Assessment and Grading

Assessment Is More than Just Grading

The words "assessment" and "grading" are sometimes used interchangeably, but it is helpful to distinguish between them.

Assessment is something you do every day as you gauge where students are in the learning process. You are assessing your students when you ask them questions, read their homework, and listen to their mathematical conversations. These assessments guide your instructional decisions regarding pacing, teaching strategies, and "where to go from here." Getting as accurate a reading as possible requires that students be observed and assessed in real situations; hence the term authentic assessment, which is used frequently in educational reform.

Assessment should be part of the ongoing educational process and should enhance learning. Unlike the standardized tests, which create a break in learning in order to take a measurement, assessment should be part of the natural flow of the classroom. When the curriculum provides a window into a student's thinking, that is a natural time to assess that student. Such an assessment need not be something you assign a specific grade to--it may be simply for informational purposes, both for you and for the student.

How Does Grading Fit In?

In a sense, grading is one of the by-products of assessment. As teachers, we have the responsibility of assigning each student a grade periodically throughout the year. Somehow, you must determine a grade--usually a single letter or number--to reflect all of a student's performance in one lump sum. Not a simple task!

The first step in deciding of how to grade your IMP students is to sit down and decide what you really value in your IMP classroom. Some of the following may come to mind:

• Completion of homework
• Group and class participation
• Progress in the concepts and skills of the unit
• Mathematical communication through written work and oral presentations

These are broad goals; your task is to construct a grading scheme that reflects your priorities.

One way to construct a grading scheme is by allocating "value dollars." Imagine that you have 100 value dollars to spend. Write down the four or five aspects of student work that you value most and apportion your value dollars accordingly.

The list should reflect your personal priorities as well as school policies, and you may find that your allotment changes from year to year. For example, I started with the following "budget":

	Homework assignments	$30
	Problems of the Week	$20
	Oral presentations	$20
	Write-ups of class activities	$20
	End-of-unit assessments	$10

Your own choices may be different. The discussion below concerning end-of-unit assessments will help explain why you might assign them only $10, compared to the traditional practice of giving major weight to final tests. Teachers find that working out these decisions together gives them all confidence in their choices, even if they disagree.

Once you've created such a list, you can then use it to assign percentages in your grading scheme. As you become more familiar with the IMP curriculum, your values may change; your grading policy should reflect such change.

Whatever system you use, it is vital that your students be informed about the grading process. Students should know where their grade is coming from. They should know what is valued and should have ways to participate in the process.

What Assignments to Grade

Although assessment is taking place every day in your IMP classroom, you will need specific tools for assigning grades. Since you can't thoroughly read and comment on all the work your students do, you need to make some choices. The overview section of each teacher's guide suggests a specific selection of assignments that represent progress toward the unit's goals.

These suggestions use a balance of activities, including assignments that focus on specific skills as well as those in which students can demonstrate a broad understanding of the development of concepts. They are spread throughout the unit and include both in-class and at-home work.

End-of-Unit Assessments

There are both an in-class and a take-home "assessment" at the end of most units. These end-of-unit assessments should be just one tool of many in your grading tool kit. They are not intended to "cover" the unit, but rather to give students a chance to show some of what they have learned. You may decide that some of the supplemental problems also make good assessment tools. The in-class assessments are intentionally quite short. You should give students the whole class period, even though most of them will need less time. That will allow you to measure how well--not how fast--students reason, think, and communicate.

Grades and End-of-Unit Assessments

Perhaps an extra word is in order about the role of end-of-unit assessments in grading.

Many of us have sometimes used end-of-chapter tests as the primary tool for grading, but we've also had the experience of seeing a "top" student do poorly on such a test. When that happens to me, I generally conclude that the student simply had a bad day and I assign a grade based on my broader knowledge of the student. In other words, I trust the judgments that I have built up over an extensive period of observation more than I trust the results of a single test.

This principle applies even more with the IMP curriculum, because you have so many opportunities to evaluate your students' work. Keep in mind that the end-of-unit assessments represent perhaps two hours of student work in a unit that may have involved twenty to thirty hours of class time and many more hours of homework.

Some "How To's" to Help with Grading

Once you have made the decision as to what you are going to grade, you need to figure out how to get it graded. Of course, the first step is to work the problem or do the activity yourself to appreciate its complexities and difficulties. If possible, discuss it with a colleague.

Here are some other tips gathered from experienced IMP teachers.

Grading Problems of the Week

POW grading is most efficiently done holistically. Holistic scoring means developing an overall sense of how well the student has done, rather than focusing on specific details. Many teachers do this by sorting papers into piles according to a broad standard (sometimes called a rubric). The teacher reads through the papers, focusing on explanation of process and solution, and puts each paper into one of the piles.

Many teachers use three basic piles--above the standard, meets the standard, and not acceptable. You might then subdivide each pile into two, and use that final sorting to assign grades. By reading student work with a focus and by limiting comments on the student papers, you can grade a class set of POWs in a reasonable amount of time.

Grading Homework

There is not enough time in the day to thoroughly grade every piece of student homework that comes in. Most experienced IMP teachers grade the bulk of homework according to completion. This can be done by stamping the homework or marking it off in your grade book as students come into class. In order to build in more accountability on occasion, you can focus on one particular part of the assignment or ask a specific question to gauge how students did.

Grading Group Participation

As you observe groups working, you will be getting insight into how well they are able to share the tasks they are assigned, and can give the group as a whole a grade on its members' ability to collaborate.

You may also find it helpful to have group members grade each other periodically on participation. You might have students do some self-reflection and grade themselves as participants in their groups. Students are typically very honest. In fact, many are too hard on themselves, so you will want to reserve the right to raise self-assigned scores.

Grading Group Projects

Occasionally, you may need to assign grades to projects or investigations done by each group as a whole. The simplest approach is to assign the same grade to each group member. As an alternative, you can give a lump sum to the group and have group members decide how to allocate it. For example, suppose you want to allow each student a maximum of 10 points on a given assignment, which would be a total of 40 points for a four-person group. If the group did B work, you might give them 34 points and have the group divide the total among themselves (and justify their decision).

Changing Over Time

As you become more experienced in teaching IMP, you will develop a system that works for you. Take time out occasionally to assess your grading scheme to make sure it reflects what you value. Also make sure it is doable--the profession needs you, so don't burn yourself out trying to be "Superreader"! Be selective in what you grade and stay on the lookout for the most effective and efficient way to get it done.