Tim Corica
@tcorica.bsky.social
Looooongtime math teacher. Believe in the dignity and respect of every human being.
Wow! That’s a level of transparency we don’t see in the U.S.!
November 7, 2025 at 10:19 PM
Wow! That’s a level of transparency we don’t see in the U.S.!
Plus, it has a great cover, and was released just as we were working on vector fields in my MVC class.
November 7, 2025 at 5:02 PM
Plus, it has a great cover, and was released just as we were working on vector fields in my MVC class.
For anyone interested in this thread, I could not recommend more strongly the book Vector: A Surprising Story of Space, Time, and Mathematical Transformation by Robyn Arianrhod! It covers the history of these ideas, and the remarkable connections between vectors, complex numbers, and quaternions.
November 7, 2025 at 5:01 PM
For anyone interested in this thread, I could not recommend more strongly the book Vector: A Surprising Story of Space, Time, and Mathematical Transformation by Robyn Arianrhod! It covers the history of these ideas, and the remarkable connections between vectors, complex numbers, and quaternions.
Nice! In MVC I would do an exercise about error in which they computed the density of a solid metal object (cube, cylinder, etc.) by making measurements and then computed the resulting error. They were surprised at the error size using displacement vs computed volume from linear measurements.
November 7, 2025 at 4:52 PM
Nice! In MVC I would do an exercise about error in which they computed the density of a solid metal object (cube, cylinder, etc.) by making measurements and then computed the resulting error. They were surprised at the error size using displacement vs computed volume from linear measurements.
Yes. I see this with my elementary students (grandkids and "tutee"). Most can't really use the standard algos mentally, but playing with place value is generally the trick, and this is a good skill and useful understanding. Of course, the question is how you "teach" mental arithmetic well.
November 7, 2025 at 2:30 PM
Yes. I see this with my elementary students (grandkids and "tutee"). Most can't really use the standard algos mentally, but playing with place value is generally the trick, and this is a good skill and useful understanding. Of course, the question is how you "teach" mental arithmetic well.
This is fun! It'd be great if there were a kid-friendly version with a context less fraught than "innocent vs criminal". E.g. soccer vs gymnast, or Ms Alvarez's class vs Mr. Trent's class.
November 7, 2025 at 2:27 PM
This is fun! It'd be great if there were a kid-friendly version with a context less fraught than "innocent vs criminal". E.g. soccer vs gymnast, or Ms Alvarez's class vs Mr. Trent's class.
I wonder why they are blocking members of congress from inspecting Broadview? /s
Bullies with badges and zero supervision or accountability. They are terrible on the streets with video cams pointed at them. Imagine them barricaded inside with no one looking!
Bullies with badges and zero supervision or accountability. They are terrible on the streets with video cams pointed at them. Imagine them barricaded inside with no one looking!
November 7, 2025 at 1:01 PM
I wonder why they are blocking members of congress from inspecting Broadview? /s
Bullies with badges and zero supervision or accountability. They are terrible on the streets with video cams pointed at them. Imagine them barricaded inside with no one looking!
Bullies with badges and zero supervision or accountability. They are terrible on the streets with video cams pointed at them. Imagine them barricaded inside with no one looking!
I'm going to delete the "wears glasses" note on my DL since I didn't wear glasses at birth.
Seriously, the point of having any bio info on a passport is for identification. If gender matters at all (and it should probably just be removed) then it should match the person, not the "birth person".
Seriously, the point of having any bio info on a passport is for identification. If gender matters at all (and it should probably just be removed) then it should match the person, not the "birth person".
November 7, 2025 at 1:23 AM
I'm going to delete the "wears glasses" note on my DL since I didn't wear glasses at birth.
Seriously, the point of having any bio info on a passport is for identification. If gender matters at all (and it should probably just be removed) then it should match the person, not the "birth person".
Seriously, the point of having any bio info on a passport is for identification. If gender matters at all (and it should probably just be removed) then it should match the person, not the "birth person".
An interesting variation (that includes a little probability thinking) would be to pick numbers one by one (from a 1-9 set of cards, or by rolling dice) and have students put the numbers in one-by-one, competing to get the largest maximum.
November 7, 2025 at 1:13 AM
An interesting variation (that includes a little probability thinking) would be to pick numbers one by one (from a 1-9 set of cards, or by rolling dice) and have students put the numbers in one-by-one, competing to get the largest maximum.
Let's not compute an expr for vertex, but reason from the orig. Want big max, so want to minimize the neg term (ax^2) and maximize the +itive terms (bx, c). bx can easily outpace c since a product, so we'll next put our energy into b. Pick smallest for a, biggest for b, and next biggest for c.
November 7, 2025 at 1:01 AM
Let's not compute an expr for vertex, but reason from the orig. Want big max, so want to minimize the neg term (ax^2) and maximize the +itive terms (bx, c). bx can easily outpace c since a product, so we'll next put our energy into b. Pick smallest for a, biggest for b, and next biggest for c.
The key is that the standard definition is a double-sided limit. That is, it exists only if the limit from the left is equal to the limit from the right. In the case of |x| of course, these two limits are different, so the limit (hence the derivative) does not exist at x=0.
November 4, 2025 at 5:03 PM
The key is that the standard definition is a double-sided limit. That is, it exists only if the limit from the left is equal to the limit from the right. In the case of |x| of course, these two limits are different, so the limit (hence the derivative) does not exist at x=0.
It's all definitional, so we can choose whatever definition we want so long as we are consistent. But I think the symmetric definition does strange things with tangent lines and other taks, so it isn't used (except computationally, as was pointed out). 2/2
November 4, 2025 at 3:06 AM
It's all definitional, so we can choose whatever definition we want so long as we are consistent. But I think the symmetric definition does strange things with tangent lines and other taks, so it isn't used (except computationally, as was pointed out). 2/2
This is called the "symmetric derivative" (en.wikipedia.org/wiki/Symmetr...).
One problem with this approach is that it doesn't behave the way we'd like at corners and discontinuities. If f(x)=|x|, is it useful to say that the derivative at zero is 0? Do we want y=0 to be a "tangent line"? 1/2
One problem with this approach is that it doesn't behave the way we'd like at corners and discontinuities. If f(x)=|x|, is it useful to say that the derivative at zero is 0? Do we want y=0 to be a "tangent line"? 1/2
Symmetric derivative - Wikipedia
en.wikipedia.org
November 4, 2025 at 3:06 AM
This is called the "symmetric derivative" (en.wikipedia.org/wiki/Symmetr...).
One problem with this approach is that it doesn't behave the way we'd like at corners and discontinuities. If f(x)=|x|, is it useful to say that the derivative at zero is 0? Do we want y=0 to be a "tangent line"? 1/2
One problem with this approach is that it doesn't behave the way we'd like at corners and discontinuities. If f(x)=|x|, is it useful to say that the derivative at zero is 0? Do we want y=0 to be a "tangent line"? 1/2
We develop rules (e.g., the power rule) from the definition, but these only apply under the circumstances that make the definition work. When we come up against something (like these holes) that we're uncertain about, we have to return to the definition.
November 4, 2025 at 2:04 AM
We develop rules (e.g., the power rule) from the definition, but these only apply under the circumstances that make the definition work. When we come up against something (like these holes) that we're uncertain about, we have to return to the definition.
To see the problem, you need to apply the definition of the derivative. You can write a derivative expression that assumes the curve is differentiable and then apply it to the (missing) point. The definition (below) requires a value for f(x) at x=4, but this does not exist. 1/2
November 4, 2025 at 2:04 AM
To see the problem, you need to apply the definition of the derivative. You can write a derivative expression that assumes the curve is differentiable and then apply it to the (missing) point. The definition (below) requires a value for f(x) at x=4, but this does not exist. 1/2
I had this exact same thought today. McConnell's explanations were vacuous and hypocritical, just as Johnson's are. If they can say s__t and not be called on it, there's absolutely no reason to expect they won't do the same when it's time to seat midterm Dems (or keep TFG in office!).
October 16, 2025 at 2:13 AM
I had this exact same thought today. McConnell's explanations were vacuous and hypocritical, just as Johnson's are. If they can say s__t and not be called on it, there's absolutely no reason to expect they won't do the same when it's time to seat midterm Dems (or keep TFG in office!).
For which there seems to be zero repercussions for ICE. The only case I’m aware of is the one where the agent threw a distraught woman to the floor. He was put on desk duty for a few days and is now back working on the street. ICE has no incentive to stop lying and brutalizing.
October 12, 2025 at 1:26 PM
For which there seems to be zero repercussions for ICE. The only case I’m aware of is the one where the agent threw a distraught woman to the floor. He was put on desk duty for a few days and is now back working on the street. ICE has no incentive to stop lying and brutalizing.
I'm ok with an informal proof of l'Hopital's 0/0 based on local-linear properties. (Zoom in, num and denom look like lines, so the ratio is the ratio of the slopes, i.e., the derivatives.) I think whenever possible an informal justification should be given, when we need something b4 we can prove it.
October 11, 2025 at 11:15 PM
I'm ok with an informal proof of l'Hopital's 0/0 based on local-linear properties. (Zoom in, num and denom look like lines, so the ratio is the ratio of the slopes, i.e., the derivatives.) I think whenever possible an informal justification should be given, when we need something b4 we can prove it.
Great! You might modify the code so that the *volumes* (rather than the radii) are proportional to the masses. That is, the "balls" are made of some material with uniform density.
October 10, 2025 at 11:06 PM
Great! You might modify the code so that the *volumes* (rather than the radii) are proportional to the masses. That is, the "balls" are made of some material with uniform density.