Math 3-6

Direct Instruction: Problem Structures


Teaching students to recognize common problem structures helps them transfer solution methods from familiar to unfamiliar problems. When students learn the structures of problems for different Operations, they develop a deeper understanding of mathematical concepts. However, research shows that students develop deeper conceptual understanding and Mathematical Flexibility when they engage in exploratory problem-solving and productive failure before direct instruction.

Use It in the Classroom

Starting at 0:40, watch how this fourth-grade teacher guides students through a four-step problem solving process. By talking through the process with her whole class, the teacher helps her students understand key problem structure components and strategies for identifying these.

  • Teachers can teach the structures of different problem types, like compare or join, by using a variety of examples. They can then have students practice categorizing problems based on their structure and choosing the appropriate strategies to solve each problem type.
  • Design It into Your Product

    Videos are chosen as examples of strategies in action. These choices are not endorsements of the products or evidence of use of research to develop the feature.

    Learn how Math Shake provides general problem structures to support student problem solving. By having the overall outline of an equation, students can practice and develop their abilities to convert word problems into mathematical equations.

  • Digital products can use visual cues, such as colors, annotations, and images, to identify key words and numbers and to highlight the underlying structures of problems. Learners can then practice coding example problems with the same visual tools and drag similar problems into like groups to practice categorizing.