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Assessing Computational Fluency

I taught 5th grade for many years before stepping into the coaching role. Every year, I had kiddos come to me who could not subtract with regrouping, let alone multiply or divide! And I’m not talking 1 or 2 students, I’m talking many. So along with teaching my grade-level skills, I had to spend significant time remediating skills from previous grade levels. Here’s my theory about why that happens. We typically teach our computation units early in the year. In many districts, grades 3-5 are finished with their computation units by winter break. Some kiddos get it, and some don’t. But we move on in the curriculum and don’t remediate what they didn’t get. That happens every year, so it’s a snowball effect that becomes a full-blown avalanche by 5th grade. And it’s not because teachers don’t have the best intentions. They most certainly do!  But they also have a million and one things on their plates.

One way to proactively address these gaps is to implement a system of assessing computational fluency utilizing brief, pure computation problems (not word problems) to assess grade-level skills. The assessments are given at the beginning-of-the-year (BOY), middle-of-the-year (MOY), and end-of-year (EOY). The BOY test is just the previous grade’s EOY test. Does that make sense? So the 3rd graders take the 2nd-grade EOY test at the beginning of 3rd grade to give the 3rd-grade teachers an idea of the students’ skills.

Our Math Vertical Team compiled data from the BOY test and used it to inform instruction. It was surprising how low the scores were at every grade level!! We decided that the teachers would remediate and re-administer the BOY Portrait again before the October vertical team meeting. That became our pattern for the year. In January, they administered the EOY test, because they had finished teaching their computation units in December. They reported their numbers in January, again in March, and just before the end of the year. The numbers went up and UP! It was the accountability piece that had been missing before.

Click here for the files containing the assessments. Keep in mind that these are aligned to the Texas TEKS, so the skills might be slightly different for common core. I uploaded them in editable form, so you can modify them to make them work for you. Kindergarten and 1st grade look a little different. We worked as a vertical team to determine what their assessment would look like. We decided that the main skill the kiddos need coming out of Kinder and 1st was knowing the combinations for ten, so that is their assessment. They use their tracking sheet all year long to determine each child’s “number”, meaning what is the largest number each student knows all the combinations for.

With each successive year, teachers save tons of instructional time previously needed for remediation. And maybe the best result? Students feel increasingly more successful! I hope this is helpful to you!

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  1. Amazing! We just started creating the same thing for our district…same format and everything!

  2. Remediation is so important! It makes such a difference for kids (and their teachers!) I love how you use data and teaming to make instruction better for all students! Thanks for sharing!

    The Math Maniac

  3. Thank you for sharing! It’s so interesting to read about different assessments. I’m printing the 1st grade one. It will be very helpful in deciding who needs more intervention.
    First Grade Found Me

    1. This is definitely just one small piece of the mathematical pie, but computation is so important. Sometimes we focus so much on problem solving (which is super important–don’t get me wrong), but we forget how important computational skills are.

  4. As we begin planning curriculum for next year I am excited to share this with my teaching team and the entire staff. Thank you for making it so accessible!

  5. Thank you for sharing this. I’ve been researching math difficulties, in particular number sense, for about four years now. By “researching” I mean, reading every peer reviewed article I can get my hands on, implementing informal action research, and keeping data to see where our teaching breaks down. I believe you are absolutely on the right track with multiple assessments COUPLED WITH REMEDIATION. My masters is in Mind, Brain and Education and if there is one thing I’ve learned about how our brains learn is that learning is fragile. What I believe happens is that we assess students before their learning is “crystalized” – or fluent. So, we assess, we think they have it, and we move on…but that knowledge wasn’t solid or we taught a procedure without a student understanding underlying concepts. BUT…even KNOWING and planning for this, I still find, to my surprise, students that I believed “had it” and when I assess them a few weeks later, I am shocked. This speaks to the need for ongoing formative assessment AND changing the way we teach math to be more aligned with the way we teach reading: phonemic awareness=number sensed; decoding=decomposing; fluency=rapid recall of facts/compositions; leveled reading & guided reading groups=remediate or advance based on individual, student progress NOT whole group; comprehension=understanding=combination of all of the above with students showing they can explain strategies as well as create problems in various ways using various methods. This HAS to occur prior to 3rd grade. Think about it, beginning in 3rd grade is when we really expect students to read for meaning verses learning to read. All the number sense skills students need to have mastered need to occur by the end of 2nd grade. If these are in place, then deeper more complicated mathematical ideas can be taught WITHOUT going back to the scaffolds that should have been there. It will require a change of pedagogy and a shift in philosophy of the way we teach and assess math.

  6. PS — follow up…yes, I saw my typos! Yikes…BUT…I want to add my appreciation because I forgot to say that part of my research, a large part, came from reading your blog, using your “products” and reading the books on your “Books I Love” list. I can’t recommend these highly enough. Yet, just like students’ “fragile” learning…knowing all of this did not guarantee student success; as you clearly illustrate by sharing that even with all your collective knowledge, it still took ongoing formative assessment and teachers coming together to look at data to get to the root of the problem (or at least one root). THANKS for your guidance to me along the way!

  7. I also like the Portrait of a Maverick Mathematician ideas, esp the brief snapshot assessments 2-5. I see the assessments themselves, but not the sheet for student names, tracking and remediation as there is for K and 1. Do you just modify one of those, or is there a sheet for 2-5 also? Thanks for all you do for teachers and learners, Donna!

    1. I actually have updated the tracking sheets for 2-5, and I’m going to be posting an update in the next couple of days!!

    2. Sounds great. BTW, I love what you are getting to do next year! It would be a dream job. And you will be great at it.

  8. I used these at the end of the year with my students and my plan is to give them to the 5th grade teachers at the beginning of the year. That way they can see where they were at the end of the year last year. I am using them the first week of school on my new kids to see where they are. Then in January to show how they have improved. We will set goals at beginning and middle of year and then review at the end of the year to see where we are! It would be powerful to send with the students to 5th grade. We have a transient population, so I know it won’t be perfect, but I love it!

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