Assessing For Learning: Assessing through Questioning

Assessing For Learning: Assessing through QuestioningAuthor(s): Ann McAloon, G. Edith Robinson and Mary Montgomery LindquistSource: The Arithmetic Teacher, Vol. 35, No. 5 (January 1988), pp. 16-18Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41194309 .

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Assessing through Questioning

You have probably been using questions to make assessments, perhaps without even realizing that you were doing so. Sometimes, a question may only reveal that a student is not paying attention or cannot repeat what was just said. A class response to "any questions?" may signal a transition to another part of the lesson. In rare moments we use questions to probe our students' understanding; this latter use of questions is addressed in this article.

Four types of questions may assist you in learning more about your students' understanding: silent questions, oral questions, written questions, and student questions. Let's examine each of these in practice in classrooms. Although each type is il- lustrated at a different grade level and with a different mathematical topic, each is appropriate at any grade level or for any topic. As you read, ask yourself how the technique could be used with other topics at the grade level you teach.

Silent Questions Our first episode focuses on silent questions. Imagine a class of kinder-

Edited by Ann McAloon and G. Edith Robinson

Educational Testing Service Princeton, NJ 0854 1 Prepared by Mary Montgomery Lindquist Columbus College Columbus, GA 31907

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garten children working with geomet- ric attribute blocks.

Today, Mr. Williams has given each child some blocks to place on his or her paper to match the shapes out- lined. He is observing Sue, a child who usually has no difficulty with such spatial tasks. By this time she has placed the two blue circular pieces in the correct places (fig. la). Mr. Williams asks himself, "Is this task too easy for Sue?"

Why doesn't he ask her? Do you see the need for silent questions?

He decides to take a minute to watch her complete the task before making a judgment. Sure enough, she quickly places the yellow square and the red triangle in the correct places (fig. lb). Now Mr. Williams asks himself, "Should I give her the sheet with the complicated design?"

This is a different stance than if Mr. Williams decides to give her the sheet with the complicated design. He is still questioning.

Sue then picks up the small yellow triangle and puts it in the middle of the square, turning it carefully to match the position of the red triangle above it. Satisfied with this re- sult, she puts the remaining piece, a large red square, over the triangle shape on the paper (fig. lc). Mr. Williams asks himself, "Didn't I make the directions clear?" Sue notices him watching her and says, "I like my pattern better than this one. The colors would not have matched if I put them where they

were supposed to go. See, each row has the same color, and they match this way too." Mr. Williams is about to ask her what she means by "this way too," but a quick look at her fingers pointing to the orienta- tion of the triangles and then that of the squares makes it clear.

What would have happened if Mr. Williams had asked Sue why she put the yellow triangle in the square? To a less confident student, such a question would have been a signal that a mistake had been made. It may have even caused Sue to find the expected solution, leaving Mr. Williams with a different picture of Sue's ability to interpret a problem in her way.

Perhaps Mr. Williams would have discovered just as much from observing as from his silent questioning, but being a constant inquirer may have kept him from being a complacent knower.

Oral Questions Asking questions to ascertain a child's understanding of a mathematical concept or process is an art. Even more difficult is asking a whole class such questions. With planning and practice, we can all improve in this type of assessment. Let's see what is happen- ing in Ms. Mimms's third-grade class. She is planning her lesson on subtract- ing three-digit numbers using the stan- dard algorithm. She makes the follow- ing list of questions: Would the answer to 594 - 268 be

about 30 or 300? Would it be more than 300?

Arithmetic Teacher



Fig. 1 Kindergartners place attribute blocks on a pattern.

Do these base-ten blocks help you explain?

What is the difference between these two problems?

A. 594 and B. 94 -268 -68

Do we know how to do any part of problem A?

Why do we begin with the ones? What would happen if I began with

the tens in problem B? Why did you cross out the 9 and write

an 8? Where did the 1 by the 4 come from? Why do we line up the digits as we

do?

January 1988

How would you write 546 - 34 verti- cally?

Why can we add to check our answer? Is the answer reasonable?

What if someone got 726 for an answer?

Do you think you could find 419 - 257?

What would you do if you were hav- ing trouble?

What is different about this problem? Ms. Mimms has thought about

some questions that she would like her students to be able to answer. Even though she may not use all of these, they will influence the way she

teaches. If the students do not know that the answer to the first subtraction exercise is about 300, then they probably do not have a good concept of three-digit numbers. If the students do not see how problems A and В are alike, then they probably have not been asked to analyze problems before computing.

Through questions such as these, Ms. Mimms will have a good idea of what some of her students know. Do you see ways to ask some of these questions that would enable her to get individual responses from all the students? For example, you may have all the children signal to a yes or no question. Oral questioning of an entire

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group will seldom enable you to make a judgment about each child, but if skillfully done it can play an important part in seeing the entire picture. You need to take time to ask individual children questions as they are working. Do not forget to ask about problems that they solved correctly. If you only ask when a mistake is being made, you will not help build the self- confidence students need.

Written Questions We can also use written questions during guided seatwork, for home- work, or on tests to assess students' understanding. A single question does not give a clear picture of a student's understanding, but the interpretation of a cluster of interrelated questions can.

Let's look at a sixth-grade class that has been studying area and perimeter. This day, Mrs. Chinn is pulling to- gether the two concepts through in- vestigations contrasting perimeter and area. After a discussion of the investi- gations, she asks the students to write what is wrong with each of the follow- ing written statements about the rectangle in figure 2: 1 . Victor said that the area was thirty-

two. 2. Linda said that the perimeter was

twelve. 3. Eula said that the area was twelve

square centimeters. 4. Jim said that if the length was two

more centimeters, the area would be two more square centimeters.

5. Wendy said that if the perimeter was doubled, the area would be doubled.

6. Bing said that if the area of a rectangle was thirty-two square centimeters, then the perimeter is always twenty-four centimeters.

7. Aira said that the perimeter of any rectangle is always a smaller num- ber than the area.

"What is wrong?" is the only question asked about each of these statements. Students' responses to this cluster of questions can clearly indi- cate their understanding of area and perimeter of a rectangle. If Monica

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Fig. 2 Which statements in this article about the figure are incorrect?

4 cm

8 cm

says that Victor and Linda forgot the unit, she may have some level of recognition that the unit is important. However, if she was unable to tell what was wrong with Jim's statement, then she probably really does not understand the role of the unit. What if Sam sees nothing wrong with Bing' s statement, with Wendy's statement, with Aira' s statement, and yet can find the area and perimeter of any rectangle? Does Sam really have a well-developed concept of area and perimeter?

Students' Questions Another way to assess students' understanding is through questions they pose. If you use this method, then you must encourage such questions. At times, you must be prepared for questions that you cannot answer immedi- ately. Here is a technique that Mr. Cortes uses to encourage questions about a set of data.

Class, here are the results of the cafeteria survey taken by the morn- ing class. Your task is to make sense out of the data and make a presentation to the principal. What questions do we need to ask about the survey or the data?

Susan: Which students did they ask? All of the eighth graders?

Tammy: When did they ask? Af- ter that terrible "turtle soup" that day?

Benje: Do we have to use all the data for each question? It seems like a lot of work.

Ralph: What type of presentation will make the principal look at the results? Should we use graphs or just tables?

Tammy: Should we try to get all the information onto one page? How shall we begin?

Ricco: What happens if the results aren't what we want? Do we have to present it anyway? After groups have been formed to handle specific parts of the survey, Mr. Cortes hears some questions like these:

Benje: The graph paper only has twenty-five squares and we have forty-eight responses. What do I do?

Susan: Is it better to use a circle graph or a line graph to show this? Or maybe we should use box and whiskers? . . .

Ricco: How do we make sure that the statement "kids who like hot dogs outnumber kids who like hamburgers by fifty" is really true? I think maybe they only sampled kids that like hot dogs; I know a lot of kids who like hamburgers better.

These questions did not come auto- matically. Mr. Cortes had worked with the students to help them learn to define a problem. They knew that he was not going to tell them exactly what to do. Stop and think about what you know about these eighth graders from listening to their questions. Could you answer Ricco? Both Susan and Benje are asking questions about making the graphs. Do you think they are at the same level?

If you are one of many teachers not fully using the power of questioning to assess for understanding, begin by choosing one of these four techniques in tomorrow's lesson. Choose another one of the four types for another day. Soon you will be mixing the types, asking and listening to more questions. Try it and observe the results. Do your students understand more or less than you thought? If they understand more, can they solve more problems? Does computation become more meaningful? Do your students think the way you do? Do your students know why they are doing mathematics? What do your students like about mathematics class? Ask, wait, and listen. Questioning can make a difference, w

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Assessing For Learning: Assessing through Questioning