Literacy and Numeracy Corner

If you attended our maths afternoon last Thursday, you likely noticed that maths lessons have evolved somewhat since you were at school. Education is an area that we all have our own personal experiences of, yet it is constantly changing in light of new information on best practices. During these articles each fortnight, we will unpack some of the concepts and terms that underpin our maths instructional model here at Brunswick North West Primary; some of these might be new ideas, some might feel much more familiar.

Within the Victorian and Australian Curriculum, it is recognised that it is not only important for young people to learn mathematical concepts, but to also develop four strong proficiencies that support their learning across all areas of maths. These proficiencies are Understanding, Fluency, Problem-Solving and Justification.

Understanding involves students making connections between related concepts and progressively applying what they already know to develop new ideas. It requires students to understand the ‘why’ and ‘how’ behind concepts, rather than rote memorisation, which allows them to apply their existing knowledge to new situations and problems. I encountered a wonderful example of a student who did not have a good sense of understanding when I was a maths coach overseas. A young student proudly recited their seven-times-tables to me (quite a feat!) all the way to 12 x 7. When I asked them what 13 x 7 was, the child responded with “There is no such thing as 13 x 7, silly!”. By contrast, in the maths afternoon I saw a student who was adding four 3-digit numbers together. The student started solving their algorithm with the hundreds column (not a preferred strategy), but was able to solve the answer correctly because they had a deep understanding of the place value system and made the necessary adjustments along the way. When the student then chose to add two larger 3-digit numbers together in their head, they came up with the correct answer quite quickly - likely because they started with the hundreds!

Fluency involves students being able to recall factual knowledge and concepts readily. Many people consider fluency as the automatic recall of number facts (most often multiplication) and while this is accurate it also includes concepts such as understanding that numbers are made up of smaller numbers (eg. I know that 8 is made up of 5 and 3, or 2 fours, it is 2 less than 10, etc). Fluency is also understanding the commutative property of addition and multiplication (we get the same solution no matter which number we start with) and the inverse relationship between addition and subtraction or multiplication and division. There’s lots of fluency involved in counting, but there is so much involved in counting I am going to save that for another article! The importance of fluency is to free up the working memory of individuals, so they are able to spend time and energy on the more challenging part of a mathematical problem or investigation. When we don’t have fluency, it is easy to lose our place, make a mistake or just find everything too hard!

Problem Solving involves students interpreting information, making choices, modeling the problem, formulating ways to solve problems and reflecting on the reasonableness of their answer. Put simply, problem solving is the application of all the mathematical knowledge, behaviours and skills that students have in their toolbox. Without opportunities to problem solve, students can be highly capable at completing algorithms, but have no idea how these algorithms relate to our world.

The problem with problem solving is that it can feel uncomfortable. Many people like the ‘clarity’ they feel maths holds: 1 + 1 always makes 2; we know there is an answer and we can solve it. In reality, mathematics does not always have an answer and if it does, the answer is not always found easily. Problem solving asks students to think creatively, persist and reflect on what they know so far - skills our students need for all subjects!

Reasoning involves students thinking about the maths they are learning or investigating. It asks them to make conjectures, analysing and evaluating data, proving or refuting algorithms, explaining and justifying their thinking to others and making generalisations. 

If you are interested in these ideas and enjoy the occasional TEDTalk, you might want to watch this video. Although the video is over ten years old and focuses on high school maths classes in the USA, Dan Meyer does talk about many of the proficiencies I’ve discussed here today.