Treviglas
See, hear and be moved by mathematics - using the principles of Accelerated Learning to raise achievement in mathematics
Chris Tomlinson, Learning Co-ordinator, Head of Mathematics, Treviglas Community College, Newquay describes his experiences of using accelerated learning methods
In at the deep end
I shall never forget my first day at Treviglas Community College as Head of Mathematics. It was not the ideal situation, as I had to take over a Year 11 lower intermediate class, half way through their GCSE course. Their previous teacher had left few records apart from predicted grades and module scores. Out of a class of 31, only seven had been predicted the magical grade C.
I did have a brief conversation with their Year 10 maths teacher, who said that the students were well trained and 'underachieving' at present. There was an equal gender split. I quickly realised I had one year to raise positive expectations and change the students' very traditional attitude to, and opinions about, maths. The students were used to being taught by a textbook and believed mathematics was all about practising techniques by completing pages of questions.
The students were well trained. The textbooks were given out by the first student who arrived and then all the students followed in automatically, sat down and started to work from chapter one of their new text book. I stood at the front of the class and asked the students to put their textbooks away. Their faces looked puzzled. I then asked them how they would like to learn mathematics. There was no answer. I gave out a simple questionnaire about multiple intelligences and preferred learning styles. From this small sample size the percentages for visual, auditory and kinesthetic preferred learning styles reflected that of a population. Of the multiple intelligences, interpersonal stood out alarmingly high compared to the others. This research study gave me some information I needed about the students. I would use this knowledge in my strategies for teaching in the lessons. Knowing what the students are good at and their preferred learning styles can really help to maximise their learning by adapting teaching methods to suit their needs.
The first lesson was titled 'The Big Picture'. The aim of this lesson was not only to gather the information mentioned above, but also to talk about the skills they would use and develop to assist their learning of mathematics. The students drew mind maps and discussed the topics they would encounter that year. The mind maps needed lots of guidance but they were a successful strategy, used in recalling and starting some topics. We visited mind maps on several occasions during the year and the students really developed this skill. The students came to realise that the skill of mind mapping is essential to give a clear overall picture of the maths they need to conquer (see Figures 1, 2 and 3). At the end of the lesson I discussed expectations with them. I told them that with hard work everybody would achieve a grade C. From past records the school's results for mathematics were at the national average. This meant that really only a small handful were on target to achieve a grade C on reflection. Full attendance was an essential ingredient and fun and laughter would play a huge part in increasing learning and changing the students' traditional opinion about mathematics.
Accelerated learning to the rescue
I had to achieve a balance of approach when inputting the content. A mix of styles was really important to gain interest, enthusiasm and to maximise learning. The classroom became a thriving source of knowledge and you could almost smell the mathematics in the air. All that time taken in preparing the classroom was sure to pay off. Some say 90 per cent of what we learn is through our subconscious. The physical environment was good and key mathematical KS4 words were situated around the room, above eye level, for visual learners. Emotionally the environment needed to be much more positive than they were used to. The students were greeted at the classroom door and soon into the next lesson I informed them of their results from the questionnaires. I talked about their talents and intelligences and how mathematics and logic did not score highly, but we could use the other intelligences outlined by Howard Gardner to aid our learning of mathematics. I used several tactics in class discussions and verbal two-way conversations:
Big hand (show me a scale of 0-5, indicating if you have understood what I have talked about).
Relay maths, to give encouragement to whole class interaction and teamwork. For example, write a fraction on the board. Give out four board pens and ask students to run to the board and write an equivalent fraction. They then return the pen to me and I give the pen out again to someone else. This lasts for four minutes and can be used for a number of exercises in maths.
Two hands up for a comment or question, one hand up for an answer.
Discuss with the person next to you for a minute or two and then contribute to the whole class discussion.
'Shut your eyes' questioning. Ask for a show of hands with eyes shut to relieve peer pressure.
Chinese whispers to produce maths chains. For example, decimal, percentage and fraction: one student gives a decimal, the next an equivalent percentage and so on, like a domino effect.
Students can always nominate a friend if they are stumbling on the answer or ask the 'audience'. This use of lifelines really relaxed the students when volunteering to answer questions. Sometimes I would throw a soft, small ball to the volunteer who then could throw it back if they had forgotten their answer or throw it to someone who could help.
When answering a question, the students were never put on the spot. Volunteers were invited or groups of students were asked for answers. It is also really important that the reply from students reflects the gender split of the class. Sometimes I used to alternate girl/boy questions that reflected the ratio of the gender in the class.
Sometimes, to break up the lesson, I would use brain gym as a learning tool to enhance the maths content I was teaching. For example, it is perfect when introducing a symbol or notation in maths for students to draw it in the air with their right hand, then their left and then both hands together. This connects both the right and the left sides of the brain and is good for motor co-ordination. It also helps the students to remember the symbol or keyword.
If the answer was ever eight then the students had to draw a 'lazy 8' in the air at any time. A 'lazy 8' is a circular movement in the shape of an eight using both right and left hands together.
A strong learning tool was visualisation. I would ask the students to shut their eyes and relax with some music playing. If I were teaching gradient, then I would tell a story that involved practical examples of gradient; for example, a roller coaster. I would tell a story and the students would describe the slopes of all the loops and the speed of the roller coaster car. This really helped to focus them on the concept of gradient. Using pieces of paper, I would ask students to produce a double doodle using both right and left hands to write the key word. This helped to focus the students on the keyword.
These activities in the brain gym related to the content were enjoyable for the students and created a positive brain environment. The students could see a real purpose to it as it was related to the content. Although you might think there is not enough time in lessons to do this, these activities actually create more time - the written part of the lesson now consisted of twenty minutes quality work instead of the usual fifty minutes taken to do the same amount of work. It helped to break up the lesson and assist concentration, giving the lesson a good flow of brain nourishment.
Bring on VAK
I had to make an impact on the students very quickly in these Year 11 lessons. More importantly I had to maximise their learning. The balance of activities I chose to input needed to reflect their learning styles. A good balance of visual, auditory and kinesthetic activities was essential. There are some teachers who believe maths cannot be taught kinesthetically. Mathematics can be taught through movement, I believe, and the students really enjoyed the lessons, having lots of fun in the process. It also helped to make mathematics accessible to all students, some of whom did not even realise that they were doing mathematics. Outlined below are some lessons and ideas that I have used for my Year 11 class, based on the levels 5-8 of the National Curriculum. The first ideas are kinesthetically based.
Transformations - Students are the shapes and play this game in pairs. A pair can reflect, rotate or translate. I would have a pack of hand-made cards with the words reflect, rotate and translate written on them. When I picked a card, if it matched the actions that the students were doing, they were asked to sit down. The winners were the pair left standing. With transformations we made up dance routines and descriptions about the routines and the type of movements we used. Some students performed the routines in front of the class. We also looked at sports videos to see the different movement that taking place. Every so often we would go for a translation around the classroom.
Running game - Using the OHP, I would put up 15 expanding bracket questions and 15 factorising questions. They are pairs to each other but the students do not notice this until the end of the exercise. Every student would be given a number and in one minute would have to decide the answer to their question. They could discuss it with fellow students. They then had to race to the board as a relay and write their answer on the board, giving the pen to the next person. To make it more of a race, I would ask them to do this before the end of a CD disk.
Human calculator - This was used for standard index form, but could be applied in other situations. Some of the students would hold up individual numbers at the front of the class that made a big number or a small number. A student holding the decimal point would come along and the class would sing, 'the decimal point jumps up and down, where are we going to move it around'. The decimal point moves along to make the number between one and less than ten. A student then holding the number ten would come along and to complete the exercise someone would stand on a chair to be a power. Obviously this lesson contains movement and uses strong visual features as well.
Horse race - Two die were thrown and the scores added together. The students were the horses, holding a number and moving along the racecourse, crossing fences when their score was thrown. I gave the students odds on each race and counters to bet with. This is a real action-packed lesson just to illustrate the concept of a sample space, but it also helped their numeracy skills and the students found it memorable and funny. It is possible to do this in a classroom and the fences are chairs to mark the distance along the racecourse. They do not actually jump a fence, just move along the racecourse.
Graph creations - When coming across any graphical function, we would always make it as a class by using the edges of the room as axes; for example, y=x2. The students would move to form the 'U'-shaped graph. I also used the drawing of graphs as part of the brain gym and students would have to draw the shape of the graph in the air. Sometimes I asked the students to use string to produce the outline of the graph and I used graphical calculators when investigating the graphs in more detail.
The followings lessons I believe to be auditory lessons, with the key being that children are doing more of the talking and listening and the teacher just directing. These activities must be monitored very carefully and time allocations given, usually quite quick and short. The teacher plays an active part by listening very carefully to what the children are saying.
Blind date - A girl would sit behind a flipchart or screen and three boys would sit the other side. Blind date can be used for many things, but here I used it to teach the properties of different types of triangles. The girl would be called Bermuda and would ask three questions in total, one at a time. Each question would require the boys to return their answers, giving one fact about the triangle they are representing; for example, Boy 1, called scalene, would answer a question, 'My sides are sexy all over. Tell me something about your sides.' His reply could be, 'My sides are unique. You won't get fed up looking at me, all my sides are different.' At the end the class, who would be watching and listening throughout, were given the role of 'Graham' to write the reminders about each contestant.
Buzz, ding, boom - If a number is in the two times table, the class say buzz; if it is in the three times table, they say ding; and if it is in both, they say boom. They can do this in pairs or as a whole class. You can ask to go backwards from ten, or make it harder by going between 30 and 50. This is quite simple for intermediate pupils, so after warming up use x, y and xy for buzz, ding and boom respectively. This is a good way to introduce algebraic expressions and you can use your imagination to develop quite complicated algebraic concepts.
Musical fractions - The students stand in a circle. I pass round different fractions, written out on laminated cards. When the music stops I call out a fraction and if the fraction they are holding is equivalent, then they win the game. You can vary the game by calling out a decimal or even use decimal numbers on cards and call out a fraction. This can also be adapted for using percentages.
Many of the lessons above contain very strong visual aids to learning. Below is an outline of a lesson I used with three-dimensional shapes that was a very strong visual lesson.
Magical shapes - I would place some wooden solid shapes under a tea towel at the front of the room. Before putting the tea towel over the shapes, the students would be allowed to look closely at the shapes. They would then shut their eyes as I took one shape away from the display. I would take the tea towel off and ask the students what shape was missing. After they guessed correctly, I would ask them to look at a shape and discuss its features. I also did this game at a different time, using everyday objects instead of the wooden solid shapes. This game really encourages good memory skills.
These lessons helped to achieve my objectives for this class. I had little time and lots of the ideas above require very few resources. If a measure of success is the number of students who achieved a magical grade C, then all expectations were exceeded - all apart from one student attained grade C or B. Initially the second module results were worse. I then had to build the confidence of the students, convincing them that it would work out in the end (see Figure 4). Obviously the students worked very hard and I used revision days, during the holidays, to enhance their revision programme. More importantly, I believe, the students had lots of fun and laughter. This to me reflected the success of some of these lessons. I certainly believe that it is possible for students to see, hear and be moved by maths.
The students followed the OCR 1666 Graduated Assessment Syllabus. They complete three modules over two years. The best of these results counts for 30 per cent of their final grade, 50 per cent of this final grade is achieved through a terminal exam and 20 per cent through coursework. The second module result was not better for the majority of students, but was sat in the November of Year 11. All but one student out of 31 improved and got a grade C or better in their third module, taken in the April of Year 11, and this was matched by a better or equivalent grade in the terminal exam.