Enhance your performance and become a better learner by attending the Learning how to Learn Seminar Series. Learn how to engage with course material at a university level and improve your thinking and learning skills.
Thinking About Your Thinking: Thu Jan 19 (mp4 video)
The ability to think about one's own thinking, called metacognition, is considered to be one of the most important skill sets. In this seminar you will be introduced to metacognition and learn how to apply it to your studies and beyond.
Embracing Failure: Thu Feb 2 (mp4 video)
A fear of failure can be extremely paralyzing. It can lead to stress, anxiety, and procrastination. In this seminar, we will discuss how to view failure, and, in particular, how to develop a growth mindset.
Learning in Lectures: Thu Feb 16 (mp4 video)
Do you find that lectures are mostly a scramble between trying to listen to the professor and take notes? In this session, I will show you how to improve your efficiency and comprehension during lectures.
The Neuroscience of Memory: Thu Mar 2 (mp4 video)
Using fMRI scans, neuroscientists have discovered a great deal about the brain. In this seminar, we will see how to use these discoveries to make learning more efficient and long lasting.
Effective Study: Thu Mar 16 (mp4 video)
There is much to accomplish in your school life and your time is a precious and limited resource. In this seminar you will learn to recognize the signs of ineffective study habits and how to redirect your efforts to study smarter, not longer.
Recommended viewing:
Learning how to learn by Barbara Oakley, Oakland University. TED talk, 2014, 17 minutes.
Learning how to learn by Barbara Oakley, Oakland University. Learning Technologies Symposium 2016 keynote lecture, Learning technology Symposium, McMaster University, 2016, 65 minutes.
Grit: the power of passion and perseverance by Angela Lee Duckworth, University of Pennsylvania. TED talk, 2013, 6 minutes.
The clip in the fifth seminar about "The Neuroscience of Memory" is from How we learn with Robert Winston by Robert Winston.
Do you find that lectures are mostly a scramble between trying to listen to the professor and take notes? In this session, I will show you how to improve your efficiency and comprehension during lectures.
Learning in Lectures (video)
Strategies:
PARSE study strategy for lectures : PREVIEW, ATTEND (GO TO CLASS), REVIEW, STUDY, EVALUATE.
PREVIEW
Preparing before your lecture will improve your efficiency and comprehension during the lecture:
Read course material: textbook, other materials as assigned.
Ask yourself questions that you would like answered in the lecture
There is much to accomplish in your school life and your time is a precious and limited resource. In this seminar you will learn to recognize the signs of ineffective study habits and how to redirect your efforts to study smarter, not longer.
Effective Study (video)
The purpose of this seminar is to teach students how to study efficiently and effectively and avoid surface studying / learning (where you study to do well on the test and forget everything the day later).
The Main Keys to Effective Study
Active, focused learning
Metacognition
Effective Study Sessions
Active Learning
Learning is not a passive sport.
Avoid writing everything your professor says.
Avoid just reading notes. Avoid over-highlighting
Math is not a spectator sport. Math is learned by doing!
To study mathematics you need to be solving problems not just reading or re-reading or repeating.
Effective Reading
While you still need to do some reading and repeating, the key is to do it as active learning not passive learning.
Effective Reading Technique - SQ3R
Survey, Question, Read, Recite, Review
Survey Phase
Decide on how many pages you want to read - do not pick too many at once. Skim (spend 2 or 3 minutes looking for the most important details. These include definition, statements of theorems, figures, tables, bold words) quickly through the section you are going to read, making a note or list of headings and key words, the important parts.
Sample of list done during the survey phase
- Older Results on the Markoff Spectrum
- Markoff spectrum
-Lagrange spectrum
-derived sequence
-table of values comparing solutions to quadratic forms
-maximal gap
Question Phase
Write down questions for yourself to answer about the headings and keywords. Give yourself a purpose for your reading. “I want to know what this is; I want to know what that means...”.
Questions based off the survey list
Def: What is the Markoff spectrum?
Def:What is the Lagrange spectrum?
There is maximal gap. Is there a minimal gap? Why are we interested in the maximal gap.
How is this related to things I’ve learned earlier?
When you ask yourself questions before your readings, you are actively engaging your mind during reading by trying to find answers to your questions.
Important things to avoid:
Reading your book like it’s a novel.
Avoid over highlighting. In the survey stage you could highlight things that look important.
Read Phase
Read the content carefully looking for the answers to your questions
Try to solve examples before reading the solution. If you can solve the problem on your own, the notes above was effective and taught you what you needed to learn. You’ve learned something valuable, compare your results to the solution. If you can’t solve it on your own, use the example to help you understand the place you got stuck. Make a note of where you got lost, which step could you not do. Then don’t just read the solution, look for where you got stuck. You are making your learning focused to where you got stuck as oppose to reading the whole thing. The goal is to move away from just reading the text.
Write down any additional questions you have. Think of new possible questions as you go on.
Tip - SQR3 before and after lectures.
Recite Phase
After you’ve read the chapter, close the book and summarize everything you read. This will re enforce what you’ve learned, and help you identify a gap in your learning. For example, if you can’t remember a certain theorem, then you need to go back to the text.
Once you are done, and you are absolutely sure that you’ve summarized everything you’ve learned, compare your summary to the summary provided at the end of chapter.
Test yourself.
Review Phase
Within 24 hours of original reading
Time management tip: review your summary
Test yourself weekly.
ADDITIONAL TIPS
Textbooks are more effective when you implement methods like SQ3R.
Effective Practice
Practice solving questions like you will have to on a test. If you can’t get question one, move on to question two. Attempt all of the questions first.
Make practice tests. Simulate the test situation. Do not solve all the problems in one chapter, then move on to the next chapter and solve the problems there. Mix it up, just like a test.
Avoid looking at solutions. You are not developing problem solving skills. On an actual test, your teacher will not provide solutions if you get stuck. The only way you can get better is by figuring out what you can try next. Figure out how to get unstuck when you are stuck.
Problem solving skills and analytic thinking are not only helpful for math, but for the real world.
Metacognition
Critically analyze how well you know each concept/question type. When you are practicing questions, think, “If this question appears on an exam. can I solve it quickly enough”.
As you learn, think about where your learning is at.
Effective Study Session
Q: How many hours should you study before test and exams?
Make a goal for the giving study session.
Study hard (focus, no distractions) for at most 1 hour.
Take a break for 10 - 15 mins. And reward yourself for studying hard. If you give yourself rewards (your mind/body will learn (like a dog lol) that it gets a reward after hard work and it will encourage you to study more.
Spend 5 mins reviewing.
Avoid distractions like music, tv shows during active studying complete focus).
After your break, if you still need to study, switch courses. Do not study the same course back to back. Space it out.
Effective Study Habits
Study at least 30 mins for every course in every 48 hours period. Never should a full day go by where you have not studied for a course for at least 30 mins. This is not always possible, so make it your general rule of thumb. Studying is most effective if it is done in short spaced out intervals.
Schedule your study sessions * Make sure it’s permanent and you can’t change it, so you get at least 30mins to 1 hour.
Take care of yourself: proper diet, exercise, and sleep (try to avoid all-nighters. When you are sleep deprived, your brain does not function effectively. Most learning occurs when you are sleeping, your brain cements everything you’ve learned).
Making a goal ahead of your sessions and work really hard for 30 mins, you will be surprised at how much you can accomplish.
Enhance your performance and become a better learner by attending the Learning how to Learn Seminar Series. Learn how to engage with course material at a university level and improve your thinking and learning skills. Learn the difference between high-school and university expectations in a mathematics course and how to study to prepare for university tests.
[video]
Learning How to Learn Seminar Series - 2017
Thinking About Your Thinking
The goal of this seminar is to show students how to learn deeply and efficiently.
“The most important thing you can learn in university is learning how to learn.”
No matter what you do in the future, whether you decide to pursue graduate studies or enter the work force, there is a 99.9% chance that it will require on the spot learning.
“The most valuable thing you can ever do is know how you personally best learn”.
It is not enough to learn, you need to figure out how to learn deeply.
Topics:
Studying vs Learning
Levels of Learning
High school vs Post-secondary mathematics.
How to study for problems that require the top levels of learning?
Your educational goals
Conclusion
Studying vs Learning
Q: What is the difference between studying and learning?
Q: Do you believe there is no difference between studying and learning?
According to Merriam-Webster: Learning is knowledge or skill acquired by instruction or study. Studying is the activity or process of learning about something by reading, memorizing facts, etc.
Q: What is something that you’ve learned but never studied?
Studying is one of the avenues for learning. “Studying can help us learn, but in many cases it is not even required to do learning. Theoretically, we should be studying to help us learn - that means studying in the right way and studying the right things.
Q: Are you guaranteed to do well on a test if you have studied lots?
Q: Are you guaranteed to do well on a test if you have learned lots?
Both do not guarantee you are going to perform well on a test.
“The most common problem: students think they have really learned the material well, but it is not until they receive their results that they discover that they have not learned the material to the level of expectations of their professor”.
The levels of learning as they pertain to mathematics:
The levels of learning from the most basic is remembering, understanding, applying, analyzing, evaluating, and to the highest level of understanding, creating.
Remembering: The most basic form of learning is remembering. “Just have it memorized!”
A question on a test at the remembering level would be: State the fundamental theorem of calculus.
Understanding: Being able to use a definition or a theorem in some very simple way. To perform calculations for example.
A question on a test at this level would be: Take the derivative of this function using the product rule. Find the eigenvalues of this matrix.
Applying: Applying some known algorithm or using definitions or theorems in a new but very simple way.
Questions at the applying level would be like curve sketching questions in calculus. Where you have a whole set of steps you need to do to solve the question.
Analyzing: ‘I like the analyzing level. The analyzing level is a type of question where after the midterm, the student comes up to me and says, “You didn’t teach me how to do that!!!”, and I say, “You’re right!!! Welcome to University!!!”
Analyzing Level: Looking at a new problem and using the content you’ve learned to solve this new problem. While the question might look unfamiliar, it’s solution requires the techniques you have learned over the semester.
The analyzing level could also include types of questions where you have to decide on a particular method. For instance, integration problems where you have to pick one of many different techniques of integration. It requires you to look carefully at the problem and then decide what you need to do from there.
Evaluating: “Often true or false problems, where the answer isn’t simple. Where you really have to think carefully about definitions or theorems to evaluate whether it is true or false. Questions at this level might require you to evaluate a large amount of data and make a prediction”.
Creating: PROOFS!!!!!!!!!!!!!!!
Note: A question is not at the “create level” just because it has the word prove or proof in it. It is possible to have lower level proof questions. For example, if your professor tells you to memorize a proof. A question involving this proof on your test would be at the remembering level.
“Creating questions are when you really have to synthesize lots of different definitions and theorems to create a new proof or a new method for solving a type of problem.
High school vs Post-secondary mathematics.
Q: What levels of learning were required in your high school (hs)courses to get really good grades?
“The vast majority of questions in hs math tests are solely from the bottom three levels.”
In university, all the levels of learning are required for students to succeed.
Most students start blaming themselves or their study habits when they struggle in their transition from highschool to university/college mathematics, as oppose to realizing that it’s not them or the course. The problem is that that they are still preparing for tests and exams the same way that they did in high school.
How to study for exams that require the top levels of learning?
You need to understand the questions at the lower levels to understand questions at the higher levels.
“Before you can solve higher level questions, you must be able to solve lower level questions. You are going to have a great difficult time applying something if you don’t even know what it is. So, first and foremost, all of those high school study techniques are still valuable and good, you still need them to do well. We now just need to add on top of them”.
Study Techniques for the lower level.
“How do you study to memorize things?”
Repeated repetition.
Cue cards
Asking friends to test you, or testing yourself.
Teaching someone
Using some sort of mnemonic (exs: Bedmas, SOH CAH TOA, ASTC (all students take calculus)) or other device to remember something.
Study techniques for questions in the understanding/applying levels.
Practice questions
Look at old examples
****Note: ‘If you are working on a practice problem, and get stuck, and then just look at the solution, and go, “I know how to do that :) “. NO YOU DON’T :( If you knew it, you wouldn’t have had to look at the solution! Be careful that you are not just trying to memorize the problems, but that you can solve them on your own.’
*****Also avoid just watching someone do the calculations.
Top Level Study Strategies
We need different techniques to solve higher level problems. For example, you cannot employ the repeated practice technique to study for questions at the creating level. “How do you repeated practice a problem you’ve never seen before?”
The strategies:
Look at someone else’s solution and try to critique it (evaluating level). Trying to decide if someone else’s argument is correct.
Look at tricky problems and try to generate your own problems (creating level). Ask yourself more in-depth type questions and literally try to create your own tricky test problems. “When you start asking yourself good questions. What would happen if I changed this? What would happen if this number was a 5? Not only are you going to be thinking more deeply about the material, but you might actually start anticipating test questions”.
Course Maps: Looking at the topics in a course and seeing how they are related. “Once you start doing this, you will start making connections to other courses and that will help your understanding of the topics”.
Discussing with your peers. Work in a group!
“Peer discussions are often better than discussing with your professor.”
“You have to justify your own solutions, and explain it a lot more carefully.”
“Your fellow classmates will have questions that you might or might not be able to answer, and vice versa ( if you’re the one with the answers, this will ensure that you understand a question. Or if you don’t understand, it means you have more learning to do).”
‘You will have to think more critically about what your peers says over your professor. Students typically think their professors are speaking the truth. If you are learning from a peer, you might question a little bit more. There might be a lot more of, “ uh that doesn’t sound right to me”. It forces you to understand at the evaluating level, because it is quite difficult to critically evaluate whether someone else’s argument is correct or false.’
“If you have problems writing your proofs, start analyzing other people’s proofs. You will find that this makes it easier to write your own proofs, because not only will you have seen what other people do well or not so well, but it’s going to give you that thought process of critically evaluating every step you do”.
“Therefore, study groups are the best way of studying problems at the higher level.”
Every student in the group can bring one or two questions so that the group can make a mock test for each student to solve individually. Once this is done, the individual test should be passed around for marking.
Note about bad study habits: Avoid solving problems in the text book in chronological order. For example, starting with section 1, then section 2 problems and so on.
Reasons to stop solving problems chronologically:
1. The material is still fresh in your mind.
2. When you are in a certain section, you know what methods you should be using to solve the problems. If you are in the integration by parts chapter, you know what you should be doing. On a test, the problems will not be in order, nor will the section from which the problem was taken from be specified. One of trickiest parts of a test is analyzing or evaluating what method you should be using to solve questions. If you are already in a particular section, you already figured that out, or it’s been told to you. So the question is now at the applying level.
Summary:
Use group work for top level problems. Do not be afraid to ask your peers questions, or teach them something they don’t know. This will make those hard test questions easier.
Still revise and practice questions at the lower levels
Your Goals
For the hardest math or cs course that you are taking this term, what grade would you like to achieve in that course?
“Aim for the stars, and if you only reach the moon, hey, you’ve reached the moon.”
There is no excuse why you shouldn’t be aiming for the highest grade. While you might not actually receive the best grade; it should be your goal. Don’t shortchange yourself. You are capable. If you limit yourself, you’ve put a cap on yourself. Do as much as you can. Learn as much as you can. Work very hard.
This requires very good and effective time management, lots of hard work, and good learning skills. As well as support from your peers, professors and TAs.
Work towards the higher levels. Figure out what level you are at (if you are working on a problem set and find that you have to look at the solutions, or get help from a professor, TA, or a friend, then you are probably not at the higher levels yet), and what you have to do to advance.
‘Every time you are studying, look at the type of question you are doing and ask, “Where does that question fall on the chart? And can I do that on my own without help. If so, yay! Now how can I get to the next level.” ’
Conclusion
You must achieve the lower levels of learning before you can obtain the higher levels.
Always try to critically evaluate where your level of learning is. The technical term for this is called meta cognition.
