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2

Probably best to refocus the question on drawing the abstract syntax tree for the expression instead. There are multiple correct answers. For example, * / \ 5 * / \ a * / \ b + / \ x y , which focuses on binary operators, or * / \ /| |\ 5 a b + / \ x y , where there's a single, quaternary (or $n\text{-...


5

There are at least 16 factors: anything of the form $5^ia^jb^k(x+y)^l$, where the exponents are all either 0 or 1. You could in fact say that there are infinitely many factors. For instance, I could say that the expression contains a factor of $5/7$, and also a factor of $7$. The only moral I can see to this example is that the normal way we talk about words ...


1

To further complicate matters, note that definitions in two of the answers (so far) either say or at least could be interpreted to say that $5a$ and $5ab$ and $ab$ and $ab(x+y)$ and $b(x+y)$ are also factors. And I've probably used "factor" to also include things like $5b$, for example if I wanted to cancel a factor from the numerator and ...


1

In my experience (German high school teacher): A factor is an operand in a multiplication and I would identify 5, a, b and (x+y) as factors. For "term", I'm aiming for a distinction between terms and equations. Thus a quite good definition of a term could be "Any legal sentence of mathematical symbols except equations". Depending on the ...


2

[I'm answering your questions in the order I usually introduce these words to beginning algebra students.] What definition would you give to your students as to what a term is? In our in-house texts, we teach that terms are: Parts of expressions separated by addition or subtraction symbols, except those between "grouping symbols" or in implied ...


3

I agree that it isn't a term. A term is a monomial and this can be simplified to 2 monomials. Certainly if I was collecting like terms, I would simplify this first. As for factors, I would count: 5, a, b, and (x+y). The reason is that if I was looking for a common factor (if this was part of a long expression with other terms), I might factor out any one ...


2

Here in Australia (NSW specifically) the highest level of high school maths in Year 12 has a topic on the logic and methods of proof. This includes general concepts of proof (symbolic logic, truth tables, the contrapositive, proof by contradiction, proof be counterexample, etc.) and some specific methods of proof. I think the best way to get a feel for what ...


3

There is no generally applicable answer to your question. In my own career I often taught while learning the material as my mathematics department began to offer more and more computer science. I learned the material a course at a time by signing up to teach it. I talked a lot with colleague mentors who knew the material. I always told my students in the ...


4

I teach at community college. That means I have a masters degree. When I first taught statistics, I had never taken a statistics course. Luckily, it was before I adopted my son. I spent 60 hour weeks, studying from many different textbooks, and asking myself questions. (I proved some results that we would never prove in our stats class.) I was an ok teacher ...


4

What is the medium of the content? If they are videos, then YouTube would probably be first option but if they are, say, pdfs, then you might have to make a blog and then upload to that there. It still might feel like an island at first but it will gain traffic from your students and then other people who find it in search results. There are also problem-...


0

Your list seems like overkill to me. As far as geometry, Kiselev is basically a rehash of Euclid, so I don't see the point in studying both. Just pick one. I don't think you need the solid geometry parts of either. If using Euclid: -- Euclid contains stuff like number theory done in an ancient style that is now only of historical interest, so if using Euclid,...


2

You don't show why, not can I see how, your change to a digital outcome from a scaled one would change the behavior that concerns you, cheating on graded homework. In contrast, I can see how changes like eliminating graded homework and replacing it with in class orictored exams would reduce, not eliminate, but reduce, cheating. Because it is harder under ...


3

Proficiency in any field requires putting some rather high number of hours of hard work (some 10,000 hours or so) into it. You have to align the incentives of would-be learners so they do put in that time. If the best way is just pass/fail or a grade system is anybody's guess, but perhaps a search will turn up rigorous studies on the matter. Note that I don'...


0

I see two options: acceleration or enrichment. Middle school is the time when acceleration becomes possible, at least in most U.S. schools. So, instead of Math 6 he would be taking Math 6/7, instead of Math 7 he would be taking Math 7/8, and instead of Math 8 he would be taking Algebra I or HS Math I in districts that have switched to integrated math. ...


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I think there is a benefit to having alternate, conflicting answers to soft questions like this. My take is to keep going with the kid. Just ask for him to go with the kids a couple grades higher, when doing math. If they don't have that because of the grade structure, than have him be independent study for a period (or see if high school is near the ...


1

Since you are in the UK, I have a few specific suggestions below. I agree with existing answers and comments that there is little benefit in rapid acceleration. The Royal Institution hosts mathematics masterclasses in some areas. See https://www.rigb.org/education/masterclasses for more information. Sometimes the sessions are for students in specific age ...


0

I would avoid accelerating any further. Be aware though that even without acceleration a talented child will have taught themselves or be able to infer without being taught much of the syllabus. The problem withh acceleration is that while it exposes the child to new material it doesn't necessarily provide intellectual challenge. A very bright child wil ...


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