Numeracy 

It’s Not Just About the Answer: It’s About How You Got There

Over many years of teaching mathematics, observing classroom teachers and speaking with leaders from other schools, I always find myself coming back to the same question and challenge: How do we get students to move beyond simply asking, “Did I get it right? Did I pass?” and start thinking, “Why is this right or wrong, and how can I improve?”

Many people think of mathematics as a series of steps that need to be followed in order to reach an answer, whereas mathematics is really about developing the ability to think, reason and make decisions based on the knowledge and skills that students have developed. This shift in thinking is something we all need to support, both within the classroom and at home.

It is important that, in mathematics classrooms, teachers not only teach the required content knowledge and skills but also explain the why and how we use those skills. By demonstrating our thinking aloud and questioning how answers have been derived, we encourage students to think more deeply about their own mathematical processes.

When students are faced with a problem, they often think, “Where do I start?”, “What do I do?”, or resort to writing the doomed “IDK” (“I don’t know”). This is because true mathematical understanding is not simply about remembering a process; it is about understanding why a particular strategy works and when it is appropriate to use it. In education, we refer to this as metacognition, which is the ability to think about our own thinking.

In mathematics, this means students should be asking themselves:

• What is this question asking me to find?
• Do I have enough information to directly find the answer, or do I need to solve something else first?
• What information has been provided that might help me?
• Do I need to convert any of the information into a different unit?
• What skills and knowledge can I associate with this question?

Then, give it a go! Start somewhere and work your way through the problem, continually asking questions of how and why.

Some strategies that we explicitly teach students in the mathematics classroom to support their thinking:

• Do not try to hold all the information in your working memory while problem solving. Write information down so that it can be easily viewed, organised and evaluated.
• Use highlighters to identify key words (e.g. predict, find, perimeter, area) or important information (e.g. a weight or length).
  • Avoid highlighting large sections of text, as this makes the strategy less effective.
• Find and write down formulas that may be useful.
• Have a clearly presented and annotated reference book with any required formulas available to refer to.
  • A common mistake with a reference book is relying on it to provide all of the information during an assessment. It should be used as a backup if you forget something or to provide formulas that do not need to be memorised.

These questions and strategies are not only valuable in the mathematics classroom but can also be encouraged at home. As parents and carers, it can be tempting to focus on whether your child has reached the correct answer. Instead of saying, “Yes, that’s right,” try asking, “How did you work that out?” or “Can you explain your thinking to me?”

Similarly, if your child is stuck on a problem or has reached an incorrect answer, rather than saying, “No, that’s wrong, try again,” or “I don’t know either,” consider modelling the process of problem solving: “I’m not sure of the answer yet. Let’s think about what we know and what strategies we could try.”

Sometimes, one of the most powerful questions we can ask when a young person who gets an answer wrong is, “Can you explain to me how you came to that answer?” You may be surprised to find that they identify their own mistake while explaining their thinking. Alternatively, you may notice a misconception in their reasoning that can be explored through further questioning.

In our Term 1B edition of the iNewsletter, we explored how numeracy is embedded into our everyday lives. These real-world opportunities are also excellent moments to develop metacognitive skills.

For example:

• While shopping, ask your child, “How did you estimate the total cost?” or “Which is the best deal for buying a particular item sold in different sizes, and why?”
• When cooking, ask, “How could we adjust this recipe if we needed to make it for more people?”
• When planning a trip, ask, “Can you take me through how you decided what time we need to leave?”
• During a game or sport, ask, “What strategy did you use?” or “Why did you make that decision?”

By encouraging students to explain their thinking, we help them become more independent and adaptable learners. The goal is not for students to memorise a set of rules and repeat them each time they encounter a question. Instead, we want them to develop a deep understanding of concepts so they can transfer their knowledge to unfamiliar problems, problems that require multiple skills, real-world situations and increasingly complex mathematical challenges.

In a world where technology can provide answers instantly, the ability to reason, justify decisions and evaluate whether a solution makes sense has never been more important.