Direct Instruction: Problem-solving Strategies
Overview
Discussing strategies for solving mathematics problems after initially letting students attempt to problem solve on their own helps them understand how to organize their mathematical thinking and intentionally tackle problems. For students to solve math problems accurately and efficiently, they must learn and compare multiple strategies, articulate why they chose one strategy over another, and flexibly apply them. However, research shows that students develop deeper conceptual understanding and Mathematical Flexibility when they engage in problem-solving and productive failure before this direct instruction.
Example: Use This Strategy in the Classroom
Watch how this sixth grade teacher models and reviews the process of dividing fractions to build Proportional Reasoning. By integrating movement with each key term, students are able to remember and apply the strategy in their problem-solving process.
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 DreamBox Learning allows students to solve problems in multiple ways. By explicitly promoting problem solving with different strategies, this product builds Mathematical Flexibility, while also developing conceptual math understanding.
Additional Resources
Additional examples, research, and professional development. These resources are possible representations of this strategy, not endorsements.
Factors Supported by this Strategy
More Instructional Approaches Strategies
Providing math tasks with high cognitive demand conveys high expectations for all students by challenging them to engage in higher-order thinking.
CRA is a sequential instructional approach during which students move from working with concrete materials to creating representational drawings to using abstract symbols.
Knowing the language of math is critical because students must use this language to understand math concepts and determine calculations needed.
Thinking of and about patterns encourages learners to look for and understand the rules and relationships that are critical components of mathematical reasoning.
Teaching students to recognize common problem structures helps them transfer solution methods from familiar to unfamiliar problems.
In guided inquiry, teachers help students use their own language for constructing knowledge by active listening and questioning.
Math centers support learner interests and promote the development of more complex math skills and social interactions.
Through short but regular mindfulness activities, students develop their awareness and ability to focus.
Instruction in multiple formats allows students to activate different cognitive skills to understand and remember the steps they are to take in their math work.
Using multiple methods of assessment can help educators gain a comprehensive understanding of learner progress across a wide range of skills and content.
When teachers connect math to the students' world, students see how math is relevant and applicable to their daily lives.
A strengths-based approach is one where educators intentionally identify, communicate, and harness students' assets, across many aspects of the whole child, in order to empower them to flourish.
Untimed tests provide students the opportunity to flexibly and productively work with numbers, further developing their problem-solving abilities.
Writing that encourages students to articulate their understanding of math concepts or explain math ideas helps deepen students' mathematical understanding.
