I don’t believe that 5th grade civics or math tests are a good idea. At that age you want to encourage children to learn by following their curiosity and if you teach math in a structured way you likely want to have instant computer driven feedback and not the idea that children are supposed to have a certain level of math knowledge at a certain age for which they get tested.
That’s fine, but choosing the question set to give the self-motivated children on which you provide the instant computer driven feedback is the same type of question; what is it that we want the child interested in X to learn?
Concretely, my 8 year old son likes math. He’s fine with multiplication and division, but enjoys thinking about math. If I want him to be successful applying math later in life, should I start him on knot theory, pre-algebra equation solving, adding and subtracting unlike fractions, or coding in python? I see real advantages to each of these; proof-based thinking and abstraction from concrete to theoretical ideas, more abstract thinking about and manipulation of numbers, getting ahead of what he’ll need next to continue at the math he will need to learn, or giving him other tools that will expand his ability to think and apply ideas, respectively.
I’d love feedback about which of these (or which combination of these) is most likely to ensure he’s learning the things that are useful in helping him apply math in a decade, but I can’t get useful feedback without trying it on large samples over the course of decades. Or, since I don’t live in Dath Ilan, I can use my best judgement and ask others for feedback in an ad-hoc fashion.
I don’t believe that 5th grade civics or math tests are a good idea. At that age you want to encourage children to learn by following their curiosity and if you teach math in a structured way you likely want to have instant computer driven feedback and not the idea that children are supposed to have a certain level of math knowledge at a certain age for which they get tested.
That’s fine, but choosing the question set to give the self-motivated children on which you provide the instant computer driven feedback is the same type of question; what is it that we want the child interested in X to learn?
Concretely, my 8 year old son likes math. He’s fine with multiplication and division, but enjoys thinking about math. If I want him to be successful applying math later in life, should I start him on knot theory, pre-algebra equation solving, adding and subtracting unlike fractions, or coding in python? I see real advantages to each of these; proof-based thinking and abstraction from concrete to theoretical ideas, more abstract thinking about and manipulation of numbers, getting ahead of what he’ll need next to continue at the math he will need to learn, or giving him other tools that will expand his ability to think and apply ideas, respectively.
I’d love feedback about which of these (or which combination of these) is most likely to ensure he’s learning the things that are useful in helping him apply math in a decade, but I can’t get useful feedback without trying it on large samples over the course of decades. Or, since I don’t live in Dath Ilan, I can use my best judgement and ask others for feedback in an ad-hoc fashion.