I prove a theorem and the house expands:
the windows jerk free to hover near the ceiling,
the ceiling floats away with a sigh.
As the walls clear themselves of everything
but transparency, the scent of carnations
leaves with them. I am out in the open
And above the windows have hinged into butterflies,
sunlight glinting where they’ve intersected.
They are going to some point true and unproven.
I argue a lot with my wife about this. Usually it’s a science question. My kid asks something that everybody knows the answer to, and my wife tell her the answer, and then I’m like WAY TO RUIN EVERYTHING.
With math, when we briefly homeschooled, I’d give my kid a “question of the day”, and give her a treat if she solved it. Usually, it involved a bunch of steps, and it pointed some concept that she hadn’t learned yet-- (multiplication, division, fractions, algebra, rates of change, etc.).
She could do it sometimes, often with hints or pointed questions. Mostly it involved her grasping that something new is necessary. And then her trying to figure out what the new thing looks like.
Of course that’s just my kid. I think she’s gifted and therefore want to treat her like a mathematician. But, that probably doesn’t apply to most kids, or even most people. Most people probably never think a lot. Instead they learn lots of answers, and then continue to learn more answers in college.
Also finding the right level is really hard. Even knowing my kid perfectly, I am still often surprised by what my kid can and can-not figure out.
Sounds like you don’t.
But, I can see you are trying.
I preferred the surprises when raising my kids.
One reason I think we need to stop thinking of “tracking” as a dirty word. If some kids are gifted and ready for acceleration, let them accelerate. You support struggling students by supporting struggling students, not by holding gifted students back.1 To that end, I think relevance is more important than fairness, and in fact if done - well, fairly - will lead to more fairness than any artificial maneuver to force full mixed inclusion whatever you want to call it.
Acceleration and being pushed to their full potential is relevant to gifted students. Scaffolding is relevant to struggling students because they get what they need to fill in their gaps in prior knowledge. Career-based intervention (or CBI, which is a growing passion of mine) is relevant for students who are varying degrees of struggling and are likely to pursue a career path that will not take them to traditional 4-year college. We have done kids a double disservice by (a) assuming that they’re definitely supposed to go to college after high school, and (b) assuming that they’re all supposed to be in the exact same place at the exact same time.
We can and should focus more on relevance by shifting from “college and career readiness” to just “career readiness” - with the understanding that some careers need 4-year college and some don’t, and one path isn’t automatically better than the other because there isn’t one best path through life.
======
1 Some people seriously believe that giftedness shouldn’t be a thing solely because of the belief that it’s inherently unfair. As a result, some places stopped accelerating students on purpose just because fairness. Apparently fairness is only for the lower end.
So am I right to conclude that my kids will likely never have the same experience I did where my teacher would give us a piece of paper with 100 different times table problems on it and you did as many as you could in 60 seconds or something and then tried to improve over time?
I was really good at that and it made me think I was good at math. I’d go on to later decide I wasn’t particularly good at math thanks to a few miserable teachers along the way, and then rediscover math in a favorable light at the start of HS thanks to a good teacher.
I tend to agree, within limits.
It was common for gifted kids in my generation to “skip” a grade and some of us skipped two years. At two years you run a greater risk of the child being much less mature and/or vulnerable in the older group. My mother was fine letting me skip one grade but told my teacher “no way” when I was offered a second acceleration. I think it was the right decision for me.
Having said that, my father-in-law went to Harvard when he was 16 and had his PhD by age 21. However there were a lot of gifted 16 year olds at Harvard in those days (1939 to 1945) and he found a community of similar young gifted individuals, primarily from Brooklyn where he grew up. He managed well within that social network but was excluded from other Harvard cliques. (Of course, that may have been more because he was Jewish and from a more modest socioeconomic group).
I certainly hope so. I had those and they were AWFUL. They were called “the mad minute” and as soon as you got one wrong the teacher stopped grading. I don’t think it was usually 100 though… usually 30 or 40 IIRC. But if you got the second out of 30 wrong and the other 29 right your score was 1/30. If you got the second to last one wrong and the other 29 right your score was 28/30. The idea was supposed to be that you should be careful enough to get each one, not skip around to find the easy ones.
I hated these as a kid, and as an educator I don’t like them much better.
If they let you skip around and didn’t stop at first error it would be more useful, IMO.
In second grade I would stop work after the first side on an arithmetic problem sheet. Mom asked me why. I said I proved I could do it on the front side, no need to do the back side.
I understand the idea… 7 x 1 is a lot easier than 7 x 6 and the idea is to make sure you know all of the times tables.
But it ends up being so insanely punitive if you make a dumb early mistake when you’re under the gun.
It strikes me as strange that we fret over “tracking” in academics, yet no one questions the same behavior in sports. “Only the gifted for this team. thanks for trying out.”
The idea of mixed-ability grouping in sports made me think of this:
We had terrible HS principal. He was a former HS coach who was friends with one of the administrators in the district and got the job he was pretty much unqualified for but I digress.
He got this great idea that the school shouldn’t have AP or honors classes and everyone should take the same basic courses. Fortunately it never went through. Now this Principal was a huge sports guy, big rah-rah type and pushed the varsity sports hard. My wife was on the site counsel and put forth in the meeting that if they were going to do that with academics they should eliminate all varsity sports and just have everyone do the same random PE courses. He had no answer for that, like many things he had no answer for but he was not happy.
Yeah, that’s why you don’t stop grading (lazy) at first error. Heck, why even give it a grade? The lesson about which is easier actually supports the concept anyway. If you know that the 1s are easy, great.
Like I said, I don’t endorse the method, just explaining the idea behind it.
We did have other tests that weren’t graded that way. But for Mad Minutes they specifically didn’t want you skipping around.
I will say this… it certainly reinforced from a very early age the idea of understanding how you were being evaluated and adjusting your strategy accordingly.
Mad Minute: Do not skip ANY problems EVER. Better to burn a ton of time on question 6 and not get to questions 21-30 as a result than to skip 6 and get everything else right. Don’t miss question 6 to get stuff that won’t end up getting graded.
Regular test: If you come across one you don’t know, skip it and move on. If there’s time when you’re done with all the ones you do know, go back to the one(s) you skipped and see if you can figure them out. Don’t miss questions 21-30 because you burned a ton of time on 6.
Knowing how to be a good test taker was a skill that came in handy at various points in life, including but not limited to actuarial exams.
Lol. In my day we had speed drills, but that sounds jack shit insane.
I get the vague idea, but maybe just don’t ask kids as many easy questions!
I don’t know if my kid’s teacher intends to give her speed drills. If not I will just find a math game for her to play.
It’s surprisingly hard to find a good one (since we live in the golden age of gaming) but I will find something.
Backgammon. Plus it’s fun. (Make sure you use the doubling cube)
This doesn’t seem like a terrible idea to me…
That sounds really stupid.
I did something like this last year for simplifying fractions. I graded it based on how many they answered and how many of those they got correct. Answering more raised your maximum score but just quickly guessing wouldn’t help. I set the number answered that would allow a perfect score based on the maximum that anyone in the class attempted (actually, it was probably about the 90th percentile or something around there).
I don’t remember my actual algorithm. I’d have to look at my spreadsheet.