To improve Math education in Singapore, much research has been done to understand how teachers teach Math. But in recent years, researchers have homed in on the other part of the equation: the learners and how they learn.
A doyenne of Math education in Singapore, Professor Berinderjeet Kaur has been a witness to how teaching and learning in Math has evolved over more than 30 years.
Two decades ago, the focus of research was on the teachers: how they taught their students, and what the common errors and misconceptions of their students are. The key question was: “How can they teach differently, so that the students don’t make these mistakes?”
Ten years later, there was a shift in thinking among researchers, Prof Kaur recalls. A new paradigm began to take shape – with the learners as the focus.
A Holistic View of Math Education
During that time, several international studies looked at student achievement and performance. “There was a concerted push towards a holistic look at teaching and learning,” Prof Kaur says. “We started looking at the interaction between three factors: the knowledge of Math, teacher and student – they form a triangle.”
Prof Kaur and her colleagues from the Mathematics and Mathematics Education Academic Group (MME AG) in NIE were part of that effort. In 2004, they joined an international research collaboration called the Learner’s Perspective Study, led by Professor David Clarke of the University of Melbourne in Australia.
“We learned a lot because that study positioned the learner very significantly in the interactive patterns,” Prof Kaur notes. The researchers video-recorded Math lessons as they unfolded in the Singapore classrooms.
“We collected data from the students, and asked them questions about what they were doing during the lesson. That informed us a lot on our understanding of the learner in the classroom.”
Looking beyond Grades
Today, the psyche of our students has become a matter of interest to educators and researchers.
Prof Kaur, for one, often reminds her student teachers during their pre-service education that they have to know the child first before teaching them. “As I always tell them, you must touch the students’ hearts first, and then the mind. Don’t go charging straight for the mind! If you haven’t touched their hearts, you haven’t won them over.”
Deputy Head of MME Associate Professor Toh Tin Lam notices that school leaders and teachers today are concerned about more than just Math scores.
“They‘re not looking at performance in exams as the only indicator. They’re also looking at other aspects of the students, such as self-motivation or academic self-concept.”
Tin Lam has just started a project with researchers from other disciplines, such as psychology and social work, to look at alternative teaching in Math and how they might affect students’ mathematical self-concept, motivation and achievement (See “Motivating Students in Math” in this issue).
“These are some other indicators we’re working on,” he says. “I believe on the whole, schools have become more receptive to what we’re doing.” In fact, they are often keen to participate in research projects by NIE researchers.
“Somehow we’ve managed to convince them what we’re doing is relevant, through pre- and in-service education,” he adds.
We should try to see things in a different light, especially when it comes to the less traditional groups of learners.
– Assoc Prof Toh Tin Lam, Mathematics and Mathematics Education Academic Group
High Performers and Low Attainers
After a decade of studying Math learners, how much do we know of them?
“How much we know is proportionate to how much research we’ve done, especially in the local context,” Prof Kaur comments. “We have a fair bit but still not sufficient.”
This is especially so as Singapore students span a wide spectrum of abilities. It is well known that they are chart-toppers in large-scale international assessments. Singapore ranked second in Math literacy skills in Programme for International Student Assessment (PISA) 2012 and first in Math for Trends in International Mathematics and Science Study (TIMSS) 2011.
There are many who do well in Math. “But as a society, we should not just be proud of these; we have to take care of the others,” Prof Kaur notes. She and some colleagues did a research project on low attainers in Math (See our previous article, “Helping Low Attainers to Keep Up” in SingTeach, Issue 31).
There were two findings that she felt were significant.
“They were keen to learn because in class, their teachers often made them feel they can do the Math.” But come assessment time, they struggled. The tests were often challenging even for better students. Prof Kaur suggests that the harder questions should be posed to these students gradually, so that they can experience success first and build their confidence.
Something else she noted was a mismatch between how these students wanted to learn and how the teachers wanted to teach.
“They wanted to learn through a lot of play, with manipulatives and some guidance,” says Prof Kaur. But the teachers tended to prefer more traditional modes of teaching and direct instruction.
MOE were receptive to their findings, and implemented interventions that encouraged teachers to show more empathy and give students more space to express themselves.
You may find that our learners are actually very interesting. They may be very quiet throughout the lesson, but if you give them the questions, they can do them!
– Prof Berinderjeet Kaur, Mathematics and Mathematics Education Academic Group
Studying learners at an end of a spectrum provides only a partial picture. Prof Kaur, Tin Lam and their colleagues hope to fill the gaps by proposing a new research project on the curriculum initiatives implemented under the current Math syllabuses. As part of the research, they want to look at lower secondary students of all abilities.
The team will video-record both teachers in action and students in the classroom. After that, they will show the videos to the students and ask them: Why was the teacher doing this? Does it help you? Which part of the lesson was important for you?
“You may find that our learners are actually very interesting,” Prof Kaur says. “They may be very quiet throughout the lesson, but if you give them the questions, they can do them!”
For Tin Lam, another way to help learners is to think of education in a different way – as a form of persuasion or communication.
Theories in other fields, such as communications, persuasion and advertising, could possibly provide another lens for looking at how Math is taught, in particular, to lower achieving students.
For example, if students are weak in algebra, a teacher can expose them to even more of it. Because of mere-exposure effect, which predicts that people will develop a preference for things or people that they are familiar with, students may grow to like it.
“But at the same time, make sure they don’t develop negative feelings about it,” says Tin Lam. “This is what advertising tries to do!”
These are just some initial possibilities that he is entertaining. In educating the new generation of students with different needs, perhaps such innovative ways of thinking are in order. As Tin Lam puts it, “We should try to see things in a different light, especially when it comes to the less traditional groups of learners.”