questions:

* What was Mr. Broudy saying about architecture?

* Why do you think he might have written this paragraph?

* How many of you know an architect?

* What does an architect do?

* What knowledge and skills does an architect need in order to do his/her job well? (Ask for justification after each response.)

3. The teacher reads the second paragraph on the transparency ("Architecture is an art form...") and asks the following questions:

* How would you summarize what an architect needs to be capable of doing the job?

* What other occupations require such a variety of technical and "people" skills?

4. The teacher reads the third paragraph on the transparency ("Problem: Imagine yourselves...") and asks the following question:

* What additional skills will be needed as a member of an architectural team?

5. The teacher reads the fourth paragraph on the transparency ("As a team, your first...") and asks the following questions:

* In what other situations are simulations helpful? (Ask for justification after each response.)

* Why will a simulation be helpful in this situation?

* What information has not been given to us about the home?

6. The teacher reads the "Rules of Play" and asks the following questions:

* What are the required characteristics of a "straw house"?

* What are some of the things that will be necessary for your team to consider before constructing the house?

D. Directions for small group

(small group)

1. The teacher divides the class into groups of four and passes out a worksheet containing directions, recording information, and evaluation information.

2. The teacher says: Each group will have approximately 20 minutes to complete a straw house, following the listed guidelines. You will be working together in groups of four, each having a special role.

3. The teacher outlines the four roles--Contractor, Blueprint Specialist, Architect, and Building Inspector--and their responsibilities.

4. The teacher asks the following questions:

* Why will it be important to encourage each other to contribute as many ideas as possible?

* Which role or roles might include the responsibility for checking for group consensus within each phase?

5. The teacher tells the students to begin the activity.

E. "Pocket questions" for PLANNING:

* How will your house meet the needs of the "wealthy entrepreneur" homeowner?

* How will you use the materials to construct the house?

* How will you make sure your house is sturdy? attractive?

* How will you know when you are ready to begin building your house?

F. "Pocket questions" for CARRYING OUT THE PLAN:

* How are you checking to see that you are following your plan?

* In what ways are you encouraging each other to contribute ideas?

* How is your structure sturdy and attractive?

* In what ways does your house meet the homeowner's needs?

G. "Pocket questions" group LOOKING BACK:

* How would you describe your effectiveness in coming to consensus within each phase?

* How did encouraging each other to contribute ideas help your group?

* How did planning help you to create a quality straw house?

* How would you rate the attractiveness of your house? Why?

* How would you rate the sturdiness of your house? Why?

(whole group)

H. Questioning for Debriefing:

* What are some examples of how your group came to consensus in solving this problem?

* What did you have to discuss and plan prior to constructing your house?

* How was this problem similar to other problems you have solved?

* What did you learn from the simulation that would help you in actually building the house?

* How would you describe your straw house? (Allow each group to share their design.)

* What makes your house unique? sturdy? attractive?

III. Teacher Reflection After the Lesson

A. Reflecting on student learning, the teacher can describe the following:
1. The students' responses throughout the lesson.

2. The students' learning as related to academic focus.

3. The students' learning as related to social and collaborative focus.

B. Reflecting on teaching, the teacher can describe the following:

1. Teaching and planning strengths.

2. Plans for improvement.

3. Questions, concerns, or targeted focus areas for future lessons.

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