What's Math Got to Do with It?: How Teachers and Parents Can Transform Mathematics Learning and Inspire Success (12 page)

The ways in which assessment reporting can affect students’ confidence as learners was illustrated poignantly by a ten-year-old student in England reporting on the standardized tests (called SATs) that she was about to take. She said: “I’m really scared about the SATs. Mrs O’Brien came and talked to us about our spelling and I’m no good at spelling and David [the class teacher] is giving us times tables tests every morning and I’m hopeless at times tables, so I’m afraid I’ll do the SATs and I’ll be a nothing.” When the interviewer tried to convince her that she could never be a “nothing,” no matter what happened on the tests, the young girl insisted that the tests would make her one. The researchers reported that even though she was “an accomplished writer, a gifted dancer and artist, and good at problem solving,” the tests made her feel as though she was an “academic non-person.”

As if the requirements that students take low-quality tests and suffer crude and demoralizing labeling were not bad enough, many teachers feel the need to coach for these tests by using similar tests in their classrooms. Many of the math teachers I have met in the United States give students a test every week, and at the end of each chapter in their textbook, that are often replicas of chapter questions. Some teachers test students more frequently, and students end up spending almost as much time taking tests as they do learning new material. Teachers rarely do anything with the tests other than score them, return the scores, then move on to the next section of work. Dylan Wiliam, an international expert on assessment, has likened this practice to a pilot of a plane flying off into the distance and hoping to land in New York. After a certain amount of time the
pilot lands in the nearest airport and asks, “Did I arrive in New York?” Whether they did or not, all the passengers would be instructed to get off so that the plane could then fly off to its next destination. Teachers in America typically do the equivalent—they teach a chapter or unit of work and at the end they give a test. They then move on to another chapter, whether students are still with them or not. Giving a test at the end of the work, with no intermediate indicators of understanding, means that teachers can do little with the information they gain from tests, apart from going over the answers to badly answered questions. Students who are confused the first time are usually confused again. With the pressure of an overfilled curriculum and a lack of knowledge about more effective assessment methods, teachers do not spend time using assessments
to improve learning
.

Teachers often treat the reporting of test scores just as badly, typically giving students only enough information to compare their performance with others. Such feedback is minimally helpful to some and has a negative impact on many. When students are given only a percentage or grade, they can do little else besides compare it to others around them, with half or more deciding that they are not as good as others. This is known as “ego feedback,” a form of feedback that has been found to be damaging to learning. A large review of research from hundreds of studies showed that such feedback has a negative impact on performance in 38 percent of cases. If students are given scores that tell them they are below others in the class, it can damage self-esteem to the extent that students give up on math or take on the identity of an underperforming student. It is really not helpful to be told that you have scored 65 percent, unless you know how to do better on the remaining 35 percent of the questions you answered incorrectly. Deevers
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found that students who were not given scores but instead given positive constructive feedback were more successful in their future work.
Unfortunately, he also found that teachers gave less and less constructive feedback as students got older. When he explored the relationship between teachers’ assessment practices and student attitudes and beliefs about mathematics, he found that students’ belief in the power to improve their own learning, and their motivation to learn, declined steadily from fifth to twelfth grade.

The standardized tests such as those imposed upon the country by the No Child Left Behind Act, as well as those typically used inside math classrooms in the United States, do not give any information that helps students improve their learning. Instead, they compare students to one another. There should be some large-scale tests in use in schools—tests that are designed to give a measure of a students’ performance at the end of a course, or to give national or state comparisons—but these do not need to be as low-quality as those administered by most states and they should not be multiple-choice tests. The AP examinations administered at the end of AP courses are a good example of a better-quality assessment that can be administered large scale and that do not harm the curriculum or learning. Inside classrooms there is room for even more improvement, and the “assessment for learning” approach has been designed to revolutionize the way assessment is used inside classes.

Assessment for learning is a form of assessment that gives useful information to teachers, parents, and others, but it also empowers students to take charge of their own learning. Assessment for learning tells students where they are in their learning path, where they could be, and what they need to do to get there. It gives learners the motivation
and the power
to regulate and improve their own learning, and there are particular ways in which parents can be involved with this new approach to improve their children’s life chances.

Assessment for Learning

Assessment for learning is based upon the principle that students should have a full and clear sense of what they are learning, of where they are in the path toward mastery, and of what they have to do to become successful. Students are given the knowledge and tools to become self-regulatory learners, so that they are not dependent on following somebody else’s plans, with little awareness of where they are going or what they might be doing wrong. It may seem obvious that learners should be clear about what they are learning and what they need to do to be successful, but in most mathematics classrooms the students have very little idea. I have visited hundreds of classrooms and stopped at students’ desks to ask them what they are working on. In traditional classrooms, students usually tell me what page they are on, or what exercise they are working through. If I ask them, “but what are you actually doing?” they say things like “Oh, I’m doing number three.” Students are usually able to tell you the titles of chapters they are working on, but they really do not have a clear sense of the mathematical goals they are pursuing, the ways that the exercises they work through are linked to the bigger goals they are pursuing, or the differences between more and less important ideas. This makes it very difficult for students, or parents, to do anything to improve children’s learning. Mary Alice White, who was a professor of psychology at Columbia University, had likened the situation to workers on a ship who may be given small tasks to do, and complete them each day without having any idea of where the ship is heading or the voyage they are undertaking.

The first part of the assessment-for-learning approach involves communication about what is being learned and where students are going. The second part involves making indivi- dual students aware of where they are in the path to success, and the third part involves giving them clear advice about how
to become more successful. The approach is called “assessment
for
learning” rather than “assessment
of
learning” because it is designed to promote learning, and all the information that is gained from assessment is made helpful to individual learners to propel them to greater levels of success.

So how is this achieved, and how does assessment for learning look different from traditional assessment in the classroom? First of all, students are made aware of what they are, should be, and could be learning through a process of self- and peer assessment. Teachers set out mathematical goals for students, not a list of chapter titles or tables of contents, but details of the important ideas and the ways they are linked. For example, students might be given a range of statements that describe the understanding they should have developed during a piece of work, with statements such as “I have understood the difference between mean and median and know when each should be used.” The statements are clear for students to understand, and they communicate to them what they should be understanding from a piece of work. Students then assess their own or their peers’ work against the statements. By assessing work against statements and deciding what they have understood, students come to understand the goals of lessons much more clearly. In reviewing the goals of a lesson, week, or unit of work, students start to become aware of what they should be learning and what the big ideas are. Parents can also review the criteria and become more knowledgeable about the ideas and knowledge students are working toward.

In studies of self-assessment in action, researchers have found that students are incredibly perceptive about their own learning, and they do not over- or underestimate it. They carefully consider goals and decide where they are and what they do and do not understand. In peer assessment, students are asked to judge each other’s work, again evaluating the work against clear criteria. This has been shown to be very effective,
in part because students are often better able to hear criticism from their peers than from a teacher, and peers usually communicate in easily understood ways. It is also an excellent opportunity for students to become aware of the criteria against which they too are being judged. One way of managing peer assessment is to ask students to identify “two stars and a wish”—they select two things done well and one area to improve in their peers’ work. When students are frequently asked to consider the goals of their learning, for themselves or their peers, they become very knowledgeable about what they are meant to be learning, and this makes a huge difference.

Evidence of the power of making students aware of what they are meant to be learning came from a very careful study conducted by two psychologists: Barbara White and John Frederiksen.
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They worked with twelve classes of thirty students learning physics. Each class was taught a unit on force and motion, with students in each class divided into experimental and control groups. The control group used some periods of time each lesson to discuss the work, while the experimental group spent the same time engaging in self- and peer assessment, considering assessment criteria. The results were dramatic, with the experimental group outperforming the control group on three different assessments. The greatest gains were made by the students who had previously been the lowest-achieving students. After they spent time considering criteria and assessing themselves and their peers against them, the previously low achievers began to achieve at the same levels as the highest achievers. Indeed, the seventh grade students who reflected on the criteria scored at higher levels than AP physics students on tests of high school physics. White and Frederiksen concluded that the students were previously unsuccessful not because they lacked ability but because they had not really known what they were meant to be focusing on.

When students are required to be aware of what they are
learning and to consider whether they understand it, this also gives important information to the teacher. For example, consider an assessment-for-learning activity called “traffic lighting.” In some versions of this, students are asked to put a red, orange, or green sticker on their work to say whether they understand new work well, a little, or not at all. In other versions, the teachers give students three paper cups: one green, one yellow, and one red. If a student feels the lesson is going too fast, he or she shows the yellow cup; those who need the teacher to stop can show the red cup. At first researchers found that students were reluctant to show a red cup, but when teachers asked someone who was showing a green cup to offer an explanation, students became more willing to show a red cup when they were not understanding something. Other teachers used the traffic lighting to group students, sometimes having the greens and yellows work together to deal with problems between themselves, while the red pupils were helped by the teacher to deal with deeper problems. Most important, the students themselves were being asked to think about what they knew and could do and what they needed more help on. This helps students and teachers tremendously, as teachers get feedback on their teaching in real time, rather than at the end of a unit or piece of work when it is too late to do anything about it, and they are able to deliver the most helpful information to students at an appropriate pace.

Methods of self- and peer assessment serve the purpose of both teaching students about the goals of the work and the nature of high-quality work and giving them information on their own understanding. For teachers, these methods also give critical information on student understanding that can help them assist individuals in the best possible way and improve their own teaching. But, as Paul Black and Dylan Wiliam have noted, these new methods require fundamental changes in the behavior of both students and teachers. Students need to move from being passive learners to being active learners, taking responsibility for
their own progress, and teachers need to be willing to lose some of the control over what is happening, which some teachers have described as scary but ultimately liberating. As Robert, a teacher at Two Bishops School in England, said when reflecting on his new assessment-for-learning approach: “[What it] has done for me is made me focus less on myself but more on the children. I have had the confidence to empower the students to take it forward.”
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The third part of the assessment-for-learning approach—after making students aware of what needs to be learned and how they are doing—involves helping students know
how
to improve, which is best achieved through diagnostic feedback. Psychology professors Maria Elawar and Lyn Corno
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trained eighteen sixth-grade teachers in three schools in Venezuela to give constructive written feedback in response to mathematics homework, instead of the scores they normally gave. The teachers learned to comment on errors (giving specific suggestions about how to improve) and to give at least one positive remark about each student’s work. In an experimental study, half the students received homework grades as usual (just scores), and half received constructive feedback. The students receiving the constructive feedback learned twice as fast as the control-group students, the achievement gap between male and female students was reduced, and students’ attitudes toward mathematics became significantly more positive.