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Summary

MAIN IDEAS

Standards-oriented instruction cannot occur without integrated assessment and good assessment cannot happen without good student-centered teaching. It is important to stress that assessment must be an integral component of instruction rather than something that occurs at the end of the unit. In that sense, this chapter compliments the foundational ideas of instruction. Assessment issues should be addressed at the same time as instructional issues. When considering an activity, teachers should not only think about how students will reflect on the desired ideas, but what will they as teachers be able to learn as students complete the activity.

The Assessment Standards

The chapter begins with a listing of the six assessment standards and a brief description of the four purposes of assessment as envisioned by the 1995 NCTM document. (T-52 lists the Assessment standards and T-53 illustrates the four purposes of assessment.) For preservice teachers, the standards are not as likely to make an impact as are the four purposes. I find especially intriguing the notion of monitoring student progress in order to promote student growth. Assessment opens up a dialogue with students, helping them see a vision of what excellence is about and how they can do better.

Assessment Tasks and Problem-Based Instructional Tasks

A good assessment task will allow students to show what they know and provide an opportunity to learn. This is exactly what a good problem-based task for instruction should do. The term performance task has had many definitions in the literature. I believe that it is essential to use the exact same definition for performance tasks or assessment tasks as is used for problems or tasks used for instruction.

Perhaps one way to approach this chapter is to say that for most classroom assessment, the teacher's job is to gather and make use of the information that comes from good problem-based tasks. It is not how to design good assessments - these are the same as the good instructional tasks discussed in Chapter 4.

Rubrics

The text provides somewhat extensive information concerning rubrics. Of all the various rubrics available, I have found the four-point rubric from the New Standards Project most useful (Figure 6.2, T-54). The idea of first sorting into two piles based on having learned the key idea(s) or not and then making a second sort to decide what needs to be done is easy to understand and use. A three-point rubric is also offered and you may have favorites of your own. It is easy to get overly involved in all of this detail so a focus on the four-point rubric is suggested.

It is useful to make a distinction between a general rubric and performance indicators. While the rubric is a general framework, the performance indicator is task-specific and can help both the teacher and the students decide what an excellent performance looks like.

Gathering Data

Observation schemes are discussed since much of the data available to the teacher does not come in written form from students. Suggestions for recording observational data are included. Contrasts with data available from the limited but traditional chapter-end tests and that available from a few performance tasks can help teachers realize how much more data is available in the latter form. Other data gathering techniques include journal writing and student self-assessments. I would let students know about these techniques and their values without making too big a deal of them. Each teacher will necessarily need to design an assessment style that fits his or her particular teaching style and needs. I would treat this section as a resource.

Writing

I am a strong advocate of students writing to explain their ideas and problem solutions. I believe that this should be an almost daily occurrence, even in the primary grades. Writing is a reflective activity and thus contributes to learning. It prepares or rehearses students for class discussions. It provides an important window into student thinking for the purposes of assessment. It can be used in helping students with their developing ideas and for communicating with parents. Written work need not be graded and in fact most of the time, should not be graded.

Since writing is such an integral part of the learning process the topic could easily be addressed as part of the earlier chapter s on problem solving or planning. It appears here due to the importance of writing so that data can be gathered.

High Stakes Tests

Almost certainly your students will soon be facing the pressures of high-stakes tests in their jobs. In mathematics, as in other subjects, the temptation to "teach to the test" is overwhelming, if not in fact dictated by the administration. It would be useful to have your students read the NCTM position statement on high-stakes testing. The essential viewpoint in this book is that attention to good conceptual development around big ideas is the best test preparation possible. However, this is an area of profitable discussion for your class.

Grading

The end of the chapter challenges readers to confront the traditions of grading. I am constantly amazed at the teacher who gives a quiz consisting of ten items, grades each item right or wrong, and enters scores in a grade book. A simple slip causes a student to receive a B grade, even when the teacher's daily interactions provide much more complete and informative information. We have a long tradition that grades must be based on arithmetic averages of test scores and that these scores in some magical way indicate learning or the lack of it. To me this is one of the most absurd beliefs in our educational system and one that may very well be worth some time discussing with your class.




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