Re: the Future of Math conversation -- I'm really chewing on your point about the software engineering background of so many education philanthropists, and how that background can invite the illusion that the right curriculum is like source code that can be compiled and run without depending on all of the specific people in the room.
Recently I got involved in an NCTM digest chat about what teachers need to do with children who come from homes where the parents do nothing about their math learning and then I read this. It seems to me that everyone is looking for somewhere else to lay the blame for our children doing poorly in math. For me it is easy to see the blame lays everywhere: in the text books, in the set up of classrooms, in the constant testing, in teachers wanting everyone else to do the teaching for them. It makes me want to scream. I see some of the answer in your writing, Dan: Really look at the students. For me in my work with the little ones the answer lies in what the classroom fosters. Does it foster exploration? Does it foster creativity? Does it foster trial and error? Can the children have meaningful conversations about what they are thinking or what they think they know? Do the children feel powerful in their ability to learn?
I hear talk about math anxiety yet teachers continue to test k's before they have had a chance to explore, try out and play. Then the ones wanting in the process are referred to remediation and we wonder where the anxiety comes from. No child would be able to walk if they had to learn that "skill" the way we teach them math.
Children need to play with stuff. They need to explore ideas on their own looking for sense making. They need time to do things over and over again if that is what they see they need or want to do. And when they get stuck or something doesn't make sense they do not need to rescued by an interfering adult who can explain why they are wrong. They need to puzzle things out, check with a friend, ask questions and be able to try and try again, I once had a student who took 42 tries until he got the problem solved. He was SO proud of himself. In most classrooms he wold not have gotten past try 3 before an adult showed him the answer.
My children don't need Chatwhatever to write their problems for them. They write them themselves and when they do this they learn as they go what a good problem needs and in the end after trying to make a problem that is "tricky" they need to be able to solve it and show their thinking. I am looking to produce little mathematicians not children who can do math.
It seems to me that the idea behind "personalize the math problem" is missing a step, or it's focused on the wrong point in the learning process.
When I talk to students about writing in response to an open-ended prompt that grants them considerable discretion over the topic and focus of the writing, I generally find that these are much harder writing assignments for most students. The reason is that most courses do very little explicit pedagogical work on topic selection and discovery practices associated with framing and refining a topic. We assume that a student will go straight at what they are interested in and that this will be a liberating and motivating opportunity, when in fact most college students (and I suspect earlier) aren't sure what interests them about the subject matter of a particular class while that class is ongoing, and aren't sure if their interests translate into a finite short piece of writing. Working metacognitively with the question "what makes something both interesting and valid in the context of a particular course?" is a really hard pedagogical challenge. It is not anywhere as easy as saying "oh, are you interested in baseball? movies? war? revolution?" etc.
I would think that for word problems in mathematics, the challenge would be "of the questions that engage your imagination and the things you're fascinated by, is there potentially a quantitative dimension to them?" I'd almost ask students to just spend a week listing questions they have that *could* be formulated in quantitative terms without any attempt to work them mathematically, and then start sorting each student's questions in terms of the mathematics they could imagine conceptually that would be needed and the data they'd need to work the problem. "What's the fastest way to earn a million dollars?" "How many onions do you need to make a bag of onion rings?" "What's the most efficient way to get on first base per at-bat in baseball?" and so on. Sometimes you'd end up saying "it turns out this question requires a really difficult mathematics that you have to work up to through a lot of other mathematics" and sometimes you'd say "We can make a word problem out of your question right now and you can solve it, here's how". If that work got a student to understand when a question is possibly or intrinsically quantitative, I think *that* would be pedagogically close to what "personalization" is meant to achieve--a kind of motivated interest in learning the skills necessary to answer the question.
One critique: your search for studies -- (I think) you imply the idea that students are not more engaged when approached with a topic they enjoy, because there is no evidence.
As an individual teacher, I have found relating the topic to a student to be an essential piece of the puzzle.
As an individual teacher, I also have found human connection with the student to be an essential piece, which is part of your article...
I think people approach social science with this idea that we can uncover laws like Newton and Einstein. --But I think there's more complexity in studying groups of children and how they learn than in observations of planetary motions. People are less predictable than celestial motion.
Thanks for including the article links. I'm coming to the conclusion that no article should be cited behind a paywall. It's impossible to judge such a paper without understanding their methodology. People put all sorts of unverifiable evidence forward these days and I think it makes us accept that we just can't do the thinking. (I know this isn't your fault.)
We’ve been advised not to use AI products for IEPs because that involves entering confidential information into the LLM, I imagine this is a major hurdle in many industries
Great post! When is teaching problem solving creating more problems? When it’s done mindlessly. Strong argument here for not using AI like a souped up textbook. Teachers matter more than tools. Learners matter most.
Though, I've personally concluded that Ed-Tech is the wrong path. As good teachers leave, we keep the barriers for new teachers high and the pay low, and we lay teachers off... we communicate our values...
Ed-Tech would be a great addition to a culture that valued education. Collectively, we seem to value the credential, the diploma, what comes with the education... but the true greats were just curious minds.
Some great product management thinking going on in this post, btw. Not this VC fake it til you make it, and probably never make it if you can find someone to buy you first, sort of thinking.
To whom is Ai evidently supporting special education? to teachers who still present decades-old documentaries in hopes students pay half of half of half attention? Having begun full-time part-time teaching in classrooms as a substitute mostly (84%) special education assisting, computer use is still a tech tool on the list of things to learn to use/teach. I also am a PAPER Education math tutor K-12 for 28 months now! And true! tutors who know how to relate to a student as another human being are prioritized despite the downsizing!
I like the snapshot tool built into Desmos classroom so we can do just that: take pictures of student work and then project them easily for the class to see. One feedback: I’d like to also be able to select the graph or whatever they are writing about to include in the album.
Whenever the Gates folks DUMP a TON OF MONEY on somebody like Sal Khan (hedge fund analyst) but it's for education... that gives me a bad vibe because it could have gone to people who know from pedagogy.
Re: the Future of Math conversation -- I'm really chewing on your point about the software engineering background of so many education philanthropists, and how that background can invite the illusion that the right curriculum is like source code that can be compiled and run without depending on all of the specific people in the room.
Recently I got involved in an NCTM digest chat about what teachers need to do with children who come from homes where the parents do nothing about their math learning and then I read this. It seems to me that everyone is looking for somewhere else to lay the blame for our children doing poorly in math. For me it is easy to see the blame lays everywhere: in the text books, in the set up of classrooms, in the constant testing, in teachers wanting everyone else to do the teaching for them. It makes me want to scream. I see some of the answer in your writing, Dan: Really look at the students. For me in my work with the little ones the answer lies in what the classroom fosters. Does it foster exploration? Does it foster creativity? Does it foster trial and error? Can the children have meaningful conversations about what they are thinking or what they think they know? Do the children feel powerful in their ability to learn?
I hear talk about math anxiety yet teachers continue to test k's before they have had a chance to explore, try out and play. Then the ones wanting in the process are referred to remediation and we wonder where the anxiety comes from. No child would be able to walk if they had to learn that "skill" the way we teach them math.
Children need to play with stuff. They need to explore ideas on their own looking for sense making. They need time to do things over and over again if that is what they see they need or want to do. And when they get stuck or something doesn't make sense they do not need to rescued by an interfering adult who can explain why they are wrong. They need to puzzle things out, check with a friend, ask questions and be able to try and try again, I once had a student who took 42 tries until he got the problem solved. He was SO proud of himself. In most classrooms he wold not have gotten past try 3 before an adult showed him the answer.
My children don't need Chatwhatever to write their problems for them. They write them themselves and when they do this they learn as they go what a good problem needs and in the end after trying to make a problem that is "tricky" they need to be able to solve it and show their thinking. I am looking to produce little mathematicians not children who can do math.
It seems to me that the idea behind "personalize the math problem" is missing a step, or it's focused on the wrong point in the learning process.
When I talk to students about writing in response to an open-ended prompt that grants them considerable discretion over the topic and focus of the writing, I generally find that these are much harder writing assignments for most students. The reason is that most courses do very little explicit pedagogical work on topic selection and discovery practices associated with framing and refining a topic. We assume that a student will go straight at what they are interested in and that this will be a liberating and motivating opportunity, when in fact most college students (and I suspect earlier) aren't sure what interests them about the subject matter of a particular class while that class is ongoing, and aren't sure if their interests translate into a finite short piece of writing. Working metacognitively with the question "what makes something both interesting and valid in the context of a particular course?" is a really hard pedagogical challenge. It is not anywhere as easy as saying "oh, are you interested in baseball? movies? war? revolution?" etc.
I would think that for word problems in mathematics, the challenge would be "of the questions that engage your imagination and the things you're fascinated by, is there potentially a quantitative dimension to them?" I'd almost ask students to just spend a week listing questions they have that *could* be formulated in quantitative terms without any attempt to work them mathematically, and then start sorting each student's questions in terms of the mathematics they could imagine conceptually that would be needed and the data they'd need to work the problem. "What's the fastest way to earn a million dollars?" "How many onions do you need to make a bag of onion rings?" "What's the most efficient way to get on first base per at-bat in baseball?" and so on. Sometimes you'd end up saying "it turns out this question requires a really difficult mathematics that you have to work up to through a lot of other mathematics" and sometimes you'd say "We can make a word problem out of your question right now and you can solve it, here's how". If that work got a student to understand when a question is possibly or intrinsically quantitative, I think *that* would be pedagogically close to what "personalization" is meant to achieve--a kind of motivated interest in learning the skills necessary to answer the question.
One critique: your search for studies -- (I think) you imply the idea that students are not more engaged when approached with a topic they enjoy, because there is no evidence.
As an individual teacher, I have found relating the topic to a student to be an essential piece of the puzzle.
As an individual teacher, I also have found human connection with the student to be an essential piece, which is part of your article...
I think people approach social science with this idea that we can uncover laws like Newton and Einstein. --But I think there's more complexity in studying groups of children and how they learn than in observations of planetary motions. People are less predictable than celestial motion.
Thanks for including the article links. I'm coming to the conclusion that no article should be cited behind a paywall. It's impossible to judge such a paper without understanding their methodology. People put all sorts of unverifiable evidence forward these days and I think it makes us accept that we just can't do the thinking. (I know this isn't your fault.)
We’ve been advised not to use AI products for IEPs because that involves entering confidential information into the LLM, I imagine this is a major hurdle in many industries
Well there it is.
Why not use a product that has a secure LLM?
Great post! When is teaching problem solving creating more problems? When it’s done mindlessly. Strong argument here for not using AI like a souped up textbook. Teachers matter more than tools. Learners matter most.
Fantastic!
Though, I've personally concluded that Ed-Tech is the wrong path. As good teachers leave, we keep the barriers for new teachers high and the pay low, and we lay teachers off... we communicate our values...
Ed-Tech would be a great addition to a culture that valued education. Collectively, we seem to value the credential, the diploma, what comes with the education... but the true greats were just curious minds.
Some great product management thinking going on in this post, btw. Not this VC fake it til you make it, and probably never make it if you can find someone to buy you first, sort of thinking.
I love your music!
To whom is Ai evidently supporting special education? to teachers who still present decades-old documentaries in hopes students pay half of half of half attention? Having begun full-time part-time teaching in classrooms as a substitute mostly (84%) special education assisting, computer use is still a tech tool on the list of things to learn to use/teach. I also am a PAPER Education math tutor K-12 for 28 months now! And true! tutors who know how to relate to a student as another human being are prioritized despite the downsizing!
I like the snapshot tool built into Desmos classroom so we can do just that: take pictures of student work and then project them easily for the class to see. One feedback: I’d like to also be able to select the graph or whatever they are writing about to include in the album.
Whenever the Gates folks DUMP a TON OF MONEY on somebody like Sal Khan (hedge fund analyst) but it's for education... that gives me a bad vibe because it could have gone to people who know from pedagogy.