My Time In SL Math A&A (Part 1)

SL Math Analysis and Approaches is a course that is usually taken over a year. Due to the pandemic, we had the entire course condensed into a semester. I had a very rough start in this course, with my first midterm grade being the lowest grade I had ever received in my 13 years of being in school. It proved to be a continuously challenging struggle to keep up not only with the content but also the rapid pace at which it was being taught.

You would think that having gone through all of this, I would be inclined to strongly dislike math. I know that that was the case for many who were in SL Math with me. However, SL Math (A&A) was what sparked a true love of math in me. And no, the IBO has not paid me to say this, nor has the International Court of Math Justice. Even I never thought I'd ever unironically say that a year from today. But I would have to say that SL Math is the reason that I got to appreciate math, and I am incredibly grateful for that experience. Even amid a global pandemic with online classes going double the pace.

The journey started in November 2021 when we started the first topic in Sequences and Series. It was the first day of class, and thanks to the wonders of online learning, I missed it because the link to the meeting worked for everyone but me. In the first class alone, a good portion of the first topic and review was finished. I didn't have a particularly strong understanding of that topic from last year either. My proficiency in math was pretty... average from grades 9 and 10. I wasn't particularly invested or interested in the subject either. I didn't understand what kind of sorcery had been done on the people who would say they loved math. In essence, by day 1 I was already behind.

This would eventually compound to become a large problem. In my opinion, work ethic and perseverance are mostly intrinsic traits that stem from determination, motivation, interest in a subject, and internal desire. When it came to math, I lacked a lot of these traits. Our teacher did not assign mandatory homework, and it was up to us what we wanted to do. The style of teaching in our class was more self-directed than I had previously been used to, which played a part in the rocky transition. In class, we would go over the concepts on a basic level once, and then the rest of it would be us given problems to attempt which would be taken up afterward. What would happen was that I would come to class, watch what was being taught, and then that was that. At that time, it didn't occur to me that I should be looking at the textbook that was posted online and trying problems. In my mind, I thought that as long as I had paid attention in class, I should be fine for the test. A mindset that had been reinforced in a lot of our classes in the past. Classes that had been a lot more teacher-guided than our SL Math course.

By the time the test rolled around, I was feeling okay. That feeling quickly went away as I wrote the test. I did not have time to finish, I forgot the formulas that were needed to answer some of the questions (I didn't realize we were allowed a formula sheet), but afterwards I had realized I completely messed up some of the questions.

Our Sequences and Series test

As you can expect, my combined score for the Topic 1 test was 17/40. Likely one of the worst test scores I had ever received. That came as a wake up call for me. I realized that the approach I had through grade 10 would not work. I had to change it.

December had come, and the next unit was Trigonometry. It was around that time that I first saw Revision Village. The videos on that YouTube channel would give absolutely incredible explanations for each subtopic that we would go through in class. So I started watching those to understand the Trigonometry concepts. I knew I couldn't afford to let myself get left behind, because we would be going through the topic at a very fast pace, and nothing would be repeated. So I made it a bigger focus of mine to pay attention, and try my best to answer the problems presented in class. I had difficulty with some parts of that topic but I made sure to go through all of the practice problems in the homework sections associated with what we were doing. Our teacher gave us a practice test near the end of the unit, which I was able to do relatively easily. That gave me a really nice confidence boost for the actual trigonometry test later in the week.

At our school, we had a Math "Support class". During our "Lunch Break", there would be a second teacher who would be in another meeting room who would do a walkthrough of problems or clarify concepts for students who needed it. I never considered joining until the day before the Trigonometry test. I joined because I was having a really hard time understanding a certain question. The clarification and help that I got in that meeting was immense. The 1 on 1 experience made a huge difference as I was able to ask any questions I needed to in order to understand without judgement. I came out of the meet feeling really good about the question that I had went to get answered. I understood not only what it was that I was supposed to do, but also how I would have known that that was what I was supposed to do. A large departure from my previous experiences in Math where I often did not understand why something was being done. I came out of that class feeling better about my understanding, and also ready to conquer the test. I started to wonder why I (or anyone else in our classes) hadn't considered joining the support class. It was an excellent resource, but nobody seemed to use it. I vowed to make use of it more often going forward, because it was such a great resource.

The next day, I was feeling excited for the test. I was really confident. We had around 30 minutes to do a paper 1 style exam (no calculator), and another 30 minutes for a paper 2 (calculator allowed). I didn't have a Graphing calculator, even though our teacher had told us we needed one. I didn't see why a normal scientific calculator wouldn't be sufficient. Paper 1 started, and I got through the first 2 questions out of 5. I couldn't figure out the 3rd question so I skipped it. The fourth and fifth ones were unlike any question I had seen before in the homework. I sat there confused as to how I was supposed to approach that question. Suddenly, before I knew it, it was almost submission time. I wrote as much as I could from guessing and then submitted. 2 questions were almost blank. The second paper went much better, but I ended up not being able to complete a question fully because I couldn't make a graph on a scientific calculator. I ended up with a 5/20 on Paper 1, and 25/30 on Paper 2.

I was feeling really disheartened with math, because I felt like I had done my personal best and still not done well. At the same time, I knew that things can't keep going like this. After all, the hundreds of thousands of people who did well in SL Math before me were just that. People as well. I let that be my guidance to do better and to get better. I would spend time online on various platforms such as Reddit and YouTube looking to read about the experiences of other people who had went through SL Math and what they had done. One of the best videos I found on the subject was from Imagifinity (https://youtu.be/HoIs6apZt5w). Her advice was some of the best I found on the subject as I could relate to it a lot. I also contacted our support teacher to ask for her advice. She gave me a very detailed list of recommendations.

Our support teacher's advice for SL Math

These recommendations really changed the way I approached studying for the subject. I would make sure to incorporate them into how I prepared for tests. I also realized that my issue lied not just on my knowledge of the concepts, but also on test taking skills. On how I approached a test, how I paced myself, how I organized my work and solutions, how I solved questions.

On our midterm report, I ended up with a grade of 66 in Math, with the average being much higher. It was to be expected given my previous results. I didn't let it phase me, and powered through to the Statistics unit. I realized that it would be better for me to have a background knowledge of what is being taught before I come to class, so that I am not sitting clueless as to how I am supposed to approach the problems we would be given in class. This is where Revision Village came in handy. I made sure to watch videos on the topic we were going through before class.

One of the things that I got from going through the videos from the Imagifinity channel, was her recommendation of keeping your camera on during online class. Her reasoning was that it not only keeps you from getting distracted, but it also makes you more engaged, and is helpful for the people who are teaching as well. It made sense to me, so that's what I vowed to do. It felt weird at first since everyone in the class would keep their camera off and barely anyone talked. It was easy to forget who was in your class, because it was just the teacher talking to a block of letters for 3 hours. Not really engaging. However, after keeping my camera on for a week, it didn't feel weird anymore, and it became easier to stay focused and to ask questions. One of the benefits is that since the teacher can see your facial expressions, she will realize it if you are confused and will go over what they were explaining again. It effectively makes the class a 1 on 1 session, even if there are 20+ other people there. They may as well not be there in that regard and it would be the same, because if you are not asking questions or staying engaged, there is no difference.

My having a background knowledge of a material before coming to class seriously paid off. I was easily able to work through the problems presented in class. When our teacher gradually gave us more challenging problems, I was still able to deduce the answer due to what I knew before. It also allowed me to ask more precise questions. I would already know from the day before what exactly I did not understand, and thus would be able to seek clarification in class.

The statistics unit was particularly Graphing Calculator (GDC) heavy. I had just recently gotten one at the start of the unit, and had very little knowledge of how to operate one. I made sure to go to every single support class. I would take the harder questions or the ones I couldn't figure out to the class and walk through them with the support teacher in those classes, asking questions along the way. Knowing how to approach the harder questions naturally made the easy ones even easier. I learned about all the different functions of the Graphing Calculator (GDC) from these support classes. It was really beneficial because some of the things I learned about GDC usage were things that we had not yet learned in my normal class.

I knew that one of my weaknesses was test-taking skills, so I learned as much as I could on how to write a test as efficiently as I could. Some things I picked up from researching online and others from my classes. Some of these included writing out homework solutions exactly as you would write on a test, always rounding to 3 significant figures as per the IB convention, using the approximately equal to sign and not the equal sign when using rounded figures, and propagating all decimal places until the final answer to avoid rounding errors. When doing homework, I made sure to make my solution neat, readable, and easy to follow for someone else.

By the time the day before the Statistics test came around, I was feeling confident in the material. However, I kept in mind that I felt the same way before the disastrous last 2 tests, and that paranoia kept pushing me forward to make sure there was not a single way I could mess up the Statistics test. By that time I had went through every single question in the textbook for the Statistics chapters. I went back and redid all the questions that I had not gotten correct on my first attempt, just to make sure I truly understood them and did not repeat the same mistake. When I had exhausted those, I tried to look for more.

I found a great resource in the Revision Village question bank for this purpose. It had a bunch of IB style questions complete with a video solution and ordered by difficulty. Since our tests (and exam) were all made from IB style questions which were written in a very specific way, it makes the most sense to practice with IB style questions in particular. I paid special attention to the command terms and mark allocation. For example, if a question started with the words "State", it meant that the answer was given somewhere in the question, which made some questions easier to figure out. This was the beauty of IB style questions in that they could be reverse engineered from the way the questions were made. Another important characteristic was the mark allocation to each question part. For example, if there was a question that was only worth 1 mark, that meant it was really straightforward to solve. This got rid of many occasions where I looked at a question and wasn't sure how to approach it, but then saw that it was only worth 2 marks meaning the solution couldn't have been very complicated. Another useful piece of information from the mark allocation was knowing exactly how much work you needed to show. Showing work and writing down steps takes time. Time that you often do not have on tests. If you have a question that's only worth 1 or 2 marks, you don't have to spend a lot of time writing out a solution. In some cases, just giving the right answer is enough to get full marks. In contrast, if a question is 5 marks, you need to make sure you show 5 marks worth of work in your solution so that you don't lose marks even if your answer is correct. From going through these questions I learned a lot about how I should be writing my solutions.

The next day was the test. I was feeling really nervous. I had been up until 2AM the previous night making sure I did not miss a single thing at all. I also made sure to review all of the GDC functions we had learned in class, plus the ones we had learned in support class to make sure I didn't waste time during paper 2. In hindsight, I feel that having gone to the support classes to learn about the GDC functions really put me at an advantage because I had more exposure to using it and thus had more comfort with it. When the test was opened, I did not waste a single second. I made sure to read through the entire test before I started, and a sense of calm came over me as I realized I knew all of the questions on the test. I put all of my test-taking skills in action. Halfway through the time we were given, I was already done the test. I used the remaining time to double check and triple check my answers. For the first time, I was feeling really good about my submission. I ended up getting a 40/42 on that test, which was one of the best moments of my Grade 11 year. It was an awesome feeling to know that my work had paid off. Now that I had found a good formula so to speak as to how to approach tests. I just had to keep it up and that would be the key to my success.

Around this time, we were assigned the task of the Math IA. Originally, we were only given 1 month total to go from our idea to the finished final draft for submission (however that would later be very generously extended). So the stress levels were very high that January. We had the December break to come up with an idea. Having been most confident in statistics given my test performance, I originally tried to go for an IA related to Statistics. However, I found a great challenge in finding data to evaluate, a rational personal engagement, and a topic that would be able to score well in the math criterion. Over the course of the December break, 2 of my ideas ended up getting rejected. I spent at least 10 to 15 hours over the course o a week trying to find a suitable idea. I wasn't able to find any topic that could fit all of the requirements of a good Math IA, and hence ended up expanding my horizons to all SL Math topics. I eventually ended up settling on an idea related to Optimization and Calculus. Even though we were far from doing the topic of Calculus in class. This meant I would have to learn the topic and concepts on my own in order to complete my IA. It would be difficult, but it was an otherwise suitable option, so that ended up being what I chose for my IA.

As this was all going on, we had moved on to the probability unit. From the support classes, I had been told that the probability unit was one of the hardest units. With that in mind, I wanted to make sure I stayed ahead. Instead of just watching the Revision Village videos, I went to read through the chapters of the textbook ahead of the class to set myself up for success. This would pay off since a lot of our class was based around learning through problems that our teacher would give us. I did not have an issue with any of the problems given in class. I would go through the textbook, again making a note of the ones that I did not get correct the first time. I also went through the Question bank questions simultaneously. However, I got to some questions that I did not know how to approach. When I took them to the support class, I learned that there were certain formulas in the formula booklet that I did not know of that I was supposed to use for the question. That's when I realized that almost 40% of the formulas on that booklet looked completely foreign to me. I took the time to make sure I learned the applications of all of the formulas in the Probability and Statistics unit. I ended up learning about formulas that we had not yet learned which gave me an advantage for the future chapters of this topic. I went through all the things that made me successful in the last test.

The time came for our Probability test, and I went through the exact same process as the last test. I went through the entire test first. I ended up recognizing one of them from my homework. I got through all the questions in due time, but the last 7 mark question was really hard. It was a long question, which ate up the rest of my time. I finished the question just in time to submit. I did not have time to check my work.

Despite that I still thought I had done well. That would be until I received the results later on. I got a 46/53 on that test. What happened? I thought to myself. As I went through the marked test, I realized they were all small errors caused from carelessness. I lost a lot of marks on the large question due to a small mistake at the start as well. I was dumbfounded afterwards. I did not have the time to check my work afterwards because of the harder last question, which led to mistakes. I did not know what I could have done to change that, which left me disheartened for quite some time.

I vented my feelings to some of my friends who study in China. One of them had done really well on the Chinese GaoKao (College Entrance Exam). She weighed in with advice.

Her advice to me was "Don’t waste time doing every single question. There is no use doing low-intensity practice. Instead, you should focus on the hardest questions in the topic you are studying as that is what will help you learn". That was very logical advice, as if I were to practice with the harder questions, not only would I save time but I would also become more familiar with the high mark questions that would be on the exam. It would make the easier questions easier thus allowing me to save time overall. So while following my earlier practice regime, I started to practice using only the harder questions from the textbook and the hardest questions from the questionbank. To improve my speed, I would practice doing them in a strictly timed environment. If the question was worth 7 marks total, I would give myself 7 minutes to do it. To make my studying more efficient, I would not work through questions that seemed, easy, repetitive, or ones that I knew I could do. This would save me time to work through harder questions.

As we worked through our final unit in topic 4 that would combine the new topics of probability distributions alongside a review of the entire topic. The weekend before the test I would wake up at 5AM everyday to work through the textbook chapters associated with our test. I followed the advice of my friend while continuing to practice the habits I had developed at the start of the topic. My paranoia shifted to making sure I didn't make these small mistakes that would cause me to mess up the question. In the support classes, I brushed up on the calculator functions and the harder questions I could not figure out.

The day of the test, I was feeling prepared. As paper 1 opened, I went through my scanning procedure of the test. All of it seemed relatively simple. In fact, one of the questions looked just like one I had done during my questionbank practice. I was able to work through it quickly, having 10 minutes left to check my work. I redid questions that had the chance to be screwed up by small mistakes to check my work, while trying to find a second way to solve a question for others to confirm I had the right answer. I was feeling very confident in my submission when it was time to submit. As paper 2 opened, I got my calculator ready. It was not as easy as paper 1, but it didn't look too bad. throughout the paper, I made sure to never clear my calculator so that I could quickly skim through my inputs to check my work at the end. As I neared the end of my time, I went back and reread every single question and made sure my final answer lined up with what was asked in the question. I was feeling a bit more nervous about this submission. I had caught a error which made me have to redo a question near submission time while I was checking my work. I was worried that I had missed something during my check.

Despite the rush in the last few minutes of paper 2, I was feeling confident about my performance on the test overall. As we started our next class, our teacher asked us how our test went. “It went well!” I replied enthusiastically, as I thought that others would echo that sentiment. To my surprise, the responses in my class were quite the opposite. I learned that some people had only finished the textbook practice the morning of the test. Or some had not done the textbook practice at all. We had a lot going on in our schedules between Math Tests, Chemistry Tests, and IAs due soon for both subjects. This was causing high stress levels in our class which is why some did not have the time to practice for the test. I had started my revision 5 days before the test to make sure I did not get jumped by surprise deadlines right before the test.

My discussion with Ali immediately following the test

I was overjoyed to get a result of 48/48 on that test. The questionbank practice with the harder questions really paid off on the second questions. The other thing was knowing the functions required for that unit. I had practiced a lot with my GDC on my own allowing me to be very comfortable with the functions required. Some of the functions were not covered in depth in class which is why the practice I did on my own time was important. I had found that practicing and learning on my own was critical to succeeding.

That was the end of our first half of SL Math, with us having covered 3 topics, gone halfway through our IA, and done 5 tests. My final mark for that term ended up being a 92. Given that this was a 66 just 2 months earlier, I was more than happy with this result. This half of SL Math had really changed me as a student as the failures early on had taught me what works and what doesn’t work. It had been an exercise in adaptability. I learned a lot about the habits needed for success, including practicing with Question Bank questions, skipping easy questions and practicing with the hardest ones available (a practice that I would go on to name Lemon Theory after the nickname of the friend who had told me about it), time management strategies for tests, the pre-reading of all content before it is started, and making sure to attend support classes to their fullest. All of these practices are what contributed to my success in this half of the SL Math class.