How do you avoid common pitfalls when teaching/tutoring?

[G01]

Hello all!

I have been toying with the idea of posting a thread like this for some time.
Currently, I am a physics tutor, and everyday I come into contact with so many students who hit certain pitfalls in their study of Physics. Whether it be finding vector components or normalizing wavefunctions, everybody hits a stumbling block when studying physics, and physics educators and tutors work to help their students/tutees to overcome these obstacles.

I thought it would be a good idea to create a thread where those interested could post a certain stumbling blocks that they or their students encountered, and how they overcame them.

I hope that this thread could be a place where people can share their teaching strategies and philosophies. The physics community as a whole can only benefit from the collaboration of educators.

Please feel free to offer or to ask for advice on explaining certain concepts that may be hard to explain or to get across.


I'll start:

I'm currently looking for a good way to explain the concept of potential/voltage to those I tutor. I use the definition of Potential Energy per Unit Charge, etc. but this seems to give some people trouble. Any advice would be greatly appreciated.



G01

 

[Ki Man]

I still find that concept somewhat tricky. My dad is a senior electrical engineer who went to UToronto and he still found it hard explaining that to me. Its almost like the story of the blind mice trying to figure out what the elephant was.

I guess the only thing that you can do in that situation is to try to be as cooperative as possible. and articulate

 

[arunma]

Hello all!

I have been toying with the idea of posting a thread like this for some time.
Currently, I am a physics tutor, and everyday I come into contact with so many students who hit certain pitfalls in their study of Physics. Whether it be finding vector components or normalizing wavefunctions, everybody hits a stumbling block when studying physics, and physics educators and tutors work to help their students/tutees to overcome these obstacles.

I thought it would be a good idea to create a thread where those interested could post a certain stumbling blocks that they or their students encountered, and how they overcame them.

I hope that this thread could be a place where people can share their teaching strategies and philosophies. The physics community as a whole can only benefit from the collaboration of educators.

Please feel free to offer or to ask for advice on explaining certain concepts that may be hard to explain or to get across.

Awesome idea! I was a physics tutor for my last two years of college, and I'm going to be a TA when I start my PhD next fall. I'm planning on going into a career that involves mostly teaching, so as you can probably tell, I'm quite interested in this topic.

I'll start:

I'm currently looking for a good way to explain the concept of potential/voltage to those I tutor. I use the definition of Potential Energy per Unit Charge, etc. but this seems to give some people trouble. Any advice would be greatly appreciated.



G01

That definitely seems like a hard one. I say this because as people who have mastered such concepts as electric potential, it's somewhat difficult to recall what it was like when we didn't understand this. The first suggestion I'd offer (and this is something that applies to physics teaching in general) is that you should insist that your students always solve problems analytically. I've found that when my students were presented with problems that involved numerical values, they were tempted to plug and chug. But in addition to being an inelegant way to solve the problem, this makes it far more difficult for them to understand what's going on. When problems with numbers showed up, I taught my students to invent variables, solve the problem symbolically, and then plug in numbers at the end. In addition to aiding in understanding, it might help to remind your students that doing problems analytically is a good way to gain partial credit. Graders typically give very little credit for numbers, especially if the number is wrong. But an analytic solution with the wrong answer is woth quite a bit of credit.

The idea of electric potential as a potential energy per unit charge seems pretty straightforward. So if your students don't understand this, then I think that they must either have trouble with the concept of potential energy, or the concept of the electric field. Either way, they're having trouble with a fundamental concept, so it's important for them to gain this understanding. First, I think you should reinforce the idea that electric field is the force on a test charge, and that the relationship between electric field and electric potential is analogous to the relationship between force and potential energy.

Secondly, you should remind them of what potential energy is. For motion in one dimension, it's extremely helpful to think of potential energy curves as a ball rolling on a hill. Electric potential is essentially the same thing. One can think of the potential of a point charge as a hill that gets infinitely steep, and a point charge as a ball rolling on that hill. If your students are in the calculus based version of introductory physics, then I think that it's also very important for them to get some physical intuition for mathematical tools such as the derivative. The image of the ball rolling down the hill physically demonstrates that the electric field (=force on a test charge) is the negative derivative of the potential.

Well anyway, good luck with your students, and I hope this helps.

 

[AKG]

What about the analogy to water? See here.

 

[Beeza]

From my personal tutoring experience and observing my peers tutor, I've found one of the biggest barriers in a "tuttees" experience is the tutor talking at too advanced of a level.

For instance, if your helping an english major struggle through a basic algebra based general physics course, there is no need to derive the work-kinetic energy theorem in front of them-- as it is likely seeing that will just confuse them more!

One needs to be able to "dumb" down the material based on their audience. I'm sick of watching other physics majors with god syndrome talk like they are some kind of genius trying to impress some physics newbies. My rant is over ;)

 

[alegoull]

I teach high school physics and definitely agree that the whole concept of potential and potential difference is baffling to most kids, even the very bright ones.

The way I teach it is by relating it to gravitational potential energy, a concept most kids are pretty comfortable with. I have them calculate the "gravitational potential" (in J/kg) at different points near the Earth's surface using a "test mass" and then have them calculate the "gravitational potential difference" between those points. Also, it's good to have them qualititatively evaluate these quantities at different points (e.g. "Is the gravitational potential larger at this point or this point? Why?"). They will then see that objects tend to move from high potential to low potential and they can calculate how much PE is lost as masses move through this potential difference. Once they're comfortable with these ideas I seque into electrical potential and electrical potential difference by replacing the Earth with point charge and asking the same questions.

This process takes much longer than simply stating the book definition but it helps them develop more of a feel for the concept. I do a very similar thing to teach the concept of electric fields, since that also befuddles most kids.

 

[ZapperZ]

From my personal tutoring experience and observing my peers tutor, I've found one of the biggest barriers in a "tuttees" experience is the tutor talking at too advanced of a level.

For instance, if your helping an english major struggle through a basic algebra based general physics course, there is no need to derive the work-kinetic energy theorem in front of them-- as it is likely seeing that will just confuse them more!

One needs to be able to "dumb" down the material based on their audience. I'm sick of watching other physics majors with god syndrome talk like they are some kind of genius trying to impress some physics newbies. My rant is over ;)

Actually, the problem here works both ways, and one can clearly see this even here on PF.

Very often, students seek help by simply presenting the exactly HW problem that he/she could not do, and that's it. There is often no explanation what exactly is the stumbling block, or if the student has attempted it. I always cringe when I see the same thing done here on PF, and anyone who has been here long enough would have seen tons of such a thing happening.

However, I cringe a second time when I see responses from people who clearly did not have any knowledge of the state of knowledge of the person asking the question. So the responses can range anywhere from basic intro physics all the way to having to know quantum field theory.

A good student will show what he/she knows and don't know. A good tutor will attempt to judge what the student does and does not know, and start from there. It has to work both ways for there to be a perfect interaction. This rule works almost in every aspect of the process of trying to understand anything.

Zz.

 

[mathwonk]

I agree with others here that the main pitfall is not scientific, but in relating to the student. As it says in Proverbs, "an impatient man cannot teach".

(But we can try.)

 

[budala]

What's the appropriate hourly rate ($) for tutoring math or physics , grade 11.

 

[mathwonk]

i always do it free, like here, since it is hard to charge as much as it is worth. you should ask around your community for the going rate.

 

[ChaoticLlama]

I mostly tutor calc, but I've noticed a lot of the same things as you've mentioned.
It's the rare individual who just doesn't 'get it'. The more commen scenario is the individual who is missing a cruical piece of understanding or skill to recognize a certain form.

The most effective learning tool is to look at the studnet's homework book, and then ask them to solve a problem in front of you. The student must be able to communicate with you, and speak to you in 100% correct mathematical/physical language. It is only then will you be able to assess the student's true ability and diagnose the problems they encounter.

A lack of confidence is a huge contributor to low grades. I have one student in particular who achieved the highest mark across all grade 11 classes, yet the individual is now struggling with calculus. It's purely due to the fact they had mastered plug & chug instead of understanding, and when faced with the challenges of AP calc shortfalls became apparent (however I blame the education system which focuses on this learning style, not the student).

accurate communication of the problem you are faced with is key. it is the greatest skill I walked out of high school with and now engineering is rather simplistic to me.

And yes, no struggling student gives a damn about proofs. don't bother.
Being able to explain a topic you understand in clear language, imparts the knowledge to your student and enhances your own understanding.
teaching and learning are two sides of the same coin

 

[G01]

Thanks a lot for the advice everyone! I was thinking about this more, and i want to know what everyone else thinks about this. Many of the people I tutor have problems with retention. I came across a lot of people who could add force vectors and find force components with no problem at the end of the intro mechanics course, yet when they reappeared this semester, many had problems adding and finding components for electric field vectors.(Remember these are not physics or engineering majors)

I think that the cumulative aspect of the material in an intro physics class should be stressed more. Students should know that many of the concepts they learn in mechanics will be back when they hit E&M, etc. This way the students will make a bigger effort to store the information for a longer period of time. Of course, their are always those who just don't care about the material, and because of that, don't retain it.

What do you guys think?

 

[robphy]

I came across a lot of people who could add force vectors and find force components with no problem at the end of the intro mechanics course, yet when they reappeared this semester, many had problems adding and finding components for electric field vectors.(Remember these are not physics or engineering majors)

I think that the cumulative aspect of the material in an intro physics class should be stressed more.

It is often not realized that "adding vectors" and "finding components of vectors" are MATH concepts... and NOT PHYSICS concepts. PHYSICS often tells you that you have to do some MATH to solve a particular problem. PHYSICS may tell you that two particular vectors need to be added... but the act of adding them is MATH... and the failure to do so correctly indicates a student's problem with MATH.

 

[berkeman]

One of the things I like to try to do in tutoring is pass along some of the mental images that I've found helpful in my learning and work. Like helping a student of trig and sine waves to visualize how a side view of a point on a spinning wheel that is translating sideways looks like a sine wave. Or how impedance vector components act in the s-plane for filters and for systems with active feedback.

And combination mental images and mental pictures that are important to memorize and get familiar with using to inuit steps in a problem. Like with trig students, I'll always help them start a crib sheet that has plots of sin, cos, and tangent on them, as well as their triangle definitions. So when they start having to deal with tan() or inverse tan(), they already have an intuition about what the asymptotes will be doing, so they don't end up running through inifinite asymptotes in their solutions.

Also, with entry engineering students, one of the biggest tricks is to get them familiar and comfortable with carrying units along in their equations. It helps them early when they are trying to figure out what to divide to get a velocity (distance/time), and it helps them later as they work out more complex solutions, because if they carry units along in each step, it's much easier to spot algebra mistakes as they happen (instead of 10 steps later when you get the wrong answer).

 

[G01]

One of the things I like to try to do in tutoring is pass along some of the mental images that I've found helpful in my learning and work. Like helping a student of trig and sine waves to visualize how a side view of a point on a spinning wheel that is translating sideways looks like a sine wave. Or how impedance vector components act in the s-plane for filters and for systems with active feedback.

And combination mental images and mental pictures that are important to memorize and get familiar with using to inuit steps in a problem. Like with trig students, I'll always help them start a crib sheet that has plots of sin, cos, and tangent on them, as well as their triangle definitions. So when they start having to deal with tan() or inverse tan(), they already have an intuition about what the asymptotes will be doing, so they don't end up running through inifinite asymptotes in their solutions.

Also, with entry engineering students, one of the biggest tricks is to get them familiar and comfortable with carrying units along in their equations. It helps them early when they are trying to figure out what to divide to get a velocity (distance/time), and it helps them later as they work out more complex solutions, because if they carry units along in each step, it's much easier to spot algebra mistakes as they happen (instead of 10 steps later when you get the wrong answer).

The carrying the units through the whole problem is definitely something that should be stressed. I come across a lot of people who screw up problems with mistakes that could have been avoided by some good old dimensional analysis!

 

[Moonbear]

This is a good topic to discuss. The most important thing when tutoring a student is to ask them lots of questions. Before you can get them past their stumbling block, you need to find out where they've tripped. It may not be the present problem you're working on, but a concept several chapters ago. My experience in teaching a variety of subjects is that students stumble most often because they are not relating concepts from one chapter to another. They have this mental dividing line that once they are done with a chapter and have passed the test on it, they don't need to know that anymore. A good tutor/teacher/instructor will help them find those conceptual relationships. Of course, that means the tutor themself must have a solid conceptual understanding of the material. I cringe to see people tutoring who just know how to solve problems really well, but don't really understand the relationships between concepts themselves, and end up just doing problems for someone else, which teaches them nothing.

So, work backward...what old concepts does a student need to fully understand a new concept. Go through them and see if they have all those foundations in place. Do they know their definitions of terms, do they know what each of the symbols for variables in an equation stand for, do they know where that equation came from, and why? Can they paraphrase without changing the meaning of something? Often, students will have memorized an explanation from their notes, but don't understand what it really means. This will be identified if you ask them to paraphrase. Listen carefully for those few key words that make a world of difference if you substitute a word that is similar by dictionary definition, but not similar by scientific definition. You need to force them into active learning, not just passive learning. Lectures are passive learning, textbooks are passive learning...information is thrown at them and they try to absorb what they can. Tutoring is a good way to get them to use active learning...have them tell you what they know and explain things to you. Ask them how two concepts relate, and if they stare at you blankly and say they don't, then you can prompt with more questions until they see the connection.

Also, keep in mind that students have different learning styles. While you may be able to appreciate the beauty of mathematical equations, or words in a textbook, they may need pictures.

So, my suggestions are general, not specific to any particular problem, because I don't teach physics, but the same teaching methodologies apply no matter what subject you teach.

 

[berkeman]

Good advice, MB. Especially the paraphrasing exercise and the linking earlier concepts. I'll use those in my next tutoring sessions!

 

[G01]

Yeah Moonbear, that's great advice.

Something that I have gotten into lately in the group tutoring sessions I work at is to have the students solve problem for me. Let's say that the students have a test the next day on, let's say, waves and wave optics, and they want to go over certain sections on different diffraction problems. I gave each of the tutees a piece of chalk and one at a time I had them do the problem on the board and explain it to their classmates that were there. They each took a turn explaining problems to others, while I would correct any errors along the way and help lead them int he right direction when they got stuck. I believe this definitely helped better than anything else we had previously done. Explaining their problem solving methods to other really helps cement the material in the brain. It's too bad that we can only do something like this when we're not over run with walk-ins wanting help(by help I mean someone to do their homwork for them.) Our tutoring sessions are a lot like the PF Homework help forums, in fact, I try to tutor the same way I answer homework questions on PF, with leading hints and letting the student put the facts together to solve the problem.