I attended John Scammell’s excellent 3-morning sessions on Formative Assessment at #TMC15. We were asked to share strategies that we may already be doing to give students feedback . I shared about how I used highlighters for this. I promised my group that I would write a short post about it, but I waited until now since I needed the school year to begin to have student samples to share.

I used highlighting to give my 6th graders feedback on their first *PoW* (*Problem of the Week* from The Math Forum).

It’s challenging, as I hope all *PoW*s are, and even more so when it’s the first one they get. I give no specific instructions on how they should write up their solution — nothing more than the usual “show all your work in order to receive credit.” I want to see what raw stuff I get on this first submission. We’ll worry about quality control soon enough.

I’m familiar with what I can expect with the first harvest of solution write-ups. One-fourth of the papers are pleasantly stellar, one-third show candid efforts (especially the ones with parents’ writings on them), another third make me get up and stick my head in the fridge to find a cold-and-alcoholic beverage, and the rest of the papers remind me that some of my 6th graders are still working on finessing the opening of their combination locks. The *other* right, sweetheart. There you go.

Years ago I taught a writing elective. I was at the beach — at the Oregon coast — because that’s where you should read and grade all writing papers. I forgot my red pen. I only had a yellow highlighter. The highlighter transformed my grading. I no longer cared so much about the writing mechanics — fuck spelling and punctuation and syntax. You got voice in your writing, kid. Your heart was wide open in this third paragraph. How did you know the rain smelled differently depending on what part of Portland you were in?

I highlighted sentences and words that spoke to me. I highlighted a brave sentence. I highlighted the weak ones too. The highlighter allowed me to interact with the kids’ writings differently. I didn’t add to or cross out anything they’d written. The highlighter didn’t judge the same way my red pen was judging.

And that’s the history of using the highlighter for me. But back to math. I have over 100 students and to write feedback for their bi-weekly *PoW *write-ups is all too time consuming. The different colored highlighters come to my rescue.

I’m going to continue using my binary scoring system because it worked well last year. I look through all the papers, separating them into two piles: papers that got it (full 1o points) and papers that fell short (1 point). These kids will get another week to revise their work and re-submit.

I use my yellow highlighter — just swipe it somewhere on their paper — to show that I’m having trouble understanding their work or that their work is lacking.

I use the pink highlighter to show that the answer is not clear, not specified, is partially or entirely missing.

I use another color (like green or blue) if the papers warrant another something-something that I need to address. I didn’t need to with this week’s *PoW* submissions.

If necessary, I will write on their papers directly. But I don’t have to do too many of these because kids’ mistakes, more often than not, are similar to one another.

When I pass the papers back, I tell students what each colored highlight means and what they need to do to revise their work, including coming in to get help from me. It’s a helluvalot faster than what I used to do.

Guess that’s it. Feels good to write in this space again.

## 19 Comments

This is awesome, Fawn.

I struggle so much with wanting to give timely, useful feedback and the time it takes to do it, leaving the last group of feedback not so timely. What a great way to expedite the feedback process!

Thanks, Andrew. I’ve tried lots of things, and so far this way works best for me. I’m not giving up the personal/tailored feedbacks when they are warranted. But overall, my feedbacks are similar enough that the color coding helps me communicate with the students just as effectively. I strongly believe in giving students feedback (why we teach at all), but there’s only so much time.

Fawn,

It feels good to read your writing in this space again!

I know that a lot of teachers would like to use problem solving more in their classrooms, but don’t know how to make it happen. Often, the need to “cover the material” trumps spending time developing student’s problem solving skills. Also, scoring “content” (right or wrong answer) is much easier than scoring problem solving, so the tendency is to focus on what is easier to for students to do and easier for teachers to score. Problem solving is fuzzy stuff. Many math teachers aren’t comfortable with fuzzy stuff.

When you have the time, I would love to hear more details of how you integrate problem solving in your curriculum. Here are some questions:

• Do you use problems that are specifically related to the content you are currently covering? Or do you consider problem solving to be a sort of “content area” of its own, so you are not tied to a specific content for your problems?

• Do you susbscribe to Drexel’s POW? Do you find problems elsewhere, such as Illustrative Mathematics or Mathematics Assessment Project?

• You give 10 points for a correct answer with a clear and easy to follow solution and 1 point for “not there yet”. Then you give those that earned a 1 another week to bring the score up to a 10. If they don’t, do you have a rubric for what score they receive between 1 and 10?

• How much help do you give?

• Do you give student’s class time to work on the problem? Are they encouraged to work together?

• Do you teach specific problem solving strategies such as

o Notice and Wonder

o Make a simpler problem

o Guess and Check

o Work backwards

o Use a table

o Use multiple representations

Any further guidance on how you integrate problem solving into your courses will be appreciated…by me and many others!

Hi Elaine. I hope to answer some of your questions. Here we go:

1. I use problems intentionally NOT related to current content. It’s too formulaic otherwise. Are they really “problems” if we knew how to solve them?

2. I do subscribe to MathForum’s PoW. (They partnered with NCTM now, so no more Drexel. Drexel’s big loss.) My problems come from 20+ years of digging through everything and anything: books, websites, workshops, college courses. Illustrative Maths (IM) and MAP don’t have the types of PS that I look for. IM has more textbook-type exercises (good ones too, but they are tied to content). MAP is awesome, and I faithfully use their tasks, but they are more for group work.

3. Either it’s a 1 or 10, nothing in between. I need to stick with this because I don’t want kids to settle for the 1. (And doing anything more takes too much out of me.) After 4 days, I have 10 of the 12 who scored 1s re-submitted and earned 10s now. I wouldn’t do this if it really didn’t motivate students and keep the focus on learning.

4. I’m available at lunch every day and after school on Mondays. I’m available after school other days too, but Mondays for sure.

5. PoWs are done on students’ own time. But parents/anyone are encouraged to work with students on these. Why not share the love? :) PS are done in class, first individually, then in small groups, then as whole class.

6. I don’t formally teach PS strategies as students are supposed to find their own strategies. Only when they are stuck [after an honest period of productive struggle] that I suggest a certain strategy. I have the strategies posted in the classroom, and we identify them when we employ them. (I don’t see Notice and Wonder as a PS strategy, it’s a great structure to begin a problem though.) And I refer to Guess-and-Check as the “last resort” strategy — it’s a common tendency when we don’t have any other strategy.

I wrote a post some time ago called, Making Problem Solving Part of the Math Curriculum. :)

Love this idea Fawn. Thanks for sharing.

Thanks, Graham, for dropping in.

Fawn, great stuff here! I was thinking of using this strategy with my formative quizzes. I might provide feedback with highlighter and allow opportunities for students to redo and return.

We just need to find ways that work for us, efficiently and effectively. Or else it’s easy to become overwhelmed and eventually give up. The highlighter works because it’s quick for me yet it gives kids the same feedback [as if I wrote them by hand] when I explain the different colored highlights to the group. It’s just oral feedback. Thank you, Matt.

I love this idea. I believe giving feedback is how we push students to think and grow and improve their mathematical thinking. Using color-coding with highlighters will get them to analyze their work and do their own error-analysis instead of me doing it for them. The added bonus is it sounds like it would take less time and I could get student work back to them much more quickly! Thanks for sharing.

Thanks, Kaci. You’re exactly right about highlighting “will get them to analyze their work and do their own error-analysis instead of me doing it for them.” The “blankness” of the highlight allows kids to fill in the blank — something is missing here, how do you account for this gap?

Way way faster to make one highlighting stroke than to write even two words. :)

Hi, Fawn,

I agree with Elaine! I would love more specifics about your process. I am intrigued by the highlighter (I taught writing, once, too, and saw quickly that the more I “corrected” on papers, the worse students felt about writing!) with math–do you use it only for POWs? Or other things?

And I would also love more ideas of where to find good problems for students who are new to problem solving (and used to more direction from teachers).

Thank you–I have been so happy to find your blog and twitter feed!

Hi Gretchen. The problem with most feedback is kids (and adults) just look ONLY at the feedback. If it’s positive, we feel good. If it’s negative, we feel badly and want to stab the person who gave that feedback. Or maybe that’s just me. :p

I use it on pretty much anything that I need to give feedback to, so PoWs for sure and other written feedbacks like their task reflections. (This is when they write for 2 to 3 minutes — timer is set for this — after doing a problem-solving type task.)

I hope my response to Elaine’s questions also answers yours.

Fawn, thanks so much for this enlightening post. I am so glad to get details about the highlighter use in formative assessment. I tried it out last week when I returned and went over quizzes with my students. I really liked how even the most easily distracted students tuned in and focused when I mentioned the highlighter color they had on their paper. One of the best ones was saying, “If you have a blue highlight on #3 or #4 you forgot the units. Remember you have to write units of measure like $ and hours on your answers.” I didn’t have to write “Don’t forget the units” over and over and they all got the message.

I’m definitely going to keep using this strategy.

Hey Fawn,

Thank you for sharing! I too want to give timely meaningful feedback and will try this out. I saw this video https://www.teachingchannel.org/videos/math-test-grading-tips and she uses the highlighter to mark where a mistake was made so students know where to fix. Thanks again for sharing!

Hi Fawn, I know this post is about giving feedback, but I wanted to comment on how rich this problem is. I plan to use it with our middle school Title 1 after school program with some questions handy if students are flailing with no success. How could we identify the possible sets of consecutive numbers? If 8 is the highest number in the series, what would the 6 numbers be? If 6 was the lowest number in the series… Then I was thinking of tying in MAA’s problem solving strategy Go to Extremes to also rule out the sets of possibilities based on the “extreme sums” of 16 and 23. This problem could be an excellent opportunity to explore that problem solving strategy. Thanks for sharing!

I think this is a really good time saving idea. It has also been my experience that students tend to make similar mistakes to each other. Do students generally understand the generalized feedback or do you often have students come up to ask questions after passing the graded paper?

This is such a great idea! I really like the 10 points or 1 point with no in-between to focus students on not settling for the 1. Thanks for sharing your greatness!

Got it: yellow = needs clarification & pink = answer incomplete. Thank you for sharing this strategy! I have been thinking about and looking for a strategy to provide feedback in a timely manner. The colors simplify work on both ends. Do you use this strategy on formative assessments, too, or just POW?

Hi Gabrielle. I use this mainly on PoW because for formative assessments, we go over each item together in class. (They go over them with peers first.) Thank you for dropping in.

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