Why Maths Mastery is Not an Abstract Idea (and 3 Ways to Make Sure It’s Concrete)

By Jasmine

CRA Method, Maths Mastery, Spiral Approach to Teaching Maths, Teach Maths

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Learn how educators can help students excel in the classroom and boost their confidence using the Concrete-Representational-Abstract (CRA) Method.

Every educator has seen students struggling in maths. Whether they are struggling to retain maths facts; failing to apply what we may see as simple; or simply deciding they are “dumb”. As educators, we feel the heartache of a struggling student and search endlessly for what will “work”; for what will make a difference in their learning journey.

When this struggle begins in the early years, students often fail to catch up. Unable to grasp simple concepts and to truly understand maths, the gap widens as new teachers/ new curriculae/ new and “better” methods are presented to try to fix the underlying problem.

In desperation to progress and to keep up with curriculum and year-specific requirements, schools and home educators most often then revert to teaching the “how” of merely getting an answer to pass a test. A formula is learnt, devoid of understanding, and the student is left dependant on the question being asked the same way for the next test.

As educators, we feel the heartache of a struggling student and search endlessly for what will “work”; for what will make a difference in their learning journey.

Often students are presented with traditional methodologies typically, books or websites with sums worked out on a whiteboard. This may be followed by maths fact recall, and completing sums in a student workbook. All of these methods are abstract and confusing to a student who learns in a multi sensory way; or who may not yet – even according to their age – have the ability to think abstractly.

According to extensive research and evidence-based findings, maths must be taught using a progression from concrete, to graphic representation, to abstract (referred to as the CRA method).

In other words, the student must touch, feel and see maths; then be able to draw it, before being able to apply it in abstract and real life situations.

When a student is taught using a CRA methodology, with the inclusion of multisensory manipulatives, they rapidly improve in their understanding, application and confidence in their own ability.

So, since you want your student to succeed in maths; since you want your student to be confident and to take maths mastery into their workplace and community, do the following:

  1. Ensure that you, as the teacher, truly understand what you are teaching, and can show this to your student using hands-on, concrete manipulatives
  2. Use hands-on, concrete manipulatives as the basis for explaining every maths concept (not just as an optional add-on)
  3. Follow the “Concrete-Representational-Abstract” methodology and check mastery of each lesson before progressing to the next.

If you are looking for a program built on this research-based approach to maths mastery; one that is based on these recommendations, and that makes maths easy to teach, email, call or visit us at www.mathsaustralia.com.au

When a student is taught using a CRA methodology, with the inclusion of multisensory manipulatives, they rapidly improve in their understanding, application and confidence in their own ability.

A strong foundation in maths mastery for Australian students will not only enhance the individual’s life skills for workplace opportunities, it will enhance families and communities, our Australian economy, and quality of life.

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