I want to start with three areas for improvement. There are always ways to do better. When I later look back at this self-reflection, I can consider how well these goals were achieved and whether my next set of goals in the future build off these.
1. Some students do not use the textbook enough. They need more incentive to do the self-graded odd-numbered homework problems. I want to try devoting the last few minutes of class to group work on these textbook problems. I can start this routine after the first midterm, once students have formed study groups and have become willing and ready to work well in groups.
2. Each term I spend some class time sharing real-life applications that are extensions of the class content (saving, investing, confidence, etc.) There is enough time for this. But I would rather exchange that time for group work (as above). I should write out these extra-curricular topics as essays for optional student reading at home.
3. When I checked the Kahn Academy site about a year ago it started with Math 60 topics. I recently noticed that Kahn Academy now has many videos for Math 20 topics. After mentioning the Kahn Academy site to my students, I did hear that several benefited from those videos. I have begun to add links to these videos, topic by topic, from my own class website. Most of this work still needs to be done.
I have written elsewhere about how I have revolutionized midterms. Before the test my website provides test-taking tips and supplies an infinite variety of randomized practice tests. During the test students work alone for the half the time and in groups for the second half, using computers at the very end to check their work and do reflection on how to study further. Midterm days are taken seriously but are less stressful. They end happily because all students leave the room with greater math understanding and self-awareness than when they arrived.
I have also written elsewhere about how this past term taught me about adding into the syllabus explicit expectations for values and attitudes. This might seem idealistic or tyrannical, yet as with group work during midterms I have found it can work if handled in a specific way, with proper timing and discussion.
During the Fall 2015 term I transformed my old Math 25 workbook into a Math 25 section of my math website. When I taught Math 25 in Winter 2016 it worked great.
Kathy's faculty Winter 2016 observation is also part of this instructor assessment process. She noted most of the things I do well while teaching.
Many of my strengths are structures and habits I have established to ensure I am always teaching at my best. I arrive at class early, start class on time, have routines about reviewing old material and transitioning to new topics, and teach from prepared notes (non-linearly when student questions prompt topic shifts). The way I write example problems involves a bunch of careful habits: how to format the problem on the page, how to use color, which details to narrate aloud, and what annotations to add for clarity when the page is used as a review reference weeks later. After class I send the students e-mails that summarize the topics covered, remind them about assignments, and if appropriate include copies of the day's board work.
Other strengths are a natural part of my personality. I am calm, yet enthusiastic and optimistic. I am helpful and patient. The students, who are initially as fearful and shy as any remedial level math students, assimilate these traits and soon handle math better in class, at home alone, and when doing group work. Kathy noted that I am comfortable with the students and they are comfortable with me; both are indeed true.
Some strengths I have worked hard to develop. My pace, volume, eye contact, and all-inclusiveness are the result of years of practice. My expertise with the math topics includes not only lecture organization but knowing in advance which details are predictably confusing, and which explanations are clearest. Much time and energy has gone into my skill with computers, fluency with the Starboard software, and composition of an extensive math website.
Kathy described the students as "quietly attentive". This is true most of the time during lecture. I think I know why.
I emphasize from day one that being Good At Math is a set of habits and study skills that anyone can learn. I assure the students that they will develop these habits and study skills: my demands will be numerous, but always explained in detail, exemplified during lecture, and clearly listed in written rubrics. During lecture I highlight how those habits and study skills avoid confusions and aid efficiency.
So the students start the term with their usual expectations of jumping through hoops because of how the instructor is picky when grading assignments, but quickly learn that the hoops are present not from my biases but because doing math well looks like that. The result is that students are agreeable—even quietly eager—to learn to mimic my methods and learn these ways of doing math. The ambiance of calm scrutiny reminds me of my past Tai Chi lessons. It is the same focusing on both what material is taught and the way the instructor moves through the material.
Kathy commented that the "calm enthusiasm" was palpable but mysterious. I should try to explain further how I cultivate that mood.
First, consider these four comments from a recent class evaluation form:
David relaxes students with quirky fun announcements, relating to them, and making ridiculously good waffles. He also allows students to revise homework as much, and whenever, they like in order to gain their best score. Some tests are done partially in groups, so if you're feeling unsure about the way you are working out a problem, you are able to review and revise with classmates-which is very helpful.
The instructor encouraged us to make mistakes and learn and fix those mistakes to learn more effectively.
It encouraged students to try their hardest and keep on trying.
Encouraging us to ask questions and how you go over EVERYTHING.
The common theme is that class time is relaxing because there is work but no worries. (Math time at home still has worries, especially having enough time each week to devote to the homework!) But during class all questions will be answered. All homework studying will be rewarded. All test confusions will be resolved. All mistakes are learning opportunities. All tries are valuable. Everything is explainable and understandable.
Second, consider these comments from e-mail and class evaluations:
> I really appreciated your patience and kindness
> this term. It was my first math class since
> high school and I was really nervous. Again,
> thanks for a great term.
He taught me how to do the math. Didn't really think I would learn it.
Great teacher good personality, won't give up on you.
I have confidence the students can succeed. They often initially do not have this confidence. Yet when they see that I can teach "how to do the math" and not just the math topics themselves, that quietly attentive mimicry begins and they slowly grow to share my confidence.
A third part of "calm enthusiasm" is revealed in these two e-mail exchanges, e-mail comment, and class evaluation comment:
>>> Here is my homework code. 3mFUJMUHNRQJNMtBQa3
>>> Please let me know how I did, thank you.
>> 13 out of 15, which probably ranks somewhere
>> between "Excellent" and "Snazzy", you decide.
> High fiving myself
> I am succeeding. I have learned a lot and
> totally eliminated my fears of mathematics
>> Thank you for all your good teaching! It made
>> such a difference. I'm not scared of math
>> anymore! That really means a lot to me.
> Hooray!...now it is time for math to be scared
> of you!
> Thank you for all you put into making our math class understandable, interesting and fun.
He was instrumental in helping me to think of math as a potentially fun subject.
Class is fun! New things are hard, and hard things are scary. But the newness is temporary, and so the scariness is temporary. It feels great when something previously scary gets mastered. The rewards of hard work are not only earning a nice grade, but enjoying how the math itself becomes fun.
The English language does not have a word that combines relaxing, confident, and fun. So the adjective I hear most often is the generic and trendy "awesome".
> Thanks so much for being an awesome teacher!
> Thank you for being an awesome teacher! I hope
> I have you for my next math class!
> Thank you so much for being awesome.
I particularly love these comments because they always come from the students who did well with that quietly attentive mimicry. In ten short weeks they grew from being afraid of math to being Good At Math by learning both what to do and how to do it well. When they say that I am awesome, what they really mean is that by copying me they became awesome in a new way.
Some students worry that their newly acquired math awesomeness is somehow connected to me, and not intrinsically theirs.
>>> Do you teach math 60??
>> Nope. Math 20 students need me. You get to
>> move up, I'm stuck at Math 20. ;-)
> Nooooo!!!! I need you.. bahumbug
That worry is unfounded. I check in with those students when I see them around their later math classes. They do fine.
> This has been one of my very favorite classes,
> probably since grade school.
> You were one of my favorite and most effective
> math teachers.
When you leave this class you will wish that you could take more classes with him as your instructor.
He was by far the best teacher. He explained everything clearly and when you needed help he was always so helpful in going over problems until you got it. I wish more teachers were like him.