“Hands down, the best thing I’ve seen in years.”

– Susan Preston, 4th Grade Teacher

And that was about an assessment! … Yes, you read that correctly, that quote was about an assessment! You know, the things that most of us working in the education system constantly bemoan. For decades now, traditional assessments haven’t been serving the best interests of students. Often times, they eat up valuable instructional time, cause students unnecessary stress, and don’t yield helpful, timely information that teachers can use on the spot to maximize student learning.

We want to help change that.

About a month ago, I had the pleasure of meeting an elementary math teacher, Susan, who was getting ready to start teaching summer school in a few weeks. She reached out to ask if we could help figure out a way to use our assessment philosophy to help her incoming summer school students. We quickly bonded over a shared desire to figure out a way to help make a tangible impact on student learning in a short time period. Susan ended up giving us the opportunity to design and pilot an entirely new assessment tool for her summer school class.

By the end of the day, Susan took her students from getting ~55% of the questions right on average to ~78% (a 42% gain!) with just 17 one-hour sessions. One student went from getting 39% of the questions right in the pre-assessment to getting ~95% right in the post assessment.

“Best thing I could’ve done in summer school.”

– Susan Preston, 4th Grade Teacher

So how did she do it? She taught precisely what the students needed to know. Rather than using the content that was prescribed, she focused on understanding her students strengths and weaknesses and using that to her advantage.

Understanding her methodology, we built an assessment tool that would help her group students based on their different understandings of various topics. In this case, after having a rough idea that students were struggling with computation, we designed an assessment to understand what processes students were using to compute, so that Susan could re-engage them with high precision.

In order to understand what processes students are using, we take an exceptionally deep looks into student answers. I was trained to be a statistician and my first job was working with the stock markets, so I generally think in probabilities and building evidence toward a decision. And in this case, each answer a student gives is not only a peek into their mathematical reasoning, but also a piece of evidence towards building an idea of how the student is thinking. We’ve found that if you design your assessment with the right questions, in the right order, you can figure out a student’s approach to almost any problem and determine what is working or not working for them. Get in touch if you are interested in talking details.

Back to the important part: Susan administered the assessment at the beginning of the summer school course. We immediately analyzed the results and identified a few groups of students based on the methods they were using to compute. We made groups that used certain processes for rounding, subtraction or general organization. We also made groups of students that we knew were likely counting on their fingers, or in their heads, and making small mistakes, etc.

To give you some more concrete examples, I’ll list the two most prevalent examples below.

1. Rounding means adding.

When we asked students to round 8 to the nearest 10, then would answer 18. Round 42 to the nearest ten? They would answer 52. To them, rounding meant adding.

2. Subtraction without borrowing (“easy subtraction” as I call it)

Students here would subtract the highest digit from the lowest digit in each place value. No borrowing or regrouping. 62 – 26 = 44. 245 – 158 = 113. We were able to see the consistency with which they were doing this across problems.

In both of these examples, students were consistent, which is a powerful place to start. If they are consistently using a strategy, we know they aren’t guessing. They have a process they’re using every time, so if we can just help them adjust that process, then they can get it right every time! And if we can help them see why their current process doesn’t work every time, we can help them gain a deeper understanding of the content.

“This is precision teaching.”

– Susan Preston, 4th Grade Teacher

Susan was able to take this information and run with it. Students using certain processes could now have special attention and those who already demonstrated understanding, could work on the something else. Susan jumped straight into rounding and the idea of place value. She was getting students to stand up and use a physical number line to see what number was closer. She had students coloring in a hundreds table and getting a better number sense.

Not every day was a success however. In order to help, we reached out to our network of teachers —tutors, teachers, math education gurus and researchers, to get her some ideas. Maybe you were one of them! We got a list of ideas to help with the subtraction issue students were having. Since students had no trouble adding, we ran a little experiment.

Let’s use “62 – 26 = __” as our example here.

Students would subtract 62 – 26 and get 44.
And then we would have them add it back.
44 + 26 = 70 …. “WAIT A SECOND!”
For some students, light bulbs went off.

We had a list of other methods to try as well:

• Breaking down subtraction into tens and ones 60 – 20 + 2 – 6
• Showing them 3 cases where their method worked and 3 cases where it didn’t. Then, have them notice and wonder why what was different about the two sets.
• Have them move both numbers down the number line until their strategy works.
  • 62 – 3 = 59
  • 26 – 3 = 23
  • 59 – 23 = 36
  • Then ask them why they got a different answer. What changed?

It’s important to recognize that not every student will click with every method of teaching, so we believe that having some backup methods to show students is a must. These can be included as extra resources for each group of students.

Assessments can be a powerful tool, but they need to dive deeply into understanding what students are doing, and how they’re thinking, not just how well they perform. There are a variety of ways to answer questions and the important information isn’t all held in the answer’s correctness. A lot of the valuable information for educators is how students arrive at an incorrect answer.

Each answer a student gives builds evidence towards how they are thinking. If you pair that with teaching methods tailored to help them understand why their method isn’t working in certain cases, we can help students build more robust understanding instead of rote memorization.

If you are interested in working with us to figure out how to help your students, please get in touch or join our community on twitter.