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Benjamin Leis commented on a post on Blogger.

Your poster on learning styles caught my eye. You might want to research some more on them. The consensus I've seen from most researchers is that the theory is flawed and they don't exist. Here's a good cite: http://www.changemag.org/archives/back%20issues/september-october%202010/the-myth-of-learning-full.html

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Benjamin Leis commented on a post on Blogger.

I was thinking about this yesterday since there were a flurry of posts (mostly panning Algebra 2 I remember Dan Meyer's in particular) and I had just listened to Stephen Strogatz's podcast in defense of "impractical" math.

I like your ideas but why stop there? The alternative (this was articulated in the podcast at the end) is to just rethink what we want the terminal parts of the math sequence to be. Discrete math is usually mentioned in these conversations the most along with probability and statistics.

I like your ideas but why stop there? The alternative (this was articulated in the podcast at the end) is to just rethink what we want the terminal parts of the math sequence to be. Discrete math is usually mentioned in these conversations the most along with probability and statistics.

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Benjamin Leis commented on a post on Blogger.

This was an interesting read. It also called to mind Richard Rusczyk's "The Calculus Trap" https://www.artofproblemsolving.com/articles/calculus-trap article.

However, I'm actually left wondering more questions after thinking about it. Something is probably wrong but its not very clear (at least to me) that acceleration is the only or even primary issue here.

1. Is it just lack of time? The primary way acceleration is implemented in most schools is compaction or skipping either at the elementary years or entry to middle school. For the most part students spend as much time studying algebra whether its at 7th, 8th or 9th grade. (There are some schools that also double up on courses at the end of high school) The amount of pre-algebra time does radically differ. But the discussion of weaknesses above pinpoints areas that are in Algebra or beyond like function graphing. I strongly suspect that if you tested the full population of students including non-accelerated ones you'd find some of the same weaknesses for that reason.

2. Is it content? I think is definitely part of the issue but another is expectations. Every standards rewrite keeps preaching the mantra of moving away from "a mile wide and an inch deep" I wonder about the rest of assessment and what areas it was probing. Is this analysis going to lead to more breadth or depth in the curriculum?

3. Is it mastery? There's a followup question whether students could have passed the areas of the exam when they where at the end of the high school courses that covered the subject. In other words, were the students given the appropriate material, appeared to learn it and then had regressed by the time they entered college? I also suspect this comes into play and it requires different adjustments. In many ways this is harder to solve since I think the entire H.S. / college gauntlet encourages bad learning habits.

4. Does College do it any better? Every level of teaching is notorious for blaming the previous years for ill-prepared students. I'd be very interested to see if a similar test was given to college Sophomores, would they do any better on retention of material. Perhaps they really are and there are models to transfer down.

However, I'm actually left wondering more questions after thinking about it. Something is probably wrong but its not very clear (at least to me) that acceleration is the only or even primary issue here.

1. Is it just lack of time? The primary way acceleration is implemented in most schools is compaction or skipping either at the elementary years or entry to middle school. For the most part students spend as much time studying algebra whether its at 7th, 8th or 9th grade. (There are some schools that also double up on courses at the end of high school) The amount of pre-algebra time does radically differ. But the discussion of weaknesses above pinpoints areas that are in Algebra or beyond like function graphing. I strongly suspect that if you tested the full population of students including non-accelerated ones you'd find some of the same weaknesses for that reason.

2. Is it content? I think is definitely part of the issue but another is expectations. Every standards rewrite keeps preaching the mantra of moving away from "a mile wide and an inch deep" I wonder about the rest of assessment and what areas it was probing. Is this analysis going to lead to more breadth or depth in the curriculum?

3. Is it mastery? There's a followup question whether students could have passed the areas of the exam when they where at the end of the high school courses that covered the subject. In other words, were the students given the appropriate material, appeared to learn it and then had regressed by the time they entered college? I also suspect this comes into play and it requires different adjustments. In many ways this is harder to solve since I think the entire H.S. / college gauntlet encourages bad learning habits.

4. Does College do it any better? Every level of teaching is notorious for blaming the previous years for ill-prepared students. I'd be very interested to see if a similar test was given to college Sophomores, would they do any better on retention of material. Perhaps they really are and there are models to transfer down.

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My new year's resolution: Fight back my contrarian instincts about much of what I read in the blogosphere.

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Benjamin Leis commented on a post on Blogger.

I've thought a lot about this post since yesterday and I have to admit I'm torn. First off, disclaimer I am a software developer and code every day. My own background included exposure to Logo back in the primary grades a long with TRS-80's in the classroom. Generally speaking my interest was kindled by the free form machines and not the logo projects which I found uninteresting at the time. On top of that, I gained most of my initial skills from projects and reading at home once I became excited about computing around say 5th grade. There was no formal CS in the rest of my school career prior to college (Although I did take the then very new CS AP Test on a lark).

My current feeling for my own children which is shared anecdotally by most of my industry friends is that I'm not very interested in formal CS topics at school. I'd be quite happy if they can get as much of a well-rounded classical education out of K-12. Basics like history and the arts are already under pressure from the relentless test driven curriculum changes. There's enough time to learn to program in college or as a hobby if they become interested earlier.

That said, there are some cool math and CS intersections like the Euler project out there that would be fun to do in high school. And I can also using coding or a tool like Wolfram Alpha for various explorations. Its already quite useful to have an infinite precision calculator when checking large modular arithmetic problems or modelling a geometry problem to see what direction a proof might take.

The problem, is I don't see technology being used in an interesting fashion most of the time when its been injected into the classroom and I'm suspicious that modern computers are more distraction for many kids. Basic programming by itself is not super interesting and honestly not that complex either but as taught currently takes a full class a year usually to cover something like Java or Python. It would only be worthwhile for me if coupled with an interesting set of projects that had to be implemented which again is hard to do.

And although the above sounds a bit down on the idea I have not made my mind up yet.

PS: for Michael programming jobs are much more subject to basic supply-demand issues than prestige. We just can't find enough candidates to fill the positions and the salaries reflect that fact. I have zero worries that a drop in prestige would arise from mandating universal coding because its hard for me to imagine us producing an oversupply of coders.

My current feeling for my own children which is shared anecdotally by most of my industry friends is that I'm not very interested in formal CS topics at school. I'd be quite happy if they can get as much of a well-rounded classical education out of K-12. Basics like history and the arts are already under pressure from the relentless test driven curriculum changes. There's enough time to learn to program in college or as a hobby if they become interested earlier.

That said, there are some cool math and CS intersections like the Euler project out there that would be fun to do in high school. And I can also using coding or a tool like Wolfram Alpha for various explorations. Its already quite useful to have an infinite precision calculator when checking large modular arithmetic problems or modelling a geometry problem to see what direction a proof might take.

The problem, is I don't see technology being used in an interesting fashion most of the time when its been injected into the classroom and I'm suspicious that modern computers are more distraction for many kids. Basic programming by itself is not super interesting and honestly not that complex either but as taught currently takes a full class a year usually to cover something like Java or Python. It would only be worthwhile for me if coupled with an interesting set of projects that had to be implemented which again is hard to do.

And although the above sounds a bit down on the idea I have not made my mind up yet.

PS: for Michael programming jobs are much more subject to basic supply-demand issues than prestige. We just can't find enough candidates to fill the positions and the salaries reflect that fact. I have zero worries that a drop in prestige would arise from mandating universal coding because its hard for me to imagine us producing an oversupply of coders.

Simplify:

(45 + 29 * sqrt(2))^1/3 + (45 - 29 * sqrt(2))^1/3

(45 + 29 * sqrt(2))^1/3 + (45 - 29 * sqrt(2))^1/3

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My solution to http://www.gogeometry.com/problem/problem006.htm

Feeling tricksier.

Feeling tricksier.

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