An interesting conversation came up yesterday regarding the proper way to grade students’ understanding of multiplication and division. Part of our most recently completed math unit was the Common Core task, which required students to use a table of information to compute one and two-step word problems using multiplication and division concepts.
Throughout the unit, we made a point of teaching various methods of multiplying and dividing. Students learned how to use arrays, pictures, tables, bar models, area models, repeated addition, repeated subtraction and more. However, based on the rubric provided in the task, if students used those methods and not explicitly written multiplication or division expressions, they could not receive credit for the work.
The discussion was spirited. Many people felt that since we taught so many different ways, it was just fine (and in fact, desirable) for students to choose the one with which they were most comfortable as long as they applied it properly. The other side of the discussion held that the task was designed for the purpose of measuring students abilities to recognize those methods as multiplication and division, and indeed, to convert their understanding to writing the sentences.
Since this task does not count for a grade and because it is our first foray into such a thing, we arrived at a consensus that a note should be made that in many cases, points awarded were not indicative of the learning that occurred or the work students did. The plan is to consider this for next year when we come up to the task again and place a greater emphasis on teaching students how to relate the chosen methods back to multiplication and division.
Three lingering thoughts I have from my students’ work:
- If the work of the problem should have been (4×4)+ (4×5) and a student simply wrote 16+20 (meaning they multiplied in their head), is that insufficient?
- If a student can multiply 3×2 mentally (or add 3+3 mentally), do they need to write it in order to receive credit when they give the correct answer of 6?
- If a student accurately computes division using pictures, is it division by another name?
I would love to read your thoughts on this, especially if you are familiar with your state’s Common Core task.