CMM - Center For Mathematical Modeling

Interview
“The confidence of school teachers comes from two things: knowledge and math thinking”
American mathematician Solomon Friedberg came to Chile to share his experience preparing prospective elementary teachers.
A few visits to classrooms were enough for him to confirm that some elementary teachers didn’t know enough mathematics to teach children and something had to be done. The chairman of the Department of Mathematics at Boston College (BC) -a highly selective Jesuit Catholic university in the United States with a commitment to both research and teaching- has been involved in many boards and committees in USA concerned with the mathematical preparation of teachers. Also he is the founder and director of the Case Studies Project at BC. Invited by the Fondef project "Tools for Training of Mathematics Teachers", developed by CMM researchers, Solomon Friedberg participated at the workshop "The ability to teach mathematics of prospective teachers of Pre-primary and basic level’ (K-8)", held in Santiago last June 16. But this is not his first visit to Chile. Last year, invited by the same project, he presented a series of talks on case studies, a method for improving the pedagogical skills of future high school teachers. Friedberg also is helping the researchers involved in this project to develop their own case studies in order to introduce this method in the curricula of Chilean universities. “They have done a really good job” he said impressed with the results of their year of hard work. During the last workshop, Solomon Friedberg talked about the preparation in Math of future elementary teachers and why they need to know mathematics. - How would be for you the ideal teacher? At a basic level, both in Chile and USA, the teachers are teachers of everything; they are generalists rather than specialists. A generalist obviously has to know how to teach, not just mathematics but everything else, but I think in particular must have knowledge of the mathematics they teach and also the knowledge of how to explain it in the way that is appropriate for the age of the child. - How do you prepare the future teachers to have that mathematical knowledge? When we are teaching mathematics for future teachers we do it very much with an eye on helping them to communicate and explain the mathematics to the students. There is a separate course in math pedagogy, which gives specific tools, methods and objects that that would help the future teacher. There is a blend, both courses –math and pedagogy- have some mathematics content and both courses are very aware that they are teaching teachers with the goal of helping them be better in the classroom. The real focus is explaining the mathematics and making them (future teachers) think again and a high level about addition, subtractions, multiplications, division, etc. The way we do it is giving them homework problems such us how do you explain to the students that they cannot divide by zero? If a child does this -some specific calculation that raises a conceptual question- what would your response be? We explain that is important to use precisely language and precisely notation and we don’t do it because is right; we do it to help the students. - Some future elementary teachers are afraid of mathematics, how do you help them? We have to recognize that there is a process and also there is a very personal kind of issue. What I do is encourage the student to come and talk to me during my office hours. Sometimes when people are afraid the professors have to make an extra effort to reach out and say to the students please come to my office. I have had some people who were very afraid of making a mistake and I have to say part of mathematics is trying things and not everything works, you have to be willing to make a mistake in order to look forward. But every person is a bit different in this regard. Their confidence comes from two things: one is from knowing and knowing that they know, and the second thing is from doing some mathematics and discovering that they can think mathematically. - What is the mathematical thinking and how it can be learned? At the basic level we want all our teachers to be able to think mathematically. What I mean by thinking mathematically is solving problems in different ways and being excited when their children come up with a new way to solve the problem, recognizing that it is okay, it is even good and exciting. We want our teachers to be comfortable enough with their mathematics; comfortable giving explanations to the child, knowing what are they teaching. We don’t want someone to say dividing 3 by 7 is impossible, of course it is quite possible, but not with a whole number answer. - Who are responsible to teach mathematics to prospective teachers at Boston College? My university got a very large grant to get faculty from the Faculty of Arts and Sciences -English professors, History professors, Geology professors, Math professors- involved with teaching our future teachers. The program created by the University encourages these people to try and see teachers in action, visit schools and then teach classes to prepare future teachers. For example, one of my colleges from the Math department has invented a new class for future teachers about Euclid. He has his students reading the original text and trying to understand the mathematical reasoning that is there and then explain it to other people in the class. It is a very rich experience for future teachers have something like that and for the mathematician it is also an excited experience.

By : CMM Communication
Date : 09-07-2008