Can We Can Improve the Learning of Mathematics?
There is, I think, sufficient data to indicate that, for both students and teachers, mathematics is the least popular subject in elementary schools, and this has been true since before I entered mathematics education over 40 years ago.
After a life time spent in mathematics education I have come to the conclusion that, despite the improvements in our understanding of how children learn, and new methods of teaching mathematics, students still leave school with a low level of numeracy. To be clear, numeracy is the ability to reason with numbers and other mathematical concepts, and includes number sense, operation sense, computation, measurement, geometry, probability and statistics. Numeracy also requires that students have an intuitive or emotional feel for mathematics that gives them confidence in predicting or calculating answers.
Many people would argue that there is no emotional aspect to mathematics, just obey the rules, get the right answer and move on. However most adults have a strong emotional response to anything related to school mathematics; unfortunately these responses are usually negative!
Intellectually students can deal with everyday calculations (after all, they are rarely without a calculator), but many lack the emotional understanding that gives confidence in predicting and calculating answers.
The problem does not lie directly with the teachers but more with the way we recruit and train potential teachers. We have a self perpetuating cycle; students don’t enjoy mathematics in school, graduate and go to university where they tend to avoid mathematics courses. They enroll in teacher education programs where they may or may not take a course on how to teach mathematics. Even if they do take a course on teaching methods for mathematics it lacks value if the participants have serious gaps in their knowledge and understanding of mathematical concepts. It is like a course on how to coach basketball if you have no knowledge of the game and the skills involved.
The student, totally unprepared to teach mathematics, now enters the teaching profession and the cycle continues.
The dilemma facing educational leaders, politicians, and society in general is figuring where and how to break the cycle.
One possible solution, which could address the problem fairly quickly, would be to have a series of courses addressing both mathematical understanding, and teaching methods for specific topics or strands of the curriculum. On successful completion of each course participants would be given a certificate to say they had been trained in that topic and were qualified to teach that topic. Over time teachers would become fully qualified to teach mathematics.
This, like most solutions to problems in education, would require financial commitment by governments, education authorities, faculties of education, and a time commitment from teachers.
At the same time the mathematics requirements for entry to teacher education programs could be made more stringent to ensure that students entering these programs will have greater mathematical understanding thus ensuring that methods courses in mathematics will be more relevant and useful.
Until we improve the entrance requirements and the qualifications of potential mathematics teachers, mathematics will be poorly taught, too many students will not achieve the numeracy skills necessary to function in today’s society, and the work done by teachers will not be given the respect it deserves.