Test-Correct-Recall.... for the mathematics teacher.

First off, I will not take credit for creating this method.  I learned this method from Greg Jacobs, a Physics teacher and all around great person from Woodberry Forrest School.

The first thing you have to make sure you have for this method is a strong rubric set up for all questions.  Most of my rubrics are based off of AP rubrics for Calculus AB and Physics B; meaning they are measuring specific skills, including the ability to explain mathematics and to set up the appropriate equations and situations.

After the test is created and all rubrics written, the students take the test.  The test is graded strictly on the rubric.  The important thing about the rubric is students can only loose a point once, meaning if they make a mistake early on, but do all of the mathematics correctly from their on out, they only are penalized the one point they missed (even if the final answer does not match up).

After the test, all of the students to corrections.  I give them a simplified rubric so they can see where they missed the points, then I give them some short questions to answer based on the original test questions.  In order to earn credit for their corrections, then they have to correct the original question and answer the shorter questions given to them.

Finally, a few days after the corrections are completed, I give a brief recall quiz based on the test.  This quiz focuses on the fundamentals and less on the calculations, and acts basically as a solidifier to commonly missed concepts.

Curve Sketching in AP Calculus

In the past, I have taught strictly the curriculum when it comes to curve sketching.  The AP exam has deemed that students should be able to look at a graph and identify aspects about the derivative or the original function based off of the given graph.

This year, I decided that instead of just looking at graphs the entire time and identifying information from the graph that I would go through the entire process of curve sketching.  So far, the students seem to be reacting well to this set up.  We have spent the past few days creating tables to allow us to graph the original function by identifying aspect of that function from the first and second derivatives.  Tomorrow I get to see the payoff, as we will be looking only at graphs and identifying (and graphing) straight from the given graph.

Lets see if this works!!

The First Day of AP Calculus AB

All students deserve a little bit of respect, especially from their teachers.  If these students are AP or Honors students, then they definitely do not need to feel patronized, especially on the first day.

Many teachers use the first day to go over the syllabus, which can create a stagnant environment, and worse, a lost teaching day.  In all of my classes, I start teaching a full blown lesson on the first day.  My goal with this approach is two fold.
1)  Set the pace that the material will be covered at instantly
2)  Show the students that I think enough of them to understand that they can read.

Below is how my first day of AP Calculus AB is structured.  Keep in mind, that I am teaching in a 45 minute time period.
1)  Hand out syllabus and review the honor code (required at the school I teach) roughly 5 minutes
2)  Numerical approximation of limits (tables generated by hand and via calculator) 40 minutes

The numerical approximation of limits is done via a student activity, which is concluded with a class generated definition of a limit.  In this process, I have also set the expectation of where all numerical answers must be rounded (3 decimal places for AP) and given a rough review of basic algebra skills.

Normally, the students are excited at the end of this class, though they are not happy with the homework assignment (generally 5 questions... I mean really, why complain).  The next day they have a short quiz to start class (error analysis with a justification) and we move forward to graphical determination of limits.  All and all, a quick start to a new year.