We make a lot of mistakes in our schools, but one of the greatest is that we seriously underestimate our children. Worried about teaching them complex subject matter in early grades, we spoon-feed them academic pabulum. And then we wonder why so many 4th graders do poorly on national tests in mathematics, reading, and writing.
Teaching young people complex subject matter in early grades may seem to some educators like a bad idea--the equivalent of suburban parents pushing their kids to do their multiplication tables before they are old enough to be signed up for school.
The political philosopher John Stuart Mill tells of his “unusual and remarkable” education in his autobiography, which recounts his experience of receiving rigorous content at a tender age. Mill’s education was overseen by his father, the Utilitarian philosopher James Mill, who believed that ordinary schooling fails to develop a child’s intellectual capacities early enough. With his father’s guidance, and in isolation from others, John Stuart Mill learned Greek by age 3 and Latin by age 8. He could carry on discussions of complex problems in mathematics, philosophy, and economics by the time he was a young boy. He wrote that the intense learning as a young child gave him a 25-year head start over his contemporaries.
Should we encourage more students--especially at-risk students--to buckle down with advanced courses in elementary school? Many believe it is wrong to encourage disadvantaged students to learn complex subjects, that it is unfair to them and only condemns them to greater failure. Nationally, students in inner-city schools are far more likely to drop out, and are twice as likely to fail to reach even basic levels of proficiency on national assessments in mathematics, compared with other students. How can they learn algebra and precalculus when they don’t learn their multiplication tables?
The answer has a lot to do with what James Mill knew intuitively nearly 200 years ago. New research reveals that the young mind is malleable, capable of abstract thought, and can process much more information than is currently offered in the schools. Foreign languages, music, and even mathematics are best taught by engaging students in activities that help them learn by doing.
It is well established that young people from all backgrounds can learn. The issue is whether teachers have the content knowledge to teach complex subject matter. Teachers must be subject-literate. It takes a highly skilled mathematician, for example, to recognize the creative and inventive reasoning underlying a young child’s right or wrong answers. A teacher who knows his or her subject turns student mistakes and digressions into lessons in mathematical logic.
Project SEED, the program I am involved in, brings expert mathematicians specially trained in the project’s Socratic-style teaching techniques into elementary and middle school classrooms. Instructors teach topics from algebra, calculus, and other college-level mathematics to students as early as the 4th grade.
Lectures are not a part of the classroom activities. Instead, instructors guide student dialogue and discourse about mathematical problems and principles. Instructors ask up to 150 questions in each class without providing a single answer. The instructors supplement the work of elementary and middle school teachers who, because of their preparation as generalists, say logarithms and differential equations are like a foreign language to them.
This type of project puts people like James Mill back into classrooms. Instructors stimulate students’ interest in learning and help guide the process. The program, which has been evaluated for more than 30 years, has led to higher student test scores in every community in which it has been used. Research indicates that Project SEED improves students’ ability to think more critically and develop a deep knowledge about mathematics.
Our work--with 20,000 students each year in Camden, N.J., Dallas, Detroit, Indianapolis, Milwaukee, Philadelphia, and the San Francisco Bay area--offers some valuable lessons to educators who may wonder how to get the most difficult students to learn more difficult content. Here are four:
Supplement the teaching staff. Not everyone is an expert in mathematics. Shortages of qualified teachers are critical in most of the school systems around the country. There are just too few people with the necessary content knowledge to teach advanced concepts. According to a recent U.S. Department of Education survey of more than 4,000 teachers, fewer than one-fourth of elementary teachers (22 percent) major in an academic subject, and fewer than half of middle school teachers (44 percent) major in any academic subject in college. These statistics, as dismal as they are, are made worse when one considers that only a handful of teachers who do have an academic major study mathematics.
The problem is especially acute in the nation’s urban schools, which serve large numbers of minority and disadvantaged students. Corporations hire consultants all the time to help fill the gap in needed personnel. Why not public schools? We need more opportunities to bring in professionals in various fields--not just mathematicians, but writers, musicians, artists, historians, computer specialists, and others who can supplement the existing talent pool while working side by side with classroom teachers and administrators.
Develop a group dynamic to engage all students simultaneously. Teaching difficult content to a large group of students is impossible if only one student has an opportunity to answer a question or do a problem at a time. In Project SEED’s pedagogy and other effective approaches, as in cooperative learning and problem-based learning, every student is deeply involved in what is happening in the class every single moment.
In our project, both verbal and silent language help convey the students’ understanding or confusion about the subject matter. A variety of other signals indicate agreement or disagreement, understanding or indecision. In such a highly interactive environment, normally shy, confused, or unruly students become adept at tackling complex mathematical concepts. The emphasis is not on delivering the right answer but the route one takes to solve the problem.
- Let the students explore. Districts need to provide opportunities during the regular school day for teachers to learn effective Socratic teaching methods and student-involvement techniques. Through these approaches, teachers can help students create their own understanding of problems and take ownership of what they learn in an atmosphere of mutual support and cooperation. Students are encouraged to take risks, be creative, and investigate ideas and possibilities. The emphasis should not be on right and wrong answers unless the goal is to cut off student participation. By learning in a discovery format, students can arrive at a deeper understanding of advanced mathematics.
Don’t worry about the test scores. When students learn the underlying principles of mathematics, algebra, and geometry, they will have the necessary foundation to take on elementary- and advanced-level mathematics problems. But more importantly, they will have developed higher-reasoning skills, the ability to think more critically and take on more challenging work. All students benefit from our instruction, even those who generally may not perform well on tests.
The test scores will come. In addition to measuring performance on higher mathematical content, researchers have evaluated our students on many nationally normed basic-skills tests, such as the Iowa Tests of Basic Skills and the Comprehensive Test of Basic Skills, or CTBS. For example, researchers found that students made 2.5 months’ worth of learning gains on the CTBS for every month of Project SEED instruction.
The program’s research base includes a 10-year longitudinal study begun in 1989 by two research and evaluation specialists from the Dallas public schools, William J. Webster and Russell Chadburn. That study has found that the supplemental mathematics-instruction program not only has led to short-term gains in student performance, but also has had an overall, cumulative effect on academic performance. The long-term benefits include higher math scores, enrollment in more-advanced math classes in high school, and fewer dropouts and failures. The study also supports claims that the program helps improve academic self-confidence and encourages students to take on more-challenging work.
The problem is not that students will miss learning arithmetic and computation by being exposed to innovative teaching and rich content. Rather, the major concern is that, once exposed in early grades, they will be stymied with dumbed-down courses later on. There is nothing sadder than a student taught complex mathematics in elementary school who must later endure a curriculum focused only on basic math.
Unfortunately, many schools are unwilling to face up to their own deficiencies and devise appropriate strategies to supplement their weaknesses. (It’s far easier to blame the kids and label them as chronic underachievers.) Few schools want to admit that their teaching force needs support from outside experts, or that traditional approaches to teaching--lecturing and drilling students one at a time--are ineffective practices that may have outlived their usefulness in today’s classrooms.
I have had the good fortune to see firsthand in classrooms nationwide that disadvantaged students need tough academic challenges, not remediation. Under the right circumstances, students considered the most difficult to teach can learn the most difficult subject matter.
