This winter/spring semester I've had the privilege of teaching two math courses to a hard working group of nurse's aides who are gearing up to enter the community college in the fall. As one might assume the students are at different places in their understanding and knowledge of math, yet work together quite well in the small group formats that comprise each of the two classes. It has been a stunning experience for myself as well--someone with more than a bit of perhaps well deserved math phobia who yet stood up when the opportunity to teach these courses opened up to me--an opportunity that perhaps many administrators would be reluctant to give me because of lack of formal experience in teaching math or significant formal educational training in the field. I spent over an hour almost every day in December and January beefing up my knowledge of math, starting with basic algebra and working backwards.
I experienced a good deal of frustration in the process and was stymied for what seemed like long periods of time learning how to compute prime factorization, least common denominators, greatest common factors, and even more, trying to figure out what role their function served. I eventually did get some eureka moments, but had put in some serious sweat equity to get there. I struggled with other basic computations also like learning how to subtract negative numbers and realizing finally that there were two steps: changing the subtraction sign to an addition sign and changing the second integer into its opposite. I couldn't for the life of me figure out that to subtract 7-2 really involved 7+(-2).
By show time I was finally at the level of knowledge that I felt confident teaching, feeling as well that I gained a concrete appreciation for the struggle that my students also experienced as they sought to learn "this stuff." What I learned as well is an appreciation both for a knowledge of the steps in working through various computations as well as an understanding of some of the thinking that went into such problems. This, along with the importance of pacing, giving a chance for each student to learn at her own rate and to experience a sense of empowerment in the process. I can't say that my teaching was always successful in establishing viable methods to teach the course content, though attention to the learning eneds of my students were uppermost in my mind.
What also stood out were persisting limitations, not in the sense of not being able to present in reasonably appealing ways the content focus of our lessons, but in the capacity to reach inward as deeply as I would have liked to both understand and explain why any given rule or procedure pertained. The underlying impulse prompting this thought is the seemingly paradoxical reflection that the more abstractly and comprehensively an instructor understands the "deep structure" of a given procedure or mathematical rule, the deeper is that person's pedagogical repertoire in providing a potentially broad range of cogent explanation. That may be the case, I would add, with someone who is reasonably attuned to the specific range of learning needs adult students have and can create a bridge between deep content and the learning challenges of specific stuents. This capacity is not necessarily a function of deep knowledge possession in itself, which, without effective pedagogies could lead to a distancing stance where the educator's very knowledge would very wellfunction as a barrier to facilitate a climate of engaged learning.
In my case I knew the materials sufficiently well to establish an engaging learning climate in our class room for most of the students most of the time. Yet, I could also sense there were levels of explanation desired by some students in some cases to which I was unable, or perhaps at some level unwilling to stretch deep enough in my own understanding to provide either the mode of explanation or a concrete enough example to bring a potentially "teaching moment" to fruition to have opened up a "eureka moment" within a particular student. To be sure there is much more for me to learn about the world of math, especially now that I have more of a taste for it, which I did not previously possess. Overall, the course has been a memorable learning experience I think for the students as well as myself, in which among a sense of seriousness, fun, has characterized our class encounters.
In these respects the the math course was much more than I anticipated would be the result when I took my initial preparation steps in December and January with much trepidation. It was, in the final analysis, as much as I possibly could have wished for and learned that I could be both successful and invigorated in the process. Thanks to my students and those administrators and a very supportive wife who had faith in me even as I doubted myself.
Adult education--you gotta love it!