Activity 2.4

Is Less More?*

Purpose:

To consider the interrelations between classroom learning and assessment

Uses:

This is an intermediate level activity. It can be used in Chapter 2 to illustrate integration of assessment and instruction and in Chapter 3 to practice task and criteria development. Prerequisites might be Activities 1.3—Post-itÔ Notes (definitions), 1.1—Changing Assessment Practices or 1.12—Assessment Principles (to look at changes in assessment and reasons for them), 1.5—Clapping Hands, or 1.11—Assessment Standards (to begin a discussion on quality) and 1.9—Going to School or 2.5—How Knowledge....(to illustrate the importance of performance criteria).

Rationale:

While there has been much talk about integrating assessment and instruction, the mechanics of how that is done can still be baffling. This activity models one approach. It involves students in self-assessment and weaves instruction and assessment together in an integrated lesson.

Materials:

• Overhead projector, screen, blank transparencies, transparency pens

• Flip chart and colored markers

• Overheads: A2.4,O1—Is Less More Purposes, A2.4,O2—Creating a Concept Web, A2.4,O3—Company Directive, A2.4,O4—Assessment of the Task, A2.4,O5—Some Questions

• Handouts: A2.4,H1—Is Less More?, A2.4,H2—Design Task, A2.4,H3—Problems (Note: Before making copies of Handout A2.4,H3, you will need to find the population of your city/town and enter this value in the appropriate blank.)

• One per group of 3-4 people:

  50-pack box of artificial sweetener
  Rulers
  Centimeter graph paper
  Scissors
  Markers and chart paper
  Calculator

• One per 2-3 groups:

  Centimeter tape
  Masking tape
  White glue
  Clear tape

• Balance: electronic or with gram weights

• Purse or briefcase containing several small packages (e.g., mints, tissues, snacks), including at least one package within a package (e.g., chewing gum)

  Time Required:

  Part A: 35 minutes; Part B: 90 minutes

  Facilitator's Notes:

  Part A: (35 minutes) Concept Web

  A1. (5 minutes) Introduction:

  a. Facilitators introduce themselves, display Overhead A2.4,O1—Is Less More Purposes, and give a brief overview of session:

  We will experience an example of a mathematics and science lesson that might be typical of today's standards-based classroom and consider the implications of such a lesson for student assessment.

  b. Divide participants into groups of 3-4.

  c. Give each person Handout A2.4,H1—Is Less More? Read the lesson objectives as participants follow along. Then tell participants:

  Try to be aware during the activity of when you think you personally have met each of the lesson objectives. Feel free to make notes on the handout to help you remember the context in which the objective was met.

  A2.(10 minutes) Hook

  a. Display packaged items at appropriate times while saying:

  I was cleaning out my purse (or briefcase) the other day and was really surprised at all the different packages that I carry around. And then I started thinking about how some things are even packages within packages.

  Demonstrate by removing stick of gum from outer gum packaging.

  When I went grocery shopping later that day, I found that I was suddenly very aware of all the packages within packages that I purchase.

  Hold up a box of artificial sweetener and ask:

  Do any of you purchase this product or one like it? Here we have 50 little packets holding the sugar substitute and then packed inside a larger box.

  b. Give each small group a box of the artificial sweetener packages. Caution them not to open the boxes yet. Ask groups to shake the box up and down and ask what they notice. Elicit from participants the idea that the box is not full. Then ask:

  Do you think we could make the box smaller and still have it hold 50 packets of sugar substitute

  Participants should say "yes" or "probably." Then ask:

  Why might we want to use a smaller box?

  Take a few responses from participants. Responses may include environmental, marketing, or economic concerns. If you want to stress science as a focus, and environmental concerns are not raised, you may want to suggest them. Then state:

  Given that there may be some good reasons for making a smaller box, I wonder why the company has chosen to make the box this size.

  A3.(10 minutes) Concept Web

  a. Use Overhead A2.4,O2—Creating A Concept Web to guide groups in exploring factors that may have influenced the design of the box. Have each group draw the box in the center of the chart paper, brainstorm factors that might have influenced the design of this package, and draw a concept web depicting the influences.

  (Note: A sample concept web generated in a recent workshop follows.)

  

  A4.(10 minutes) Large Group Sharing:

  Call on one person from each group to briefly describe the group's concept web. Allow about 2 minutes per group and ask for comments or questions.

  Part B: (90 minutes) Design Task B1. (10 minutes) Company Directive

  a. Tell participants that you understand that the artificial sweetener company is interested in designing a smaller box to hold the 50 packets. Display the Company Directive (Overhead A2.4,O3). Explain that each group will be given the opportunity to meet the Company Directive. Groups are going to take on the role of designers and attempt to help the company with this task by trying to design a smaller box.

  b. Ask participants to look at their box again. Pose the following question:

  If I asked you to design a box that used less material and to prove mathematically that it used less, what would you have to know or be able to do?

  Capture their responses on a blank transparency. Be sure to elicit from participants that one thing they would have to know is how to find out how much paperboard there is in the original box and in the new box. Give groups 5 minutes to discuss how they would determine how much material is in the box. Call on one person to share ideas from each group. Be certain participants know what materials are available (e.g., rulers, tape, glue, the triple beam balance). Important: Check to see that everyone understands the different ideas before going further.

  c. The Design Task: Distribute (one per group) Handout A2.4,H2—Design Task and explain the Design Task that addresses the Company Directive. Participants will design (and if desired, use the existing box to build) a smaller box that can still hold all 50 packets of the sweetener. They will record all measurements and computations, and compute the percentage reduction in paperboard of the new box. DO NOT ALLOW PARTICIPANTS TO BEGIN THE DESIGN TASK YET!

  B2. (10 minutes) Assessing the Task
  Use Overhead A2.4,O4—Assessment of the Task to tell participants that before they work on the design task, they need to consider how they might assess successful completion of the task. Remember that the task is designed to practice working cooperatively as well as to practice problem solving and application of knowledge.
  Allow 8-10 minutes for groups to develop criteria/strategies for assessing the quality of performance on the design task, including the actual package design. Stress the importance of writing value-neutral statements that encompass each important objective of the activity and can easily be assessed. Be sure each group has included a strategy for assessing mathematical and/or science skills, concepts, and group skills. Make sure chart papers are easy to read and visibly posted.
  B3.(30 minutes) The Design Task

  a. Tell participants they will have 25 minutes to re-design the box and complete the design task. Point out the variety of materials available on the supply table for their use. Tell participants they should keep in mind the assessment strategies/criteria that are posted around the room as they complete the design task.

  b. Pass out the problems on Handout A2.4,H3—Problems. The problems cannot be completed until they know the percentage reduction in paperboard of the new box.

  As participants work, the facilitator should move around the room with notepad in hand. Refer to each group’s posted criteria and jot down notes about your perception of the extent to which each group is meeting their criteria. Be careful not to compare groups.

  c. Ask groups to prepare a display of their completed boxes, problems, and summary paragraph at their tables.

  B4.(5-10 minutes) Round Robin Sharing. Have groups rotate from table to table to quickly examine each group's finished product. Allow no more than 1 minute per station. (Or, see Optional Extension.) B5.(10 minutes) Assessing Student Performance and Lesson Objectives

  Point out that performance on the activity was assessed using a variety of strategies for a variety of purposes. On flip chart sheets, have small groups prepare a list of different strategies that were used, along with the purpose of each. You may need to stimulate the discussion further by providing any of the following examples:

  a. To assess individuals' attainment of lesson objectives: self-reflection, confirmation (or not) by peers, teacher observation during group work

  b. To assess group performance: group reflection on how it met its own criteria, production of a product that met specifications, self or teacher examination of problem sheets, and summary paragraph

  You may also wish to say that in an ideal classroom setting, the facilitator would later collect and review each group’s written calculations, summary paragraph, and problems. S/he would then meet with each group for a consultation to compare the instructor’s assessment of the task with the group’s assessment. Together, they would then identify areas for additional study and develop suitable activities for building strengths and enhancing learning of specific skills and knowledge.

  B6.(15 minutes) Closure

  Referring to the list of assessment strategies generated above, use Overhead A2.4,O5—Some Questions to facilitate a discussion about the following questions:

  Are these assessment ideas and strategies different from traditional assessment approaches? If so, how are they different?

  What are practical realities of using these kinds of assessment strategies in the classroom?

  What are some implications for teachers, parents, course grade, etc.?

  Close by acknowledging that there are a variety of assessment approaches that can be integrated into instructional lessons. Each provides a different kind of information about the students. Traditional assessments allow limited approaches to assessing students. By incorporating a wide variety of assessment strategies into classroom teaching, different student and teacher learning and teaching styles can be accommodated.

  Optional Extension—60 minutes

  After groups have viewed each other’s displays, have them select one of their criteria and generate an expanded description of what might be considered an excellent response. After sharing these with the large group, facilitate a discussion about how samples of student work allow refinement of the criteria.

   

  ___________________
  *This activity is based on a classroom activity written by Ann Anderson, entitled "Mathematics in Context: Measurement, Packaging, and Caring for Our Environment." Published in the March 1994 issue of School Science and Mathematics (Volume 94, Number 3, pp. 146-150), it is used with permission of the editors