WHY IS MATHS TAUGHT DIFFERENTLY NOW?
Telling or asking?
Many of us were taught Maths through telling. Our teachers told us how to ‘do’ maths and then we ‘practised’ until we could ’do’ it independently. The learning theory was that if we were ‘told’ how to ‘do’ it and ‘did’ it enough, understanding would follow…
The problem was that in many cases, understanding never followed, whether or not we could ‘do’ the maths. However, it was thought we ‘understood’ if we arrived at the correct answer. If we didn’t arrive at the correct answer, we were simply ‘told’ how to ‘do’ it again!
We now know that this is not an effective way to develop deep understanding of Maths
Maths is conceptually based, not skills based. Understanding of one concept is needed to understand another concept, and another concept, and another concept….
Children need to develop understanding of concepts, and the relationships between concepts, and not merely ‘do’ maths.
When we ‘tell’ children about Maths, we find out what we understand!
When we ‘ask’ children about Maths, we find out what they understand!
Questioning allows us to identify misconceptions, build on incomplete understanding and ensure children are learning from their leading edge. It also lets us know whether children did learn what we intended them to!
More importantly, questioning allows children to identify what they currently understand – and don’t understand! Questioning allows children to work out how they fit in with current understandings, and grapple with new understandings that doesn’t fit with their current understandings.
Questioning allows children to grapple with problematic knowledge – otherwise known as confusion! Confusion is great because it means that we are learning! It means we are addressing new knowledge that isn’t fitting in with prior knowledge. It means we are addressing knowledge that is beyond our current level of understanding – thus expanding our understanding! Neurologically, we are searching for a connection to prior understanding. If we find a connection, we get that ‘aha’ moment! If we don’t find a connection, our brain settles down to learn. Giving up when we are confused is the worst thing we can do!
Questioning allows children to understand the way they are thinking. If children understand the way they think, they can understand successful and unsuccessful thinking and think in successful ways intentionally.
Questioning allows us to identify how children are thinking. Children need to think additively, multiplicatively and algebraically:
Additive: Thinking in terms of Addition and Subtraction. Children think additively until the end of Year 2 when they add, subtract, multiply or divide. Multiplying and dividing is additive in Year 1 and 2 because children are skip counting. Children continue to think additively when adding and subtracting from Year 3 onwards – because addition and subtraction are additive concepts! Children will also continue to think additively about place value.
Multiplicative: Thinking in terms of Multiplication and Division. From Year 3, children need to think multiplicatively when they multiply, divide or find fractions. Thinking multiplicatively begins with children see multiplying by 2 as making a number 2 TIMES larger, rather than having 2 of the number. Children will begin to think about Place Value both additively and multiplicatively. Unless teachers consciously help children develop multiplicative thinking, which goes well beyond repeated addition, it may not happen for many children (Jacob and Willis, MERGA Conference 2001)
Algebraic: Finding patterns and relationships. Our brain is hard wired from birth to find patterns (things that happen over and over again) and relationships (when I do this, that happens).! Children need to be looking for patterns and relationships in everything they learn – maths included! As soon as kids start learning how to count, and then add, subtract, multiply, and divide, they are encountering algebraic thinking. (Leslie Blair: It’s Elementary: Introducing Algebraic Thinking Before High School)
Questioning allows children to explain what they currently understand. Learning research tells us that to learn we need to think, then speak, then write. Speaking – putting thoughts into words – is essential to learning. Thought is not merely expressed in words, it comes into existence through them. (Lev Vygotsky: Thought and Language).
Questioning allows children to develop the mathematical language. Maths is full of precise language – almost like a foreign language! Once we can speak ‘maths’ we can understand and explain. Learning the language of maths is exactly the same as learning any language – you need lots of opportunity to speak it! Asking and answeringquestions provides children with the opportunity to develop their mathematical ‘meta-language’ (understanding the language as well as using it as vocabulary).
Primary Maths Videos use questioning for all of the reasons listed above! Children pause the video to respond to questions. If you are sitting with your child, you pause the video to engage in discussion with your child – you may find your
understanding and maths language deepens too!
Primary Maths Investigations and Reflections use questions for all of the reasons listed above! Children explain their thinking and strategies, and reflect on their understanding. If you are sitting with your child, ask them the reflection question – you may find your understanding and maths language deepens too!
While the end goal is the ‘correct’ answer, we are looking for deepening understanding and increasing capacity to explain!