Delibrate Practice. Lesson 12

 

In prior lessons we learned some of the key principles of memorization:

·       Lesson 1: encoding, consolidation, retrieval, reconsolidation

·       Lesson 2: getting motivated

·       Lesson 3: paying attention

·       Lesson 8: making associations

Photo by Jonathan Chng on Unsplash

We will learn how to implement these principles in this lesson on Deliberate Practice. Anders Ericsson and his colleagues came up with the idea of deliberate practice during the 1990s, based on their study of musicians. The researchers saw that deliberate practice requires considerable time investment, but it is more than just repeating what you are trying to master. It is not “drill and kill.” It is practice in which you:

·       Have a clear long-term objective in mind.

·       Plan what you need to do in detail.

·       Monitor how you executed the plan, with attention to specific details.

·       Noticing what to avoid and what to repeat in the future.

·       Apply corrective feedback to adjust the plan if needed and remind yourself what you need to do different next time.

·       Affirm and reward yourself for progress.

·       Get coaching from an outside source, like a teacher.

·       Keep raising the standards for acceptable performance. 

When I transitioned from a D student in the 4^th grade to an A student in the 7^th grade, I think the change was made possible through deliberate practice. Though I did not understand much about deliberate practice, I did intuitively use some elements of it. Penmanship class was likely the turning point, because deliberate practice is baked into the learning. When I looked a drawing of a cursive “a” and tried to duplicate it, the results were tangible and immediate. I had to think about where my drawing missed the mark and what I needed to do to make it look better. I had to keep repeating the process until what I produced looked like the instructional example. Aside from the utility of learning cursive, this may be the most beneficial example of teaching penmanship in school. Few schools do that these days.

 

Until you have mastered the learning goal, deliberate practice is a cyclic process that is repeated again and again. Most everyone has had this kind of learning experience at some point, usually when they are trying to perfect some kind of physical action. If you were in school band, for example, you used deliberate practice to memorize sheet music and master your instrument. If you were in a sport, you used deliberate practice in perfecting the movement skill sets.

If you did not have these experiences, here is one you can try right now: To perfect learning how to stand on one foot in a yoga pose, you could just do it repeatedly without thinking about what you have to do to make it work. Try it. You will see that does not work well. Now try it again, focusing on a visual spot far away and think about what muscles in your foot you have to activate to keep you balanced. These deliberate tactics will train you much faster to master this task.

Deliberate practice is not limited to physical movements. It is equally applicable to mastering school work. The practice objective might likely be to perform better on exams or to develop competence you know will be required in later courses.

Study sessions need to be strategic. That is, at the time you are studying, you need to think about what you need to do to make your memorization better. You may need to pump up your motivation level. You will need focus and self-discipline to work outside your comfort zone. Perhaps you need to invent better mnemonics. You need to think about how often to repeat self-testing forced recall. You need to contrive ways to apply what you are trying to learn. You need to take practice quizzes and solve related problems. You need a way to check on the completeness of your understanding. You need to have a way to check on the correctness of your recall and establish criteria for satisfactory mastery.

Next Lesson:

Especially difficult learning tasks

Sources:

Clear, James  (n.d.) Deliberate practice and how to use it. https://jamesclear.com/deliberate-practice-theory

Keep, Ben (n.d.) Deliberate practice in the classroom. The Learning Curve. https://www.the-learning-agency-lab.com/the-learning-curve/deliberate-practice-in-the-classroom

Learning and Memorizing Math. Lesson 11

There was a time that I thought that understanding math was more useful than memorizing it. A certain amount of memorization is essential, especially for lower-level math. For example, you need to memorize the multiplication table up to 9 x 9 in order to be able to multiply two four-digit numbers.

In elementary and high school, this was not an issue for me, because I did not have to work very hard to understand or memorize it. In college, however, they threw engineering calculus at me, and that was a very different story, not so easy. This was in second semester of my freshman year at the University of Tennessee. I struggled to understand the formulas and going into the final exam, my grade was an F. In desperation, I gave up trying to understand the calculus concepts. Instead, I memorized all the formulas we had covered in the course and the kinds of problems that each could solve. I made a 100 on the final exam, which converted my F to a C. While the memorization served a useful purpose, my lack of understanding would surely have doomed me if I had been in a curriculum that required more advanced classes later.

Now, many decades later, I discover that a similar experience happened to the author of an article published by the Dana Center. The author, Monette McIver, liked math before she went to college, and it was relatively easy. But college math was too challenging, and she too realized that maybe she should just focus on memorizing what was necessary rather than trying to understand. She actually got an undergraduate degree in math that way. She laments having to do this, however, because she really wanted a career as an engineer, and she did not end up with needed level of understanding.

So, what should you do when faced with overwhelming math challenges? I say, memorize it, in order not to be overwhelmed, but as you move along, keep striving for understanding. And seek out the teachers who are good at explaining the math. While the modern focus on understanding math, as in “New Math” and “Common Core,” is commendable, it too often leaves students confused, and they don’t learn the basics either. There is a certain utility in memorizing multiplication tables, even if you understand the principles well enough to build a table. The trick is in discovering what should be memorized to free you to apply that knowledge for higher-level problems. Here are some basic principles that might help:

1.     Use the math you do know to help you figure out the math you do not know. For beginners, work on developing number sense. For example, when asked to solve 7 x 8 question, someone with number sense may have memorized 56, but they would also be able to work out that 7 x 7 is 49 and then add 7 to make 56, or they may work out ten 7’s and subtract two 7’s (70-14). Alternatively, know that 7 x 8 means 7 rows of 8 or 8 rows of 7, to enable you to realize that 7 x 7 = 49 plus 7 makes 56. Mnemonics are very helpful with the memorization: for example: 56 = 7x8 is the numbers 5 6 7 8 in order.

2.     Solve many problems at the level you do understand. This will reinforce the memorization, and seeing the same issues in different contexts will gradually build up understanding.

3.     Try to identify, understand, and memorize the really crucial concepts and definitions that underlie many other math ideas. Examples include words like function, theorem, angle, tangent, sine, cosine, derivative, integral, matrix.

4.     Learn a special case of a math concept first and then generalize to more abstract extensions as your understanding improves.

5.     Whenever feasible, make drawings to illustrate a concept.

6.     Find good learning sources. Many are on the Internet. One of the best sites is Kahn Academy

7.     At the appropriate age, master algebra. It is fundamental to most of higher math.

8.     Develop mnemonic devices, but only for basic ideas and don’t overdo it. The point is to use memorization as an adjunct to mathematical thinking, not as a substitute for it.

In one lesson, I can’t cover much mathematics, but I will choose a fundamental of trigonometry to illustrate my point to identify what is useful to memorize and what you need to think through. To remember the core ideas of a triangle, the features you need to memorize are labeled in the figure below.

First, realize that the lines are measures of distance (a,b,c,). For future reference you could think of lines a and b as y and x axes of a graph, but this is not relevant here. The lines could be labeled anything. Notice also there are three angles (1,2,3). They also could be labeled anything. Mathematicians like to use Greek and for angles, they often use theta (θ). Angle #1 is a special angle, called a “right” angle. I don’t know why it is called “right,” but you might think of it being the right angle to focus on in a triangle: because it is 90^o by definition, the sum of the other two angles is also 90.^o Can you figure out why the other two add up to 90? On a scratch sheet, draw two triangles stacked against each other to form a square and a horizontal line running from top left to bottom right. The box has four 90^o angles if you remove the diagonal line. On the right you see that if you flip line b to form a straight line, you have created a 180^o angle, and if you keep on moving the line around, you create a circle of 360^o. I have no idea why a circle is defined as having 360 degrees. Some mathematician early knew it would be useful to carve a circle up into angular pieces and for what ever reason decided 360 would be a good number (not too small, not too big).

See that there are three boundaries, a, b, and the longest one, c, which is always defined as the hypotenuse. At about this point, you should be asking, “What is the point of all this? What is the ultimate objective?” The answer is that trigonometry allows you to calculate certain dimensions without actually having to memorize or even measure them.

At this point you must memorize that in a right triangle the longest line (c) is called the “hypotenuse.” Each of the two variable angles has a line opposite to it and the other non-hypotenuse line is called the adjacent side. Sine is arbitrarily defined as opposite/hypotenuse, cosine as adjacent/hypotenuse, and tangent as opposite/adjacent. In the diagram above, the sine of angle 3 is a/c, the cosine is b/c, and the tangent is a/b. With these ideas firmly cemented in memory, you are now free to explore the mathematical consequences and uses.

Sine, cosine, and tangent are just names; they could have been called anything. But they are useful because they are a way to label the ratios of the lengths of any two sides of the triangle. If you divide the denominator of the ratio into the numerator, you calculate the length of the third side without having to measure it.

You could, for example, measure on of the angles with a protractor and now instantly know the degree of the other angle that is not the right angle of 90.^o If angle 3, for example is 35^o, then angle 2 is 55.^o

Note also that the two non-right angles are complementary. They sum to 90^o and moreover, the sine of one is equal to the cosine of the other. The equations can be consolidated, as follows:

Sin 35^o = a/c, Cos 55^o = a/c, therefore, the sin of any angle, θ, = cos 90 - (θ).

With these few examples, you can see the usefulness for learning math of combining some memorization with reasoning.

                                 

Next Lesson: #11. Deliberate Practice

Sources:

https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-complementary-angles/v/sine-and-cosine-of-compl

 

McIver, Monette. (2018). Memorization versus understanding. Better approaches to teaching mathematics. May 26. https://www.utdanacenter.org/blog/memorization-versus-understanding-better-approaches-teaching-mathematics

Learning from Lectures, Readings. Lesson 10

 Effective learning takes much less time if you “study smart.” To “study smart,” you need to approach learning in a deliberate way. To study smart, think about the strategies and tactics you need to be using to master a learning challenge. Be aware of any need to change strategies and tactics that are not working well for you.

Best learning occurs during lectures and videos if you make it a point to be alert and aware. The best approach is to think about what you are trying to memorize. Ask yourself questions about the information, such as:

·       What is missing that would be useful to know?

·       What do I not understand?

·       Where can I get this explained better?

·       How can I apply this information to what I already know, to other parts of the course, to other courses, and to different kinds of problems?

·       What new ideas does this give me?

Think about the information in different ways, in other contexts. Think about how the information relates to what you thought you already knew. What is new about it that you need to incorporate into your knowledge arsenal? 

Readings

Anybody old enough to be taking these lessons on improving learning and memory knows how to read. Right? Not necessarily. First, we have to address how students are taught the mechanics of reading. Significant numbers of people were not taught phonics, which was the traditional way of teaching literacy for hundreds of years in almost all languages. Then some educators thought learners could just skip the phonics stage and move directly to “whole-language.” The basic idea of whole language reading is to prevent learners from breaking down sounds in a word individually, but to fix the eyes on whole words and associate them with prior knowledge.

I think that the correct way to literacy is to begin first with phonics. Then as learners master the sounds of the alphabet, they can sound out strange words and decode their meaning. Once phonics is learned, whole language becomes a way to read words, rather than consciously sounding out each syllable. The International Reading Association (IRA) has supported the inclusion of phonics in the whole language approach to literacy.

Actually, this still leaves the problem of plodding along one word at a time. Optimal reading requires clusters of multiple words at a time, speeding the amount of material accessed. Thinking about word clusters imparts linguistic meaning faster and better than plodding through one word after another.

To see word clusters properly, you need to train you eyes to pop along from one fixation point in a line to the next point to the right, then the next, and so on. You might not know that everything the eyes see, whether it is text or nature scenes, results from quick snaps of eye movement from one fixation target to another. These quick jumps are called saccades. The trick is to expand the size of the visual target that is seen with each snap, that is, increase the number of words you see at each snap of the eyes from fixation point to the next fixation point. Just by trying to do this, you can increase the number of words seen at each fixation. At first it may just be one or two words. Soon, your eyes will take in four or five words with each snap of the eyes. This kind of training requires deliberate practice, but if you think hard about what you are trying to do, it starts to become automatic. Good readers take in a whole line of text in a book, for example, in two to three eye snaps. Tests show that readers with average reading speed can double or triple their reading speeds with no loss of comprehension.

Key points to remember:

·       Preview the reading material to get a feel for what it is like.  Note the heading and subheadings. Think about the overall scope of what is covered and not covered.

·       Think about your purpose ahead of time. Ask yourself, “What am I supposed to get out of this reading?” “What am I supposed to understand and remember.”

·       Skim first, looking for the paragraphs that matter the most. The first and last sentences in a paragraph usually provide the best clues as to which paragraph is most important.

·       Make yourself interested in what you must read. You punish yourself by allowing boredom.

·       Adjust your pace according to the denseness and difficulty of information.

·       Try to reduce the number of times you skip back to re-read. If this is a problem, work on your concentration and focus. Don’t let you mind wander when you read. Definitely, do not multi-task.

·       At first you may want to move your finger or a pointer underneath each line to guide your eye snaps. But as you practice and get better, try to eliminate this crutch.

·       Do not move tongue or lips to simulate saying the words inside your head. If you tend to do this, make it a point to hold the tip of your tongue against the roof of your mouth.

·       At each eye snap, THINK about what the words, as a group, mean.

·       Make sure you actually see all the words at each fixation point. If you can’t see all the words at each fixation, decrease the number of words you expect to register until you get better at this.

·       As you realize you are getting better at these eye snaps, increase the speed of snapping.

·       Pause from time to time to reflect on what you just read. Ask yourself to recall the information you just read. Ask yourself how you could and should use the information. Ask yourself how the information fits you existing knowledge and understanding. Ask yourself what you still do not understand? Ask yourself what information you need or want that has not been covered yet.

·       When you finish, DO SOMETHING with what you just read. Self-quiz. Write notes. Report to others what you just read. Use the information in a different way.

 

If you search on the web for “learning how to speed read,” you will find numerous explanations of how to improve reading mechanics. There are even computer apps that help train your eyes attend rapidly presented words, one at a time in rapid succession. See the review of 10 of these apps at https://bookriot.com/best-speed-reading-apps/. Many apps use the RSVP method in which words are presented at a preset speed. Sprint has a free browser based trainer that allows you to increase the number of words presented each time, which helps you learn how to expand the size of the visual field. However, this method fails to teach you how to snap your eyes across a minimum number of fixation points per line of text (see video at https://www.youtube.com/watch?v=kmDMrxUSXKY). I have not found any apps that train you to do what really matters: snap your eyes appropriately across each line of text and engage larger and larger visual fields with each snap.

Lectures

Many of the thinking aspects mentioned above for reading apply also to learning from lectures or on-line videos. Lectures and videos may demand more attentiveness that reading because it is not so easy to slow things down or pause or go back to reconsider information that did not register well. To help information register more effectively, it helps to do some advanced preparation. Good teachers may give you a reading assignment related to the lecture. The more you learn from this pre-reading material, the more you will comprehend and remember from the lecture.

This brings up the point that the goal for lectures or videos is to learn as much as you can at the time. You may not get a second exposure to an unrecorded lecture. A classroom environment presents a special challenge. Once there, you are more or less trapped and your time is pre-committed. As long as you are in class, you might as well bring your A-game so you get the most out of your time commitment. Students who are charged up, fully expecting to aim to remember everything presented in class, are the most likely to remember the most. Be as engaged in discussion if it is allowed. In my experience both as a student and an instructor, I have found the best kind of engagement is asking good questions silently to yourself or of the teacher when questions are solicited. Asking good questions requires deep thinking and deep thinking is the best kind of memory rehearsal. Such thinking and the Q&A that follow obviously can help understanding.

Everything learned in class is something you don’t have to study much after class. Besides, being fully engaged in classroom activities makes class more interesting —certainly more useful.

Get “up” for class, expecting to remember everything.

It should go without saying that you need to be rested. Sleep is vastly more important for learning than you probably realize. Not only does being rested keep you from wasting your time by dozing in class, but memory of what was presented in class is largely consolidated that night as you sleep.

Students should take notes during the lecture or watching a video. But in my experience, they get little good advice on how to take notes. Perhaps this is a good time to re-read lesson 5 on note taking. Note-taking is the standard process whereby information is transferred from the teacher’s notes to the student’s notes (sometimes without passing through the mind of either). The problem is that students are too busy writing notes and not busy enough thinking about what the teacher says and means. Good teachers hand out note outlines before class so students can pay attention to the lecture and get engaged with

Such “skeleton notes,” give the student freedom to leave out things they already know or can figure out. This approach really pays off when it comes time to study for exams.

Note taking should be minimal. Follow the principles given for reading. The idea is to think about what is being said, asking yourself or the teacher questions, expressing the ideas in your own terms, making mental images, and so on. What do you do in case you miss some key information while doing all this thinking?  If the teacher permits, use a tape recorder and use variable speed, so you can slow down for difficult parts and speed up through parts that are not particularly useful.

Next Lesson: Lesson 11. Learning and Memorizing Math Concepts