In the United States, students are typically taught a variety of ways to solve word problems. These strategies often include drawing a picture of an object or animal, for example. In early grades, that may work. But as students move on to larger numbers, word problems become more complex as do the skills required to solve them.
Studies have shown that students who can visualize a word problem through modeling are more successful at problem solving and accuracy. This has been documented in Singapore—one of the top performing nations on the Trends in International Math and Sciences (TIMSS) report—where model drawing is used extensively across grades. Using models helps students transition from concrete manipulative work with word problems to the abstract step of generating an equation to solve contextual problems. By using models, students can successfully tackle more and more complicated word problems as they move through the grade levels. This puts them firmly on the path to algebra and future success in all their mathematics endeavors.
What Is Visual Modeling?
Basically, visual modeling (also known as Model Drawing or Problem Solving) is a systematic method of representing word problems and number relationships. Using a concrete-pictorial-abstract approach, teachers build deep understanding of math concepts. Students learn how to use rectangular bars to visualize the problem and decide what operations to perform. Rectangles are easy to draw, and make it easy for students to recognize larger numbers and proportional relationships. Word problems require students to have many skills—the ability to read, understand, strategize, compute, and check their work. Even the most capable students can find these demands overwhelming. With visual modeling, students have a step-by-step approach to help them organize their thinking and turn problem-solving into a doable activity.
When Can Visual Modeling Be Introduced?
Early learners can use visual modeling to solve basic addition, subtraction, multiplication, and division problems. Most children at this age enjoy seeing abstract relationships represented by concrete images. They may model them with the real objects of the problem, such as a toy car or stuffed animal. They learn, at a very early age, about patterns, generalizations, and number relationships—important lessons to be drawn on in later work. In addition, their confidence in dealing with math problems grows.
In more advanced grades, visual model can be used to teach ratio, rate, percent, multi-step, and other more complex problems. Over time, they may progress from realistic portrayals of the items in the problem to multi-purpose representations such as circles.
The Benefits of Visual Modeling
Singapore transformed math education and student performance in less than a decade. By integrating the model drawing approach into your classroom, you can build good number sense and the ability to solve complex problems, plus you can:
- Bring problem solving to life. Model drawing is an extremely powerful visual method that enables students to see, manipulate, and understand how problem solving works.
- Develop your students’ confidence. This is a prerequisite to higher achievement.
- Challenge your gifted students with proven techniques to extend word problems.
- Improve higher-level thinking and raise test scores.
- Eliminate the mystery from problem solving. Visual modeling is simple, clear, and manageable.
- Save teaching time. You won’t need to re-teach problem-solving skills. Students will catch on quickly.
- Get students excited about math and problem solving. Math will be more engaging, meaningful, and fun.
Introduce a visual approach to word problems in your classroom. SDE offers a webinar that shows you how to bring math understanding to a whole new level. Check out Model Drawing: Next Steps by award-winning educator and math coach Ricky Mikelman.