Schema-based instruction, which teaches students to focus on the underlying structure of math word problems, improves learning for students of all levels.
I became interested in looking for better ways to teach math problems because of my daughter, who suffered brain damage in early childhood which inhibited her development of language skills. Despite this delay in developing language, she showed great understanding of mathematical concepts at an early age. I remember being amazed when she showed us how the calendar repeats itself every 28 years and quickly mastered her multiplication tables. However, she continued to have a difficult time solving math word problems.
The Problem with Math Word Problems
She’s not alone. Many students – both in mainstream and special education – struggle with math word problems. It’s easy to get lost in the problem’s surface details, rather than understanding the mathematical language and concepts and applying the relevant operation to solve the problem. For the past six years, I’ve been studying the effectiveness of “schema-based instruction,” a teaching method that helps students categorize and organize problems into different types and identify strategies based on the underlying mathematical similarity. I believe that schema-based instruction can be a powerful tool for math teachers and parents to empower student success.
Math word problems have traditionally been problematic for many students. A student may read two problems and believe them to be different because of the language and situation presented. For example, a problem about how far a bicycle can travel at a certain speed and another problem with a scenario involving a spaceship might appear to be very different – but at their core are similar rate problems. Through schema-based instruction, we help the student focus on the underlying problem structure and represent the problem text using visual schematic diagrams that show how quantities in a word problem are related.
Schema-Based Instruction in Math
I’ve been studying the promise that schema-based instruction has for elementary and middle school students. It is well documented that many students, especially those struggling in math, jump immediately into calculating the answers when solving math word problems without understanding the premise and reasoning whether the answer is meaningful. With schema-based instruction, we get to the essence of a math word problem by having the student identify what type of problem it is (ratio, proportion, percent of change, etc.) and the relevant information needed to solve the problem. Then we teach them to use schematic diagrams that help them visualize how quantities in a word problem are related. Because comprehension is particularly difficult for many students struggling in math, we provide schematic diagrams as they translate and integrate information in the problem into the representation before they are taught to construct their own diagrams.
We also teach problem solving procedures grounded in reasoning and focus on building “metacognition” skills. This means guiding students to think about what they are doing and why they are doing it by asking, “What type of a problem is it? Is it similar to or different from others that I have solved before? What solution strategy is most appropriate? Is the answer reasonable?” By framing their thought process in this manner, students can identify what they need to solve for, which of the multiple ways to solve the problem is best and – most importantly – how to differentiate between the relevant information and the irrelevant information in a word problem.
Schema-Based Math Skills Spur Success
For the past five years, we’ve been testing the effectiveness of schema-based instruction with more than 7,250 students and teachers. In Minnesota alone, we’ve worked with teachers in 50 different school districts around the state. After promising results here, we added districts in Florida and Utah to add demographic and geographic diversity to our sample.
No matter the state, city or demographics of a district, we’re finding that schema-based instruction works. Students who participate in schema-based instruction classrooms outperform students in the control classrooms that continue to follow their district’s mandated textbook approach. Interestingly, we found that this improved performance compared to peers was consistent whether the student was in special education or conventional classroom settings.
This is true for teachers as well. We studied teachers that were experienced in schema-based instruction and teachers who were novices, and found that the outcomes for students were the same no matter the teacher’s level of experience. The improvement in student outcomes is maintained over time, even if the teachers do not participate in additional professional development training related to schema-based instruction. In general, the teachers that participated in our study love the schema-based instruction techniques they’ve learned and plan to continue to use them in their classrooms.
Tips for Encouraging Success in Math Word Problem Solving
Schema-based instruction is a powerful tool for teaching math word problem solving. Below are some principles for improving all students’ math word problem solving skills.
- Ensure that classroom math instruction not only includes sufficient problem solving activities but also focuses on foundational mathematics content (e.g., number sense, place value) to support and accelerate the learning of students at risk for math difficulties.
- Make word problems and situations mirror real life experiences that kids will encounter. My work with middle school students shows that the more relevant and pertinent to real life we can make math, the more students will buy into learning and doing math.
- It is important that all students who have persistent math difficulties, even those in middle school, receive word problem solving interventions of sufficient quality and intensity (more focused time, small group instruction) to accelerate their progress.
- Explicitly teach and review the language used in mathematics so that students understand what is being asked in a problem and how the problem should be solved.
- Students at risk for math difficulties need instructional support (e.g., explicit, systematic instruction, opportunities for corrective feedback) to make sense of word problems.
- Develop students’ ability to monitor and reflect as they solve word problems. Use prompts (e.g., What is this problem about and what do I need to solve? What are the steps to solve this problem? Does the answer make sense?) that require students to think through the problem-solving process. This practice is important, because it enhances mathematical metacognition by requiring students to both express their own thinking and listen to the ideas of their peers.
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