This is my first post so I'm not too sure of whether I am posting this in the appropriate format, or whether this post is appropriate or not - please let me know if it's not.

I am a first year university student who is intending to become a high school teacher after I finish my undergraduate studies. I am wondering if there are many other school teachers in this community and what particular methodologies you implement. I am seeking out discussions on teaching methodologies that people use, why they use them, and what is successful about them. In the lead-up to my career as a teacher, as of a month or so ago, I have begun compiling a document of methodologies and techniques I intend to use to maximise my effectiveness of a teacher.

A particular thing I would love to discuss is philosophies on teaching science. I strongly believe that it is *very* important for me to include a component on rationality in the curriculum, because too often students are taught "science" without first being taught how to think about science.

Some of my experiences tutoring math over Skype:

One-to-one tutoring is superior to one-to-many tutoring.

One-to-one tutoring can be structured as a conversation with lots of back and forth and keeps student participation high. It also means the teacher can adjust their teaching style to that particular student's level and personality.

One-to-many tutoring is more of a performance on part of the teacher and is quite different. The students are much more passive in this situation. I don't know how to do this well.

The most important thing is to

get the student to talk out loud about their thoughtswhen they see a problem. If they're intimidated or confused, it's very useful to ask the student what particular bit of the problem causes the confusion. (Is it because there's an x in the denominator in the fraction 2x in an equation you need to solve? Or is it because you need to differentiate cos(x2) and the student doesn't know how to handle the x2? Etc.)Being able to identify and name the bits of the problem that gives them difficulty is a skill in itself and requires practice. When they do name them, you have a great opportunity to develop empathy with the student by reflecting their thoughts back to them. ("Yes, when there's an x2 inside the cosine it really is a bit more tricky to differentiate than we're used to!" Etc.)

Then you can remove the complicating factor and solve a simplified, related problem. (E.g. what if the equation had 2x instead of 2x? Or what if it was just cos(x)? Would the student then be able to solve the problem?)

Then you add back the complicating factors incrementally until you get to the original problem, explaining how to deal with the complicating factors using a similar problem with different numbers/functions, etc.

Optimally,

the student should be teaching meand telling me step-by-step what I should write down (and how) as we solve the problem, with me only playing a supporting role, giving suggestions when the student gets stuck. Or even better: with me prompting for suggestions from the student, which we then try out, whether or not they work.This role-reversal, with me being just a robot-hand and the student being the controller, gives great insight into their thought process and helps debugging it. (E.g. are they able to recognize that we can use Pythagoras because we have a right-angled triangle? Do they know the correct rules for multiplying together two parentheses? Etc.) It probably also strengthens the student's memory.

Some students are closed up and will simply say "I don't know." I find it's important to encourage them to guess, sometimes wildly, and then receive that guess non-judgementally, and then try it out. If it doesn't work, you can nearly always learn something from *why* it doesn't work. Does it *almost* work? Does it get us *closer* to the right answer? Or further away? (E.g. if dividing by x makes the equation more complicated, the student himself will often notice that the opposite approach, i.e. multiplying by x works better. Etc.) This also works as a free-recall exercise, helping the student connect related bits of memory together.

Removing the student's fear of math and self-labeling defeatist attitudes, and increasing their self-confidence is more important than any theorem you can teach them. But you cannot attack these beliefs directly. They will fade away by themselves in proportion to how many problems they solve successfully and how they learn to deal productively with problems they don't immediately understand.

If I at any point during the session get frustrated or negative or judgemental, I lose. The student will not look forward to the sessions; they'll become cautious of guessing because you shoot them down; and they'll be reluctant to tell you their working out in fear of being judged.

Polya's /How To Solve It/ has a useful list of questions to ask yourself (and therefore also the student) as you go about solving problems.

E.g.

Not a school teacher, but I've been teaching a kids' programming class for two years, and a math class for the past few months. I also did more math teaching in the past. My advice is to find one or two students (better if they aren't too smart or motivated) and start teaching them on a regular schedule, in person, as soon as possible. By all means, bring your own ideas and be all excited about them, it's more fun that way :-)

That's the #1 thing you must do. Start arranging it today. This hour.

I also teach a kids programming class currently. I also run youth movement activities for kids most wekeends and on holiday camps!

Cool! What's your approach to teaching programming? What age are the kids? Sorry for prying, I'm just very curious.

So the kids I teach are about 7-12 years old.

Still in early stages, I've only been teaching them for 5 weeks so far (1 hour per week).

My approach is to set them onto a task, and get them to attempt it on their own. If they are struggling, I tell them that before I will help them they need to just try a few of the first things that come to mind, see what happens, and if they still need help I will walk them through figuring it out for themselves.

Only very rarely do I explicitly tell any of the kids how to do a specific thing.

Thanks! :-)

What kind of tasks? Is it a game like LightBot, or an educational tool like Scratch, or a real programming language straight away?

We use the block courses of the website Code.Org. It's similar to scratch in some regards. Not familiar with LightBot.

Teaching is not about methodology; it's metis, not episteme. (I am also not a schoolteacher but I have taught at CFAR workshops.)

I love cousin_it's suggestion that you should start teaching a student regularly as soon as possible, but I have an additional suggestion about how to spend that time: namely, your goal should not be to teach anyone anything but to find out how students' minds work (and since anyone can be a student, this means your goal is to find out how people's minds work), and how those minds interface with the material you want to teach. E.g. if you attempt to teach your student X and they're not getting it, instead of being frustrated at how they're not getting it, be curious about what's happening for the student instead of getting it. How are they interpreting the words you're saying? What models, if any, are they building in their head of the situation? Etc. etc.

My first response to the question about teaching science is whether that's a subject in the curriculum in the first place. The standard curriculum includes teaching scientific findings but little about teaching science.

If you are actually free to teach about science Keith E Stanovich's How to Think Straight About Psychology. Stanovich has a great description of what science is:

The book also discusses other elements of the scientific process that are important to understand.

A Year of Spaced Repetition Software in the Classroom is an interesting post by an actual teacher about using Anki inside of his classroom.