This blog was inspired by discussions with former students who were enrolled in my Math 4050 class, Advanced Perspectives on the Secondary Mathematics Curriculum. These students were senior math majors at UNT who were within a year of graduating and seeking employment as a secondary mathematics teacher in the Dallas-Fort Worth metroplex. One goal of my Math 4050 class is demonstrating to these future teachers that the lemma-theorem-proof-corollary paradigm that they’ve learned in college-level mathematics courses is indeed applicable to understanding why familiar concepts taught in high school are indeed true. Another goal is filling in the holes in the mathematical backgrounds of my students so that they would be better prepared to enter the teaching profession.

My students told me that they really enjoyed my course and wished that there was a way that they could continue our conversation after the course was over. (One student’s precise words were, “I wish there was a Dr. Q app on my phone.”)

Just what I needed… a really good idea giving me something else to do.

I remember well when I first became interested in the professional development of mathematics teachers. One day, a local high school teacher (sadly, I’ve forgotten his name) was roaming the halls of my department, knocking on my colleagues’ doors and looking for someone who would be willing to answer his questions. He was an AP Calculus teacher and had some questions about the mathematics he was teaching, and so he went to a place where he thought he could get some help. We made an appointment for him to see me, and for about an hour he asked his most pressing questions. (The two that I remember are “Why is ?” and “Why do we teach students about numerical integration, like the Trapezoid Rule and Simpson’s Rule, if they can exactly evaluate every integral in our textbook?”) I answered his questions to the best of my ability, and he thanked me and left.

And then I started thinking about this encounter.

I had a lot of respect for my visitor. He knew what he didn’t know and showed a lot of initiative to rectify these gaps in his knowledge, with the hope that he could become a better teacher after our conversation with this bit of professional development. Then It occurred to me that there must be plenty of other teachers out there that are in similar circumstances but perhaps do not have the initiative to roam a university’s hallway in search of help.

More than 10 years later, I am now directly involved in improving both the quantity and the quality of the secondary mathematics teachers that UNT produces, of which this blog is a natural outgrowth.

This blog does not aim to answer common student questions like “How to factor this polynomial?” or “How do I solve for in this equation?” (There are plenty of excellent websites out there, some listed on my Resources page, that give good step-by-step instructions of such problems.) Instead, this blog aims to address the *whys* of mathematics, providing readers with deeper content knowledge of mathematics that probably goes well beyond the expectations of most textbooks. As well as an audience of current and future secondary teachers, I also hope that this blog might be of some help to parents who might need a refresher when helping their children with their math homework. I also hope that this blog will be interesting to students who are interested in learning more about their subject.

Interspersed with these serious topics will be various anecdotes, vignettes and video clips that I’ve used to engage students in my classes. One of my overarching goals as an instructors is to make my students actually want to come to class, and I try to use humor, applications, and history to achieve this goal.

In writing this blog, I’m assuming an audience fairly similar to my former students who are now my colleagues in the education profession, working in secondary schools in my part of the country. I assume that readers are fairly conversant in the language of mathematics but perhaps (1) have occasional holes in their backgrounds that they’d like to address, or (2) have a good working knowledge concerning a mathematical algorithm or procedure but would like to gain further insights as to why the procedure actually works.

Before going any further, I’ll be the first to say that a deep content knowledge of a subject (like mathematics) is a necessary ingredient to successful teaching, but it’s not sufficient. One of the best fish-out-of-water stories that I’ve ever read concerned an award-winning professor at Harvey Mudd College who decided to spend his sabbatical year as a high school teacher in a large urban school district. He certainly had deep knowledge of his subject but had to navigate issues with classroom management, pedagogical techniques for engaging students, communicating with parents, and a whole host of other issues that are common struggles for first-year high school teachers. (And lest anyone think I’m being critical, I readily admit that I doubt that I would have done much better in similar circumstances.)

I welcome comments from people with all mathematical backgrounds and levels of expertise. I do requests that discussions are kept civil and constructive. Comments that do not meet these criteria may be deleted, and I may block repeat offenders. I will take requests for topics. That said, I am not interested in requests for solving homework problems, but questions inspired by the solution of a homework problem are appropriate and welcome. Also, please keep in mind that I do have a fairly demanding day job, and so there may be a delay in answering even excellent ideas for postings.