When it comes to deciding upon an approach to teaching maths, thoughtful homeschooling parents and educators take the time to research all of the options, consider their individual children and students, and make the decision that is best for their own classroom.
If you’ve done the research, then you understand how lively those discussions about mastery vs. spiral can be! In case you haven’t had the opportunity to weigh-in on the debate, here are a few important things to consider:
What is the difference between both styles of teaching?
"Mastery based approach" and "spiral methodology" are terms used to describe the typical methods for teaching maths.
More specifically, students in a mastery maths program learn maths concepts in increments; the learning of each new concept builds on previously mastered skills. As a great example of this point, the Brighter Maths Pink Level teaches students to master multiplication, including memorising the facts and learning how to regroup multiple digits, which therefore prepares them to move to the Yellow Level where they master division.
Alternatively, the spiral approach to teaching maths offers numerous topics at once, offered one after the other, yet not necessarily related. These topics repeat for each progressive level so that the material becomes more complex as new concepts are added. But each topic may be revisited only once every six to twelve months. An example of a spiral approach program may be designed with year three content covering simple multiplication facts; the following year they would begin multiplying two-digit numbers; in the next subsequent year the student might revisit multiplication with three-digit numbers. There has just been a large time gap between the initial instruction given to the student.
In both approaches, the student learns identical maths concepts just in different orders.
At Maths Australia, our Brighter Maths program aligns with the science of learning and research-based recommendations whereby mastery is ensured before the student progresses. And whilst both approaches to maths mastery strive for similar outcomes, the results seen in most Western education systems can attest to the inherent shortcomings in the spiral approach.
In the 1990s, when the U.S. began participating in international testing for maths, they discovered that U.S. students performed significantly lower than other students. Much of this has been attributed to the spiral approach to teaching. Countries that preferred a mastery approach such as Japan and Finland produced top-performing students! Subsequently, Western educational programs, educators, and textbook publishers began to research and analyse the mastery approach to teaching maths.
Why choose a mastery-based approach?
Although the educational community agrees that mastery learning is the best practice, some educators still critique this model of teaching. Their main concern is that the mastery approach does not provide students the time or opportunity to review material that was already learned. Maths Australia's Brighter Maths program addresses this by including Cumulative Review of previous lesson content at each and every new lesson.
Another concern of the mastery approach is that students are forced along the same path and have little to no opportunity to delve into extended levels of application. To address this, Brighter Maths progresses the student through a concrete - representational - abstract methodology that is integrated within the student workbooks. This approach supports confidence and engagement through ensuring the student can relate what they have learnt to their everday life. The lesson plans suggest additional games and fun extension activities to enhance the learning experience, ensuring that the student does not experience cognitive overload through too much information or too many representations.
The final criticism of the mastery approach is its focus on individual concepts, one at a time. In the Brighter Maths program, as the student progresses, each new concept mastered is connected to the same manipulatives; this provides students with a cohesive foundation upon which to build their success in maths. We believe that student need accurate, clear and explicit instruction, as well as time to embed this in their knowledge base before progressing too swiftly to yet another maths concept.
With my thorough review of the entire Brighter Maths Curriculum in relation to ACARA, I can confirm that Brighter Maths indeed meets the requirements of the Australian Curriculum…If there is no explicit lesson as yet to teach a certain concept, teachers can teach this concept through another strand. For example, halves and quarters can be taught with time and related to 'past' and 'to' on the clock. Additional lessons are being added, alongside Maths Australia's recent program upgrades and Australian content being more fully integrated."
Enter your text here...
Jan McArthy
Jan McArthy, Senior Numeracy Consultant for NT Department of Education
As research advances what we know about effective maths instruction and the Brighter Maths program with its interconnected manipulatives, students will come to understand and enjoy maths even more fully.
To review more research and evidence-based recommendations that are integrated within Brighter Maths, visit our Research page.
If you'd like further information, you can contact us directly
Because every student deserves a brighter future!
The Team at Maths Australia