Helping students transition from High School to University

[L-x]

I am in the rather unique and exciting position of being able to design an extension curriculum for some gifted Physics students who are in their final year of high school. The goal of the curriculum is to help prepare them for university physics with tools and ways of thinking, without just teaching them physics content that they will then have to re-learn at university. For example, some things I am planning to include are:
- how to use different frames of reference, probably in the context of an introduction to galilean relativity
- how to approach problem-solving (https://arxiv.org/ftp/physics/papers/0508/0508131.pdf is a great read as a starting point)
- how to connect the mathematics they've studied to their A-Level Physics curriculum (some of the mathematical concepts they meet in maths but aren't explicitly linked to the physics A-Level are vector and scalar products, differential equations, and matrix algebra)

I am, however, interested to discuss with others which parts of university required the biggest conceptual leaps, especially when those leaps can be more gently introduced earlier. Again, the idea is very much not to just teach first year content, but more to provide a gentle introduction to tools (for example changing reference frame) which are both vital and intitially difficult to grasp.

This is a UK-based school, and the students will all be studying A-Level Physics, Mathematics, and Further Mathematics. Syllabuses are easily available online but in my brief attempt to convert to American qualifications it looks like they will have seen much more maths than someone taking AP statistics and AP calculus, and about the same amount of Physics as someone taking AP physics 1 and 2, but as much as someone taking AP physics C.

Thanks!

 

[e-pie]

Maybe a lecture about the philosophical perspective of what physics really is, an account of the great scientists who made the subject a part of their daily life, how we use it everyday, some little insights on higher branches of the subjects would be a nice way to motivate and imspire the students to study the subject.

Like when I teach Maths, to a new batch of students, the first 1,2 classes I tell them stories of how Galois shouted for not passing the Ecole Polytechnic entrance test, how Cauchy wrote 600 pages of research, how the mathematical space surrounds us, how ripples in water can be studied using mathematics etc etc. This sure motivates some students. I do not expect all.

 

[e-pie]

The actual teaching depends on the type of students intended.

A course in non-rigorous calculus, vector, Newtonian Mechanics and the limitations of it, how it was expanded(The Science of Mechanics by Sir Ernst Mach is a great read here) would appeal to the students more.

You can use interactive graphs of functions, Mathematica may come handy in this. Lectures by Feynman( on YouTube) will cover the “inspire“ part.

AP French Newtonian Mechanics and Kleppner Kolenkow's Mechanics, Calculus by Lang or Thomas or Stewart will cover most of the material you are intending.

Practical experiments and lecture series like they will get in college is also a nice idea.

 

[Andy Resnick]

I am, however, interested to discuss with others which parts of university required the biggest conceptual leaps, especially when those leaps can be more gently introduced earlier. Again, the idea is very much not to just teach first year content, but more to provide a gentle introduction to tools (for example changing reference frame) which are both vital and intitially difficult to grasp.

In my experience teaching both algebra- and calculus-based intro physics courses, a nearly uniform difficulty students have is understanding how 'the real world' gets abstracted into 'physics world' and the underlying motivation to model the real world as 'solvable problems'. Most of my students in these classes are either engineering majors (calc-based) or health science majors (algebra-based), and they really struggle with understanding how the simple, clean, abstract problems they work on in class have any relationship to the messy world they live in. To be really clear, just because a homework problem uses words like 'road', 'car', 'wheel', 'rope', etc. doesn't mean the students agree that the problem has any relationship to real cars, roads, wheels, etc.

To help the students, I try and work in as much 'estimation problems' as possible, so they begin to understand that oftentimes, a simplified model can account for 90% (or more) of observed behavior.

 

[berkeman]

- how to use different frames of reference, probably in the context of an introduction to galilean relativity
- how to approach problem-solving (https://arxiv.org/ftp/physics/papers/0508/0508131.pdf is a great read as a starting point)
- how to connect the mathematics they've studied to their A-Level Physics curriculum (some of the mathematical concepts they meet in maths but aren't explicitly linked to the physics A-Level are vector and scalar products, differential equations, and matrix algebra)

I can think of a few things that may be useful:

• Be sure they understand how to carry units along in their calculations to help to check their work and to be sure that the units make sense. They should understand how to convert units by "multiplying by 1" with the correct selection of units in the numerator and denominator of the "1" fraction to do the unit corrections. Learning this trick early in my undergrad was a big "aha" moment for me, and less than 10% of the students in my class already knew of this trick.
• Find some good visualization tools for common problems and show them to your students, to get them used to coming up with visualizations that help their understanding and memory. For example, it's helpful to memorize the graphs of the trig functions and be able to sketch them quickly to help with intuition on problems that involve trig functions. It's helpful to be able to visualize the 2-d Complex Plane extended into 3-D by adding a time axis, so that you can visualize complex functions that have a time dependence (this is used in EE a lot for signals). Show them animations of an EM wave propagating along the time axis, and point out the relationship between the E and B fields as the wave propagates. Etc.
• Teach them some intuitive tools for approaching problems with variables, like thinking about what happens in an equation if one of the variables is made very large, or very small, compared to the rest of the variables. This can often give some intuition for how best to solve the problem, and helps you to guess about what the answer should be.

Hope that helps. Let us know what-all you come up with.

 

[mpresic3]

This seems to be a unique opportunity.
When I conducted recitation and lab sections at three universities, I found that students often had holes in the knowledge of individual and collective facts that they should have learned in high school or earlier. This is not surprising because many science syllabuses downplay the learning of facts in favor of scientific processes and methods. Both have a role. Let me propose an example.

One day the instructor of the course told me a student in my recitation section missed the final, through no fault of their own, and told me to give the student an oral make-up exam. As the student was known to be very conscientious, the instructor told me to grade quite liberally.

I was about to find out how well the student could think on their feet. I had in mind to have the student determine the density of the moon to show it wasn't green cheese.

The student would have to find the Mass of the Moon, and the volume of the Moon.

Teacher: Can you find the volume of the Moon?)
Student: I am having trouble.
Teacher: What is the volume of a sphere.
Student: 4/3 pi r squared.
Teacher: (Here I was pleasantly surprised. The student knew how to compute the volume from the radius)
What is the radius of the Moon?
Here the student went for the table in the back of the textbook.

Teacher Did you ever learn the size of the Moon in School?

The student did not know. Back when the teacher was growing up, astronauts were actually traveling to the Moon. It was common knowledge that the diameter of the Moon was (very roughly) one-fourth the diameter of the Earth. This approximation would lead to a fair approximation of the density. At least the rough approximation would still not lead to a "green cheese" moon with density 1 g / cc.

The student was too young to remember these times.

I told the student to use 1080 miles for the radius. The student converted to meters and continued.

Teacher: We are going to use Kepler's third law relating the period of the Moon's orbit around the Earth to find the mass of the Moon.
What is the distance from the Earth to the Moon (approximately)

Here again a complete blank from the student who moved towards the book.

Student: One-Million Kilometers? (this was just a guess)

Again I thought when I was growing up, and astronauts were moon-bound, it was common knowledge among college bound HS students the Moon was 1/4 million miles from Earth.

I corrected the Student
Teacher: Use 238000 miles.

The student converted this to kilometers and then to meters.

Teacher: We are going to need the period of the Moon's orbit around the Earth. How long does it take the Moon to circle the Earth?
Student: It is in the book.
Teacher: Suppose we use common knowledge.

Teacher: Does the Moon orbit in a day? (blank look from the student)
Teacher: How about a week? (blank look)
Teacher: How about a month? (still no sign of recognition)

Teacher: It is a month. That is why it is called a Mo-on-th
Student smiles.

Teacher: use 29 days.
Student does the conversion to metric.

Finally the student needs the value of GM.

The student moves towards the textbook.

Teacher: Let's not look it up.
Let's equate Newton's gravity GMM/ R squared to mg. What is g

Student: (triumphant) 9.8 m/s^2
Teacher: good. What should we use for R

(Here I had the student draw a hanging mass so there was no question R was the radius of the Earth)

Teacher: what is the approximate radius of the Earth

The student once again moves to the textbook.

(It seems to the teacher that this is common knowledge)

Teacher: Well how far is it around the Earth? We can divide by 2 * pi
Student: I do not know.

I relented,

Teacher: Use 3900 miles for the radius?end


You get the idea. The student does OK until they need individual (once) commonly known facts about our planet and moon that the teacher learned (actually in middle school).


I assure you this was a school where the average SAT verbal and math combined was about 1400 (in the year 1980). I could give many other examples.

These were very smart students with holes in their general knowledge. They are textbook relient. This is even a bigger problem now that the internet allows them to look up even more.

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The story does not end here. I am told a story of a job interview where the interviewer proposed to sell a toy to every school child in the US and asked given a particular start-up cost would it be profitable. The conversation went like this.

Interviewer: (wanted the interviewer to assume the school age market was 10% of the total population) What is the population of the US?.

Applicant: I do not know.

Interviewer: Make an approximate guess.

Applicant: One-million people

Interviewer: You know this isn't right. The greater metropolitan area of this city alone is a million people. Can you make a better guess.?

Applicant: One-billion people

Interviewer: (incredulous) You think there are one-billion people in the US

Applicant: Well you said it was more than a million.

As crazy as this sounds this came from a true interview from a candidate from a good school with a great academic record.
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To make a very long story short. It may be time to ensure the student retains facts that were once relegated to "common" knowledge.

 

[mpresic3]

correction to the previous post. The student told me the volume of the sphere was 4/3 pi r cubed and of course they were correct