Getting Students to Explain their Solutions

When I started my physics career, I had two excellent resources. 1) My math skills were solid. 2) My spacial reasoning were also solid. This got me very far in physics. My largest downfall was that I was not good at explaining the results of my work. I often dreaded the last one or two question on Professor Brüning's problem sets that asked to delve deeper into the results of the calculations. Over time, I have improved my abilities in this area significantly over my career. I improved by doing lots of problems, explaining my solutions and my thought process with my peers, and being forced to expand my understanding when teaching others. Of course understanding the results of a calculation is one of the most important skills a physicist needs and I want my students to be good at it.

Furthermore, in the job market employers are always looking for scientist with good communication skills. As much as I want them to wow their professors at university with their robust answers, I really want them to be comfortable explaining their thought process in the written word. To be able to show future employers that they are exemplary scientific communicators.

To do this,

• The meaning of a solution is linked to the process of getting there so I ask my students to explain their solutions. 
• I go through a problem solving unit with my physical science students that promotes verbalizing their thought process.
• I model explaining my solutions as much as I can remember to do it slash have time to do it.

For this post, I just want to focus on getting my students to explain their solutions. 

I just want to know and I want them to know their thought process. If they make a small angle approximation I want to know why they did? To get an analytical solution. Because the book does it. Because the pendulum can only be displaced by a small angle. I want to know why.

As an incentive I make it part of my rubric.

• 2.0 The solution to the problem is justified through the language of mathematics and using clear and concise english to explain each step.
• 1.8 The solution to the problem is correct, but it lacks a sufficient explanation mathematically or otherwise.
• 1.5 The solution contains minor errors. Such as a transcription error.
• 1.0 Contains a major error.
• 0.5 The question was attempted.
• 0.0 The question was not attempted.

I know that marks are a poor incentive in the long run, but I don't know how else to initiate my student into the habit. I've also toyed with the idea of not grading them on the content of their explanations, but just insuring that they are there. Some students struggle with understanding the material and if they battle it out on their problem sets then I'm cool with that. I want it to start a conversation with my students. I haven't been good at this yet, but it is something I'm working on. 

Examples to come, hopefully.

Later gator. JMS

A great engineering/physics question.

It is still very early in my teaching career and I'm not by any means reaching my own standards, but I did come up with this question that I'm proud of.

Light travels from air into some unknown medium as show in the figure.

1. Is the index of refraction larger or smaller than in air? Show a proof explaining your choice?
2. Calculate the index of refraction of the unknown medium using a protractor. Note that the index of refraction in air is 1.0003. 
3. What is the critical angle between air and the unknown material?
4. Draw an accurate path for a light beam that travels from the air into the unknown medium and reflects at least one time inside the medium.

I just finished marking this question. Most students did an excellent job of question 1. I'm proud of that. 

Question 4, however, left most of my students in the dust. In a weird way, this also makes me proud. Some students just drew an incident line inside the medium being reflected that was larger than the critical angle. Another group of students just threw their hands up and listened to the cries that there is no angle that will work. Other correctly drew pictures with an incident ray that goes into the unknown medium from the left side surface, refracts, then reflects off the top side surface. This is the correct answer, but then when they tried to get correct angles they failed and said it was  impossible. They failed because the reflected angle is much larger than the critical angle. They started their reverse engineering by stating that the reflected angle was the critical angle. Their failure I attribute to my own inaptitudes as a teacher but now I know about it. 

If you have an idea on how to improve the question please leave a comment. If you know how to help me teach the skills my students need for the fourth question that would also be helpful.

Anywho, that it is for the today. 

Mr. Samson

Bugil Academy : I got a Job!

Hello World,

I got a job working at a school in Cheonan, South Korea. My school, Global Leader Program (GLP), is part of a larger school Bugil Academy which is a boarding school. The GLP is a program funded by some large corporation here and is designed to prepare Korean students for western colleges and universities. The students have had to write tests to get into the school, so they are all motivated and academically astute. A great deal of courses are Advanced Placement, the curriculum created by the CollegBoard.

My job is to teach physics. Which is great because that is my training. Though in teacher's college I have been leaning more towards teaching Math. My curriculum is AP physics C and B based. Because the classes are small and have relatively few behavioural problems, I'm excited to develop my curriculum for when I go back to North America.

How do we teach 21st century students with web 2.0?

The students of the 21st will have a very different experience then the one I grew up in. For one teacher’s will no longer be the most easily accessible source of knowledge. I think this will lead to a shift in the role of a teacher. Lectures are most likely going to be a very small part of a teachers job. This is already true in elementary and junior high, but I see trends in secondary to move away from the model. It is only a matter of time before it spreads to University. Why should I listen to my professor lecture on Newtonian Mechanics when I can go on iTunes to watch a professor from M.I.T. do the same thing for FREE? Why should I limit myself to the degree requirements of a university? Why can't I tailor my education to my needs? The knowledge is out there. It is NOT our job to disseminate information.

So where do we carve out a place for ourselves as teachers for these students? For one we need to embrace the web as a tool for teaching.



Furthermore, we are expert learners; we have the know-how to discern the truthiness of information. Our job will be to show students how to engage with the information, how to produce it, and how to share it with the world in a safe and credible way. We will be moving towards giving our students a media literacy with course outlines like the topics shared in Dr. Alec Couros’s blog post “90+ videos for Tech. & Media Literacy”.

The interactive web capabilities of the web 2.0 are engaging youth to create, participate, and most importantly give them a place to share their world view. Teacher's shouldn't be fighting with their studentshttp://www.blogger.com/img/blank.gif to listen in class and stop going on facebook. We need to help them go on twitter, blogspot, youtube, and wikipedia to help them create the content they want. With this we will have to carry on Larry Lessig's discussion on copyright and patents.

This will go a long way since we have no idea what challenges our students will face when they become employees. The pace of innovation is growing at an exponential pace. In my life I have seen the death the death of the Renaissance Man and know even the analog in a subject like Physics is over. There is not a single professional academic who knows the breadth of knowledge that spans all of their department. There is such a connection between subjects physical chemistry, medical physics, bio-physics, geo-physics. We connect them all and yet we still have separate buildings for these connected subjects. Our students will need to navigate the plethora of options and find their way in it. I’m not sure how this is going to happen and how we can help except to be one of many mentors they will need on this journey.

The one thing I’ve seen recently that has inspired me is Raghava KK’s TED talk “Shake up your story”. Raghava makes the case that we should not strive for the Renaissance man in the sense of breadth of knowledge we should focus on breadth of view points. We should be cultivating empathy so that our students who will deal with a more connected world will be able to understand the people from other cultures they will interact with. And as my friend Jun Allard said to me not long ago you can't farm out empathy. In the current economy isn't that something we should build on.

21st Century Students and Web 2.0

The students of the 21st will have a very different experience then the one I grew up in. For one teacher’s will no longer be the most easily accessible source of knowledge. I think this will lead to a shift in the role of a teacher. Lectures are most likely going to be a very small part of a teachers job. This is already true in elementary and junior high, but I see trends in secondary to move away from the model. It is only a matter of time before it spreads to University. Why should I listen to my professor lecture on Newtonian Mechanics when I can go on iTunes to watch a professor from M.I.T. do the same thing for FREE? Why should I limit myself to the degree requirements of a university? Why can't I tailor my education to my needs? The knowledge is out there. It is NOT our job to disseminate information.

So where do we carve out a place for ourselves as teachers for these students? For one we need to embrace the web as a tool for teaching.Furthermore, we are expert learners; we have the know-how to discern the truthiness of information. Our job will be to show students how to engage with the information, how to produce it, and how to share it with the world in a safe and credible way. We will be moving towards giving our students a media literacy with course outlines like the topics shared in Dr. Alec Couros’s blog post “90+ videos for Tech. & Media Literacy”.

The interactive web capabilities of the web 2.0 are engaging youth to create, participate, and most importantly give them a place to share their world view. Teacher's shouldn't be fighting with their students to listen in class and stop going on facebook. We need to help them go on twitter, blogspot, youtube, and wikipedia to help them create the content they want. With this we will have to carry on Larry Lessig's discussion on copyright and patents.

This will go a long way since we have no idea what challenges our students will face when they become employees. The pace of innovation is growing at an exponential pace. In my life I have seen the death the death of the Renaissance Man and know even the analog in a subject like Physics is over. There is not a single professional academic who knows the breadth of knowledge that spans all of their department. There is such a connection between subjects physical chemistry, medical physics, bio-physics, geo-physics. We connect them all and yet we still have separate buildings for these connected subjects. Our students will need to navigate the plethora of options and find their way in it. I’m not sure how this is going to happen and how we can help except to be one of many mentors they will need on this journey.

The one thing I’ve seen recently that has inspired me is Raghava KK’s TED talk “Shake up your story”. Raghava makes the case that we should not strive for the Renaissance man in the sense of breadth of knowledge we should focus on breadth of view points. We should be cultivating empathy so that our students who will deal with a more connected world will be able to understand the people from other cultures they will interact with. And as my friend Jun Allard said to me not long ago you can't farm out empathy. In the current economy isn't that something we should build on.

Tennis

So the other day I woke up with a great idea to center some math (and science around); Tennis.

The idea would be to watch several tennis players playing aces where they send the ball down the line. Hopefully this will generate some questions such as

• how fast the ball is going?
• how do they get the ball to hit the line?
• why do they make noises when they hit the ball?
• how does the spin of the ball effect the motion of the ball after it hits the ground?
  
• etc...

From this you could get into approximating the path of the ball as a straight line. With the aid of similar triangles students could calculate the speed by knowing the dimensions involved. By knowing the position the ball strikes and the height of the tennis pro and reach. Getting the tennis players height seems to be like an easy stat but the reach might be harder to get. In order to solve that part of the problem some statistic could be used to explore the ratios between height and reach etc.

In order to get a deep analysis the students could then move on to 2d projectile motion and see how the values change in this realistic model. Then what would happen if air resistance would be a factor?

A small victory.

Today, I got a call from Mount Saint Vincent University. Now I have a interview to enter the education program at MSVU tomorrow at 1 pm. One step closer to the goal post.

I'm going to go over my application and think about things I would like to mention.

Cheers.