Whilst visiting Australia, Bruno Reddy, CEO of Maths Circle, linked up with Brendan Lee. Brendan is the host of the Knowledge for Teachers Podcast, and is currently a Senior Teacher at Comleroy Road Public School. In Brendan’s own words ‘Bruno is one of the pioneers in maths mastery’, and with Bruno’s background in psychology, this episode is jampacked with teaching theory, educational strategies, and digging into the science of learning so we can understand how children learn.
You can listen to the podcast on Spotify here:
1. QUESTIONING AND UNDERSTANDING
How we pose a question is instrumental in cementing understanding. As Bruno says, teaching is more than just training children to pass exams, or to regurgitate information; the aim is to provide children with a comprehensive and full understanding of the information they are acquiring.
Bruno expounded on Variation Theory. Variation Theory explains how a learner might come to see, understand, or experience a given phenomenon in a certain way and the importance of presenting the same concept in different forms. Implementing measures to ensure variation in teaching methods goes beyond rote memorisation and encourages a more profound comprehension of the underlying principles, preparing students for real-world problem-solving.
So, considering the link between effective questioning techniques and instilling deeper conceptual understanding, here are some of the strategies Bruno and Brendan discussed:
Chunking and Repetition:
Cognitive Load Theory emphasises the limited capacity of our working memory. Presenting information in multiple ways helps to avoid cognitive overload, improving students’ retention. Chunking and repetition of questions allows complex problems to be broken into smaller, more manageable parts. Isolating and repeating each step enhances students’ decision-making skills and reduces the mental strain on students, facilitating better understanding and retention.
The Concrete, Pictorial, Abstract (CPA) approach involves teaching with a sequence of concrete manipulatives, visual aids, and ultimately, abstract symbols. Using tangible objects, children build a foundation to familiarise themselves with the abstract concepts in maths.
Central to CPA, is the value of ‘multiple representations – representing the same concept or construct in different ways to aid understanding. For example, using Cuisenaire rods, arrays and bar models to represent a multiplication fact. On TT Rock Stars head to ‘Interactive Tools’ for a host of multiple representations.
Questioning with minimal difference is, well, posing questions slightly differently each time. The key word here is minimal. Each question that is introduced should be slightly different from the one before, providing children with a familiarity in their learning process, whilst also allowing them to develop their knowledge. For instance, in maths, 5 x 6, as well as 6 x 5, then moving onto 5 x 7.
Examples and Non-Examples:
Often, teaching is demonstrating to children what a concept IS; what it means, encompasses and answers. To do this, you may show working examples. On the flip side, showing learners what it is NOT, will provide them with an enhanced, well-rounded understanding.
2. RECALL
High Frequency of Thought
Spaced Learning and Little and Often
Low Stakes Quizzing
3. MATHS ANXIETY
Encouraging children to see themselves as capable mathematicians is crucial for alleviating anxiety, and this is achieved by creating feelings of success. Here Bruno reiterated the importance of evidence based teaching strategies such as minimal different questions, examples and non-examples, and low stakes quizzing. Generating a calm yet fun atmosphere in the classroom can work wonders for minimising feelings of stress; tune into the TTRS playlist or run rock days!
As well as creating a joyful and engaging space, children should feel like they are in a safe space to make mistakes. To achieve this, we as adults should be acknowledging and celebrating our own mistakes! This normalises errors and contributes to creating a culture where everyone feels empowered to contribute without fear of shame. Additionally, acknowledging mistakes as a fundamental part of learning sets the foundation for happy and successful lives as adults, emphasising the importance of embracing challenges and learning from them.
Instilling children with confidence is paramount to us at Maths Circle. We have introduced as many anxiety mitigating strategies as possible to help cultivate feelings of success: low-stakes quizzing, timer-free practice and additional accessibility settings. You can read more on how we enhance the playing experience HERE.
Check out Brendan and Bruno on social media:
Bruno:
Twitter: @BrunoReddyMaths
LinkedIn: Bruno Reddy
Brendan:
Twitter: @learnwithmrlee
Facebook: @learningwithmrlee
Website: learnwithlee.net
You can catch the podcast here:
