## Reflections after the first week

I just finished Reluctant Disciplinarian by by Gary Rubinstein, which sums up my own inclinations toward being a “softy”.  The things I take away from this book include:

• Start the first few weeks of class with lessons that have clear expectations for students and, in my case, may be similar to what students are used to.  This sets up the students for a minimum of culture shock.  To this baseline I can slowly add more pizazz.  The time that I have spent “substituting” for my CT have been a convenient baseline.
• Be mindful about over-talking and over-sharing.
• Criticize one’s own lessons with a list of “cons”.

My tendency is to become so absorbed by the content and zany lesson that I forget to respond to student needs.  Any misbehavior is then so shocking that I deal with it too publicly, thereby alienating the rest of the students.  I have seen firsthand how a “softy” becomes the “mean teacher”.  I have also seen that it is possible to improve, and so I hold that hope going into the next week, the beginning of which my CT will again be gone.  I will have to prepare the students for an upcoming test.  Reviews are always hard for me to do well because every student has different needs.  I know that the students will be expecting a review game on the last day before the test, so I hope that my CT was able to put something together.  If not I will have to invent something.

This Monday is also the first day of official classes for my University.  I wouldn’t be so worried by this, but I am also studying to take the Praxis Secondary PLT this Saturday, and it has been quite some time since I took Educational Psychology.  I’m finding that the questions are IMHO so poorly written that the right answers are flawed, which leads me to reject them and try to find truth in another answer.  As a result, I’m not doing so well on the practice questions, so I will need to put in quite a bit of studying all week.  If anyone from ETS reads this, I suggest that rather than rewarding the top 15% (for Excellence!), you reward the top 5% by refunding their testing fees.  If you offer to refund even other materials (like your lousy online review course with terrible questions), you may even encourage more people to buy those.

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Due to an unexpected event, my cooperating teacher had to leave for a few days, putting a substitute in charge of the class.  Thus begins my student teaching!

On the plus side (opposite the minus of being unprepared), my CT has already prepared lessons, which will give me the chance to teach in a similar manner as I get started.  This should make the classroom management situation a little easier.

## First non-professional-development day

Yesterday was a semi-productive inservice day.  None of the inservice topics were new to me, but we were tasked with improving on a previously written lesson using differentiated instruction.  Seeing as I had no previously written lesson plan, I assisted one of my CTs with improving one.  I plan to try to write one later using differentiated instruction methods to satisfy the principal’s call, but I haven’t yet selected a topic.  Although I agree with differentiated instruction in principle, I find myself getting anxious over a tendency to cater to each student’s preferred modality rather than build on weaker ones.  Surely some balance in this dialectic exists?  Perhaps even synthesized into a harnessing of group diversity to advance individual learning à la Japanese mathematics?  I like the idea of improving stale lessons, but the process lacks the accountability and collaboration of lesson study.

Today was the first day with students.  I assisted only in a minor capacity while trying to learn student names, something at which I am exceedingly bad.  The day, however, passed without incident, so I shall use the remainder of my evening to make some flash cards to help me learn student names (and for later when asking questions).  The one thing I will note, which carries increased salience now that I have read The Teaching Gap and its comparisons with Japan, is that there were an aweful lot of interruptions to class today.  The teaching could not help but be fragmented, though the teachers did the best they could.

I’ve also pondered over the last few months the many ways to teach factoring.  With a general quadratic trinomial $ax^2+bx+c$, the ac-method usually results in numbers that are unnecessarily big.  Instead, I start from separate prime factorizations of a and c.  This builds on the idea of natural numbers being “bags” of prime numbers (the “Bag Model”).  Just like the guess-and-check method, this one takes practice.  It’s similar to the X-method but different.  I haven’t settled on one form yet and have developed a filtering-based approach (only using prime factors indirectly to generate factor pairs and much like the X-method) and a “spin” approach that is visually appealing but not helpful.  This got me into a digression on the combinatorics of “possible” factorizations based on the first and last terms, which turned out to be more complicated than I thought.