Helping students comprehend word problems is a challenge for most Kindergarten to 3rd grade teachers. Traditional methods, like relying on keywords, often leave students without a deep understanding of the math involved. 

For 1st-grade teacher Matt Spirakus, Structures of Equality (SoE) offers a more effective way for students to approach and solve word problems. In an interview, Matt shared how using SoE has transformed his teaching, the shifts he has made in his instruction, and his advice for other educators curious about SoE.

A new approach to word problems

When Matt first started teaching years ago, his classroom instruction focused on traditional strategies like keyword identification. But he knew this method wasn’t fostering deep comprehension.

Valerie Faulkner, a mathematics subject expert and former professor, was one of the early adopters of my approach to helping students use the structures as a reading comprehension tool to make sense of word problems. She shared some of my work in a professional development session Matt attended, and the concept of SoE began to reshape his thinking. 

He implemented what he learned for the next 5 or 6 years. “I’ve kept those lessons that Val had shared, and implemented them in the classroom… I feel like my students have a really good grasp on thinking through the problems,” he explains. This switch in focus allowed his students to visualize relationships between parts and totals, leading to a more meaningful understanding of the situations occurring in the story.

Then, his entire school decided to go all in and, along with Valerie, I provided training for the K-5 teachers. With this newfound support and the available, free resources, Matt has been able to take his work with SoE to the next level.

Q: What were the biggest changes you made in your teaching when you started using Structures of Equality?

A: Well, I had been teaching kindergarten up to this year. So I think my mindset changed a little bit about how I’m coming at these word problems and using the structures. Last year in kindergarten, we were really looking at the setting and what was happening in the problem. This year, we’re focusing on understanding how we set up our bar, our structures, and how we’re going to come about using it.

This shift wasn’t just about introducing new visuals but also about helping students find  and label the parts of the problem, which becomes essential in solidifying their understanding. It’s one of the components that makes the structures superior to bar models. 

Q: What has been the response from your students?

A: I think it was easy for them to see where the pieces go. After a little bit of practice, I feel like we are able to identify the addends and the total if it’s provided there. The hardest part was getting them to write it. It took some practice to get my 1st-graders writing down the labels and putting into words really what the math main idea was. It is a big change of mindset getting kids to think, alright – I’m not going to worry about the numbers right now. I’m going to really think about what’s being presented in the problem. It’s a mindset change for our staff too.

This is the real challenge of implementing SoE – while students internalize the structures, writing down their thinking requires patience and consistent practice. We’re asking them to slow down and make sense of the math.

The power of visualization in problem solving

Using SoE allows Matt’s students to engage with word problems on a deeper level. Instead of rushing to solve based on numbers, students now start by identifying the context of the problem (math main idea), determining what the parts and totals represent, and labeling them accordingly. “We focus on what’s being asked in the problem before jumping into calculations,” Matt explains. This approach slows down the process and encourages critical thinking, giving students a framework to break down the problem piece by piece.

Matt’s school embraced this shift as well. During Professional Learning Community (PLC) meetings, teachers discuss their experiences using Structures of Equality and share resources like anchor charts to guide their students. “The anchor charts have been great for reinforcing what the structures look like and how to apply them,” says Matt. 

They’ve also found the free resources on my website, YouTube, Facebook, and in my weekly emails helpful. 

Q: What were some initial challenges in implementing SoE, and how did you overcome them?

A: I think the hardest part was getting the kids to write it… the most time-consuming part was those 1st-grade writers writing down the labels and putting into words really what the math main idea was. That was difficult because they hadn’t really been asked that before. It takes some practice, but using some sense-making strategies helps with that.

The challenge isn’t necessarily in the concept of SoE itself but in teaching students how to articulate their thought process. 

Q: How has your school responded to the use of SoE?

A: Teachers from kindergarten up to 5th grade are finding that they’re able to use and apply the structures, and it’s helpful in the classroom. I thought the upper grades, like 4th and 5th, would be resistant, but they love it too. I think it has to do with the common language we’re using K through 5. We’re not going to be learning different styles as the students are moving up, so they’re getting used to this structure early on.

The common language across grade levels makes the approach easier to adopt throughout the school. As students progress from kindergarten to 5th grade, they build upon the same foundational skills, which ultimately makes word problems less daunting in the upper grades.

Advice for teachers new to Structures of Equality

For teachers who are just beginning their journey with Structures of Equality or are struggling to implement it, Matt’s advice is simple: be patient and trust the process. “With anything that’s new, it’s going to take a little bit of time for students to pick up and understand. But I think the students are gaining so much by using the structures and understanding what’s happening in the problems.”

He emphasizes that while the process may feel slow initially, it builds a much stronger foundation for students in the long run. The payoff is not just in solving the problem but in developing a deep understanding of the math and the relationships within the problem.

Key Takeaways

• Move beyond keywords: Structures of Equality shifts the focus from keyword-based problem-solving to understanding the relationships within the problem.
• Bar models offer concrete visualization: Bar models (the foundation built upon by the structures) help students visualize the parts and total of a problem, making abstract math more tangible. 
• Labeling is essential: Although challenging at first, labeling parts helps students break down and fully comprehend the math main idea.
• Patience leads to results: Trusting the process and allowing students time to engage deeply with SoE leads to greater understanding and long-term success.

Conclusion

For Matt, Structures of Equality has changed how his students approach word problems. The method not only transformed his classroom but also gained widespread support across his school, helping students develop a deeper understanding of math through visualization and structured thinking. As Matt puts it, “This is the best professional development I’ve been to in 16 years, and it’s the one that I keep referring back to. I can’t speak highly enough of it.”