Activity 3.4
Assessing Learning: The Studentís Toolbox

Purposes:

1. To practice matching different assessment tasks to the student learning to be measured

2. To practice developing ("opening up") performance tasks

Uses:

This is an intermediate level activity that can be used in Chapter 1 to illustrate the need to match assessment method to the learning targets being assessed, and in Chapter 3 to assist teachers to design assessment tasks that match various learning targets.

Prerequisites might include (a) an activity on the rationale for alternative assessment (e.g., Activities 1.1-Changing Assessment Practices..., 1.6-Comparing Multiple-Choice and Alternative Assessment, or 1.12-Assessment Principles); (b) Chapter 1 text or Activity 1.7-Target Method Match; and (c) Chapter 2 text or an activity, such as 2.3-Ms. Toliver, illustrating integrating assessmenty tasks into instruction.

Rationale:

As assessment initiatives seek to provide educators with the tools to gain insights into complex learning outcomes, discussions of assessment methods and task type can be overwhelming. This brief activity uses a toolbox metaphor, developed by Dr. David Clarke, to clearly illustrate different learning targets that can be addressed by slightly changing what began as relatively straightforward test items.

Materials:

Overhead projector, screen, blank transparencies, chart paper and pens

Overheads A3.4,O1-Assessing Learning Purposes and A3.4,O2-Mathematical Tools

Handout A3.4,H1-Mathematics as a Set of Tools

Time Required:

20-30 minutes

Facilitator Notes:

1. (5 minutes) This is a whole group presentation to set the stage for more detailed activities on expanding or creating performance tasks. Use Overhead A3.4,O1-Assessing Learning Purposes to highlight the purposes of this activity.

2. (5 minutes) Show the first section of Overhead A3.4,O2-Mathematical Tools and make the point that "opening up" our existing mathematics (or other) tasks so they can assess more complex student skills does not have to involve massive development; rather, it is possible to open-up tasks with some careful but simple changes.

Some additional points to make: Traditional assessment items have heavily focused on answering the question of whether students have a particular mathematical tool in their "toolbox." But complex problem solving and other powerful mathematical thinking and investigating that we now expect as outcomes for learning demand more than "possessing the tools"-they demand understanding, using the tools in real world contexts, and knowing which tools to use in particular situations.

3. (5-15 minutes) Continue revealing each box on Overhead A3.4,O2 while reviewing the examples that illustrate each type of question.

After looking at each box, ask participants to be clear on which learning targets each successive "opening" addresses (to reinforce the notion of target-method match). For example, you might say: In this activity, the learning targets to be assessed are stated in the vocabulary of the tool box metaphor. State the learning targets measured by each task in the language of your local content standards.

Possible answers: Tool possession=knowledge; tool understanding=knowledge; tool application=reasoning, problem solving; tool selection=reasoning, problem solving, math connections, communication in math.

4. Close with an invitation to experiment with opening-up the tasks currently in use and pass out Handout 3.4,H1-Mathematics as a Set of Tools.

Variation: Trying Out Opened-Up Tasks

Materials:

Party favor streamers, crepe paper or string

Lined or unlined paper

Time:

45-60 minutes

Facilitatorís Notes:

1. (5 minutes) While presenting each box on Overhead A3.4,O2-Mathematical Tools, invite participants to actually do the tasks shown individually or with a partner. Prompt participants to discuss with their partner or with another pair the intellectual demands of each and provide additional examples of tasks aimed at answering the central question within each box.

2. (5 minutes) Following try out of the first task, (Is the tool in the student's toolbox?-"What is the average of 19, 21, 23, 25, and 27?") ask participants if itís possible to complete this task without understanding the concept of ìaverage.î (The answer is "yes.") Note that much of our traditional assessment is centered only on the "tool possession" questions.

  1. (20 minutes) To carry out the second task, participants form into groups of 5 (the number is essential). Each group is given a streamer. This task ("Using only the streamer, find and display the average height of your group.") gets at the question: Does the student understand the tool? When groups are done, ask them to (a) describe what approach they took to the task, (b) whether each approach really leads the group to the "average" (rather than the median or mode), and (c) what more they might learn about the students' understanding of "average" following this task.

(Note: Instead of the streamer activity, you might ask participants to do the other question in the box: "The average of five numbers is 23. What might the numbers be?" A useful extension of this task, underscoring emphasis on student understanding, is to ask participants if they can generate rules that could be used for similar average tasks. This results in a clear indication of whether the concept is understood. Some recent examples of generalizations: (a) "Add up all five numbers to get the sum. No matter what numbers you choose, as long as they add up to that sum, and you divide by 5, the average will be the same." (b) "Start with the number in the middle and go up and down equal increments on both sides." Ask the group to check the possible rule to see if it works.)

4. (5-10 minutes) The third task is "You are one member of a household of 5 people, whose average age is 23. What could be the ages of the other four people and who might they be?" It focuses on the question "Can the student use the tool well in a real world context?" Point out that while this is not an extremely "authentic" task, it is one that students respond to with great enthusiasm and energy-creating interesting family structures and then trying to communicate why certain ages are found among the members of the family. Ask participants how they might modify this task to match their own local context. Ask what they would know about student understanding of "average" from this task and what responses to the task say about students' ability to make mathematical connections between a real work situation and school math.

5. (10-15 minutes) The final sample task is one that demands students in small groups to independently select appropriate tools when presented with a situation that does not name the mathematical tool(s) that should be used. The task in the example is a Fermi Problem to which students must bring their experience, knowledge base and reasoning skills. Participants (and students who are given this type of task) are prompted with powerful closing questions: How good is your answer? Why?

6. You can extend this activity with an opportunity for participants to open-up tasks they have brought to the session or provide sample tasks that they can expand and critique for each other as critical friends.