Thanks for building the MIST Academy community! I interview all new students nowadays, and it definitely helps. I am also running Alabama ARML practices. Unfortunately I don't have as big a reach as you did in the Birmingham area, but I hope my online students from around the states are able to gain what I gained from attending classes at MIST. Most of my students are from outside AL now. Hopefully I am continuing your legacy of teaching a bit in my own way.
Congratulations on seeking out new methods in education and for capturing your wisdom for posterity. And of course many thanks.
It’s clear the ancient techniques are serving society and civilization poorly. The industrialization of education (and medicine) have been massive errors (or, more charitably, necessary phases of imperfection in the evolution of both). A more personal approach to both is sorely needed. No doubt it takes huge amounts of energy and enthusiasm.
I would be interested in hearing about any of your students who decided to become teachers themselves using your methods. Did you have more advanced students teaching the less in your schools?
Aug 9, 2022·edited Aug 9, 2022Liked by Mathew Crawford
Listened to the whole video on my walk today. It was great!
I felt a deep sense of gratitude for the countless hours my dad spent educating me as a teenager after school hours and on weekends. At the time I hated it, and he certainly was not as patient as you, nevertheless he took countless hours out of his own schedule to educate me. That 1-on-1 instruction is invaluable.
I like the fact you did no shy away from starting with a hard question for each new problem and then broke it down into easier scenarios depending on their comprehension, yet always managed to eventually help the student answer the original hard question on their own. (State the goal, establish the competency level, then figure out the best way to get them to the goal whilst remaining extremely attentive to how they respond at each step.)
Loved her accent and the way she could speak perfect English and Spanish seamlessly.
Thank you for taking the time to put this together and providing a guide for others to follow. Much appreciated.
------
I'm amazed at how sharp young brains are. Given the right conditions and instruction they can absorb so much information. This gives me so much hope for the future. Thank you.
I appreciate the way you and Iris developed the rules for each more complicated counting problem. More impressed with your patience (wonderful) and Iris perseverance even when for a time she seem stuck. She never gave up.
I homeschooled my children. When I looked at math education and textbooks for 6-8th grade I became appalled with the fact that almost no new concepts were taught 3 yrs in a row. When it came time to teach algebra, I decided to use a college algebra and trig text. The text was out of print but was very good with great example problems. My oldest graduated with a chemical engineering degree and my youngest graduated cosmetology school.
The best video I have seen on education is:
2+2=5 | Two & Two - Nominated as Best Short Film, Bafta Film Awards, 2012
B"H" Re interview technique, I had a similar mo teaching 1st college students at 1st tier SLACs computer programming. I too used interviews (but slyly and continuously) in the form of weekly progress reports in classes of about 2 dozens to 30 students. Every student every week wrote in his / her own words progress report 100-300 words (questions, thoughts, knots, venting, summaries). Sundays I analyzed reports & Monday in class did review of points most unclear, best q, funniest quip etc. See some samples here https://web.archive.org/web/20210527141211/https://twitter.com/daniel_bilar/status/1397913183113801745
"I felt the problem was even broader—that everyone is at a dramatic disadvantage anywhere there is not a healthy culture of learning math."
But math is hard. "The easy path is always mined."
Similarly, a solid background in chemistry and physics helps one to understand systematic error and error analysis.
NB Cool physics factoid: A substance that absorbs a particular frequency of EM radiation will always reflect that EM radiation, but the reverse isn't always true. Some things reflect, but don't absorb. (e.g., mirrors) The reason is because the index of refraction (IOR) is complex. The real part has to do with reflection and the imaginary part has to do with absorption. Also, the IOR varies with EM frequency for substances. My physics research had to do with measuring reflectivity for a straight chain alcohol and comparing it with a straight chain carboxylic acid containing the same number of carbons. I uploaded the reflectivity data to a computer, which ran a Fast Fourier Transform on the data to generate absorption values which I then compared to a library of absorption values for the alcohol and carboxylic acid components. I found absorption for a C=O in one set of data, but not in the other. QED. Nothing new theoretically, but there was practical application in space exploration and in medicine.
Great teaching Mathew! It may be easier to teach the factorial method of counting prior to the choose method? (i.e. first, keep the number of items/people to choose positions equal to the number of positions available). Great approach to teaching all these concepts. I love it.
I love this approach for persons of a ages. You are doing a great service for all of us. If you have books (math stuff in particular) that you can recommend please do.
You said you worked with 2000 students or more, not counting time at AoPS. But how much time with each student, and did you really achieve a ratio of greater than 8:1 students to teacher?
I literally have your AoPS number theory book within arms-reach right now. I'm about to begin teaching it to my student this semester (I homeschool.) But I cannot imagine Socratic methods scaling to every day instruction except in the hands of the most gifted teacher and equivalently gifted students.
We have brick and mortar AoPS in our town; they're grinds. They aren't taught socratically even though they're problem based. Online AoPS grew but didn't scale; quality has suffered, and now their goals have shifted. When ed schools became enamored with constructivism,they invent TERC and Everyday Math which became fuzzy math appreciation. Modern schoolteachers can't possibly use the Socratic method because they don't know a good idea from a bad. They wouldn't recognize a contradiction.
Moreover it is exhausting to do this and to do it for every subject every day. There's another reason Socrates did it with adults, too. There were premises (even if false) on which to hang an argument. And of course, when he did succeed with the youngerish, they killed him. We should proceed cautiously.
Excellent! My grandfather was a Math teacher and would sit down with me and do math problems when he came to visit and I think that is what fueled my interest in the subject. I had some good and bad experiences in school, but I always loved math competitions. I did not enjoy my college statistics class, but now I'm having to go back and re-learn everything just to keep up with everything that is going on. This lesson made crystal clear what had always been kind of a fuzzy concept.
I saw a Math teacher with a different approach. Works for a class, where you have different levels of students.The main idea is that you have different answers to math questions. You have an easy answer, and some more complex answers.
That way students can feel satisfied that they can answer the question. And then they can explore from interest the more complex answers that are possible. The system works well in magic squares, number patterns, fill in the +/-/*/div etc. Because you always get an answer with little effort, it invites to continue and stay focused.
I think this same system can be applied to statistics & probabilities, graphs, geometries, etc. Always have an easy answer, and let the smart-ass people explore more complex ones.
What you describe in the video: "How can you make this simpler?" Seems a good idea too. It is hard to make it simpler in a correct way. So you may need to explore those variants too.
In my experience, 5 girls never can choose a seat.
Warning: Don't flip the coin imaginary times. Then you may end existence.
Thanks for building the MIST Academy community! I interview all new students nowadays, and it definitely helps. I am also running Alabama ARML practices. Unfortunately I don't have as big a reach as you did in the Birmingham area, but I hope my online students from around the states are able to gain what I gained from attending classes at MIST. Most of my students are from outside AL now. Hopefully I am continuing your legacy of teaching a bit in my own way.
Congratulations on seeking out new methods in education and for capturing your wisdom for posterity. And of course many thanks.
It’s clear the ancient techniques are serving society and civilization poorly. The industrialization of education (and medicine) have been massive errors (or, more charitably, necessary phases of imperfection in the evolution of both). A more personal approach to both is sorely needed. No doubt it takes huge amounts of energy and enthusiasm.
I would be interested in hearing about any of your students who decided to become teachers themselves using your methods. Did you have more advanced students teaching the less in your schools?
Listened to the whole video on my walk today. It was great!
I felt a deep sense of gratitude for the countless hours my dad spent educating me as a teenager after school hours and on weekends. At the time I hated it, and he certainly was not as patient as you, nevertheless he took countless hours out of his own schedule to educate me. That 1-on-1 instruction is invaluable.
I like the fact you did no shy away from starting with a hard question for each new problem and then broke it down into easier scenarios depending on their comprehension, yet always managed to eventually help the student answer the original hard question on their own. (State the goal, establish the competency level, then figure out the best way to get them to the goal whilst remaining extremely attentive to how they respond at each step.)
Loved her accent and the way she could speak perfect English and Spanish seamlessly.
Thank you for taking the time to put this together and providing a guide for others to follow. Much appreciated.
------
I'm amazed at how sharp young brains are. Given the right conditions and instruction they can absorb so much information. This gives me so much hope for the future. Thank you.
I appreciate the way you and Iris developed the rules for each more complicated counting problem. More impressed with your patience (wonderful) and Iris perseverance even when for a time she seem stuck. She never gave up.
Thank you both
I homeschooled my children. When I looked at math education and textbooks for 6-8th grade I became appalled with the fact that almost no new concepts were taught 3 yrs in a row. When it came time to teach algebra, I decided to use a college algebra and trig text. The text was out of print but was very good with great example problems. My oldest graduated with a chemical engineering degree and my youngest graduated cosmetology school.
The best video I have seen on education is:
2+2=5 | Two & Two - Nominated as Best Short Film, Bafta Film Awards, 2012
https://www.youtube.com/watch?v=EHAuGA7gqFU
You will have to read the subtitles because I believe the language is Persian (Farsi)
B"H" Re interview technique, I had a similar mo teaching 1st college students at 1st tier SLACs computer programming. I too used interviews (but slyly and continuously) in the form of weekly progress reports in classes of about 2 dozens to 30 students. Every student every week wrote in his / her own words progress report 100-300 words (questions, thoughts, knots, venting, summaries). Sundays I analyzed reports & Monday in class did review of points most unclear, best q, funniest quip etc. See some samples here https://web.archive.org/web/20210527141211/https://twitter.com/daniel_bilar/status/1397913183113801745
IMHO a math PhD educator collaborator may be willing to write an extended version of your post & submit to JRME https://www.nctm.org/publications/journal-for-research-in-mathematics-education/
Was at school a lot of years ago and hated math. When’s the next lesson? can’t wait!
Great stuff, thank you. All of the kids in my family gets a math focus because it falls under the category of "Things other people can't do".
You can only make money 5 ways. Steal it, inherit/win it, marry it, do something other people don't want to do, or do something other people can't do.
"I felt the problem was even broader—that everyone is at a dramatic disadvantage anywhere there is not a healthy culture of learning math."
But math is hard. "The easy path is always mined."
Similarly, a solid background in chemistry and physics helps one to understand systematic error and error analysis.
NB Cool physics factoid: A substance that absorbs a particular frequency of EM radiation will always reflect that EM radiation, but the reverse isn't always true. Some things reflect, but don't absorb. (e.g., mirrors) The reason is because the index of refraction (IOR) is complex. The real part has to do with reflection and the imaginary part has to do with absorption. Also, the IOR varies with EM frequency for substances. My physics research had to do with measuring reflectivity for a straight chain alcohol and comparing it with a straight chain carboxylic acid containing the same number of carbons. I uploaded the reflectivity data to a computer, which ran a Fast Fourier Transform on the data to generate absorption values which I then compared to a library of absorption values for the alcohol and carboxylic acid components. I found absorption for a C=O in one set of data, but not in the other. QED. Nothing new theoretically, but there was practical application in space exploration and in medicine.
Great teaching Mathew! It may be easier to teach the factorial method of counting prior to the choose method? (i.e. first, keep the number of items/people to choose positions equal to the number of positions available). Great approach to teaching all these concepts. I love it.
I love this approach for persons of a ages. You are doing a great service for all of us. If you have books (math stuff in particular) that you can recommend please do.
It sounds more like you taught an 8 th grade or thereabouts math class rather then " opened " and " closed a school " .
You said you worked with 2000 students or more, not counting time at AoPS. But how much time with each student, and did you really achieve a ratio of greater than 8:1 students to teacher?
I literally have your AoPS number theory book within arms-reach right now. I'm about to begin teaching it to my student this semester (I homeschool.) But I cannot imagine Socratic methods scaling to every day instruction except in the hands of the most gifted teacher and equivalently gifted students.
We have brick and mortar AoPS in our town; they're grinds. They aren't taught socratically even though they're problem based. Online AoPS grew but didn't scale; quality has suffered, and now their goals have shifted. When ed schools became enamored with constructivism,they invent TERC and Everyday Math which became fuzzy math appreciation. Modern schoolteachers can't possibly use the Socratic method because they don't know a good idea from a bad. They wouldn't recognize a contradiction.
Moreover it is exhausting to do this and to do it for every subject every day. There's another reason Socrates did it with adults, too. There were premises (even if false) on which to hang an argument. And of course, when he did succeed with the youngerish, they killed him. We should proceed cautiously.
Excellent! My grandfather was a Math teacher and would sit down with me and do math problems when he came to visit and I think that is what fueled my interest in the subject. I had some good and bad experiences in school, but I always loved math competitions. I did not enjoy my college statistics class, but now I'm having to go back and re-learn everything just to keep up with everything that is going on. This lesson made crystal clear what had always been kind of a fuzzy concept.
I saw a Math teacher with a different approach. Works for a class, where you have different levels of students.The main idea is that you have different answers to math questions. You have an easy answer, and some more complex answers.
That way students can feel satisfied that they can answer the question. And then they can explore from interest the more complex answers that are possible. The system works well in magic squares, number patterns, fill in the +/-/*/div etc. Because you always get an answer with little effort, it invites to continue and stay focused.
I think this same system can be applied to statistics & probabilities, graphs, geometries, etc. Always have an easy answer, and let the smart-ass people explore more complex ones.
What you describe in the video: "How can you make this simpler?" Seems a good idea too. It is hard to make it simpler in a correct way. So you may need to explore those variants too.
In my experience, 5 girls never can choose a seat.
Warning: Don't flip the coin imaginary times. Then you may end existence.