When we hear the word ‘Mathematics’, we are likely to have a variety of reactions. Some smile as Maths was a subject that came easily to them, while others start to feel ill as they remember their days of struggling with meaningless numbers on a page.
Often our reaction is due to the way that Maths was taught to us.
Mathematics often meant an imposed system of dealing with numbers: learning a ‘set way’ to do something. This is based on the idea that the teacher has the knowledge and they ‘pour it in’ to the student — the student being a passive recipient of that knowledge. Facts, skills and process were often memorised without understanding or knowing how or why to apply that knowledge.
Many students were left with feelings of failure, if they didn’t understand, hence the all-too-common comment, “I am no good at Maths”. This negative feeling is often carried through to adulthood.
Similarly, there are myths such as boys are good at Mathematics, while girls are good at English. It often appears that there is much gender stereotyping when it comes to Maths.
Is there even such a thing as a good Maths teacher?
As teachers at the Victoria International School of Sharjah (VISS), we look around at the great things going on in Mathematics classrooms — students are active, engaged and happy: many of the activities are fun. Children are involved in measuring, comparing, playing games, writing, talking, working on computers, explaining and much more during Maths lessons. The goal of each teacher is to be a highly effective teacher of numeracy.
So what should we be teaching in Maths?
Students need the capacity and confidence to understand and apply mathematical concepts, problem solve, collect and analyse data and to make connections within mathematics to meet the demands of learning at school, work, home, community and within civic life. That is what numeracy is — mathematical skills for life. It is more than just learning your times tables! Let’s look at what some of the characteristics of effective numeracy teaching look like in practice.
To understand and apply mathematical concepts, students need to be taught, using good physical and mental ‘models’ to develop these concepts. These models may be in a variety of forms — a physical model may range from the first use of plastic counters to show simple numbers, using a string of 100 beads to show the idea of percentage to folding paper rectangles to demonstrate fractions.
Ideas in maths should not be just seen in isolation to each other.
Students at VISS are specifically taught to make connections between the ideas. When a student is learning about decimals, for example, they will compare them to fractions and percentages with the same value. Previous learning is reinforced and overall mathematical knowledge is deepened by the connections made.
VISS has produced its own set of ‘times-tables’ cards for each student to practice the multiplication facts at school and home. Knowing these facts gives students the confidence and capacity to solve problems quickly.
How to differentiate Maths in the classroom
Every child in the classroom is at a slightly different stage: students learn at different rates and in different ways. Giving exactly the same work to all students in the class will mean that the more able students will be bored as it is too easy for them and it could stifle their learning. The less able students will struggle with the same work and become stressed and unhappy.
Effective numeracy teachers know they need to challenge each student at their own level. All students need to think deeply, understand, explain their thinking and problem solving. Our job as teachers is to take the student from where they are in their learning journey to further along the path.
One way we do this at VISS is to pre-test students before the start of different topics. This means that they will be given some form of assessment to determine exactly where they are in their learning journey.
Then the teacher will carefully analyse the testing and may group students with similar learning needs. Specific activities are planned for the different groups. While one group may be working closely with the teacher in a session, other groups work independently on a variety of activities, all selected specifically for their unique learning needs.
Another way we provide differentiation within the class at VISS is to use ‘open questions’. What is an open question? It is one where there is a variety of possible responses, not just one right answer.
Students have to think deeply to come up with the answers and will vary in their response, according to their level. To illustrate this concept, consider the opposite of an open question — a closed question. A closed question could be 5x4=20, easy to do for some, harder for others.
A better question which would provide a variety of answers would be ‘what possible numbers might multiply together to give the answer of 20?’
Students may use counters to work out that some answers could be 10 by 2, 5 by 4, 20 by 1. Other children might draw diagrams to work it out, yet others just write the possibilities.
Some children might give one answer, others more. The teacher roams the room, prompting and challenging each child to go further in their thinking about the question. By answering open questions, all students can achieve success and be taken further in their learning journey.
Giving students the capacity to question is crucial. As Guy Claxton (2003) articulated “good learning starts with questions, not answers”. Students who are given the opportunity to question and to make connections will develop deeper understanding with the content.
Teaching and learning Mathematics can be fun, challenging and interesting. Both teachers and students are partners on the journey together.
Helping girls like mathematics
Why is it that there is a perception that boys are better than girls at Maths when researchers have studied gender differences in Mathematics performance and concluded from a meta analysis of 100 published studies, that in fact, females outperformed males, even if by a slight amount, with the possible exception of problem solving?
One reason is that often girls do not have positive role models either at school or at home, who will openly admit they were good at Maths. Even those who were good Mathematicians will downplay their achievements.
This creates a perception amongst females, that males are superior when it comes to areas of Mathematics. When confidence as well as the expectations are decreased, then performance is also affected as self-confidence in Maths influences actual results. Girls who have a negative perception of their ability in Mathematics will be outperformed by other more confident but less able students.
Females also have a need for understanding and reasoning. Studies conducted in the UK have concluded that “Mathematical reasoning, even more so than children’s knowledge of arithmetic, is important for children’s later achievement in mathematics”.
Girls in particular need to have the opportunity to develop their reasoning skills, as opposed to rote learning and need to be given opportunities to discuss their thinking and reasoning behind certain mathematical problems.
Boys tend to be more practical and try to grasp the meaning of what they are learning. Girls, on the other hand, tend to be more methodical in their approach by learning theory and formulas and this may lead to them not being able to apply their learning to new situations.
At VISS, girls and boys are given the opportunity to work within their strengths, as well as being challenged to think and work outside their comfort zone so that they are able to increase their skill base. Helping girls like mathematics
Why is it that there is a perception that boys are better than girls at Maths when researchers have studied gender differences in mathematics performance and concluded from a meta analysis of 100 published studies, that in fact females outperformed males, even if by a slight amount, with the possible exception of problem solving?
One reason is that often girls do not have positive role models either at school or at home, who will openly admit they were good at Maths. Even those who were good Mathematicians will downplay their achievements. This creates a perception amongst females, that males are superior when it comes to areas of Mathematics.
When confidence as well as the expectations are decreased, then performance is also affected as self-confidence in Maths influences actual results. Girls who have a negative perception of their ability in Mathematics will be outperformed by other more confident but less abled students.
Females also have a need for understanding and reasoning. Studies conducted in the UK have concluded that “Mathematical reasoning, even more so than children’s knowledge of arithmetic, is important for children’s later achievement in mathematics”.
Girls, in particular, need to have the opportunity to develop their reasoning skills, as opposed to rote learning and need to be given opportunities to discuss their thinking and reasoning behind certain mathematical problems. It is important therefore that we as teachers provide opportunities where students can share their findings and explain their understandings. The justification of their answers is the crucial element to making connections.
There is no doubt that boys and girls think differently and learn differently. Boys tend to be more practical and try to grasp the meaning of what they are learning. Girls on the other hand tend to be more methodical in their approach by learning the theory and formulas and this may lead to them not being able to apply their learning to new situations. This can be compared with how males and females may approach putting together a cabinet.
Males will generally open up the box, look at all the pieces and try to work out how to put it together. A female will look at the instruction manual and follow the procedures step by step. Whilst the result may be the same, the males may have a better understanding of how they fit together because they have needed to ‘work it out’ and therefore may display a more advanced problem solving capacity. In order to provide well-rounded individuals, we as VISS teachers are adept at providing tasks and activities which suit both genders.
Girls and boys are given the opportunity to work within their strengths, as well as being challenged to think and work outside their comfort zone so that they are able to increase their skill base.
