One of the above comments is true. In the modern classroom, if you wait to get everyone’s attention, you won’t be able to teach anything. That is especially true in today’s math classrooms. Many students are not motivated to learn. Math is objective and cumulative. It is easy to see where someone is on the spectrum of math understanding. However, ...
OP: "Refuse to teach without attention."
In my role as chair, I attended an instructor's class where he really
refused to advance until he was certain the students were all with him, via detailed verbal feedback. The students responded, stopped the presentations and asked questions.
I've changed my own teaching as a result of watching how this can ...
They are basic, friendly pieces of pedagogical advice. Most pre-college teaching is very much STILL in this mold.
Where we fall down is in high-end universities and graduate schools, where pedagogy is less emphasized in the paradoxical belief that harder material should be learned with worse training methods. Or that smart students don't need/benefit from ...
I'd say yes, and I'd go with binary if you had to do any one alternative base simply because it's so relevant to computing and technology, and in my experience teaching discrete math, once you understand binary, related bases like octal and hex are pretty simple to pick up. But I don't think the converse is necessarily true.
Ideally I'd like math and CS ...
I can't answer the OP's questions, but I'll just mention that
a local 6th-grade teacher (in the U.S.) has a successful unit on base-$5$.
It is mentioned in the recent article below. Sometimes he called it "star-fish math."
"Math for Grades 1 to 5 Should Be Art."
Mathematical Intelligencer. 42, pages 64–69, Dec. 2020.
I remember getting my first 18 inch slide ruler. I had worked hard, poison oak filled, hours making fire breaks in the Oakland hills to make enough money to get it. It was aluminum, had a spring loaded cursor that slid like it was greased, and the C and D scales (I think) lined up perfectly. It was huge and had scales I was never going to use. I loved it.
Not a proper acceptable answer, just an expansion of my original comment:
A literal/direct/mechanistic recitation probably involves a lighter cognitive load than a quirkier sentence-translated recitation. So:
one times five equals five
six times seven equals forty-two
eleven times twelve equals one-hundred-and-thirty-two;
one (copy of) five is five
I think for first learning, it is easier to think of the former, not the latter. So two twos make a four. After all, what is "times", for someone new to it.
But by the time you are doing the whole multiplication table (and six sevens is pretty high up into it), you've got more familiarity with multiplication and can just start saying "times&...
I think the multiplication table should be learned, but only up to ten times ten. As a student I would appreciate a teacher that made the task as easy as possible, and part of that is teaching only what is needed. The teacher can tell students that they can be glad they don't need to learn it past ten times ten.
There is a naturalness of stopping at ten ...
As with Ben C, I agree that kids differ in their abilities. Usually lower, slower than the people who frequent this site. Case in point, the casually name-dropped Tom Apostol calculus, is not typical. So, "I have met kids" is not a good indicator for general ability. You are dealing with a population of non-identical units. People are not ...
Found this after debating with my 8th grader son trying to bounce players of diagonal walls in a canvas js based game of his own making:
I agree with many posts above that we have it all backwards. Vectors don't come into our lives through physics anymore, but through video games and early coding.
Kids do translation of stuff using scratch in pre-k. They ...
A common error I see when teaching function composition is students seeing it as multiplication. Many factors contribute to this, but examples with multiplication in them don't help:
Q: Let f(x) = 2x and g(x) = x+1. What is f(g(x))?
A: f(g(x)) = 2(x+1)
Some students will see this and think that the answer somehow involves multiplying f(x) by g(x).