I recently wrote a TL Knowhow article on the topic of preparing to teach classes, with an emphasis on classroom and especially public school teaching (You can read it Here). Many people have requested I write something that focuses on how to teach. This is much more difficult. Whatever I write will be controversial and difficult to justify. Regardless I decided to compile some suggestions that focus on helping another learn, and are applicable to a much larger audience than my previous article. Instead of discussing classroom teaching this article addresses much more generally how to help another person understand something. It is as applicable for private tutoring or discussions between friends as it is for working as a professional school teacher. It is my opinion that everyone falls into the demographic of this article, although some people need to heed its advice more than others.

Disclaimers:

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Without further ado, here are my suggestions for how to help others learn, as well as some insights I have made through experience and observation:

Clarity:

Being clear in your meaning is one of the most important aspects of teaching (most of the time). This does not just mean to be clear when explaining content, but also when giving instructions, identifying expectations, or providing justifications. If you want your learner to figure something out on their own, that's fine, but make sure information is either given to them or withheld from them rather than somewhat given in an unclear manner. Minimizing unnecessary confusion is very difficult and usually takes a lot of experience to accomplish.

Information given to your learner(s) in passing is often ignored or quickly forgotten. If you and your student carefully come to a conclusion together, it's fine to expect them to recall and apply it a few minutes later. However, if while the student was working on something you also mention a useful additional fact, don't expect them to recall it later. This may seem obvious but teachers tend to do this all the time. A more frustrating example is when a professor doesn't write down a due date for an assignment anywhere and then mentions at some irrelevant moment how (s)he expects it handed in on a certain date. Then the date comes and the professor is wondering why so many students don't have the assignment completed...

Put yourself in the learner's shoes:

It can be difficult but you need to anticipate what will be challenging about the learning process for a given lesson (and for a given student). What would be the necessary thought process of the student in order to accomplish the lesson objective(s)? Is that a realistic thing to expect of your student? My experience has been that usually students diverge from the thought process you planned more quickly than in your worst nightmare! That's okay, so long as you are prepared for it though, and are often checking to see what the student's thought process actually is at any particular moment.

Can you reasonably expect students to learn the new 'thing' based on their prior knowledge? This also takes experience to develop: both measuring the student's prior knowledge quickly, and reasonably determining how much help the student needs to apply it to the new material. Try not to assume students will effortlessly recall things they learned a long while back, even if they were quite skilled at it. There was a period of time when I could integrate sin^2(x) very easily. Today I needed to do it for a side project and it took me a few minutes to figure out what method I was even supposed to use! If I had been working with an experienced teacher they would have quickly identified that I did indeed learn the relevant math methods and just needed a small push (or some time) to figure out the procedure. They would not have told me how to do it immediately, nor would they have been surprised that I couldn't quickly solve the problem.

Avoid giving information when possible:

If there is a way for a student to come up with an idea on their own (such as the formula for average speed), try to help them come up with it themselves. In some respects this is the most challenging and most important part of teaching (and sometimes the most rewarding). Giving information is not teaching. Helping the student to teach themselves (I don't mean to imply a laziness on the part of the teacher here) is preferable. If students will learn the years that world war 2 started and ended, let the student figure it out using another resource besides your voice, your powerpoint, your whiteboard, or just generally you. This won't be possible for every factoid, but should be strived as much as you can allow.

Explaining things:

Even if you try to do the right thing and teach through guidance rather than pure explanation, there are times when you need to explain things. My observation, depressing as it may be, is that most people are bad at explaining most things, most of the time. The pitfall is that people tend to focus their attention almost entirely on the topic they are trying to explain, rather than focusing a good deal on the learner's intake of the explanation. Similar to putting yourself in the learner's shoes, you need to think about how you can word your explanation in order to help the learner understand whatever it is you want them to get. It's quite difficult to simultaneously extract information from your brain and think about how to implant that information effectively into someone else's mind. Nobody said teaching was easy. Well actually, many people did, but they are usually bad teachers... and they are probably bad at explaining things.

Identifying misconceptions:

Before teaching or explaining something you should try to determine what are the most common misconceptions people have that might get in the way of the learner understanding the new material. In other words, probe your student before starting a component of a lesson to see where they stand. If you do identify misconceptions, try to deal with them sooner rather than later. Without going into too much detail or education theory, people who learn things incorrectly cannot 'unlearn' them. They instead 'pave over' the old knowledge with new knowledge, leaving traces of the misconceptions or error behind. A musician and educational expert I knew said he originally learned to play the piano without having a teacher. He came up with his own system for how to cross over his fingers when playing scales. Unfortunately, it was a bad method that makes it really difficult to play harder pieces later. Eventually he got a teacher who showed him the proper method to choose which fingers to hit each key with. When this guy gets drunk enough however, he finds if he sits at a piano and tries to play pieces he ends up reverting back to his original fingering scheme, crossing his fingers over at the wrong time. This is literally decades later and he is still susceptible! I'm pretty sure that alcohol is not the only reason why this could be a problem, but you should get the idea.

You are the master learner:


When you are teaching something new to another person, it's better for the learner to think of you as the master learner. What this means is that a veteran student of the content is helping a novice student of the content become a veteran themselves. By being the master learner instead of the 'teacher,' you are more similar to your student. This will sometimes make it easier for your student to receive help from you than if you were their learning 'supervisor.' I think it's easier to take someone's learning advice when they themselves once needed it (learner) rather than they were born with the knowledge (teacher). Obviously this isn't true, but it's how students often perceive teachers without meaning to! This master learner concept can be applied to a public school classroom teacher as much as it can to a friend tutoring a classmate. The teacher is no less a student of the content than the lesson's target is... they are just further along in their studies.

Ask questions:

Asking questions is an important part of teaching. Usually, phrasing something as a question instead of a statement helps your students to think about it (more active learning). On the other hand, when you phrase something as a question (or if you actually want to ask a question), pause sufficiently for students to process the question and think about it. If possible try to make it obvious (without explicitly stating it) whether your question is rhetorical or you are actually interested in a response. Like other parts of teaching, clarity is very important for questions. Be as specific as possible. For example, instead of "so what happens if mass distribution is less symmetric" (vague) try "how are the perturbations affected by a decrease in mass symmetry?" (more specific, without leading too much) Avoid asking questions that don't make conversational sense. For example "are there any questions?" is strange because you are asking a yes or no question as to if someone has a question. Do you want a student to respond "no" or even "yes"? "What questions do you have?" is better because it elicits the actual questions from the students. I've heard from distinguished educators that there is actual research which shows that the latter phasing gets more responses from students. In summary make sure your phrasing asks questions in the way you want them answered. Instead of "do you know the equation for a circle" try "what is the equation for a circle?" unless you want students to yell out "yes" or "no" which you probably don't. Most 'smart alec' responses from students are an indication that you should have worded your question differently.

Be polite when students give wrong answers:

Be diplomatic when a student gives an incorrect answer. While not every student needs to be coddled... especially if they already know you don't think they're stupid/uneducated, a little leniency goes a long way. Try to find merit in the student's response even if it isn't the correct answer to your original question. If you ask a student what the cause of World War 1 was, and the student replies "to prevent the Holocaust" they are wrong for at least two reasons. Obviously, the Holocaust overlapped World War 2 instead of World War 1. Also, the Holocaust wasn't really the 'cause' of World War 2. Some teachers/tutors would respond to that answer with "wow, you are way off" or "no" which is just about the worst thing you can do. The teacher may not even mean it as any type of a negativism, but the best way to stop a learner from learning is to make them feel bad/stupid. You could instead respond "you're thinking of a different world war!" and let them come to the realization of their mistake if they can. This may seem like a trivial difference with just saying "not the correct answer" devoid of all emotion. However, you have given their answer credence... it just isn't the answer to your specific question. Notice it wasn't necessary to address both mistakes at the same time in the reply. Suppose the student responded "oh, yea, that was WW2, um, oh yea WW1 had to do with tons of alliances and some assassination" it is better than you initially responding "no, actually WW1 was caused by a large number of alliances and a relatively small assassination which triggered an increasing scale of events." You could then move on from there to help the student get a better picture of what happened. At some point if you came to revisit WW2, instead of saying "you thought the Holocaust was the cause of World War 2, but it wasn't really; it was when Nazi Germany started invading other countries" which is just giving them information they may or may not already know, try "you said before that the Holocaust was a cause of WW2 (little white lie; they said it was THE cause), but there were others. What other causes were there?" It is almost impossible to overestimate the insecurity of most learners, and the power of the ego.

Be careful when trying to demonstrate something:

Using a demonstration (whether it be a cool piece of equipment, java animation, or video) can be very helpful when teaching something new, but make sure you are clear how it relates to what is being learned. If someone needs to learn about hyperbolic trigonometric functions, you might tell them to look at http://upload.wikimedia.org/wikipedia/commons/b/bc/Hyperbolic_functions-2.svg and it might be a very helpful picture for learning sinh/cosh. However, don't assume that because you gave a rudimentary explanation of what sinh/cosh are, and showed the picture to the learner, that the learner now understands what a sinh/cosh is and how it relates to sin/cos. Effort needs to go into helping the student interpret the picture and checking to see what the student does/doesn't understand about the picture. Think of it this way: if I interviewed your student right when you were showing them that picture and asked them "why is your tutor showing you this picture?" what would the student respond? The student doesn't need to be able to explain hyperbolic trig functions at that point, but they should be able to identify what role specifically the picture serves. In contrast, there are times where you show the student something and want them to figure out what the purpose of showing it was. This is okay so long as it is your intention, and thought has gone into why this is how you are proceeding with the lesson.

Helping the learner visualize something can be difficult, and usually fails when you 'wing it':

This segues on the previous section since you are using a demonstration, however I want to specifically focus on quick sketches and illustrating configurations using your fingers/hands. If you are "winging it" your sketch or hand demonstration is probably very confusing. Most of the time when someone tries to explain what something looks like, pauses to think for a second, and then starts fake drawing something on a table with their fingers, I have no idea what they are trying to show me. Even make-shift diagrams are often really confusing... especially if things aren't labeled. An example of poor attempts to help with visualization is when someone tries to give directions to me for how to drive to a particular location. The exchange may go like this:

Me: How do I get from building x to building y by car?
Them: Okay, so you... oh you make a left out of the lot and then fork right where the... ok let's say HERE is Bay Blvd draws random line on table with finger and you're coming THIS way moves finger in random curve along table ...you should see the administration building HERE taps table with finger in random spot which tells you you just missed the right fork for the road which goes to building y.
Me: what someone looks like after they are killed in the movie "The Ring"



Give students time to process, think, and try new things:


Be reasonable about how much time a student will need to complete a task, whether it be thinking about the answer to a question, reading about new material (it's slower than when you read it to review it), or completing a written/physical task. If you want your student to calculate the sin values of 0, pi/6, pi/4, pi/3, and pi/2, you might think they need about 5-10 seconds for each one, but it will probably take the student a while to interpret each question (like, what does each of those angle mean, and what does it look like on a unit circle, and how to I do sin again?). Don't cut them short after 20 seconds assuming they did it all. If you don't want them spending a good minute on that activity, don't give them the activity. If you think the student will be able to finish much more quickly that's fine, so long as you are prepared for the case where they won't. Most importantly, when you ask questions and the student doesn't respond, pause before saying anything. Answering questions is actually very mentally taxing. You ears needs to convert the sound waves into a signal, turn the signal into words, turn the words into sentences, interpret the sentences, and only THEN start thinking about the new material and what the answer to the question might be. A question that you are expecting is easy to process, and you probably already know the answer. A question asked by your teacher often is unexpected, difficult to process, and on TOP of that requires much more time to come up with an answer. If a student comes up with a ridiculous answer, don't freak out. They might have just goofed in one of the many steps involved in answering a question, and with a little more time will come up with a less ridiculous answer. Whatever you do don't criticize the student for giving such a ridiculous answer as most of the time this will make it harder for them to learn. If you can't help but laugh at an answer, do your best to let your learner know that such a moment is normal and sometimes happens when discussing a topic such as the current one. I see this all the time, both in real life and even on TL.NET: overracting to a bad/dumb answer and criticizing the person for it. It only makes sense if you legitimately have malicious intent.

Assumptions

You've probably noticed a great deal of overlap between all of the topics here, but a little redundancy for the most important points is probably a good idea. A danger when trying to teach or tutor is to make incorrect assumptions. To an extent this is unavoidable, but you should try to minimize it. Here are some examples of assumptions you should try to avoid as much as possible:

1. The learner is already fully comfortable with prior topic X so I can assume they know it as they learn topic Y
   
2. I was a little unclear, I suppose, but the learner understood what I meant anyway, I'm pretty sure
   
3. The learner understood what I was alluding to / implying
   
4. The learner can take it from here; they won't need any more help to reach this next objective (note: it's okay to let them try it, of course)
   
5. The learner examined all available information as they were supposed to
   
6. The learner knows why I am asking them to do thing X (this one is really important!)

Conclusion:

The most important thing you can do to improve your teaching is to be reflective. What this means is to think about how your recent lesson/tutoring session went. Feel free to get feedback from your student. What they say or recommend isn't necessarily true, but you should give it some credence. If they say something was confusing, it doesn't matter how confident you are you explained it as clearly as it has ever been explained... there is room for improvement. It's not even your fault necessary. Every lesson ever implemented has had moments where students were unnecessarily confused. A little bit of confusion isn't always a bad thing, as it's actually somewhat authentic (happens in real life situations). However, clarity in instructions, expectations, and purposes is paramount.

Brought to you by the TL Knowhow Team
Written by: micronesia