A few weeks ago I attended an all-staff PD at the County Office. During the morning session we scored samples of 2-point short-text items from grades 4, 8, and high school. It was time well spent.

I wanted to duplicate that experience for my students with two goals in mind:

- See how well they can interpret and use a scoring rubric.
- For them to attend to the same thoroughness and precision in their own solution writing when it’s their turn in May.

What I had my students do:

#### 1. Get to know the short-text item.

They worked on the grade 4 item below. This was intentional to diminish any math anxiety and to keep our focus on the scoring of the task.

While it was good to learn of my kids’ different solutions, it was also disheartening — but not too surprising as they are the same ones who struggle mightily — to learn that 20% of my 6th graders did not get the correct solution for this grade 4 item.

#### 2. Go over the solution.

I collected their papers and just had a couple of kids share their strategies to the whole class. Considering 1 out of 5 kids in the room didn’t quite know how to solve the problem, this step was really for them.

#### 3. Get to know the item-specific rubric.

I gave the kids quiet time to read the rubric, reminding them that they would use this rubric to score 9 students’ solution responses. I told them that they could expect to return to the rubric over and over again as they scored each response.

#### 4. Score the responses.

I gave them quiet time to fill out *Score 1 *column of this handout*. *I reminded them that this was one of the main goals of the task — to score the sample responses fairly and accurately using the item-specific rubric.

Why are you giving this response a 1? What is it missing to not get a 2? What does it have to earn a 1 and not a 0? Keep referring to the rubric! Does spelling matter? What does your rubric say about spelling errors?

After everyone was done filling in *Score 1 *column, I asked them to talk to their neighbor/s and only fill in *Score 2* column if they changed their mind. (They were not to erase any score in *Score 1 *column.) This also made it easy for me to see how many scores they’d changed their mind on.

My favorite thing in the whole wide world is to listen in on their conversations about math.

#### 5. Reveal the actual scores.

[The actual scores are on 2nd page of handout above.]

If the whole class agreed with the actual score for a particular student response, then we moved on. But if anyone disagreed, then I had that student tell the class why. Then I had another student who agreed with the answer to share his/her reason.

Out of 66 students, 24 students scored 9 of 9 correctly, 19 students scored 8 of 9 correctly, and 6 students scored 7 of 9 correctly.

That meant 65% of my 6th graders did this scoring-using-a-rubric better than I did. Whatever.

I also asked the kids to write a couple of sentences about what they got out of doing this. Most of their responses echoed these:

This was helpful to me because now I know I need to be much more thorough with my work and explain why I might of did something.

This was helpful to do because it let us see how these problems are graded. Even though the problem was for 4th grade, I think the grading scale of conclusion and math will be similar or the same for all problems like this.

I believe this was helpful because when I take the test, I will be more aware of the questions and what is expected of me. I will make sure to always back up my answers with evidence.

## 8 Comments

Using the scoring rubric on their own work is an awesome idea. It will help de-mystify the test, among other things. Thanks for sharing. We are also SBAC testing soon.

This is great, Fawn! I did something similar with a problem from the ACT ASPIRE, but I didn’t want to create a whole other problem. Glad to be able to use this one!

My last step, after we go over the sample responses, is to get the kids to go back to their initial work and grade it using the rubric. They usually realize that they didn’t put in enough effort in their explanations. Then I have them rewrite their explanations to get full credit.

I understand the benefits this has for kids taking the test (and for teachers evaluated based on test scores). However …

(1) Does this help the students improve their mathematical writing?

This is a sincere question and not intended as snarky criticism. I see some good points and bad and would love to hear other opinions.

In the grading rubric, they are given points for actually answering the question (useful) and for giving supporting evidence (also good). However, there is nothing really about explaining their thinking or communicating mathematics. For example, do they have a nice model they used to calculate 10 * 1.5?

(2) Reinforcement of The One True Answer myth: All the answers take the same path, or part of the path: 10* 1.5 = 15, 15 10, so “no?” I’m sure people more clever than me (aka students) can come up with other good approaches.

(3) Does the question reinforce number sense and mathematical thinking? No, who makes lemonade (at home) that way? One clue is in the number of lemons theoretically required for 16 ounces = 10 2/3 lemons. No one does. You squeeze your lemons, see how much juice you have, then measure out the other ingredients (mostly sugar) to suit.

However, I’d note that the rubric does give full points for someone who correctly calculates 15 and says it is “close.” Does that mean they are saying it is ok to go ahead and make lemonade or not? I would love to hear if any students talked about this part of the rubric.

I see several explorations inspired by this question:

– how much juice do you get from a lemon? how much does this vary from one to another? does it vary by who is squeezing?

– how do we make lemonade and suit the constraints of our materials (probably amount of lemon juice)?

– how does our lemonade taste for various different recipes (more/less sugar)? One of the rare opportunities to use taste for mathematical comparisons!

Since it is the hot season where I live, tomorrow is a perfect time for this investigation with my own kids at home. However, we will use limes instead of lemons, so our data won’t directly relate to the question as written.

I think this exercise helps kids improve their writing, especially if you get the kids to grade their own responses and rewrite them. I just did the lesson in 1st period today, and I even projected some kids’ work that was a 1/2 and talked about how make it a 2/2 (I have brave kids in 1st period).

I also think that exposure to the rubric would help the students write better responses to the next problem of this sort. Here is the example I used in my class, from ACT ASPIRE:

Sorry, here is the follow-up question I would use:

“A student thinks that the sum of 4.3 and 8.4 is 12.7 because 4 + 8 = 12 and 3 + 4 = 7.

The student then adds 3.7 and 2.6 and gets 5.13 because 3 + 2 is 5 and 6 + 7 = 13.

Identify the mistake in the student’s procedure, and explain why the procedure won’t always work.”

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