Two of my questions:
1. How to make Maths meaningful for the average student.
2. See 1.
This question came up on the ctg100 forum and it is my wish that my answer is thought provoking – enjoy!
This is my first post here, I am not a school teacher. I am passionate about maths and my mission in life is to make maths fun! I travel round schools doing just that, with soap bubbles and balloons, so that makes my task easy! You will find that I use the term “learner” instead of student or pupil, since I believe that it keeps us all aware of their role in the group, since you can’t learn for them :0). I am a constant learner of maths and ideas for learning it.
I love your question and I have spent the last five years investigating this very matter. I hope that you find something useful in my answer – I found that once I started writing I couldn’t stop! Please forgive me :0)
The essence of making maths meaningful is to bring the subject matter to life and allowing the learner to think for themselves, giving them the responsibility for their own learning. Facilitate the LEARNING of mathematics, as opposed to “teaching” it and allow each learner to assimilate the concepts in their own way. This may sound obvious and I know that applying it can be tough for a teacher on a tight schedule, therefore choosing exercises that use several items on the curriculum at once, would be highly beneficial. All humans (unless they have specific challenges) are natural born mathematicians and our job is to increase their skill and knowledge about mathematics, ensure that we keep them open to mathematics (we all start out open and too many children are subsequently shut down to it) and the fact that you are on this forum means that this probably doesn’t apply to you. Since others may read this, I will say it anyway :0) – it is ESSENTIAL that we don’t transfer any negative feelings we have around maths. I believe the last point is impossible, since subconscious signals will be transmitted by the teacher and received by the learners, so the only way I know of removing the problem is through education – so that any teachers that had a fear or hatred of maths are “cured”.
7 techniques to make maths meaningful:
1. ASK the learners for ideas and then find ways of using their ideas in a constructive way, this empowers them and shows them that you listen and care.
2. Give them confidence, if you’re not sure of something, investigate it as a class. It is important for them to have confidence in you of course and demonstrating to them that learning is a lifelong activity is a good thing, it also shows them that learning can continue after they leave school.
3. Use mathematical thinking exercises where “Every answer is a good answer because every answer leads to learning” and progress towards assimilation of the concepts at a level of true understanding.
4. Facilitate from the back of the class, where once a question is posed, the learners go up to the front to present their views to the rest of the class. This builds a culture of confidence, enthusiasm, trust and respect. It is essential that your class does not do any cruel teasing, which WILL discourage the timid participants. You are looking for an atmosphere in you class where everyone “wants a go” and encouragement for all – including those REALLY silly answers is constructive. I use “you are thinking! Keep on thinking!” in those situations, together with some questions if appropriate.
5. Bring every exercise alive using props that generate movement and feelings (soap bubbles and balloons do this). The excitement they feel about the props is ideally transferred to excitement about the topic!
6. As soon as you give the answer, the thinking stops (in most cases). It’s OK to leave a question open – how many times have you been mulling over a problem and the solution has come to you at an unexpected moment. If you are still finding blank looks at the end of a session, see what happens if you leave it open and then come back to it on a regular basis as a starter. If you give them the answer, they may react with relief but your learners are unlikely to be able to then tackle to matter on their own.
7. Ask the learners how they worked through an exercise. This is a real eye opener. It is a powerful demonstration of just how important it is to allow each individual to think in their own way and it shows all the learners that it’s OK if their way isn’t exactly the same as all the rest. You can teach a method, however, learning a METHOD is not the same as learning the maths. It was only recently, in a session with Mike Askew, that I realised I didn’t understand division of fractions.. whilst I knew the METHOD very well, I discovered that I DIDN’T understand the concept. A great exercise to do with other teachers or any group of grown ups involves mental arithmetic. Give them a series of fairly simple calculations, ensuring that they will reach a number in the thousands – the answer is not important here… then ask each individual what their process was and more importantly, how they visualised it. Ask them to describe their internal number line. You should get several different answers. Some of which might be a true revelation.
Making maths meaningful (the triple M!), that’s what it’s ALL about, isn’t it!
i. The Cambridge University Nrich website www.nrich.maths.org
ii. Do a course in the learning of mathematics at the Open University. This July, they are having the last ever residential course – EVERY person teaching maths should do it.
iii. Read ANYTHING by John Mason and or Sue Johnston-Wilder, starting with Thinking Mathematically and Fundamental Constructs in Mathematics Education
iv. Join the ATM (Association for Teachers of Mathematics) and come to our annual conference in April www.atm.org.uk
v. Any ATM book – they are all aimed at making maths meaningful.
It is my hope that you will have found at least one useful point in my answer.
Best Maths FUN! Regards
Founder of BUBBLZ! Making Maths FUN!