An Interview with Prof. George R. Thomas

Question: You stated in your essay "Why MathPath?" that remedies for the malais in education must be sought. In your opinion, what are these remedies?
Answer: Observing, as I did, that remedies must be sought is easy. Prescribing the remedies is not. Now, even before considering remedies, we need to know what the problem is - note that we are pointing the finger at ourselves rather than at other countries. Let us simplify the problem as this: The student in junior high or high school in general is not getting the concepts. Let us also simplify and say that the fault does not lie with students, parents, the surrounding society, or school funding, or even with the shortcomings of a particular teacher. In short, let us say the problem is with content and pedagogy.

What is taught and how it is taught is then our question. Let me just consider the latter and offer some solutions that I think might be appropriate in 2004 A.D.

Student Islands in school classes
In considering how math is taught, we are led to considering the common practice today - the traditional lecture method. The efficacy of the method is an ongoing debate. My feeling is that in a given course, say in junior high or high school especially, lecture is sometimes appropriate while at other times it is not. Regardless, I believe that a class should be split up into groups of size between three and six - this size is an interesting topic for investigation. The groups should form islands of desks and chairs facing the front of the class, with room between islands for the teacher to walk about. There are several advantages to forming islands. Let me mention three: (a) Whereas only about 30% [2] of the students follow the lecture in a traditional class, the percentage would be much more with the islands. (b) The islands are suitable for having the class do problems. They can discuss problems right there. "The main audio-visual tool, the most dependable and responsive component in any coordinated instructional system, is the classmate of the student."[2] The islands can compete with each other - for the very intelligent, this might be more fun than TV football. (c) An island system enables large class sizes, say 50 as opposed to 20. This would result in immense cost savings in education. What we need is not small class but larger classroom.
Homework
Homework given to students must be carefully selected and coordinated regarding time and quality. Both time and quality are important for homework or you harm the student. Too much time spent on homework will not only not improve grades but also adversely affect the student's social development. A rule of thumb is 10 minutes total for each grade. Thus a grade 3 student would be required to do about 30 minutes of homework a day, whereas a grade 12 student would do about two hours. And that is not all math but all subjects combined. This involves coordination among teachers. Quality of the work assigned is equally important. The photocopied math sheets are the easy way for the teacher. But the standard "math sheet" is boring. No wonder, most students don't like math! Doing the homework in any subject should ideally make for an excited, happy, and engaged time for the child. The drill sheets in math do not evoke this. So, go for assignments that involve not only practice, for some amount of practice is useful and even necessary, but also calls for a brain response different from practice.
Teacher Training
Implement proper teacher in-service and out-service training (sending them, for example, to at least the regional meetings of the NCTM).
Teacher pay
Pay them - being in the most important profession in the world - salaries that are attractive relative to other professions. Where is the money? Take it from the savings from increasing class sizes by forming Student Islands in class. I am not advocating the same salary for all teachers.
Adequately Qualified Teachers
Ensure that high school and middle school mathematics teachers hold degrees in mathematics. Re-certify them periodically using national criteria.
Lowering teaching load
Distribute the heavy work load so that each teacher has adequate daily in-school preparation time to be more effectively involved in "INSTRUCT! I'm ON" - instruction.
Testing student understanding
Look for ways - perhaps, through nation-wide or at least state-wide exit tests ( not multiple-choice format) for each grade - to test student understanding rather than skill; this will reduce the mechanical drilling and the teaching of tricks to pass tests.
Disallowing calculators in middle school and high school math classes
Calculators should be banished from the school math classrooms, for these implementers - is there such a word? - of algorithms might confuse the student that real mathematics also includes computation. The devil called "product sales" has gotten hold of the unsuspecting school teacher or the bribed calculator-pushing mathematician (speaking at NCTM and other large teacher meetings). The only justifiable need for a calculator in the mathematics class room is to check a time-consuming graph, but the advantage is small compared to the harm in the student's over-reliance for simpler chores. Let every math teacher acquire a confident familiarity with the graphs of the six trigonometric functions, the conics, the exponential function, the logarithm function, and the 1/xⁿ function, and let every student memorize the multiplication table, instead. A calculator is indeed an aid to computation in statistics classes; but statistics is not mathematics; it is applied mathematics.