During her visit to ISB last week, Erma Anderson, the internationally renowned math consultant, addressed why, at the International School of Beijing (ISB), students no longer learn math the way their parents were taught it.
Originally a high school math and science teacher, Ms. Anderson worked with the National Science Teachers Association (NSTA) for ten years, on projects involving the design of high school science curricula and on professional development for teachers. As Assistant Project Director of the Council for Basic Education's Schools Around the World project, she facilitated the development of several state and district science and mathematics curriculum frameworks and consulted on the international benchmarking of standards. Currently, Ms. Anderson is a math and science consultant with the Office of Overseas Schools AERO project, improving programming and training teachers at 124 schools internationally.
One of the drivers for Ms. Anderson’s approach to mathematics is the pace of change in the 21st century. Today’s schools are preparing students for careers which either may currently not exist or which may be radically impacted and restructured by technological advancement. Either way, today’s ISB students will be called upon to solve problems never encountered before, using technology that hasn’t been invented yet. “We show children that math is not a set of rules they’ve got to memorize; math is a way of thinking,” said Ms. Anderson. “Because, students who learn self-confidence, adaptability, and problem solving develop a mentality where no matter what life throws at them, they can figure it out.”
Ms. Anderson says the theory of constructivism in education underpins this approach: children learn and understand math by forming their own understanding of the techniques, processes, and systems which make up the language of math. “We want students to have a more substantial, less fragile understanding of math. When I have only rules to remember, if I forget a step, I’m lost. But if I have an understanding of the problem and why the math works I can communicate, collaborate, and invent my own rules and strategies for solving it,” said Ms. Anderson.
She said that at ISB, students learn how the math works - the procedures, rules, and algorithms, but crucially they also understand why the math works. By providing multiple approaches and opportunities for students to question, experiment, and explore, teachers make certain that students have the necessary depth of understanding and procedural fluency. Along with drawing out connections between the problem and previous material, the teacher facilitates inquiry, collaboration, and communication, introducing new ideas and skills to ensure that student understanding is complete. In old-fashioned education, often teachers themselves had a superficial understanding of math concepts; standing in front of the class and demonstrating a method which the students drilled repeatedly. “That method doesn’t work, and it’s never worked,” said Ms. Anderson. “Teachers need to deeply understand the concepts themselves, provide a great context for learning, and then closely observe what skills the students are missing in order to resolve the problem.”
Students understand the computational and procedural skills, have reasoned their way to the conceptual understanding more thoroughly, and deepen their understanding across a range of scenarios, in order to learn “where” math works. ISB teachers design problems to elicit each student’s prior learning and which requires them to apply that knowledge in a new context. “A well-balanced math program must address the applications for math and we always relate the learning to real-world scenarios,” said Ms. Anderson. “We are focusing on building skills to solve problems.”
At ISB, math is not simply calculation and the application of shallowly understood math tricks. It’s a way of thinking: asking perceptive questions; collaborating on solutions; and developing a problem-solving approach to math and life. “I hear all the time from parents and teachers that they wish they themselves had learned math this way,” said Ms. Anderson.