I have thought a long time about the mathematics qualifications of "the mathematics teacher." For better or worse, I'd like to share my ideas. This is lengthy. So, if the topic isn't interesting, just delete my posting now.
Also, I thought that I would state my summary first so that those who don't agree with me don't have to waste their time reading this post. So: In summary, I don't think that the quantity of mathematics courses makes a teacher a better teacher of mathematics. Yet, there is a minimum of background a teacher needs for certain levels of instruction. It is my opinion that the pedagogy, understanding of the child and the deportment of the teacher probably make more of an impact.
I wish to thank those math-ed college and university professors who are trying to do the best job that they can educating our future mathematics teachers. I know that many subscribe to this list. You all not only know mathematics, but you also realize the importance of the way it is taught.
First of all, in teaching mathematics in K-12, there is the ideal, and there is the real. I am drawing this from my own many years in mathematics education, my own course work, and my reading. Thus, the presented opinions are subjective.
Ideally, an undergraduate major is the minimum mathematics qualification for teaching mathematics. Now, who are the mathematics teachers?
We know that the elementary teacher, K- to approximately 6th, teaches all subjects, and is usually in a self-contained classroom (this is where students stay in one classroom all day with the same teacher). What mathematics background is this teacher expected to have? If it is to be a mathematics major as an undergraduate, what about the language arts, social studies, art, science, music, etc., that the elementary teacher teaches? Should we expect the elementary teacher to have a separate degree in all areas? Obviously, this isn't practical. From my experience in teaching in the elementary grades, a background in The Calculus really isn't necessary. However, a sound understanding of concepts through rational numbers is. It is my opinion that teachers in the elementary grades should understand the topics covered in high school. And, they should understand how and what they teach prepares the student for continued mathematics study. Yet, I also believe that an understanding of good pedagogy, child growth and development, and learning theories are essential to mathematics teaching in the elementary grades.
I guess I'm saying the obvious. The more complex the mathematics you are teaching, the more mathematics background is needed. Yet, this is not all.
In middle school, teachers start departmentalizing. In my opinion the middle school teacher needs a strong mathematics background, but not necessarily a mathematics degree. And, in the real world many districts are looking at middle school teachers to form a team approach. Thus, often the mathematics teacher will also teach another discipline in middle school. In many states, these teachers don't need mathematics certification. What is being encouraged is a background in middle school education. This is because it is felt the middle school student has so many affective and social needs.
In my years of teaching, my undergraduate and my graduate mathematics degrees have been most helpful in teaching high school subjects. I have used my mathematics background in middle school to enrich my teaching and to give the students a sense of the flow of mathematics. But, I can't swear that it was necessary. I did have a precocious student to whom I taught pre-calculus to in eighth grade.
Frankly, my graduate degree in psychology has helped me more in K-8 mathematics education. It has helped in secondary education and in teacher education, too, but on a lesser scale. I think it is important to understand the whole child while teaching mathematics. Just being a math major in the university wouldn't have given me this background.
I am working with learning disabled student right now. He is exceptional in the language arts areas. However, he (age 11) can remember his tables. He has had flash cards, records, etc. He still has problems. What do I do? I let him use the calculator; I encourage him; we use tricks to help him remember basic facts; and we do algebra which he understands. I would never have any understanding about teaching mathematics to such a wonderful child without course work and much reading about theories of learning. And, I still don't know enough to help him as I would like.
I love mathematics. I love working out problems that I find in the MAA journals, in Quantum, etc. I find these stimulating exercises. What is important, too, is that my students see that I enjoy doing such. My modeling of my love and appreciation of mathematics are essential to generating such in my students. I suggest all teachers, K- whatever, need to also model their love and appreciation of mathematics.
That's my $.02.
Math History Lives!
Karen Dee Michalowicz VQUEST Math Lead Teacher/Trainer Upper School Mathematics Chair Virginia Quality Education The Langley School in Sciences and Technology 1411 Balls Hill Rd, McLean, VA 22012 USA 703-356-1920(w) E-Mail: firstname.lastname@example.org Fax: (703) 790-9712 --or-- KarenDM@aol.com