Lynn Arthur Steen, professor at St. Olaf College and former president of the Mathematical Association of America, writes that the mission of mathematics education has changed from identifying and educating a minority of students gifted in mathematics to raising the standards to provide mathematics proficiency for all students.
He reports that although high schools are teaching more college-level mathematics, colleges are teaching enormous amounts of high-school mathematics. Instead of focusing on their core responsibility to educate all students proficiently, schools accelerate some students to college-level work and neglect others who are functionally innumerate and unprepared for college-level math.
These neglected students outnumber accelerated students by 10 to 1. The result is continued poor average performance on standardized tests. Steen reports that this pattern of acceleration mixed with neglect continues in college.
Few math departments apply as much effort to improve the quantitative literacy of all students as they do to enrich the mathematical education of their majors. The standards movement in mathematics seeks to change that.
Traditional focus has been on minority of gifted math students
In Steen’s opinion, mathematics is central to the global movement to democratize education: it supports the increased need for post-secondary education, the technical demands of the high-performance workplace, and the conceptual skills required to live and work in the information age.
Research shows that most students learn mathematics best when they encounter it in familiar contexts. The traditional curriculum may have served the minority of gifted math students adequately, but it is not suited to educate the majority of students. Disagreements between mathematicians and educators have centered around the pacing of curricula and approaches to teaching.
Now that the mission of school mathematics has changed to “mathematics for all,” new methods are needed, writes Steen. Currently, the political solution for addressing educational under-performance is high standards enforced by high-stakes tests. Steen contends that when states create the tests that are required for high-school graduation, they measure competency on only the lowest third of their curriculum. Even this low target causes problems for many students who have to take the test several times.
Advanced content squeezed out of testing
In Steen’s opinion, the consequences of such high-stakes tests are huge and almost entirely bad. To ensure politically acceptable passing rates, the advanced content specified by standards is squeezed out of state exit tests and thus the content in the overall curriculum is diminished. Instruction focuses on passing tests rather than on understanding mathematics.
Instruction directed at helping students pass tests can accomplish its goal, but does not foster the kind of deep understanding that students must have to be able to use mathematics in higher education or in the high-performance workplace. High-stakes testing neither reveals nor increases students’ understanding of mathematics.
Meaning of mathematical proficiency for educators
Mathematicians and educators have recently united around two ideas that bridge their differences: the meaning of mathematical proficiency and the understanding that is required to teach it. At every grade level, proficiency and understanding are far more complex than many have realized. Although it is possible to race through the traditional curriculum, finishing algebra in eighth grade and completing calculus by twelfth grade, students who do so end up mathematically impoverished.
Steen believes that calculus should be taught in college and that the high-school years should be used to explore not only algebra and geometry, but useful subjects such as data analysis and discrete mathematics, probability and modeling, statistics and computing. The connections between these subjects will promote deep understanding of mathematics and equip students with the quantitative skills they need as employees, consumers, parents and citizens.
Steen believes that for students to develop mathematical habits of mind, they need to see and do mathematics everywhere, not just in math class. As writing is now accepted as a part of the entire curriculum, so mathematics should be accepted.
If our goal is for all students to learn mathematics, we need to greatly increase the number of teachers who understand it deeply and are able to guide students’ learning effectively. Low salaries, competition from industry, and poor working conditions make recruiting math teachers unusually difficult.
Assumptions about teacher preparation for math not well-founded
Because of the nationwide need for math teachers, the mathematics community has recently agreed on important principles for preparing teachers. Colleges need to be encouraged to implement these new guidelines. The challenge is to develop in prospective teachers a robust and flexible understanding of mathematics.
Steen says that two assumptions that underlie current teacher preparation are not well-founded. First is the belief, entrenched in state certification requirements, that elementary school teachers need only a cursory knowledge of mathematics represented by two courses or six credit hours.
Second is the belief that secondary school teachers will be mathematically well-prepared if they complete a major in mathematics. Both beliefs ignore the crucial importance of pedagogical knowledge — the translation of mathematical ideas into strategies for teaching in the form of problems, lessons, and tasks that will help students gain mathematical understanding.
What teachers need most is to understand elementary mathematics from an advanced perspective. Even prospective teachers who understand higher mathematics well often have little idea how to translate that understanding into a form suitable for younger students.
Achieving mathematical proficiency for all students is a monumental task, but Steen sees some cause for optimism. Mathematics now penetrates almost every aspect of life and work, so students have greater opportunities to see how math is used and to recognize its value.
Since the previous debates about math education have been largely unproductive, mathematicians and educators are beginning to work together to build a consensus and clarify areas of difference. Many educators are beginning to understand the value of looking at mathematics as a united enterprise from kindergarten to college.
“Achieving Mathematical Proficiency for All, Moving Beyond the Math Wars” The College Board Review Number 196, Spring 2002 Pp. 4-11.
Published in ERN September 2002 Volume 15 Number 6