Physics/math: how much knowledge does a high school teacher need?

[haushofer]

Dear all,

as some of you may know I'm a math/physics teacher at a teachers education in Holland, where we prepare teachers at pre-university level high school. We focus mainly on teachers who are already licensed to teach in the first three years of pre-university high school ("2nd degree"); for the last three years (4,5,6) they enroll with us to obtain a "first degree".

Of course, some of the curriculum in our education they'll also teach at their pupils, at a lower level. But some topics they'll never teach to them. One example of this is Linear Algebra; of course high school pupils need to solve equations, but they'll never encounter matrix equations or vector spaces. I also taught quantum mechanics to physics teachers, which goes pretty beyond they'll teach their own pupils.

So that made me think: how much do teachers need to know to stand above their pupils? Has there been any research on this topic? I'm also intending to do some research on my own, but I thought maybe other teachers here are also interested in the topic and can add to the discussion ;)

 

[.Scott]

I'm all for pushing statistics over calculus. Calculus is very STEM-oriented. Statistics is much broader.
Knowing how to read a study and understand how it applies to your situation. For example, is deaths per mile important? What about deaths per passenger mile? How do studies hedge against the placebo effect?
How are studies designed?
Different parts of the community have different criteria for studies. You need five-sigma to claim a new particle discovery on Physics. You need a more complicated evidence-based studies for drugs or medical procedures.
It's important that High School student recognize the limitations on N=1 studies.

 

[gleem]

There is a lot of talk about QM and its counterintuitive behavior, which is commonly referenced in the media. It is reasonable to teach an elementary introduction to quantum principles. In my opinion, it would be of value.

Here is a program from the University of Chicago on teaching quantum mechanics principles to high school students. I hope you find it useful.

https://teachquantum.pme.uchicago.edu/_gl=1%2Amnb3hs%2A_gcl_au%2ANDA3MjcyMzc1LjE3NzYyNzU5NDE.

 

[berkeman]

So that made me think: how much do teachers need to know to stand above their pupils?

I'm not sure I like the metaphor of "standing above their pupils", at least in a STEM teaching environment. I've tutored numerous folks over the years (not for pay) in math, science and engineering courses, and I always felt that my best contribution was passing along some of the intuitive understanding I have acquired over the years, including mental models of difficult subjects. For example, in trigonometry, I find it helpful to have mental images of plots of sin, cos, tan in my head (plotted on the same horizontal axis), and visualizing many trig problems as lines on those plots.

In algebra word problems, I try to pass along my intuition for how to figure out what variables to define first, and how to start writing equations that interrelate those variables to get a handle on the word problem. In EE problems involving Linear Systems, stability and the s-domain and similar, I like to pass along the intuition that you get by visualizing the 3-D complex space plots of H(s) as below:

https://lpsa.swarthmore.edu/Representations/SysRepZPK.html

So I guess my reply to your question is that it is best if the teacher not only has adequate knowledge of the subject they are trying to teach, but has a more in-depth understanding of the subject including the intuitions they have developed by working with the subject and solving hard problems over a long period of time.

 

[sbrothy]

I've written papers for people from Technical School and Computer Science at university bachelor level for pay. Sometimes it backfired as they didn't understand the papers I wrote for them, so I ended up having to teach them for several hours (sometimes days) making the price they paid moot or downright ridiculous.

Their censor told them to their face that he didnt believe they had written it themselves but as he couldn't prove anything he had no choice but to give them pretty good grades (10 on the 03-13 scale used here).

My point is that sometimes education and good grades prove nothing at all.

 

[gleem]

New research shows a maths-free framework using diagrams for total beginners could transform the way schoolchildren learn and understand quantum theory.

This is from this article: https://www.cs.ox.ac.uk/news/2280-full.html

This research has resulted in a book:

Quantum in Pictures: A New Way to Understand the Quantum World by Bob Coecke (Author), Stefano Gogioso (Author)​

available in paperback at Amazon https://www.amazon.com/Quantum-Pictures-New-Understand-World/dp/1739214714/?tag=pfamazon01-20

 

[haushofer]

I have a feeling my question was not properly formulated. Let me rephrase it:

How much surplus knowledge does a teacher need to be considered a good teacher?

One reason I'm asking this is because in Dutch teacher's educations more and more time is spend on pedagogy and didactics, at the cost of the the math and physics (subject content).

 

[sbrothy]

I recently read several books (or studies if you will) about education methods. (Sorry it's in Danish and probably hasn't been translated). As you mentioned didactics and psychology it was pretty much in line with how educational methods have changed with developments in psychology and pedagogy.

EDIT: And I realize that doesn't answer your question at all so I don't know what I'm doing. :)

 

[Andy Resnick]

So that made me think: how much do teachers need to know to stand above their pupils?

In the US, teacher licensing requirements vary from state to state. Even 'worse', different types of school (public, charter, private, etc...) are allowed to have their own requirements.

In Ohio (maybe not the best example), a minimum requirement for STEM teachers is "[Licensure] Candidates must have a bachelor’s degree in a field related to the subject area they will teach from an accredited college or university."

https://sboe.ohio.gov/educator-licensure/apply-for-a-new-license/stem-teaching-licenses

My 2-second search of other states seem to all share the requirement of a "bachelor’s degree in a field related to the subject area they will teach from an accredited college or university", and I will simply note how vague that requirement really is... Oral Roberts University is fully accredited, FWIW.

 

[Andy Resnick]

How much surplus knowledge does a teacher need to be considered a good teacher?

Not to be glib, but that is a bad question. There is no agreement on what, exactly, results in someone being "considered a good teacher".

 

[gleem]

How much surplus knowledge does a teacher need to be considered a good teacher?

My thought was to show current methodology for teaching QM in secondary schools, so that it would provide some guidance on the depth of knowledge one should have. You should have enough knowledge to deliver a presentation accessible to the least capable learner and provide the necessary insights for the most interested one.