Assessment and grading:

How will they look different?

≥What we assess and how we assess it communicates what we value.≤ (National Council of Supervisors of Mathematics, 1996)

A teacherπs goal in assessing is to gather evidence that the student has made sense of a concept.

Assessment and grading will be different in any standards-based mathematics program as compared to a traditional program. Though teachers will still give tests, quizzes, projects, and/or other more traditional assignments, assessment no longer just means putting a score or a letter grade on a paper according to how many answers are correct; it now means truly attempting to understand the thinking of each student in order to help him/her to progress. As a result, the criteria for grading change. In student work, teachers will be looking for strategies used, explanations given (if required), and the actual answer(s). Many teachers will be using rubrics as a way of putting scores on work. A general example of a rubric that the teachers might use has been provided below. If a parent has a question about a score, he/she should be able to look at the rubric used for that task and understand the score (rubrics will not be provided for every task since many tasks will be graded on similar rubrics, but a teacher should be able to provide the rubric if requested). High scores will be obtained when students give what might be considered an ideal answer to the question, given the learning that is expected to have occurred at that point. Here is an example task from third grade:

There were 57 people who each had 6 marbles. How many marbles did they have in all?

Give your solution. Show how you solved the problem, and explain how you know your solution makes sense.

(third grade student)

I counted by 6 fifty-seven times and got to 339. I know this makes sense because each time I counted a 6, I was adding one more group of marbles to the count.

Analyzing this solution: The method does make sense for the reason that the student stated, and in fact the student explained this well. However, the answer is wrong – it should be 342. So this is not an ideal response just because of that.

Also, beyond what we see in black and white, we need to consider what was expected of students at the point the task was given and what is expected in our state standards. By the end of third grade, students need to multiply and divide by single-digit numbers.

If this were early in the year in third grade, or even halfway through, this solution strategy might have been acceptable because it was logical. So, on a typical 4-point rubric, the task might have earned a 3 because the answer was incorrect. But, if it were the end of the year, the score might have dropped to a 2 because the strategy was not efficient. A 4-point solution might have been, I knew six 50s were 300 and six 7s were 42, so I added the 50s and the 7s and got 342. (If 339 had been listed as the answer, 3 points should probably have been the score.)

Thus, rubric scores, along with any assessment in this program, will reflect the level of mathematical thinking of the student as well as whether the answer is correct.

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