A blog advocating autism through my own personal experiences and insights.

Archive for the ‘School’ Category

My First Teaching Experience

As I mentioned before, this past summer I taught my first course. The Pure Math Department at the University of Waterloo offered me such an opportunity last January to which I accepted. I was very pleased because I had been waiting for such an opportunity since it’s usually the case that pure math PhD students at Waterloo are offered such an opportunity before completing their degrees. I had done well so far in the CUT (Certificate of University Teaching) program that the university offers to its PhD students and have explained my positive experience in this program in Learning How to Teach (I have since completed it). I had done two guest lectures for a couple of courses where one of my PhD supervisors was the actual instructor and they had gone well. I was also pleased that that the course they offered me was a third year pure math course in Elementary Number Theory, which is my research speciality and one of my favourite mathematical subjects.

The course was set to begin in May and run through August where I would be lecturing three hours per week for about 12 weeks. I did prepare a lot beforehand though and spent a lot of time preparing a course outline and lecture notes. I managed to get a lot of resources from another PhD student who was teaching the course that winter, including various lecture notes and sample midterms and exams from him and various professors. I also got a textbook on Elementary Number Theory out of the university library that I was familiar with and that I liked and that contained almost all of the material I need to cover. I ended up basing most of my lecture notes out of the material in this book, the rest out of the sample lecture notes. By the time it had come to actually teach the course I had done up all of the lecture notes and had put together a first assignment. I felt pretty prepared.

As I taught the course, I used my lecture notes in a bit of a unique way. As the weeks went by, I would post the relevent lecture notes up on LEARN. LEARN is a website that a lot of professors and instructors at Waterloo use to organise their courses and upload course materials such as course outlines and assignments. My own lecture notes consisted of all of the material that I would cover, but with a lot of blank spaces. For example, a short proof of a minor result I would leave blank and for longer proofs I would write down a few steps of the proof and leave the class to fill in the details. The idea here was that before each class the students would print off the lecture notes, take them to class, and fill in the rest as I went through my lectures. As a student and instructor, I felt that such a strategy minimizes the amount of writing students need to do during the lecture, while maximizing the amount of listening and participating they do to help them get a stronger grasp of the material. As a student, I was in a class before where the professor used exactly this strategy and found tht it really helped me follow along, which was why I decided to try it out. I was pretty pleased when this strategy seemed to work and that a few students even printed them off to follow along. In my course evaluations, some students even praised this strategy. I will therefore continue to use this strategy for future courses I teach.

The first day I lectured, I was pretty nervous. It did, however, go very well and I looked forward to the next one afterwards. After each subsequent lecture teaching came more and more naturally to me. I also used various other strategies in my lectures that I learned from being in the CUT program. For example, I used the teaching method think-pair-share to give students a chance to apply what they have learned without having it be formally graded. Think-pair-share is a strategy where the instructor poses a problem that can be solved in a couple of minutes to the class. The class tries to solve the problem, and then spend another minute conversing with a partner on their answer to the problem. Also, one time earlier on in the course, I used the one minute paper method, which is a strategy where the instructor hands out sheets of blank paper to the students, giving them a prompt relevant to the material covered in that particular lecture. The students’ answers are not graded. Rather, the instructor collects them and picks the three to comment on without revealing the authors. Here I used the prompt of asking them about the most confusing part of the lecture. I then looked over their answers and spent the first few minutes of the next lecture answering three of their questions thoroughly.

Overall, my first teaching experience was a real success and I look forward to doing it again.


Learning How to Teach

Having laid out my plans to continue on in academia after my PhD, I have become aware that there is another set of skills besides good research ability that I need to have and that is teaching ability. Back a few years ago, it was common for potential professors getting their PhDs to not get any training in teaching at all, but simply to learn as they went along. Some succeeded in this way, while others not so much. There is a big difference between being an expert on a certain subject and having the skills necessary to teach it effectively. Fortunately, however, more and more universities today are recognising that actual training in teaching and not just becoming knowledgeable in a subject area is a good idea to set up for future potential university professors. The University of Waterloo has certainly recognised this need and has set up two programs for graduate students to take if they wish to make teaching part of their careers. One of the programs, The Fundamentals of University Teaching, I completed this past summer and the other, The Certificate of University Teaching (CUT), I have just begun this fall. These programs are run by the Centre of Teaching Excellence who greatly encourage any graduate students to take them if they wish to continue in academia. The former is a program that any graduate student can enter into. It requires attending at least six workshops where we learn different teaching methods and styles. It also requires giving three microteaching sessions.

Ever since entering my PhD, I’ve always known I would like to be an instructor of a course before graduating. I have spoken of this desire with the pure math department, and one of my supervisors has let me step in for him as a guest lecturer in two undergraduate classes he’s teaching in the past couple of weeks. The experience was a little anxiety provoking since I’ve never taught a full class period before, but it went reasonably well both times. The first time I did it, he supplied me with the notes that I would teach from. He sat in and provided me with great constructive feedback afterwards. The second time he only gave me a topic with which to teach the class and let me write up all the notes. He reviewed them the day before I would be lecturing and said they were all right. My second supervisor then attended the lecture and said afterwards that my teaching went really well and that I had improved on a couple of things that my other supervisor had noted about the first time, such as my use of whiteboard space. I asked a lot of questions to the students during the lectures to help keep the class engaged, which seemed to work each time. I also experimented with a learning activity that I learned in the teaching programs, which is called a one minute paper. This is where at the end of the lecture I got the students to write down anything confusing on the topic. I also made the second lecturing experience part of my CUT program in so far that I got a staff member from the Centre of Teaching Excellence to supervise my teaching as well.

While still no concrete plans are in place in my teaching a whole course, I know I’m on my way to making this happen. I have proven myself as an excellent researcher within the department and I am now proving myself to be good at teaching as well. I just have to be patient and let things unfold.

A Switch in Passions

I have experienced a change in myself over the last half year that has caused me to reassess my life and where I’m headed with it in terms of goals, ambitions, etc. As I have elaborated throughout this blog, I have three large passions that I’ve rather built my life around: math, philosophy, and fiction writing. In the last half year, however, I have found that one of these passions has intensified, but that the other two have waned. While I am unclear as to why this occurred and whether this is anything temporary or permanent, I do feel the experience is worth sharing.

I’m currently completing a PhD in pure mathematics. When I entered the PhD program, however, I was fully aware that my other academic passion in philosophy was just as strong, if not stronger. As such, I considered doing a second PhD in philosophy after being done with the math PhD. I knew I had to make my applications as strong as possible to go for a graduate degree in philosophy. I had, after all, only done philosophy as a second major in my undergrad and did one graduate philosophy course during my master’s in pure math and wasn’t sure how this atypical philosophy background would be looked upon. As such, I made plans for making time to take some philosophy courses while completing my math PhD. I first, however, wanted to complete the major requirements for the math PhD including the course requirements and the written comprehensive exams before I attempted additional work in philosophy. It took two years for me to complete these requirements and afterwards, during last summer, I made plans to take another graduate philosophy course.

The strange thing about this was that when I signed up for a graduate philosophy course I felt I was only taking the course to strengthen my application. I wasn’t sure how passionate I was with philosophy at the moment, but I also knew my chance in taking philosophy courses was limited and so I signed up for one anyway. While the course was good and interesting in its own right and I did quite well in it, the more the course went on the more I realised I was no longer feeling passionate about it the same way I used to. The experience was rather surreal. It’s hard to describe, but I didn’t and still don’t, feel like the same person I was when I was very much into philosophy. I know for sure I was still passionate about it a year ago, and it’s hard to explain why the passion waned. During this third year in my math PhD, however, my mathematical research has picked up and I’ve made a lot of progress on two separate projects, both of which I’m very excited about and that I feel has led to an increased passion in math. As such, I ended up deciding to continue on in math and try to obtain a post-doc position in math afterwards, rather than going for another degree in philosophy.

My passion for writing fiction has also unfortunately waned. Like philosophy I cannot explain why this would be so and that I certainly felt this passion a year ago. In fact, I was feeling it up until last September. Last summer, I was doing a bit of research and plotting for a novel I was going to write. Yet, when October came around, it unexplainably vanished. Of course, I was busy not only with my PhD then, but also with the philosophy course I mentioned above. I therefore thought that it would be pointless to try pursuing writing at such a time regardless and thought I would attempt writing again this winter.

Winter has come and gone and very recently I tried to see if my passion for fiction writing really had waned. Even though I still didn’t feel like it, I forced myself to sit in front of my computer for on average half an hour per day for two and a half weeks to see if this passion could be recovered. I was coming up with a lot of good ideas for my current novel and didn’t think I was experiencing writer’s block. Unfortunately, much like with the philosophy, I felt the passion in plotting a novel had just been stripped away. After two and a half weeks was up, I thought it pointless to continue since I had hardly been feeling it for the time I wrote.

Again, I cannot explain why a 10 year old writing passion would suddenly disappear. My mind could just very well be caught up in my math PhD research for the moment and sub-consciously casting these other endeavours to the side or it could be something more permanent. If, however, I feel that philosophy and fiction writing are not suitable to pursue at this point in my life, then I won’t be pursuing them, at least not right now. If, later on, they come back, then I will act appropriately. For example, I could pursue a graduate philosophy degree later in life or somehow squeeze my way into a philosophy department after becoming a math professor. There have indeed been a number of philosophers who have started off their careers as mathematicians. As for writing fiction, that is something that has almost no constraints. All I need to do if the passion comes back is to pull up Microsoft Word on my computer and write. It all comes down to trusting your instincts to tell you what’s right for you and to be prepared to have regrets along the way. People change, people switch careers and endeavours, and have interesting life paths. As I have learned from this experience, even a passion that you can have for a long time and feeling that it has defined who you are can change.

I do miss my philosophy and writing passions and do wish I still had them. It is like having a desire to desire something. It took a bit of time to accept that this happened, but I also feel it has led to a new level of self-acceptance for me. Also, it has currently made time for other things, such as reading, doing Zumba, planning things with friends, which are things I still enjoy.

Tribute to my Nazzer Grandparents

This fall has been quite an eventful time for me. For starters it has been one of the rougher school terms for me, but I still made quite a bit of progress in it (more on that in the next blog post). On the other hand, however, one of my grandmothers passed away, which happened at the end of October. My family was able to fly me home for a memorial service we had for her in early November and I got to see a lot of family I didn’t normally see regularly growing up (everyone on my mother’s side of the family lives quite a distance away). It still seems only yesterday that my maternal grandfather passed away in Summer 2005. My Nazzer grandparents lived very near us and, as such, they were an important part of my childhood. I gave speeches at my grandfather’s memorial service when I was only 16, then at my grandmother’s 90th birthday party 4 years ago, and then again at her service this fall.
My relationship with my grandfather Don Barkeley Nazzer was a really good one. For one thing, we both had intellectual minds and we would talk about math and stuff (he was a civil engineer). When I was 12, for example, I started exploring my grandfather’s books and he ended up giving me quite a few intellectually stimulating books. In one of the books he gave me (if you really want to know what the book is it’s Mathematics: A Human Endeavour by Harold R. Jacobs) he even wrote inside the cover
“This book is now the property of John Charles Saunders. From his grandfather, Don Nazzer Dec. 26, 2000. Enjoy it!”
Looking at this handwritten note today is what helps keep his soul alive inside me and knowing how proud he would be of me if he could see where I was today. Back then, as well, I was very interested in antique calculators and I started to collect slide rules. I was fortunate enough that my grandfather had two of them that I got and still have in my possession. I also had other fun times with him. When I was a kid, my grandparents had bought me a lego set for my birthday. I wish I could say that we had built it together on that day, but I actually just let him build it first and I sat behind him, occasionally looking over his shoulder. Also, when I was a teenager he taught me how to use a ride-on lawnmower for mowing the grass at their summer place.
I also look up to him, as well as my grandmother, for their healthy lifestyles as well and how independent they both were until each of them passed away. My grandfather’s passing was very unexpected even at his age of 86 ½ and when he was in the hospital from multiple heart blockages the doctors were very impressed with how healthy a man he was. The only possible sign would be that my grandmother had gotten a little more dependent on people during the last year of her life, but she was still living alone inside her own house even up until her passing two months shorts of her 94th birthday (which would have been today and more amazing still my other grandmother who’s still around is still living alone inside her own two-storey house at 97 so I certainly have some very good genes!). I feel it’s the way we should all go, living life to the fullest until it’s time to go.
My relationship with my grandmother Margaret Irene “Sunny” Nazzer was also good, but it was a little different. She certainly loved me just as much. I’m glad she lived long enough to see me now and was always proud of my accomplishments and my intellectual mind. Unlike my grandfather, however, she was an extrovert (which I like to think is at least partly where I got my own extraverted qualities from so it looks like I inherited something good from each of them). When I was little and my parents brought me in to visit them, she would try to get me to talk more than I naturally did, even though it was like pulling teeth sometimes. My parents would also have my grandparents look after me and my sister sometimes and one time when my grandmother was tucking me into bed she would sit by my bedside and listen as I told her stories based on childrens’ movies I had seen. After my grandfather passed, she attended my high school graduation, my undergrad university convocation, and even convinced my parents (who were initially a bit hesitant in allowing her) that she should fly out to see my masters’ convocation even though she was 91 at the time!
Since my grandmother’s passing, I have inherited a few more of their belongings too. My grandfather has this neat mouse pad for his computer that looks like a rug with a complicated rug pattern on it and I also got a lot of his cuff links. As well, I also inherited a rug and a large wicker chair and a wooden case that my grandfather had since he was younger than me.
Both have been cremated and their ashes are now buried in a cemetery near where their summer home is. My memories of them will be life-long cherished.

How Anxiety Works For Me

I know it’s been a while since I’ve last posted, I’ve had a lot going on over the last little while. But at least I’m taking the time to make a post now.
As I’ve told about in previous posts, I’m working up to my next attempts at my PhD comprehensive exams. The first one, which is Algebra, will be at the beginning of February. I’ve been studying since September for it so hopefully it’ll work out this time after unfortunately failing it last year. There are four main subject areas for the algebra comp and so far I have three of them more or less mastered. The last subject I’m studying right now is the strongest area and I did very well in it on the comp last year. Hence I’ve saved it for last and it’s coming back to me pretty easily so far.
Back in October, however, I felt anxiety start to mount again, however, and I went to the Student Success Office at the university to book an appointment with an advisor there for some academic advice. I’ve since had three appointments with her and so far it’s been well worth it. We delved deep into what was causing the anxiety and it’s really helped a lot. Even though the algebra comp is only a month and a half away I’m feeling considerably less worried about it than I have about the comps ever before.
One of things we talked about was how anxiety actually hindered my academic experience and we talked through the steps. It was a cycle. The first phase was feeling anxious, which led to the second phase of letting feelings of anxiety and anger overwhelm me. Then the third phase was letting these feelings completely blind me. By this time, I’m aware I’m not getting much accomplished, which causes the fourth phase of panic mode. The fifth phase was not carrying out the given task I was trying to complete to the best of my ability because of the panic. Finally to complete the cycle, this led directly back to feeling anxious.
We then talked about how to break the cycle, specifically between the first and second phases. It was okay to feel anxious when trying to complete a task, but I couldn’t let it expand to overwhelming feelings of anxiety and anger. To help, we found supporting evidence that of everything I had going for me: my intelligence, my undergrad professors high opinions of me, every struggle I’ve taken to get to where I am (in second year of a PhD in pure math now), I’ve gotten research published in the past and am currently getting more research published.
There were also various factors that was causing the anxiety. For example, there was the issue of what my future job would be and how failing the comps would impact that and what kind of backup plans were necessary. My advisor got me to make a list of all the resources I already had if I ended up failing the comps again (and which she properly emphasised was a big “if”). For example, I put away a lot of money from my NSERC scholarship that I had during my Master’s and I still had financial support if necessary from my parents. Then just like how we broke the anxiety cycle, we looked at everything that would say I would survive and succeed no matter what. Specifically, the things we came up with were that I am intelligent, I am hard working, I have good references, I have research published, and I have a Master’s in Pure Math from Waterloo. Then she gave me a list of reminders I could read every morning until the exam to further build my confidence, some of which were as follows (and which I have been reading):
Failing the comps is not about your IQ it is simply about learning how to handle anxiety – which you are in the process of learning.
I do belong – I have worked hard to be where I am and I have tackled many obstacles
I understand and know most of the material, I have a great start.
Finally, it’s also been approved that I have the comprehensive exams split up between two days. The usual time that students get for them is 3 hours each and the last time I wrote them I got 4 ½ hours each, which I found out when I wrote the comps the first not enough extra time so I now I’ll be getting double time. For each of the exams, I’ll be getting half the questions one day and then the other half the day after. I suspect this will decrease some of the anxiety as well. Instead of getting a sheet full of 9 major questions all coming from different areas of algebra or analysis (the subjects of the exams), I’ll only be looking at 4 or 5 questions at a time and thus will be able to manage them a bit more.
It’s now just a month and a half before the algebra exam is over and done with. Once that time period comes to an end and I’ll have passed it, I’ll have a new confidence level for preparing for the analysis exam, which will be in May. I’ll be celebrating wildly.

Dealing with Failure Part 2

It’s been awhile since my last post. Alas grad school got out of hand again, yet optimism has flowed back once again. The last struggle I’ve had with grad school has been about failing my first phd comprehensive exam, in Algebra, back in January. I’m afraid my second phd comprehensive exam in Analysis, which I took in May, I didn’t pass either. Like with the algebra exam, however, I was borderline close. Unlike the algebra exam, however, I ended up getting a lot more advice of what to do the next time I prepare for the comps, which has been enlightening as well.

I did suffer from extreme anxiety when I wrote the exam, which was I believe is mainly due to the time constraint. Even with the extra time granted by the disability office, I still found the amount not enough for this exam, and I couldn’t seem to complete enough of these exams to pass and feel like I could’ve completed more on these exams if more extra time was granted. As such, I found it pretty difficult to pace myself which unfortunately caused a lot of anxiety when I took the exam, which I also feel had an affect on my performance.

I got the useful advice of putting pressure on myself to answer questions in as short as time as possible when I start studying again, which will help decrease the anxiety when I take the exams as well. A week before I wrote the analysis comp I did a dry run on an old comp I hadn’t even looked at a week before and thought the dry run went better than the real attempt so I’ll practice that more often. I also heard the department has had some successful PhD students who failed both comps the first time but then passed both the second time, which is encouraging as well.

And because I studied so hard and did all of the right things for the second exam, it has made it all the more apparent to me that timing is the real issue. And because of that I’ve been able to pull down the resources I need. My disability advisor actually completed a master’s in pure math at the University of Waterloo herself and attempted the PhD comps herself and knows what they’re like. We are thus currently coming up with a plan to get more extra time. She is also granting that shortly before I write the exams for real the second time that I write a few practice past exams at the disability office, which will make it easier to be more comfortable when I write the real ones. Another drawback on the analysis comp had been that my anxiety caused me to not even read past a few words on a couple of the questions, again the time constraint contributing significantly to this problem. With all the advice/resources described above, however, will also help eliminate this problem. I also made another visit to the psychologist I’ve been seeing and got some useful feedback regarding remaining positive and focusing on the process instead of the result.

Graduate school continues to be a struggle, but so far I have found that my struggles so far in it have resulted in a positive net gain overall that may have not resulted had the struggles not taken place. My first term of my master’s didn’t go that well, yet I persevered and as such I took twice as many courses covering a lot of areas in more depth in math. Had I not received five PhD rejections last year, I would not have had the opportunity to do original publishable research while still in my master’s (the paper of which I’m pleased to announce has been accepted for publication in International Journal of Number Theory and I will be presenting it at the Canadian Number Theory Association at U of Ottawa this week). Similarly, after I pass my comprehensive exams next year (assuming I do pass them and remain in the program), I will have spent twice as much time studying the material than if I had passed them the first time. It thus wouldn’t surprise me if this resulted in me being truly versed in both the broad branches of pure mathematics that are algebra and analysis. The material will be staying with me well after the exams and thus being that much easier to recall, teach, and apply throughout the rest of the time I do math.

Building a Support Group for Students with Autism

Another term of university has passed. And like most of my past university terms, it went great. It was also a special term because it was the first term of my PhD. My two courses I took this term went well and I’ve been studying hard (and continue to study hard and successfully) for my first PhD Comprehensive Exam that will take place this January. And I’ve also found happiness in being in Kitchener-Waterloo for the next four years of my life. Thus I more or less know what will happen in the next four years of my life. It is very nice and really comfortable to be in such a situation (especially after all the trouble I had with grad school to get to this stage)!

One of the advantages of being in a somewhat permanent position like this is that I have the flexibility to plan more long term goals. It is to form a Support Group for Waterloo students with autism and Asperger’s. I took the initiative to start such a group during my Master’s (see Gaining Power). It was put into action nearing the end of my Master’s, which was unfortunately the time I started receiving PhD rejections and as a result, the Disability Office agreed to take over my group as it looked like my time at Waterloo was nearly over. The Disability Office has so far put on occasional social events for the group during the past summer and fall, which I participated in and enjoyed. Since Waterloo has changed their minds and has let me into the PhD and I have taken a term to make sure I’m properly settled I can go back to continue to help students with autism/Asperger’s after all!

Besides social events for this group, I also want support meetings. I would gather our students to talk and release what they are feeling about that particular week and/or ways in which having autism/Asperger’s has impacted us. Earlier this month, I contacted the Disability Office about my plans and they were more than happy to let me carry this out. Likewise I’ve also received a couple of positive replies from the students themselves. So it looks like things are getting set for the new year ahead. And assuming all goes well it will be something I can continue to run at the university for the next four years.

It is my Christmas gift to the Waterloo students with autism and Asperger’s.