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Strategies for Developing Mathematical Understanding


Making Math Accessible for All Students was a topic discussed in a webinar that fits our thinking about mathematics.  One strategy used to make mathematics accessible to students with learning difficulties is the Concrete-Representational-Abstract instructional sequence, also referenced as CRA. This is a research-based strategy with the purpose of ensuring that students truly have a thorough understanding of the math concepts/skills they are learning.

When students who have math learning problems are allowed to first develop a concrete understanding of the math concept/skill, then they are much more likely to perform that math skill and truly understand math concepts at the abstract level. This sequence helps to make the invisible visible through models, drawing, manipulatives, etc.

Below you will find some additional strategies to use in the classroom:

1. Allow mathematics to be problematic for students.

• All students need to struggle with challenging problems

• Teacher must refrain from doing too much of the mathematics

• Problem solving leads to understanding!

2. Focus classroom activity on the methods used to solve problems.

• Opportunity for students to share one’s own method

• Hear alternative methods of solving a problem

• Examine the advantages and disadvantages of these different methods (efficiency)

Class discussions should revolve around sharing, analyzing, and improving methods. Mistakes become opportunities for learning.

3. Determine what mathematical information should be presented and when this information should be presented.

• Presenting too much information too soon removed the problematic nature of problem

• Presenting too little information can leave the students floundering

Implementing these strategies and developing student behaviors such as; discussing, explaining, writing, representing, and presenting are necessary for ALL students to experience success. Research indicates that active and regular participation in the classroom- not only reading and listening but also discussing, explaining, writing, representing, and presenting- is
critical for success in mathematics.

Students understand best when they explore concepts through purposeful activities and investigations. Through organizing
key concepts and big ideas into rich tasks, teachers create learning experiences that give more time for students to become proficient and explore deeper mathematical concepts.

Additional information can be found at:




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