Teaching "x = 'why'"

Previously, I shared in this blog the experiences of a Washington Post reporter who went back and spent a year taking high school math. A lot could be learned by returning to the classroom. Having been in a profession offers new perspectives, certainly a new vantage point, to see high school education. These are anecdotes yet useful insights can be drawn from all of these. Another useful immersion has been recently described by Harvey Mudd College professor of mathematics Darryl Yong. Professor Yong spent his recent sabbatical teaching high school math classes in a large urban school district. Yong wrote a wonderful piece describing his experiences as well as his thoughts on this unusual excursion in the Notices magazine of the American Mathematical Society:

http://www.ams.org/notices/201210/rtx121001408p.pdf

The piece illustrates an example of how higher education may be able to help society understand the needs of basic education. For such an immersion to be genuine, it is important that classroom conditions are not altered simply to please a guest lecturer in high school. Otherwise, it defeats the purpose of experiencing first hand what it really means to teach elementary or high school. Professor Yong clearly did not receive special treatment as the following excerpt demonstrates:

...As a final illustration of the kinds of frustration that teachers face, here is an excerpt of a letter I received from my school district a few weeks after the end of the school year.

Dear YONG, DARRYL:
Our records show that you have received an overpayment as a result of a change that was processed in June 2010. The total adjusted gross amount  of your overpayment (reduced by any
retirement contribution) is $12,197.66. This letter is intended to advise you of  your options in repaying the identified overpayment.

The letter was not signed by anyone, there was no contact person listed, and there was no phone number to call! The letter seemed to make it impossible to contest the overpayment; it only listed options for repayment and threatened referral to a collections agency if the amount was not repaid....

Seeing the above proves to anyone without any doubt that this immersion was real and what Yong has to say about teaching in high school reflects a genuine scenario. What he describes in his piece is therefore worth our time. His reflections provide a deeper vision of basic education seen through the eyes of a professor in mathematics. And here are the main points, which he appropriately calls lessons, that he raises in his essay:

• Basic education schools are complex. Even this is still an understatement. When schools fail, explanations (or excuses) offered are usually too simplistic, thus, depriving society the complete view to address properly the problems. In the Philippines, the old ten-year curriculum described as congested has been pinpointed as the main culprit in the poor state of basic education. The explanation, however, is more of a justification to go to K to 12, than a sincere and in-depth examination of the situation. These are excuses and are no different from knee-jerk comments made by high school teachers regarding how poor they perceive elementary school education is. As Professor Yong writes, "Simplistic diagnoses are dangerous because they encourage quick fixes. Instead of long-term plans for systemic change, school reform becomes a series of short-lived fads that cause teachers to become jaded by unfulfilled promises of improvement." This explains in part why reform after reform, problems in basic education remain. 
• It helps to have a teacher who has mastery of the subject content but this is no guarantee for high student learning. Yong cites a study made by  Hattie (John Hattie, Visible Learning: A Synthesis of over 800 Meta-Analyses Relating to Achievement, Routledge, 2009.) that shows that a how a student views himself or herself with regard to the subject counts significantly towards the learning outcome in that domain. If a student begins with a perception of weakness in mathematics, this has serious implications on the student's performance in math. Thus, if student's performance correlates with what we perceive as high quality teaching then effective teaching must be able to address and correct a student's preconception of the subject. Perhaps, this is a major difference between an effective and an ineffective teacher. The following excerpt from Yong illustrates this vividly:

I initially spent a great deal of time thinking of fun or creative lessons that would get students excited. These lessons rarely worked because they were often too complicated or inappropriate for my students’ mathematical development. Instead, I began to design my lessons and accompanying student work so that (1) all of my students could successfully complete the first problem or task independently, and in which (2) the sequence of problems/tasks matched my students’ tolerance for challenge and self-concept. 

This strategy not only increased student learning but also eliminated most of the discipline issues in my class and relieved the pressure of having to develop whiz-bang “fun” lessons every day. 

• There is a great need to understand correctly what the teaching profession entails. No different from the practice of medicine, the teaching profession is an ongoing learning. Only with the realization of the emotional, physical and intellectual demands of teaching, would society understand and begin to truly respect teachers. If society treats its physicians in a similar manner as teachers are currently treated in the Philippines, for example, one could only wonder what will happen to the quality of health care and medical services.
• The last lesson Yong shares is that the "Written curriculum does not matter." What matters is what actually occurs inside the classroom. In this respect, the teacher serves a central role.

Yong's experiences are rich with insights and I invite everyone interested in improving the state of basic education to read his article.