Recommended Study Strategies

Students taking their first linear algebra course often ask instructors how to succeed in the course. While the study strategies work for each student will very from student to student, there are some general advice that instructors can offer to students taking their first linear algebra class.

In past offers of MATH 1554, instructors have sometimes held an activity in canvas that asked students to describe the study strategies that they want to use to reach their goals. Or they ask students to: imagine a scenario along the lines of imagine yourself three months into the future: the class has completed. Looking back on your experiences in this class, you feel satisfied because you reached the goals you set. What did you do to reach your goals?

Each time the survey is run a few themes emerge from the responses. Below are a few examples of what students wrote, grouped into themes that emerged from the data.

They are presented in no particular order.

Are there ideas here that you can implement in your studying this semester?

1. Solve Many Problems

To understand linear algebra means being able to solve problems with linear algebra. That takes practice. Below are a few comments that students wrote on solving many problems.

Practice, Practice, Practice, Practice ... I think that's it. I never really realized, but it's literally practice that's got most of us where we are: whether we practised simple addition of 2 digit numbers in the 2nd Grade, or practised History past papers in the 8th Grade.
I plan to practice old quizzes, old exams, MML quizmes/extra practice, and (if they become functional) the extra quizzes on Canvas in order to gain practice on the material from a variety of sources. This strategy will expose me to many different types of problems, many using different wording, and therefore will require me to understand the concepts on a deeper level.
Extra exercises will allow me to improve my ability to solve problems and will allow a greater grasp of the concepts. Extra exercises also increases the odds of being more familiar with assessment problems.
And, I plan to use the study feature on math lab, along with the textbook problems and worksheets to master all of the material fully.
I will complete all the extra problems in the book and practice as much as possible to better my critical thinking skills.

2. Schedule Your Time

Scheduling your time with a digital or physical calendar helps you make sure you are making time for the learning you need to reach your goals. Below are a few comments that students wrote on this strategy.

I would like to have a plan for the future, like having a planner or a strict calendar. In the past, I could not understand the people keeping full calendars; being a high school senior, I understand what it means to have a strict schedule, and I started to think that I should keep one myself.
I have started using Microsoft To-Do this year, where I can track everything I need to do on one platform and make plans on when things need to be worked on.
I plan on checking my assignments every day to make sure I'm keeping up.
I have a planner with when due dates are, which allows me to turn in items earlier, and not being forced to turn in right before due dates. This way I have more freedom of when I work on things and turn them in.
I've become more organized and made sure that I've written out all my due dates, tasks, and events out on a piece of paper in my binder, as well as on Google Calendar. I also have separate desktops open on my computer to divide up my courses and keep myself focused on the task at hand and able to move into another task easily. I've also gotten a binder for this class and split it up with a section for notes, worksheets, and practice problems from the textbook.
I decided to use my planner and create a designated study/homework time. I realized that I need to visually see my time being split and organized in order for me to figure out what to do. These soft "deadlines" really encouraged me to work with a schedule and in fact, I felt a sense of achievement after finishing these "tasks."
I planned out my days and stuck to the schedule as much as I can to accomplish everything I want to.
I have a Google document where I write down all of the work I have assigned in each class, and I color code the assignments by when I want to finish them by (Before next class, before week ends, urgent, etc.)
So far, I have made myself a calendar mapping out all my activities and events throughout the month, giving me a visual representation of how much time I have to complete my work.
I wrote all quiz and midterm dates into my agenda at the beginning of the semester so that I would be prepared for any assessments and have plenty of time to study.
I had a master calendar in which I recorded my work in all categories, including Linear Algebra. This way, I was able do my work and study ahead on days where I would not have time later.
I laid out a sort of calendar for myself so I knew that regardless of the work I had to do that day for other classes, I made sure I prioritized my textbook readings. I also timed myself so that I made sure I was able to answer problems in a timely fashion.
I bought a planner this year to plan my work earlier, and make short term goals
I started creating a to-do list every morning before I start the day so that I know all the tasks that I want/need to complete that day

3. Pace Yourself

Linear algebra is a subject that draws connections between several inter-related concepts. So as you are learning linear algebra, realize that understanding how concepts are related to each other and how to apply them may take time to learn. Pacing yourself helps you ensure that you have time to see these connections and ask help as you are learning them. Below are a few comments that students wrote on pacing.

This semester I'm continuously budgeting my time in one hour blocks, putting in proportions of each class to expose myself to content 1-7 days ahead of where we are in lecture; This schedule is subject to daily adjustment.
Study 1 hour a day: through supplementary lectures, practicing textbook problems, etc. Start all assignments at least 2 days early and finish them on time (starting them early will allow me to look at them as more of an opportunity to learn and less of a stressor/something to rush through)
I try to stay a little ahead of the content's due dates so I have time to ask for help or complete any extra practice I need.
I've realized now that the MML homeworks alone are not enough practice for me, so I want to start doing ~10-15 practice problems from the textbook for every topic every weekend (~30-45 problems total for that week's lessons).
I will plan to do every Written Assignment at least two days in advance to give me time to thoroughly check over everything.
For organization, I have already found an application that allows me to compile of my work in the same place. This has been able to keep me on track with deadlines and make sure I never miss an assignment.
I intend on reading the textbook before class/ recitation and allotting an hour or two everyday to study and prepare for 1554.
I studied multiple days in advance
instead of doing homework the minute its assigned, I would do it a few days before the due date to be in good synchronization with the syllabus.
I studied at least a little every night, especially the night before lecture. I didn't wait until the night before to study for tests or to work on my assignments.
I made a decision to be better prepared for lectures and exams by being more engaged outside of the classroom. This included attempting my homework early, so I could ask better questions during lecture
I intend on reading the textbook before class/ recitation and allotting an hour or two everyday to study and prepare for 1554.

4. Attend and Participate in Lecture and Studio

Make the most of the time that you have in lecture to check your own understanding of course concepts and deepen your understanding of course concepts.

I plan to show up to lectures and studios to ensure that I am able to not just read the material from the textbook, but also to hear it explained by an experienced instructor. Additionally, studios give students a chance to practice what they've learned with other students.
The day before the lecture, I always check the schedule and preview the materials that I'm going to learn. The next day, I attend the lecture and ask questions that I had yesterday. After that, I attend every recitation and review the materials.
I want to watch and understand all of the lecture videos by taking notes on each slide.

5. Optimize Your Study Strategies: You Can Apply Them to More Advanced Courses and Projects

As you develop strategies and habits that work for you in this class, you develop habits that can carry you forward towards your long term career and academic goals. A few comments from students regarding how developing study habits in this class connects to their long-term goals are below.

As the course continues, I will try out different strategies and routines to see which proves to be most successful. Then, I can use that strategy next semester and in other college classes down the road.
My success in this course will help me determine next year's classes and my college major at the end of this year.
I'm sure that I will take higher level math courses in college, so the learning/study habits that I develop in this course will carry on into the future. and it's important to learn from all the mistakes that I make.

6. This Course Can Seem Difficult at Times. Keep Pushing Forward. Use Your Mistakes as a Guide.

Make the most of the mistakes you make as you are progressing through the course. They tell you where you need to focus your time to be more prepared for upcoming assignments and exams in the class. Below are a few comments students wrote about overcoming challenges and learning from your mistakes.

I plan to adjust the previous actions listed depending on my performance on course assessments. If my expectations were too low and I don't do as well as I expected, I will assess what I misjudged or how I messed up and will put effort into fixing that mistake. I can then use these self-assessments to gauge the expectations that a GT class has of its students to carry me through future classes.
I also plan to take the assignments and quizzes very seriously and always trying to understand the questions and the solutions and understanding my mistakes if they are made.
Learning from mistakes and understanding how to comprehend and solve each problem is important for me to reach the goal of getting not only a good grade but a well-built foundation of my understanding of linear algebra.
My first goal is important to me because if I am trying my hardest to succeed in a class, it will instill beneficial traits in me such as persistence.
I learned that I needed to keep pushing forward.
To maintain a growth mindset, I will not get upset about the questions I miss but rather work to understand why¬† I missed them and how I can improve in the future.
Keep pushing myself no matter how hard it gets by setting goals and doing all my homework.
I focused on my weak spots rather than focusing on my strong steps, being able to do that helped me get better and perfect my skills before each quiz/midterm.
I also looked over old quizzes and tests and made sure that I understood my mistakes and did not make similar mistakes in the future.

7. Develop Community: Ask Questions, Answer Questions

The benefits of discussing course concepts with others are numerous. Besides helping you clear up any specific confusion that you may have, you can also benefit from explaining concepts to others. Below are some of the thoughts that students wrote about connecting with instructors, teaching assistants, and other students in the class.

Use what I learn from the class as well as actively seek discussion from my peers to better understand the subject.
I plan to speak with my family and with a friend with whom I am taking the class in order to practice speaking the language of Linear Algebra. There are many potentially confusing vocabulary terms describing important concepts, and successfully solving problems will require the ability to speak the language that the problems are written in. Talking out loud about the material will help me to become more fluent in the language that I will be required to speak.
I would utilize Piazza no matter how stupid the question sounds to me, and I would attend office hours to ask the TAs questions I have.
However, to get an A in this class, I will need to make an effort ask questions during office hours.
I will form a habit of "teaching" difficult concepts to my dad, because I have found that teaching is the best way to solidify things I have learned.
I plan to work together with the people taking the class with me at my highschool in order to make sure I fully understand the content of the course. I also plan to ask my brother, who is in college and has taken linear algebra courses, as well as my parents for additional help if I need it as they have taken linear algebra in college and have textbooks on it in case I need them
Start journaling and track my daily habits on paper, set reminders and have people who are close to you to cheer you on!
I also asked for help when I needed it from friends who have taken the course before.
I discussed with my peers whenever a challenging problems were in front of us.
I studied each night, communicated with friends, utilized all available class resources, and prepared with the practice exams.
I would go to office hours whenever I needed help. I wouldn't be afraid to collaborate with my peers and TAs. I would (hopefully) reduce the anxiety I have before examinations through these things.

8. Minimize Distractions When Studying

To make the most of the time you set aside for the class, whether it is a lecture, studio, or studying for an exam: try to put away anything that might pull you away from what you were there to do. Below are a few ideas on what students wrote with regards to staying focused while studying.

I have learned that working away from my phone helps me stay focused, hence I plan to implement that.
I'm cutting down on social media use and messaging apps. Recently, I've put my phone permanently on Do Not Disturb mode (no notifications unless it's an emergency). I'm also working on some sleep strategies to stop me from being so tired.
I want to work on the learning the course content and the assignments efficiently by isolating myself from distractions. This is particularly difficult since the course is online; however, I am really enjoying this class and it feels easier to avoid distractions.
Also, I've also tried to reduce the distractions surrounding me so I can stay more focused. For example, I keep my phone in another room so that I can focus on the work on my laptop
Turned off my phone during class

9. Read the Textbook: Before Lecture and After Lecture

The pace of linear algebra is fast enough that no matter how fast or slow your instructors and teaching assistants teach the material, you will get more out of lectures and studios if you come to class prepared. Read the textbook to get a better idea of what you are learning, before it is covered in class. Below are a few ideas that students wrote about reading.

Read each section of the textbook before class
The day before the lecture, I always check the schedule and preview the materials that I'm going to learn. The next day, I attend the lecture and ask questions that I had yesterday. After that, I attend every recitation and review the materials.
I believe deeply reading the textbook for each unit and understanding how the many different theorems and definitions relate with each other will greatly help me grasp the concepts found in the course.
I need to make sure that I make use of the resources I have to ensure that I understand all of the content and understand why they make sense. The textbook is very helpful in this aspect so i make sure that I have been reading it thoroughly.
I hope to reach my goals by reading the textbook everyday, and rereading sections that I do not understand the first time during my class time.
I opened the textbook and read ahead the night before a lecture and really felt prepared for the material when it was exposed to me again the following lecture. For example, when working with vectors and using them to find if systems are consistent or not, I understood that the lecture really well because I read ahead before.
I started assignments as soon as I got them and at least skimmed the textbook before going to lecture.
To reach these goals, I recorded any homework into my agenda the moment it was assigned in class. I also checked the Canvas weekly so that I would know exactly what assessments were coming up and stayed on top of all of my homework. I also read the textbook ahead of every lecture to ensure my grasp of the content was improved, and finally sought help at office hours or among peers when something was unclear to me.
Make sure to study and read the textbooks every day for at least 30 mins.
After each lecture, I read the textbook to deepen and solidify my knowledge of what we had learned in class.
I lightly reviewed the lecture material + textbook before most lectures, so I wouldn't be totally lost.

10. Apply Strategies to Help You Reach Your Own Goals

Everyone is different. Every student taking linear algebra will have their own individual learning and/or career goals. Some students who take this class are in their last semester at Georgia Tech. While for others this is their first college level math course. There are many high school students who take this class through a distance education program. But whatever your individual learning goals happen to be, realizing what they are and connecting your study strategies to them can help you reach them. Below are a few study strategies that were specific to the goals that students had in the class and beyond.

I will read through and try to reconstruct as many proofs as I can for the topics of this course (who also wrote that they are a math major and want to have a firm conceptual understanding of linear algebra, so that I'm prepared to continue in their major)
Additionally, I will be using two other reference texts (the 1553 text and Anton) just in case I feel as though a concept in the Lay book is not explained sufficiently. By working on MML problems before class, I will be able to apply the concepts I have learned to see how well I truly understand them. This way, I can gain a grasp on concepts before they are covered in class, which will help me to better understand what is covered in lectures (written by a student who wanted to improve their critical thinking and problem-solving skills)
While working on problems, I will be sure not to let myself work through them thoughtlessly. It is important to critically analyze what the problem is asking for, what method could be applied to answer that question, and whether or not the results that were found actually make sense. It is easy to make many mistakes by not going through this process, and going through this process helps to build critical thinking skills that will be of benefit to me not just for this class, but for my future classes as well.
Try to apply the topic where appropriate in my everyday life, and do my best to see how it provides insight to different areas.
I want to conduct a thorough analysis of the coding/math behind web search engines to help me understand how linear algebra can be embedded in code or simply used in an effective manner to produce the search engines we use daily.
Lastly, I plan on simultaneously coding visual CS programs that required linear algebra. Another possible application I would like to practice is the coding of mechanics, which requires much vector work and processing using a variety of theorems and equations.
I want to actively research many areas in biology while exploring linear algebra and provide beneficial solutions that help the community.
Do some research in how linear algebra is applied in machine learning.
I think I would correlate the topics we learn and relate them to CS.
In order to reach this goal, I researched the connection between Linear Algebra to statistics and Industrial engineering. I found great sources on Wikipedia.
Obtain a thorough understanding of linear algebra and develop my programming skills to intertwine the two disciplines.
I regularly attempted to incorporate linear algebra into my programming assignments in CS 1331.
Make sure to read self-help books and watch online videos to further improve my self-management process and studying skills.

11. Take Care of Yourself

Last but definitely not least: please take the time to care for your health as best you can. Everyone comes to linear algebra with a different set of circumstances and interests. But anything you can do to help you stay healthy can help you be at your best can help you reach the particular goals that you have for this class. Here are a few examples of what students have written about managing their health in order to succeed in this class.

I will not miss opportunities to spend time with my friends/go to games (if we can because of Covid) due to school work because I will not need to do things at the last minute. This will allow for more schedule flexibility and spontaneous activities.
Last, to reduce stress levels, spreading out the work load will be key, If I let the work compile and I procrastinate, it will only make things more stressful.
I get distracted easily, so I will have to work on that. Less distracted --> more time for schoolwork --> more sleep.
To reach my first goal (stay in shape and eat healthy), I walk with my dog. My golden retriever is a little chubby, so it motivates me even more to work out and train my body.
I decided to learn how to cook over the winter break. I also decided to make a fitness routine that I plan on religiously following.
I also got enough sleep the night before to wake up for the 8am lectures.
Went to sleep early before tests
In order to reach these goals, I maintained good habits all throughout the semester. I made sure to do my homework on time and study well in advance of my tests while also caring for my mental health by exercising and meeting new people.
I set up a daily priority list whenever I felt overworked or stressed. To finish the year strong, I needed to be consistent and kept to the schedule by working out the things higher on the list. As more activities got checked off, I became more efficient at using my time. To keep the healthy mindset, I needed to make sure I had time for myself to breathe mentally and exercise both my body and my mind.
I know that, even if I don't understand the homework/lecture material, I can always go to you or any of the TAs to ask for help. Finally, I would try to get as much sleep as possible before tests and exams. For me, that has been a crucial factor that makes the difference between doing well and not doing so well.