by Angela Andrews
October 2000
In a recent talk, "Why the New Standards Won't Work," a renowned mathematics educator gave several reasons but lay the major blame directly at the feet of poorly prepared elementary teachers who don't understand mathematics. I was about to agree with this remark when the speaker went on to share the opinion that anybody who could not explain the mathematics behind finding the square root of a multidigit number had no business teaching mathematics in the elementary classroom. This statement was both arrogant and disrespectful, and I wondered whether I had just put my finger on one of the major problems with preservice education.
It is always easier to blame the victims than to teach them.
To improve preservice education, we must take basic steps to help mathanxious and mathavoidant students, who are casualties of their previous mathematics education but who are drawn to elementary education, become competent and confident mathematics teachers.
Step 1: Respect the student.
A major problem with undergraduate mathematics is that is it taught by mathematicians—those for whom the subject comes easily. Recognizing the difficulty of the subject is hard for them. Although the secret of education lies in respecting the pupil, those for whom mathematics comes easily are often disrespectful of students for whom it does not. College teachers often riddle their lectures with such disrespectful remarks as "It's easy," "Couldn't be simpler," "This isn't rocket science, you know," and so on. Such teachers often use only their own preferred methods and procedures to explain mathematics. Once, in a methods class, after I explained my thinking about a problem by using a paperfolding model, my professor told me that my method was inefficient and would have been unnecessary if I had understood algebra better. Perhaps so, but his negative attitude toward thinking that differed from his own "more efficient" way did nothing to nurture either my mathematical confidence or competence. Perhaps college teachers might treat their preservice teaching students with more respect if they recognized the potential "gift of the mathanxious teacher." Such teachers are already motivated by their own struggles and want to ensure that none of their students have the same difficulties. They may be more open to trying approaches that differ from the ones that permeate a rulebound curriculum.
Step 2: Recognize the limits of time.
Although we wish for more preservice mathematics courses, we must face the fact that elementary educators are generalists, not specialists. They do not have enough time to cover everything. Rather than lament because elementary educators don't understand enough mathematics, we must focus on helping them understand and teach fundamental mathematics well (personal conversation with Liping Ma). Then, recognizing that the object of education is to prepare people to educate themselves, we must instill the desire in prospective teachers to want to continue learning after graduation.
How do we do this?
Step 3: Bring passion to the subject of mathematics.
According to an anonymous source, "Whosoever would kindle another must himself first glow." Like many preservice students, I had strong negative emotions about mathematics. These feelings began to reverse when a teacher caught me with her "glittering eye." She was passionate about mathematics and didn't care who knew it. Her classroom was an adventure—full of activity and insight, providing for investigation, reflection, and discourse. She taught me to take risks and to think deeply about simple things. She engaged my heart as well as my intellect. I was turned on to mathematics for the very first time, and I haven't been the same since. I am compelled to learn and grow as a mathematics educator. Unfortunately, this did not happen in a preservice classroom—but it could have! The preservice classroom is an environment that either nurtures or stunts students' growth as mathematics educators. If you really believe in better mathematics education for all, let it start here.
Angela Giglio Andrews, A.G.Andrews@dcmrats.org, is an early childhood educator and teacher at Scott Elementary School in Naperville, Illinois. She has taught preservice methods courses at National Louis University, in Evanston, Illinois, and was a member of the PreK–2 writing team for NCTM's Principles and Standards for School Mathematics. 
