This quarter I have greatly benefited from my study group and office hours to make my education richer and engaging. This would not have been possible if I did not embrace being uncomfortable when actively seeking help.

Starting with the first week of the class, I made the effort to keep my camera on despite being the only one besides my professor in a lecture of over 30 students. When attending office hours and discussion in the first and second week, I messaged other engaged students to gather contact information and establish weekly zoom calls to review our homework. I believe being consistently present and often asking questions demonstrated my will to thrive in this class and made my classmates more willing to engage with me.

If I had not done this work within the first two weeks, I would have been less inclined to reach out further into the quarter, so forming the habit early was vital to my success.

To get to this point, I have had to battle with myself and imposter syndrome. Having always struggled in school, these years of failures have often left me with a lot of limiting beliefs about my capabilities. These beliefs often made me less inclined to engage with others as I did not feel like an equal to my peers.

I have had to learn to acknowledge and gradually remove the power from these beliefs to uncomfortably expose my vulnerabilities and receive help from others. As a result, not only have I greatly benefited from this experience, but my peers have shared their gratitude with me for taking charge in creating a supportive learning community.

I have received a lot of help and guidance in my academic journey, so it is crazy to believe that I have the tools and knowledge to currently help empower others as well.

Trust the Process.

This is the motto that has stuck by my side through the hardest of times. I wish that I could say the end of my hard times in academia are near, but that moment barely seems to be getting any closer. It is easy for me to fall into the trap of knocking myself for not being the prototypical 22-year-old graduate making money in the corporate world. More now than ever, I just need to trust the process.

I am 24 now and I do not know when I will graduate, but I will! I have struggled for a long time to believe this, and a lot of that self-doubt is attributed to my history of failing math classes throughout high school and college. However, rewriting my narrative and therapy are powerful tools that have helped me get back up after being knocked down countless times. I used to be ashamed to reveal my history of struggling with math, even to this day I sometimes find myself falling back on that narrative. It has been a pleasant surprise for me for people to find my story inspiring. People are often in disbelief knowing I am a math major and finding out I have not given this path up despite all the years of setbacks I have encountered.

It always makes me smile when I can help someone with math and they tell me, “yeah, I’m just not a math person,” and they look at me in disbelief as I tell them I am the same way, and that I have a track record to prove it!

My progress towards my bachelors degree has felt awfully slow recently. Every hard-fought quarter and only ending up with a D or a C hurts. Six years into this process, and I feel as if I should have it all figured out by now. For years, every essence of my soul was fixed on coming back to UC Davis and thriving in this environment to validate my worth as a student. Starting at a new school in the middle of a pandemic was not what I envisioned, but it did teach me something. I did not need a new school to validate myself, I am the same person I always have been. I have picked up a lot of knowledgeable gems on the way here, but I have been capable and worthy the whole time. Without recognizing this, it is easy to fall prey to any perpetuated narratives that tries to push me out of academia or make me feel like I am not good enough to be here.

F**k that.

I can choose to see all my experiences as failures, or opportunities to learn and grow from. I know many of my “failures” are yet to come, “failures” so big they might discourage others from continuing, but I have been pushed to the bottom and counted out my whole life, there is nowhere to go from here but up! The logistics and timeline of getting my bachelors might not yet be evident, but I must let go and have unwavering faith that I will get there. I need to trust the process.

For my readers:

What motto has resonated with you along your journey and why? (In a more fun way to say this, what motto would you tattoo on yourself and why?)

One of the great things about being human is always being able to improve your craft. As much as I wish I could have been a perfect student by now (six years in higher education), I continue to learn about myself, skills I want to develop, and habits I fall back on. Here are three ideas that I want to reflect and expand upon to hopefully serve me in the future.

Getting Feedback

Without a doubt, getting feedback is one of the most important aspects of my learning. Making sure that the feedback is received early and often is just as important. A personal pitfall of mine is placing myself within the trap of thinking that I should not ask for help when I have fallen behind. I always deceive myself into believing that I will ask for help once I have caught up to the current lecture. However, I need this message to get lodged into my head. I will always be behind! Therefore, I should never be using that reasoning to justify me not asking for help, otherwise I will never get to it. I know that it hurts my pride to admit when I am struggling but asking for help often saves me so much time and alleviates me of so much pressure. It is funny and a bit sad to realize that I know what I need but find myself always looking for reasons to justify why I should not ask for help. Just do it! In addition to feedback being received early and often, I have found honest and raw feedback from my peers to be just as pivotal for my success. Getting genuine feedback from peers who understand the difficulty of learning the same material as me makes the learning much more engaging and less daunting. Within the context of feedback, it is very empowering and validating to be able to freely express my concerns without worrying about the power dynamic and politics that can be present when engaging with professors.

Focused and Diffused Approach to Learning

This is an idea that still requires a lot of exploring on my part, but I found it to be a reoccurring theme as I struggled through my lecture. I believe it is safe to assume that being focused is great, but sometimes I felt as if it also hindered my learning as well. Perhaps my gaze was too focused on following through with my notes and textbook in a rigid and linear way. When my attention was more diffused and freer with no specific structure to follow, I often found myself being more capable of breaking down information and finding a spot for it in my concept map of the content. In the same way that reflection does not call upon a concentrated gaze, I feel compelled to begin my study sessions with the same form of diffused thought.

Full Immersion

Inspired by the “Math Sorcerer” on YouTube, I want to be fully immersed in a subject matter. This implies that beyond my scheduled studying, I also want to engage in pleasure reading of the material or related material. This idea really appealed to me because I often found myself discontent with the content I was learning. I have a deep appreciation for math, but all the stress associated with deadlines and grades made me want to do anything else but math sometimes. By setting aside a time slot to randomly engage and be okay with not yet knowing math as one reads it, one can not only cultivate their excitement for the subject, but also continue to learn! Whether that engagement is a focused reading with pen and paper at hand, or whether it is a leisurely reading, I can still gain so much from this experience.

For the audience: What are some reoccurring ideas/themes about your own learning processes that you would like to explore?

I used to really enjoy learning! Having been in higher education for six years now, I feel as if that ambition has been picked away at more and more each quarter. The emphasis on grades is mentally taxing!

I want to be the best student I can be. However, in the eyes of the current educational system, that means specializing in memorizing specific ideas and using them too often in abstract ways. I have always wanted to relate ideas to other concepts in real-life, and as a result bring my education “to life.” But there is no reward for that, if anything, I lose time I could have spent continuing the cycle of memorizing enough to pass but not understand.

University favors strategic learning in place of deep learning. As vital as deep learning is for being successful in industry, it is too often neglected and not incentivized. Unfortunately, any beneficial deep-learning gets pushed to one’s free-time, if you have the privilege of having a lot of free-time during college. This unfortunate factor leads to the loss of so much talent. But for now, many of us including myself will have to get by with strategic learning until we are granted a diploma.

With only so much amount of time in the day, I have felt the need to evaluate what my priorities have to be as I sit through my lectures. Although each lecture is only about 50 minutes in length, to dissect and engage with every 15 minutes of content takes me around an hour on a good day! So each lecture takes me about 3 to 6 hours. While I am okay with 3 hours to each lecture, the 6 hours per lecture tend to set me back and create scheduling issues for the future. I would like to find a way to break down 50 minutes of content consistently within 3 to 4 hours, but I do not know if its possible. However, I do know that if I’m going to be spending all of this time engaging with math lectures, I might as well learn deeply, and hopefully efficiently, by keeping some principles in mind. Thus, I sought out advice on how to deepen and better my experience with math from How to Think Like a Mathematician: A Companion to Undergraduate Mathematics by Kevin Houston. 

Luckily for me and other readers out there, the chapter Reading Mathematics offered just what I was looking for. Before I demonstrate my list of principles from the advice offered in the book, I  want to acknowledge that I struggle to be consistent with large lists. Therefore, I have chosen the four most important principles that I believe can keep me best engaged and efficient in my learning. 

“Before reading decide what you want from the text. The goal may be as specific as learning a particular definition or how to solve a certain type of problem.” – page 16

Trudging through a lecture for hours with no end near in sight is incredibly intimidating. I have found it to be very helpful to skim through the lecture or notes (if provided), to seek out important definitions, equations, or ideas. At least by initially having a roadmap of the content, I can anticipate how long certain topics will be and if they will be related to other presented topics beforehand. Therefore, this principle allows me to consider the relationships of ideas as I learn about them. Also, if I notice that there are few topics to cover, I am not as discouraged when I am taking hours to get through one topic, knowing in advance that there are fewer topics to cover.

“The first reason for using pen and paper is that you should make notes from what you are reading – in particular, what it means, not what it says – and to record ideas as they occur to you.” – page 17

For me at least, I benefit from writing “what is says” and then “what it means.” By slowly writing down what I see in a lecture video or a textbook, I understand better what the author is trying to teach. As soon as I reach any hesitation or vague understanding, I make sure to comment my raw thoughts and confusion in my designated commenting area with a contrasting blue pen to my main black pen. This principle has helped me in recognizing and tracking and addressing my patterns of confusion.

“The second reason [for using pen and paper] is more important. You can explore theorems and formulas by applying them to examples, draw diagrams…Physicist and chemists have laboratory experiments, mathematicians have these explorations as experiments” – page 17

Following this principle, I make sure to not concern myself with fully understanding a theory or idea before looking at an example. Although I have a stubborn habit of rereading something and thinking about it until it makes sense, it has also been helpful to attempt related problems which can then reveal how and why the theory works. Although I would think that understanding the theory is vital to solving a problem about that theory, sometimes solving the the problem is vital to helping me understand the theory. I guess you could say that you can read about a subject as much as you want, but finally interacting with it is when you learn whether you truly understand it.

“Ask ‘what does this tell us or allow us to do that other work does not?'” – page 19

This principle pairs well with the first principle as it forces me to be in the driving seat of my learning. If I happen to get caught in the lull of simply memorizing without understanding, constantly asking this question throughout the lecture can help me stay engaged as I relate it to something I already understand. In other words, build your concept images!

Thanks for reading. (:

Question to the audience: How long does an “hour’s worth” of reading/lecture take you to understand on average, and why?

Plan, act, and reflect. As defeating as it is to know events have not turned out as planned, it is just as empowering to know that one can adapt to the circumstances.

These last two weeks in school I had high hopes for a stellar start to my quarter, but I have found myself falling behind early. Thus, I dedicate this post to demonstrating my plan, act, reflect cycle. I previously had a post on my plan for the quarter, so I will be reflecting on how my week has gone using those ambitious goals.

I have seen a lot of people rave about time-based goals instead of completion-based goals, so I thought I could change the way I schedule to get a better experience. I designated specific amounts of hours to study per day, but it had pain painful to see myself not complete the tasks within that time. Moving forward, I will focus on keeping my number of tasks per  day low, but doing everything in my control to get those done. Perhaps, having an additional stress of time is just something that does not work well for me. In addition to setting amounts of time to study, studying in intervals seemed like a great idea that I know has worked for many, but it was not working for me. Studying in intervals of either 25 or 50 minute study sessions often left me disrupting my studying as I was beginning to enter “the flow state.” Although the idea of taking breaks often was initially appealing, for me the hardest part was starting, so I rather not have to constantly test my willpower by restarting that process often throughout the day. To manage these completion-based goals, I used google calendar which I believe is very helpful. Although I do not want to be as strict as I previously was, having a loose structure of when I expected to study throughout the day helped me carryout through my day with intention.

I have often found lecture notes and my textbook to be a good enough source for me to have a great understanding of the course material. However, I have found myself in an environment where these resources are still leaving me curious and confused about certain content. I have had to learn to replicate the feedback of others in forms such as online math exchanges and videos. I have to keep my system of collecting knowledge robust and flexible to be able thrive in the new environment I have found myself in (upper division math, online pre-recorded courses). It also saves me a lot of time to seek out online resources after a few attempts instead of staring at a textbook or lecture slide until I get it an hour later.

Lastly, this is my first time taking a full course load, I can’t spend as much time leisurely diving deeply into content for the sake of my own curiosity. I need to be able to get through my lecture notes quickly (around 2 hours), and spend more time on exercises and homework problems. I was too often taking 3 to 4 hours to rewrite my notes for each class, leaving me little time to do homework until right before the due date. However, I definitely need to do spend time doing homework daily throughout the week so I can get more feedback and not feel so pressed for time. As active as I was during my note-taking, it will never be as active as solving problems because that quickly makes you realize how much you do or do don’t know.

Although I have talked about a lot of things I want to change, I also want to acknowledge how far I have come since beginning my journey in college since 2015. It’s a privilege to be in higher education, and I’m grateful to have the opportunity to study and grow as a person!

Every quarter, I sit and think about where I fell short in terms of my potential as a student navigating higher education. I have many skills that work for me now, many I probably even do unconsciously, but I am always looking to refine my workflow.

In the past I have fallen for the trap of wanting to address every aspect that I would like to change, but over multiple years I have learned that change is slow and gradual. Although I feel as if I have several weak points that can be improved, to supplement the student I am today, I have narrowed down some solutions to implement this quarter. I will omit personal goals (working out, video blogging, cooking, etc..) from this list, but I still take them into consideration when planning.

However, I would not have been able to come up with solutions if I had not spent time at the end of my quarter reflecting on things I wanted to improve. Here is that raw list of complaints:

• “Because I am struggling to follow along with lecture, I have no idea what is going on. I do not even know what I am confused about and what to ask questions about. My time in lecture feels wasted, and thus I occasionally skip lecture to instead study previous lectures and then eventually I catch up on a recording of the zoom lecture. I feel as if I should be regularly attending lecture to ask questions, I wish I could be prepared and feel engaged in the live lecture. I had originally planned to prepare for each lecture, but whenever I began to fall behind, I was confronted with the decision of previewing for the next lecture or reviewing the previous lecture, and I chose the latter every time. Perhaps I should not think about completing one before the other, but instead distribute some time apart for both.”

• “Throughout my first three weeks, I found it incredibly difficult to match my previous 6-8 hours of studying daily. I beat myself up for not keeping up with that goal, I would like to set my goal lower in the two to four hour range and gradually increase it. Also, I should take into consideration that studying from home (covid-19 time) for multiple hours is so much more demanding from studying at a library. Start with smaller increments of time for studying, perhaps I must build up my focus like a muscle.”

• “I feel as if college is a unique atmosphere where I can learn beyond the classroom through students, faculty, and organizations, but I did not get that experience this time around during zoom university. I know that clubs and some departments make some effort to maintain that social aspect of learning, but I have not made the effort to engage. I am on several mailing lists and have ignored online seminars, lunches with faculty, and clubs. Get involved! Perhaps I was scared for my first quarter back that I would not be able to manage being involved in extracurricular activities and balancing school, but now I know that I am capable with my academic success from last quarter.”

• “I’m glad I created flash cards for my math classes, but I’m sad that I did not use them enough to make them beneficial. As I wrote my lecture notes, I created the cards, but I only ever practiced with them 2-3 days before an exam. If I want to see some benefit, then I’m going to have to focus on frequency of practice and place more emphasis on flash cards that I struggle more with.”

• “I tend to underestimate how behind I am because of how I organize my notes. I store all my first drafts of lecture notes together, and gradually replace them when I update my notes for each lecture. However, at any given time my set is complete and mixed with finished notes and my first drafts. I believe that my final notes need to be an independent set so that when I see the most recent lecture notes, I have the last notes I updated instead of the most recent lecture which I have not yet studied.”

• “I need to make scholarship writing a habit.”

After reading these, I can feel my exhaustion in my endless pursuit for being “the perfect student.” For future reference, I should write about what I did right too. The little wins are also important! By being specific in my reflections, I have been able to create my 2021 Winter Quarter Game Plan to address these problems through a few new tools and goals. Although my game plan does not show my already developed habits and study-skills, it does show the direction I hope to move in.

Winter Quarter 2021 Game Plan

Here is some bonus footage of my first game plan from Winter Quarter 2017 at UC Davis. As you can see, my goals are fewer and now more specific than before.

Winter Quarter 2017 Game Plan

I will be expanding upon this post with a video about implementing this game plan on top of my current study skills once I receive my syllabuses to tailor the video to my specific needs for the quarter! Stay tuned!

The use of flash cards to train with active recall is something I have been wanting to incorporate for a long time. It was not until my latest quarter that I finally began to implement this study tool, but from that experience I learned so much about how much more effectively I can be using this tool. To further expand upon my intuition about learning, I sought research-based principles from How Learning Works: 7 Research-Based Principles for Smart Teaching by Susan A. Ambrose.

The initial problems that I ran into were that I did not take into account what I was struggling with, how often I was practicing, and whether I was actively learning or just relying on short-term memory. From reading Ambrose’s book, I realized I was neglecting her components of learning.

“Research has shown that learning and performance are best fostered when students engage in practice that focuses on a specific goal or criterion for performance,targets an appropriate level of challenge relative to students’ current performance, and is of sufficient quantity and frequency to meet the performance criteria” (127)

I did not have a specific goal or criteria when using flash cards, and I lacked the frequency of practice to make them effective. I have already developed the habit of creating the flashcards, but I need to create the habit of using them. A small sustainable metric for me would be 10 minutes of daily practice. To address having a criteria for performance, I need to implement strategies that keep the level of challenge consistent but dynamic. By reading the same flashcards repeatedly and for too long, my brain became less occupied with active recall, and relied more on short-term memory.

Two of the strategies I will be using are interleaved practice and distributed practice. Interleaved practice entails introducing various approaches to avoid reliance on short-term memory. In the case of flash cards, I will stop separating my cards by chapter, and continuously shuffle my cards in a random order to always get new combinations of questions. To better demonstrate this idea, I’ve included two tables. The above table has randomized columns, whereas the bottom table has the same column multiple times. After several iterations, resorting to a strategy based off the second table will allow you to memorize the sequence of the questions and answers instead of forcing you to work on actively recalling solutions.

A	B	C
B	C	B
C	A	A

vs

A	A	A
B	B	B
C	C	C

With interleaved practice, I can also target my weak areas by focusing on cards I consistently struggle with, instead of continuing to use my time on cards I have already mastered. Distributed practice is the act of spacing out practices to several shorter sessions instead of one long session. I often found myself using the flashcards only within the week before the exam, which lowered the frequency and thus lowered my potential of learning gains to be made. Therefore, I plan for the ten minutes of daily practice to help me take advantage of learning efficiently.

I hope to invite you to join me in using Ambrose’s principle of reflective learning to reflect upon our study skills and adjust them accordingly.

“Goal-directed practice coupled with targeted feedback are critical to learning” (125)

An important study skill I have continuously tried to implement into my arsenal of tools is previewing material before lecture. The idea of being exposed to material more often would obviously make me better at retaining and understanding that information. I could use this benefit to be more engaged in lecture and ask more questions. In addition, the better understanding from lecture can save me time that I would have spent trying to understand the lecture during my lecture rewrites.

From Susan Ambrose’s How Learning Works 7 Research-Based Principles for Smart Teaching, her principle “Students come into our courses with knowledge, beliefs, and attitudes…it influences how they filter and interpret what they are learning. If students’ prior knowledge is robust and accurate and activated at the appropriate time, it provides a strong foundation for building new knowledge” (4) directly contributes to the idea of developing some prior knowledge to then efficiently expand upon.

So why have I consecutively failed to keep up with this habit of previewing lecture material. By the way, this blog post is just as much for me as it is for the next person. By identifying some of my pitfalls, hopefully, I can save you the trouble of making these same mistakes. I have narrowed down the issue to two different aspects of scheduling: setting time-based goals instead of completion-based goals and creating a habit through routine. Lastly, I did not have a method for how to preview material.

Pitfall #1: Completion-Based Goals (AKA Chasing Rainbows)

What do completion-based goals have anything to do with previewing lecture material? Time after time, I find myself in some variation of this scenario, I have multiple tasks to complete including: previewing for the next lecture, reviewing for the previous lecture, and some assignment related to previous lectures. My reaction every time has been to throw previewing out the window and dedicate my time to masterfully reviewing the previous lecture, and then spend whatever little time I have left over finishing an assignment. I find myself in this situation often, and thus abandoning lecture previews becomes a habit, even though I originally set forward to make previewing a habit of mine. This is the result of spending more time than anticipated on completing tasks, otherwise known as failing to follow through with completion-based goals.

Current Solution #1: Time-based Goals

Instead of completing each assignment one-by-one whether on schedule or not, I will begin to dedicate time to each assignment, regardless of my progress on it. For example, if I had six hours to dedicate to the three tasks, I could designate time to each task like two hours for review, three hours for homework, and one hour for preview. Not only would I get exposed to all three tasks, but I could also get a better understanding of the necessary time to complete each task later.

Pitfall #2: Lack of Routine, Lack of Habit

Just like rewriting my lecture notes, previewing my lecture notes is optional. Thus, I have more often relied on motivation instead of discipline to get me to routinely preview lecture material. However, rewriting lecture material is habit I routinely follow through with, unlike previewing lectures.

Current Solution #2: Habit through Routine

One thing that can help with that is setting aside a weekly routine where I preview material at the same time every day. I can get rid of the spontaneity of previewing by treating it as a physical class, where I must routinely be physically and mentally present. I highly recommend setting aside at least an hour the night before a lecture. I personally would avoid previewing right before lecture, as I can easily exhaust and overwhelm myself right before class. But do what you must do!

Pitfall #3: Aimlessly Previewing

If you’ve ever tried to read a page out of a math textbook, I think we can both agree it’s taken us multiple rereads just to get a bit of understanding from one paragraph, and sometimes even just a sentence. Yes, that can be very demoralizing, but that is why it is important to distinguish between reading a textbook and a novel. Do not expect to read the textbook like a novel!

Current Solution #3: Strategic Method for Previewing

When previewing material, it is important to keep in mind what you expect to get from that one to two hours spent. From skimming the lesson and paying attention to bold and highlighted texts as well as examples, we should hope to deduct the following:

• What is the big picture of this lesson?
• What are the main ideas/key words in this section?
• What is being asked of in the questions?
• What is being given in the questions?
• How does this lesson relate to or expand upon previous lessons or previous courses?
• What am I confused about?

Being able to relate the lesson your previewing to previous knowledge can make covering the content afterward much easier to digest. As a learner of the material, we have concept images of how everything relates to each other. Thinking about relationships and how new information fits into our concept images is shown to be effective as explained with “researchers have also found that if students are asked to generate relevant knowledge from previous courses or their own lives, it can help to facilitate their integration of new material” (Ambrose, 17). Therefore, when spending our time previewing information, we should emphasize the context of how this new information fits into the agenda of our curriculum if possible.

Lastly, it is important to identify what confuses us, so that we can get that addressed as soon as possible. Preparing questions will also ensure that we stay engaged in lecture as we will be listening for the solutions, and we could also ask the questions when relevant. We much rather find out what we do not know before the exam instead of on the exam. So, fail early, fail often, and fail forward my friends!