You’re looking at year-by-year state test scores in math for two similar middle schools in the same school district. They begin in similar starting positions.

What happens beginning in 2017 for the school represented by the blue line? How did they make such strong improvements while the other school remained stagnant?

## Quick Background

In order to answer the questions above, it will be helpful to have some quick background info on Math ANEX.

Math ANEX has been working on repairing the way students are assessed in mathematics. Rather than solely scoring correctness of answers, we have been building assessment tools that focus on uncovering students’ mathematical thinking.

The big question we’ve been grappling with is: How can we help educators take this refined assessment methodology and use it to directly impact student learning?

The answer is something we’re calling “learning cycles”. We define a learning cycle as any period of time that covers some specific learning goal or material. This can be very broad (think Algebra 1) or very specific (think introducing decimals).

Within a learning cycle, we believe there are key activities that can help make students more successful. Based on the results we’ve seen with our partners, we believe this is an approach that can deliver a broad impact within our education system as a whole.

## The Four A’s

The learning cycle has four distinct steps. The four A’s make it easy to remember.

**1st Step** **— Assess**

To start, we need to capture insights into how students are thinking about the identified topic and material. This can be done with student interviews, collecting old student work, or doing an assessment activity.

**2nd Step** **— Analyze**

The second step is to perform an analysis of what we’ve collected. By gaining a deep understanding of how students are **thinking** about the topic, we’ll be able to design the next steps of instruction with precision. This can be done by mapping out our own plan, doing research, or engaging in professional learning with someone who has expertise in this type of work.

**3rd Step** **— Act**

Next up is running the plan with your students. This may be adding a math language routine. Or perhaps a re-engagement activity that presents popular student answers for group analysis. There are countless routes to take here. This step is all about honoring and engaging with the specific ways students are approaching the topic in order to help them make progress.

**4th Step — Achieve**

Finally, we’ve got the reflection stage. Once again, this is all about figuring out how students are thinking about the topic. How did they grow? How has their thinking, approach, or comprehension evolved? We want to help students celebrate their growth. It’s important for students to see the progress they are making, in real time.

It’s also important to think about how to help create a better experience for them for their next learning cycle. How was the learning cycle from their perspective? Is there anything we can change? If we can share our results, did anyone have more growth in certain areas, especially in the movement between one type of student thinking to another?

## Can This Approach Actually Make A Difference?

With the learning cycle now defined, why do we believe that this can be a catalyst to improve our educational system? For one, it’s an opportunity to come together to get very specific on ways to help each student (or group of students) based on the specific way they are thinking about a topic.

Let’s look at a simple example:

Students who answer “61” and “111” are missing some key concepts around the idea of what the equals sign means in this context. What type of re-engagement would best help those students? We know that whatever we can do for them, probably wouldn’t work for students who got the answer “1”. We have various ways to re-engage each of these students, based on their own unique ways of thinking, but it would be incredible to have a body of research on what was most effective for which students. Using that data, we could then understand how to best help any specific group of students based on how they are thinking, their other skill sets, motivation, etc.

## Learning Cycle Example

Another reason we think this approach can deliver results broadly in education is because members of the Math ANEX team have been doing it for years — and the results for students have been astounding.

Let’s start with a learning cycle that is a difficulty for a lot of students — summer school. We ended up meeting a wonderful teacher this past summer who wanted to make the biggest possible difference for her students. One of the main complicating factors in summer school is time. In this teacher’s case, she only had one hour a day with these students for a total of just three weeks.

We looked at the students’ previous work from the last year and gave a quick 15-minute assessment. This gave us ample material on how to best help them. We worked with this teacher on the best practices to help her students and let her run with it. Three weeks later, they took a similar assessment and improved from an average score ~55% to an average score of ~80%.

“This is precision teaching.”

— Susan Preston, 4th Grade Teacher

We were also thrilled to see that these students retained their new skills in the new school year. Susan requested to have as many of them in her class as she could.

## Results Over Time

It’s great to see this type of result in a focused, short-term learning cycle, but what does the impact look like over longer periods of time? We ran 6 learning cycles per year for a middle school and measured them against a similar school in the same area with similar demographics and similar starting state test scores.

What we saw over the course of three years was that students participating in these learning cycles drastically improved their understanding of mathematics, and it showed up in external metrics, like state test scores. It’s incredible to see the change that we can make for students by deeply looking into how they think and designing ways to help based on that data.

## The Power of Re-Engagement Activities

Re-engagement activities are the crux of step 3 of the learning cycle: Act. These activities allow students the opportunity to talk about their ways of thinking and learn about other students’ ways of thinking. Let’s take a quick look at just how impactful these activities are.

In one of our recent learning cycles, there was one week when about half the teachers weren’t able to do a re-engagement activity based on their students’ thinking. The data that arose was very telling.

Even though they started further back, students who did a re-engagement activity came from behind and made huge improvements, and actually finished ahead of the other group. While the students who did not do a re-engagement activity, their performance remained about the same.

## Interested in hearing more?

If you would like to learn more about learning cycles or implement them at your school or district, contact us today and let’s talk about how we can help.