There are many different word problem approaches used in mathematics classrooms. But one common struggle is prevalent through all of them. Teachers and students alike grow increasingly frustrated when approaching story problems.

Common concerns from teachers include:

• My students don’t understand what the problem is asking.
• They don’t know which operation to use.
• My kids get frustrated and give up easily.

If you’ve ever worked with students on word problems, you’ve likely come across these scenarios. With so many strategies out there, what actually works?

Structures of Equality (SoE): A Reading Comprehension Tool

I developed SoEs after facing the same frustrations as many of you. I was tired of seeing my students get discouraged when facing story problems. I tried every strategy I could think of and experienced the most success with Singapore Bar Models.

Here’s what works with bar models:

• Use a mathematical model to represent a story
• Help students visualize word problems
• Help develop problem solving skills

Here’s what doesn’t. I found I still had students that could draw a bar model and not completely understand what was happening in the story, or what the model represented.

I decided to take what worked and build upon it.

Foundations of Structures of Equality

As much of the work I have done is derived from the Singapore Bar Modeling concept, it’s important to understand why they work.

“Singapore Math is able to teach at a slower pace and in more depth because it focuses instruction on essential math skills recommended by the Curriculum Focal Points (National Council of Teachers of Mathematics)…That surprising results, slower pace resulting in more rapid progress works for students who perform on, above or below grade level.” “Singapore Math: Simple or Complex?” Education Leadership 65 No 3 N 2007

This style of teaching, along with the use of bar modeling has proven to be a successful combination for the country of Singapore. They have repeatedly been leaders when it comes to TIMMS (Trends in International Mathematics and Science Study) testing. While I recognize there are many different variables involved, we can’t look past the use of modeling as a key contributor to their successes.

SoEs and bar models: a comparison

Bar model representation:                               Compare SoE representation:

How SoEs enhance bar models

These are the only models you need to diagram any problem type in the elementary Common Core standards. After explicit instruction and repeated exposure, students begin to understand which types of stories lend themselves to which structures. Instead of endless possibilities, they can organize their thinking easily.

Structures of Equality (SoE) are graphic organizers that help students map out a math story. The 3 different SoEs are:

• Parts Equal Total
• Compare
• Repeated Equal Groups

A SoE is made of three crucial elements. When a student includes all three, it indicates comprehension. They MUST:

• Contain values (numbers)
• Have labels (units of measure, the things you are counting…)
• Represent equality

Students must understand what is happening in order to utilize SoEs. They know which parts of the story are represented in each part of the model, the relationship between those parts, and where the equality within the relationships exist.

This solves the issue of students not knowing which operation to use.

Do SoEs work for all students?

In last week’s blog, we looked at data from a classroom with full implementation of SoEs. Proficiency scores exceeded expectations, and there was growth for ALL students, regardless of their starting point.

SoEs provide an equitable approach to classroom practices. They increase active engagement which increases learning outcomes for all students.

You’ll still have students who struggle with decoding the words in a story problem. You will need to provide additional scaffolds and supports for this part of the process. Once they can decode the story, SoEs support the reading comprehension process.

Conclusion

SoEs provide a comprehensive tool to tackle the challenges that come with solving word problems in math classrooms. Inspired by the approach of bar modeling, they help students visualize word problems and promote problem-solving skills by offering a clear framework to understand story problems.

What’s Next?

Each of the next 3 weeks will be dedicated to an in-depth exploration of the structures, one each week. If you’re on my email list, you got a few quick tips around the Parts Equal Total Structures, and a sneak peek into a classroom conversation. If you haven’t joined my email list yet, subscribe for exclusive access to resources before they’re made available to the public.

References:

• http://nces.ed.gov/timss/table11_2.asp, http://nces.ed.gov/timss/tables11.asp (International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2011)
• “Singapore Math: Simple or Complex?” Education Leadership 65 No 3 N 2007
• https://www.dpi.nc.gov/nc-2nd-grade-math-unpacking-rev-june-2022/open