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Trial and Error Helps Brain Development Professor Jo Boaler, who teaches mathematics at Stanford, has looked into the reasons why children struggle when being taught the subject.
When the 7-year-old son of one of her colleagues declared that he no longer liked maths, his mother asked him why. His response was ‘because it always asks for answers without teaching us anything’.
This story, like thousands of others, shows how primary school children may think that the objective of maths can be quite hazy in comparison with other subjects. This might seem quite ironic, given that the nature of maths dictates a clear answer.
If we really want to make sure every child gets the best possible mathematics education, we’ll have to
change our approach.
There is a myth that some people are made to do maths and others aren’t – but it is, in fact, just a myth.
There’s really no such thing as a ‘mathematical brain’. In fact, maths mastery is down to finding the
right teaching method for each person.
By tackling your addition and subtraction or trigonometry maths worksheets with an individualised method, you can become a true mathematician!
Neuroscience has identified a strong link between a pupil’s opinion of themselves and their academic success.
Everyone is capable of achieving success with the right approach ¦ source: Pixabay
Science has proven that the human brain is capable of growing both physically and in capacity as well as shrinking, depending on how it is used.
This phenomenon was demonstrated by a study of London taxi drivers who had to memorise every London street in order to obtain their licence.
The capacity of the brain (thanks to the hippocampus) increased, whilst those of retired drivers, who no longer needed this information, began to shrink.
When it comes to mathematical concepts, trial and error means that your brain develops because of the heightened levels of concentration that come with being stuck on an algebraic problem or understanding where you went wrong in calculus. The high level of brain activity causes neurones to multiply, meaning you can arrive at the correct answer in even less time the next time you try a similar problem.
Although this doesn’t necessarily mean that making mathematical errors will give you the gift for maths, it does show how
certain approaches can be more effective than others in overcoming maths blocking.
Trial and error works for all kinds of mathematical disciplines, including geometry, polynomial functions, differential equations, multiplication and division, quadratic equations and even graphing a parabola!
In a world where perfection is the aim and efficiency is the game, learning this way shows a different side to learning math, where error is not necessarily a bad thing.
The Boaler Method to Learn Maths
Another study on children learning maths showed that the brains of those who encountered problems when it came to the subject behaved differently to those of children who demonstrated good math skills.
This phenomenon was noticed by Prof. Jo Boaler, who noticed that different area’s of the children’s brains lit up when they tried to tackle a set of maths questions.
Boaler’s teaching methods include
representing maths visually and monitoring students’ progress by discussing their views toward their strengths and weaknesses on a regular basis. A study of these methods has shown that any child is capable of understanding maths when the teaching is adapted to their needs.
Prof. Boaler estimates that
only 2-3% of the population experiences real difficulty in learning maths, and therefore the rest of the population is fully capable of learning the subject, including at high level.
People who have studied maths using traditional learning methods are often surprised when introduced to the visual method, as it goes against their brain’s understanding of the inner workings of mathematics. This is because the part of the brain that is used to visualisation is completely different to the part that deals with numbers.
Boaler’s methods bring maths to life to suit all types of learning style ¦ source: Pixabay
The reason these methods have been so successful is the way in wich they encourage both halves of the brain to work together. The logical left brain benefits from the creativity of the right brain and so for people who learn visually or creatively, this is incredibly useful.
Learning Maths Requires a State of Mind
More and more teachers are noticing how a student’s confidence in themselves can affect their progress in maths.
Approaching maths puzzles with a
positive state of mind changes the learning process and produces better results.
As the appreciation for the importance of this notion grows, teachers are looking for ways to bring this approach into the classroom.
According to Prof. Boaler, children are more capable of learning about math than any other subject.
Making maths fun is the secret to engaging children in the math curriculum ¦ source: Visualhunt
Teachers often fail to see the potential in a child and doubt their ability to reach the higher levels in school math. This creates a problem for the children they teach, who, in turn, begin to hold the same beliefs about themselves.
Boaler says that difficulties of creating a positive mindset come about when children are met with yes/no questions, since answers are either completely right or completely wrong, so there is no basis for constructive learning.
She proposes a visual alternative, where the educator works with pupils to open up a dialogue which offers different points of view and therefore different ways of arriving at a solution to the maths problem.
So rather than sitting through endless math worksheets and quizzes on adding and subtracting, triangles, word problems, surface area, math symbols, telling time, and linear inequalities, only to be met with a tick or a cross, students should be able to actively solve problems in the form of addition games, for example.
Leaving students to find their own solutions to interactive math games lets them use their creative side and improve their maths problem-solving skills, whilst helping them learn about their preferred learning strategies. This method will help student to appreciate the applications of math in real life.
Fun maths games for kids such as maths bingo can be a particularly helpful resource if you’re a parent or maths tutor who wants to encourage maths revision of topics that have been covered in class, for example. There are plenty of maths websites such as
BBC bitesize maths and Hooda Math which offer online maths games and math aids, for example. Learning Maths Without Pressure
Of course, pressure can be good sometimes. It motivates us to do better and appeals to our competitive side.
However, another study carries out by Prof. Jo Boaler at the
University of Chicago showed that constant pressure and particularly stress caused by time constraints can actually cause a mental block. The result of this is that the brain is not able to be 100% efficient in its processes.
When it comes to school math and other math courses, obstacles caused by pressure to do well are all too common.
This is particularly the case for children who suffer anxiety in school or who lack self-confidence. Increased pressure means that these students focus on the stress and can lose their way.
Quite often, the math teacher will call on their pupils to answer questions in front of their classmates. This quick-fire format reinforces the idea that calculation speed counts.
The irony is that even mathematicians with a math PhD don’t process numbers that much faster than the rest of the population, they just use certain mental maths techniques to make calculations easier. You don’t have to be a math genius – such techniques can be learnt by anyone to make mental arithmetic more efficient.
The Programme for International Student Assessment (PISA) for Maths Tuition
Often considered as a measure of performance in many subjects including mathematics for many countries around the world, the
PISA is of great interest to certified teachers and others in the teaching profession who want to see how their country is performing on the global stage.
Studies carried out by PISA show that children living in countries where maths is taught through memorisation rank worst overall. On the other hand, those who take a different approach and view mathematics as a network of different processes which follow the same rules tend to do a lot better.
PISA’s studies have also shown that repeating tasks is an ineffective way of learning.
So forget about learning that multiplication table by heart and put times tables into the form of a cool maths game, for example. Students need a productive way for approaching math problems from different perspectives to arrive at the same answer as well as clear explanations of each mathematical process.
The countries with the highest rankings learn by doing ¦ source: Visualhunt
Jo Boaler’s methodology of learning by doing has revolutionised the way maths is taught across the USA. Boaler has written several books for teachers who wish to use her methods in the classroom, and she also offers free online maths lessons.
More than one hundred thousand educational institutions have trialled Boaler’s methods and a recent survey has shown that 96% of their students hoped to continue to study maths even if they encountered difficulties along the way.
Is Learning Maths Stressful for a Maths Tutor?
Funnily enough, maths teachers themselves may become anxious when it comes to certain topics. This is usually because their understanding is based on how their teachers taught them when they were younger, using outdated and ineffective methods.
Primary school teachers seem to be among the worst affected by this.
Working on communication and visualisation, and discussing different solutions to maths problems are invaluable to children learning maths.
Encouraging creativity and figuring out the best individual learning strategy for each learner will help with learning in the long term.
Effective learning starts with a positive state of mind
Teachers can apply these new teaching methods to help children discover that
maths is fun!
The approach to national curriculum maths obviously needs to change if all children are to be offered equal learning opportunities. Teaching math in a one-size-fits-all fashion is shown to be far less effective than helping students understand how mathematics works and how it is relevant to their everyday lives. This is where the tailored approach of tutoring comes in. With a class of 30 or so pupils, it’s hard for teachers to respond to the specific needs of each individual, so for students who are worried about falling behind their peers or need a hand with their maths homework, private tuition could be the answer.
One to one tutoring is often the best form of adaptive learning since the tutor focusses on each of their students rather than textbooks. Receiving private
maths help allows children and adults learning maths to perfect their skills and gain confidence in the subject.
Tutoring can help all kinds of people, from those getting to grips with KS1 maths to
maths revision GCSE students preparing for their exams, to undergrads who need a hand with their maths degree, and even adults who have no formal maths qualifications!
So learn maths online or in person with a one on one tutor or private maths teacher and discover the maths geek in you!
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