Three Goals

In addition to content mastery, these are the three goals I have for all students enrolled in AP & College level math at JHU CTY Online.

1. Improved articulation of mathematical thinking. 
2. Realizing there is no shame in asking questions.
3. Ability to find and use resources external to those directly provided in-class. 

(1) Many students enter calculus with a phenomenal ability to perform complex calculations in their heads and then write the (often correct) answer on the page without any indication of what thought process led them to this (often correct) conclusion.  I applaud and am impressed by this ability, but in AP & College level math I design my problems to have more than one solution and I want my students to be able to clearly articulate how exactly they arrived at theirs.  I wrote up a short "guide to mathematical writing" to help students understand what is expected of their mathematical writing. For example, in AP Calculus, I ask that students "explain all of your calculus reasoning, relevant algebraic steps, interpret your answer in the context of the problem, and don't show arithmetic please." I encourage students to use LaTeX, as many of them often go on to study a field of math, science, programming, or engineering. (here is the LaTeX starter guide and videos I created for them).  

(2) Asking questions is generally stigmatized (I blame awful legislation such as NCLB which forces teaching isolated facts on irrelevant tests) but among bright students it is even more of a social stigma. For a student who identifies him or herself as intelligent, it can be difficult to admit that you may not know something and having to ask someone, anyone, a question can be (internally) viewed as a weakness.  Of course, this is incorrect, but the myth persists and I always try to bust that myth whenever possible.  I ask students what software they are using, what programming languages they are studying, or what books they have ready or music they have listened to lately and let them know when "I've never heard of that before!". 

(3) Often a student will ask me a question only after they've read this or that section 20 times over or watched this or that video the same number of times and they still don't get it.  At that point I am glad to walk them through where their current understanding is, then give them a different perspective on the problem and they usually have an "ah-ha" moment.  I use that moment to explain the notion of using external resources -- if your book or video isn't doing it for you -- find another one!  I even built an entire website based around this concept.  Learning how to find and use external resources is a skill I wish I would have learned sooner, so the earlier I can get it to my students, the better off they are.

By the end of their class, many students often say that they felt truly challenged, but rarely frustrated, and that they feel glad that they can find a way to express all of the awesome mathematical ideas which have always been buzzing around their brain via graphs, LaTeX typesetting, animation/video, etc.  and that they are better able to avoid banging their head against the wall through focused searching for extra resources and not being afraid and/or ashamed to ask someone for help.  

Getting students to this point requires building a good rapport that is based on regular communication.  I take pride in the fact that I and my staff have success with this approach and that we are continually striving to get better.  

Thank you for reading and if you have any comments, questions, or concerns, please feel free to contact me!  

Twitter @mathteacher1729

My student resources website