Teach 180: 14% (Day 130)

On Thursday, seven of twenty-two students didn't take the AP Statistics test that was scheduled for that day.  Absenteeism and apathy among my seniors is rampant.  If I recall correctly, I gave 13 of my seniors incompletes for the current reporting period due to work not being turned in or an assessment that had not been taken yet.

Some of the students have missed multiple days of class and the fact that they had to learn half of the current chapter via screencasts on snow days did not help.  As a stat teacher, it made sense for me to gather some data.  The table below shows the overall average percent absence was 14% over the past two weeks.

A lack of "touch points" has been a problem for many teachers this year.  One Algebra 2 teacher in my department greeted her students on March 26th with "Who are you again?"  She hadn't seen the students since March 9th due to days when she wouldn't normally meet with them, spring break, snow days and the standardized testing day.

Our math departments (middle school and upper school) will be meeting on April 19th to discuss what we have chosen to leave out of our curricula this year and the impact it will have on students as they move through the sequence of math courses.  In future years, we may offer AP classes in math, but we may no longer have any time to review before the AP exams.  This will be especially true if we need to take content from lower level courses and move them into upper level courses.  Our current bell schedule will be the death of our AP math program without a coordinated, major overhaul of the curriculum in the next two years.

Teach 180: Bounce Off! (Day 129)

One of the things I love about our new schedule this year is that I have more time to spend with my advisees.  They are seniors this year.  As college decisions come in, I can sense them starting to relax.  Today in advisory we spent about five minutes discussing the assembly period from the previous day. Then, we played a game "Bounce Off!" (Thank you AP Stat Secret Santa for the gift!)

     

Students read the rules and then decided to make their own rules.  The rules became modified as we played the game for a nearly 30 minutes.  After the first game, they were laughing and having so much fun that I decided to join them.  There wasn't much math involved in this game, but it did get me to thinking math-related questions, like "What is the best bounce height?", "What is the best bounce angle?" and "What is the optimal distance from the board?"   These questions will need to be saved for another advisory meeting.

Teach 180: Discovering the Antiderivative (Day 128)

Today in Calculus students were introduced to the idea of the antiderivative.  I wanted them to discover how to take the antiderivative of xⁿ where n ≠ -1.  In addition, I hoped they would discover the reason why +C is necessary when finding an indefinite integral.  I began by having students fold a piece of paper into thirds.  On the top third, they wrote a polynomial function of their choice.  On the middle third, they wrote the derivative.  Then, I had them fold the paper in such a way that the original function was inside.

Next, students traded folded papers with their neighbors and were instructed to find the original function - the one that was now folded inside the paper.  After they had written down what they thought f(x) was, they were allowed to open the paper and see if their function matched the original function.  Here, you can see a sample paper.

This led to the discussion of three main ideas.  First, did you get an exact match to the original function?  If not, why not.  If the original polynomial function had a non-zero constant term, then it was very likely that there was not an exact match.  This led us to adding +C to show that there could be constant added to the end of the original function.  Tomorrow we will consider this as a family of functions.

Second, how did you actually figure out the exponent and coefficient in front of the exponent when you were trying to undo the derivative?  What procedure did you use?  Most groups could articulate adding 1 to the exponent.  But only two groups were able to describe dividing by the new power.

Finally, we looked at why n ≠ -1 when we wrote our general rule for taking the antiderivative  of xⁿ. What would happen if we added 1 to the power and divided by the new power?  Raising a number to the zero power isn't a problem, but dividing by zero IS a problem.  It was at that point that a student recalled that the derivative of ln(x) is 1/x.  So, the antiderivative of 1/x would be ln(x).