How I Learned Maths
If I reflected on how I learned maths when I was in primary school (it’s like many years ago), I felt I did not have the chance to absorb and understand the big idea behind the learning itself. Why do I learn this? What connections should I make? Why do I have to learn this? How can this be useful or help me to understand how things work? I believe I have many more questions which I had not had a chance to get clarifications. I am not saying the old practices had ruined my understanding of maths or my perspectives of learning maths, it’s just I have always had this thought, ‘I wish I……’ in my head. Textbooks, exams, pages of exercise, memorizing the facts and rules, homework …. It felt like a never-ending ‘drilling’ practices and I survived.
It’s Not a Prescribed Learning
And now, I am playing the role as a teacher and I always tell myself that the learners should understand whatever they are learning.
Many parents are always surprised when they find out that we do not use any textbooks for maths. We do have a curriculum which shows the expectations but not text/workbooks.
How children learn is not based on a particular prescription. Children enter the learning stage with their previous knowledge and experience. They will continue constructing their knowledge in a different way and in a different stage. Child A knows to count up to 50. Whilst child B is still developing the understanding of number sense. In such a situation, the teacher can’t just tell them to open the book and do page X, regardless of what they understand or not. Some children may be ready to transfer and apply their understanding into their lives, whilst some are still struggling with understanding the notations. When following a textbook, children seem to be forced to move forward. Once you complete chapter 1 and have done chapter 1 review, you will be guaranteed that you understand concept A. Unfortunately, that’s not how learning works. Therefore, learning is not a prescribed journey. It’s a journey which allows learners to create their own prescriptions, what works and doesn’t work.
Let Them Talk
It is important to encourage learners to share their understanding. ‘I understand but I don’t know how to explain it.‘ The children may say this but that means they do not 100% understand yet. What’s still confusing? Which part can’t you explain? What can help you explain your thinking – manipulatives, blocks, pictures, counters, etc.?
At the beginning of this academic year, a fresh and young teacher told me about the math talk. She mentioned that she would like to do a maths talk in her class. At that time, I was not sure what she meant by maths talk. After a while, I realized it’s just a different term I use. Yes, of course ‘maths talk’.
The idea behind the maths talk is to encourage students to articulate their mathematical reasoning which relates closely to their critical thinking skills. For me as a teacher, this allows me to listen and assess their understanding of concepts. I always tell them that if you understand something, you should be able to explain your thinking. If not, then you may have something that is still confusing you.
I have always enjoyed listening to their conversations. This also provides them with an opportunity to develop the sense of being knowledgeable and being open-minded at the same time. #WODB and ‘Two Truths and One Lie’ are the two activities which can develop their mathematical reasoning.
‘Which one does not belong?‘ is one activity that I have used since the beginning of the year. I used it to assess their prior knowledge and to see who can articulate their thinking.
What do you see? Do you see the pattern? What makes it different from the other three? Do you see what others see?
As the learners shared their thinking, I could see their understanding of numbers sense, operations, patterns, etc. They also understood that others may have seen a different pattern from what they saw.
2 Truths and 1 Lie
When I told them that we are going to play two truths and one lie, they were wondering what it is. Is it like ‘truth or dare?’ Not exactly the same. 🙂
I have been following John Orr’s blog. I have been inspired by some of the maths activities and strategies that can be adapted to plan concept-based inquiry maths lessons. I joined John Orr’s online training at the annual virtual math summit during my summer break (organized by Build Math Minds).
Two truths and one lie is one of the activities that can be used to start a might fight.
A rich discussion and arguments would be evident throughout the activity. I just started introducing this to the fourth graders. Since we have been learning about factors and multiples, I created a few prompts to get them to think about factors and multiples.
Many of them were able to share their reasons behind the lie. ‘I agree/disagree with …because…..’ ‘I notice that…….’ When they’re asked to create their own 2 truths and one lie statements, many of them were still confused on how to phrase the statement which can be understood by others. More practice is required. However, listening to their arguments about the truths and lie has shown how their thinking and understanding of the topic/concept.
What other strategies am I going to you to get the learners to develop their critical thinking skills and articulate their mathematical reasoning? How effectively do these strategies help learners to develop their maths and thinking skills? What do other educators do to engage the learners and develop a growth mindset when learning maths?
Look forward to hearing more ideas and thoughts on teaching and learning maths.