## Marzano’s _Classroom Assessment & Grading That Work

I thought that I would do a couple of book reports this summer. I have been hearing about Marzano for years, and I thought that I should finally read some of what he says about Standards-Based Grading. The book I read is Classroom Assessment & Grading that Work.

I read the book about a month ago, so I do not remember everything. However, below are the ideas that stuck with me.

First, you should use “topics” for your class, and there should be about 15–20 of them. These are akin to standards in SBG. Whenever you test a standard, you should give the student a question in three parts. The first part should be basic details and/or facts that you would expect every student to know, the second part measures whether students understand what was covered in class, and the third part asks the students to go beyond what was done in class. I am teaching real analysis in the fall, so I am going to give an example for real analysis on the topic of compactness:

1. Is the interval $[2,3.5)$ compact?
2. Show that if $S \subseteq \mathbb{R}$ is a compact set, then the supremum of $S$ exists and is in $S$.
3. Give an example of a metric space $M$ with a set $S \subseteq M$ such that $S$ is closed and bounded but not compact.

I don’t love my example, but I hope it gives you an idea. You then grade the students answer according to the following rubric:

• A student receives a score of 4.0 if she is able to answer all three questions (“I can make connections that weren’t explicitly taught.”).
• A student receives a score of 3.0 if she can answer the first two questions (but not the third) without mistakes (“I can do everything that is taught without mistakes.”).
• A student receives a score of 2.0 if she can answer the first question (but not the second or third) without mistakes (“I can do the basics without mistakes.”).
• A student receives a score of 1.0 if she can answer some portion of the questions with help.
• A student receives a score of 0.0 if she cannot do any of the questions, even with help.

Half scores of 0.5, 1.5, 2.5, and 3.5 can be defined in a reasonable manner (Marzano does this in the book). Marzano claims that this scoring system leads to a roughly normal distribution.

Marzano then suggests that each topic is graded in one of two ways: either you find a function of the form a*x^b “of best fit” for each topic to predict where they will be at the end of the semester (using software). I will not be using this method. He also recommends using the “Method of Mounting Evidence,” which basically means that you keep track of all of the student’s scores within a topic (e.g. 1.5, 2.0, 1.5, 2.5, 2.5, 3.0, 2.5). Once you are convinced that a student’s “true score” is at a certain level, you mark it down and then look for evidence that they surpass it in future assessments. For instance, in the example list of numbers above, the second 2.5 is in italics, which might indicate that our hypothetical teacher thinks that our hypothetical student has convince him that she is definitely at 2.5 level for this topic. On assessments following that corresponding to the italicize score, the teacher will be mainly looking to see if the student jumped to a 3.0, 3.5, or 4.0 as her true score. And is she gets, say, a 1.5 on a future assessment? The teacher just returns the assessment and asks her to correct the missed “easy” work, with the assumption being that the student just had a bad day rather than no longer knows the material.

You can assess students as many times as you like, although Marzano recommends assessing students you are unsure of more. This seems entirely reasonable.

It seems possible that a student could get the hardest question correct but not the easiest question. Marzano mentions this possibility, but basically says that he assumes that a student who can answer the hardest question should be able to answer the easiest. So, ideally, the assessment writer would write questions in such a way that this is true.

At the end of the semester, the student’s score for each topic is just wherever they ended up with from the Method of Mounting Evidence. Marzano then talks about ways of averaging together the topic scores, although this is not particularly of interest to me. His other method for determining a final grade is something akin to what many of us to already, which is creating rules like, “A student gets a B for the semester if no topic score is below 2.0 and the majority or 2.5 or above.”

The two ideas that I am thinking a lot about are:

1. Topics should be assessed at different levels, as with my real analysis example. I have been heading this way for a while now, and maybe this is the year to try it.
2. You can give grades based on whether a student can solve it with help. I think that this is brilliant. However, I still need to figure out how to assess this in a reasonable way with 75 students. But I like it.

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