What's left out is that Math Academy started small as an experiment with in-person instruction providing advanced math to 5th or 6th grade students in Pasadena Unified. I have no insight into why and how they moved to a technology platform though I have watched from afar as they have done so. The original approach was never meant to educate all students.
If you believe that students should have an opportunity to learn advanced math at an earlier age or more advanced math than what's set out by grade-level standards, which I know is not always the case, two issues with the original in-person approach are equity and scale. Who gets to participate and who is left out? And, assuming you can mitigate or live with the equity issues, how can you reach more students given the current systems and resources available?
Math Academy seems to have seen technology as the way to address at least the latter. I am not sure they have considered the former. Obviously, their platform and approach leaves much to be desired.
However, I wonder often what are better options that are more equitable and can reach more students who are ready for advanced math?
I ask as a parent in a district where there is no longer tracking in math until high school. Some teachers, like the one we currently have, allow for one 30 minute session of "advanced math" per week for selected students with a volunteer, in this case me, a former teacher. There are other students who would benefit from participating in this group but don't. I have a feeling its related to many of the issues we all know as to why they are not offered this opportunity given there are other kids who are seem quite capable of doing advanced math from what I witness and hear from the students I work with. I wish these kids had the opportunity to do more.
And yet, what I do weekly is not sufficient for most of the kids in the pull-out group. Some of the kids I work with, including my own, are utterly bored in class because of the slow pace and low level of the concepts. This doesn't seem fair to them either.
Thanks for this explanation of what good teachers do. I thought you were going to talk about home teachers who teach only computation. I am sure that is a problem, too. Talking about math is the real value. Being able to defend our answers, in any arena, shows learning- understanding.
This takes some guided practice and time to demonstrate (and practice) student learnings.
Noting that selection effects can "curate their student body so the students have fewer disabilities, fewer special education and language needs" doesn't invalidate the premise that it can work. It's unlikely anything works for everyone, especially in the realm of varied disabilities and special education needs. One teacher won't come close to stretching across every variety of student either, but you would not conclude they're ineffective because a rigorous application process biases their school population.
Sure, Math Academy and platforms like it can work for SOME students and for SOME definition of "work." But that isn't their claim. Their claim isn't "this can work." Their claim is this works 4x faster than "a traditional math class." But traditional math classes aren't required to work for SOME students. They're required to provide a free and appropriate education to EVERY student. That's the fallacy here.
The selection bias in the examples you noted is key. And knowing how to get the derivative (procedural math) can be orthogonal from conceptual understanding, as you cleverly demonstrated with your kids. Anything worth learning takes work for the vast majority of learners.
While teaching them this little stupid mathy trick, I literally had the thought that "this is going to make actually understanding the derivative harder for them later."
I can see that! I also have a kiddo around your kids’ age. I haven’t taught them derivates yet :), but we’re learning multi-digit arithmetic through a concrete-pictorial-abstract method. I am the tutor, not AI. At this age, it’s so important to have human-led learning. I do see some of the merits of AI and apps down the road when they’re older—but I’m not planning to outsource this process right now! Plus I enjoy teaching math, so that helps.
"But on some level everyone knows you get the big results (in education) through selection effects. The only question is whether you are paid to not know this."
So true...and unfortunately "private" education is literally paid to not know this...and public education is under attack as it seeks to confront it...
🎯 Several commenters noted after the recent NAEP results that students in Catholic schools scored higher and at lower cost than students in public schools. I, someone who is not paid to not know what is going on, might suggest that selection effects are at play here. Others, paid to not know what is going on, have implied that we should turn over the education of our nation's kids to the US Conference of Catholic Bishops, who seem to have figured out the secret to better, more efficient education! C'mon, folks!
I've encountered this framing several times lately, so I want to understand the argument better. Is the point that "public education underperforms because it accepts everyone and so there's a high variance in the student population?"
Yes. Selective private schools (or public magnet schools) have academic requirements for admission, so their achievement data looks great. Is it because of the teachers? Or is it because their student population is already more likely to academically succeed? Clearly, in my view, the latter is the answer.
If they set a height requirement for admission to Harvard, they'd be able to brag about how tall their students were, but would that mean they had a meaningful impact on the height of their students? Not necessarily.
The single most important, mostly ignored, aspect of all education data is the impact of selection effects.
As a former board member of Vanderbilt Charter Academy in Holland, MI, I encouraged the board and leadership to engage in progress monitoring, rather than outcome monitoring...this I believe provides more accurate information. Economic and social factors of the student body also impact outcome measurements, ESL, family stability etc.
I always appreciate your insights. I suppose, before we have anyone trying to "redefine math learning" we should, most importantly, define math learning. The challenges associated with reading through your state's curricula, matching your learning objectives and assessments with the conceptual underpinnings of the math at hand and then clearly targeting your "state's goals" is difficult for an experienced teacher with ultimate control in their classroom and probably impossible for most inexperienced teachers. If we are going to "win at math", we will first need some better definitions, hopefully with the guidance of these experienced teachers.
When I homeschooled my boys for one year during Covid, one was in Algebra the other in Geometry. I knew Algebra had a state test and I wanted to make sure my son learned all he should. I used my state standards, but they were unclear. I used a state specific textbook (it was great and aligned well with state standards), I used "StudyIsland", it was good because teachers from each state had aligned it with state standards and I used a well known publisher's online platform (I had used this publishers college platform and LOVED it when I taught). The "well known publisher" had standards NO WHERE NEAR my states standards-the concepts labelled Algebra I for the state of PA included about 40% of the content slated for Algebra II here in PA. The amount of time I had to spend "picking and choosing" content made the online platform valueless-StudyIsland was 25x more helpful. Now, the best aligned product, StudyIsland, is no longer available for families or individuals so if your district doesn't adopt it, a teacher must "cobble together" a curriculum that might align with state standards or receive a stale set of guidelines created long ago.
We really could use a national set of standards that guarantee a certain level of math understanding for each grade. We should be in the habit of helping teachers and families understand the definition of "math learning" for a grade and working together to not only meet but exceed that goal. Until we define math learning, it will consistently be a victim of being undefined which will allow companies to constantly redefine the objectives to suit their desired results.
What he said.
Was intro'd to a true believer this week and agreed to a chat.
Me: "So um yeah, I organized this tiny Harvard AI conference last spring - "
"Amazing! Finally someone on our side, there so many naysayers, we have to tell people how AI is really transforming already..."
Me: "Oh wait. No this was I guess a naysayer-ish conference. Convince us you see a path here around the 5% rule, and nobody could."
We had a good laugh.
What's left out is that Math Academy started small as an experiment with in-person instruction providing advanced math to 5th or 6th grade students in Pasadena Unified. I have no insight into why and how they moved to a technology platform though I have watched from afar as they have done so. The original approach was never meant to educate all students.
If you believe that students should have an opportunity to learn advanced math at an earlier age or more advanced math than what's set out by grade-level standards, which I know is not always the case, two issues with the original in-person approach are equity and scale. Who gets to participate and who is left out? And, assuming you can mitigate or live with the equity issues, how can you reach more students given the current systems and resources available?
Math Academy seems to have seen technology as the way to address at least the latter. I am not sure they have considered the former. Obviously, their platform and approach leaves much to be desired.
However, I wonder often what are better options that are more equitable and can reach more students who are ready for advanced math?
I ask as a parent in a district where there is no longer tracking in math until high school. Some teachers, like the one we currently have, allow for one 30 minute session of "advanced math" per week for selected students with a volunteer, in this case me, a former teacher. There are other students who would benefit from participating in this group but don't. I have a feeling its related to many of the issues we all know as to why they are not offered this opportunity given there are other kids who are seem quite capable of doing advanced math from what I witness and hear from the students I work with. I wish these kids had the opportunity to do more.
And yet, what I do weekly is not sufficient for most of the kids in the pull-out group. Some of the kids I work with, including my own, are utterly bored in class because of the slow pace and low level of the concepts. This doesn't seem fair to them either.
Good Morning Dan,
Thanks for this explanation of what good teachers do. I thought you were going to talk about home teachers who teach only computation. I am sure that is a problem, too. Talking about math is the real value. Being able to defend our answers, in any arena, shows learning- understanding.
This takes some guided practice and time to demonstrate (and practice) student learnings.
Teach On,
Mrs. J.
Noting that selection effects can "curate their student body so the students have fewer disabilities, fewer special education and language needs" doesn't invalidate the premise that it can work. It's unlikely anything works for everyone, especially in the realm of varied disabilities and special education needs. One teacher won't come close to stretching across every variety of student either, but you would not conclude they're ineffective because a rigorous application process biases their school population.
Sure, Math Academy and platforms like it can work for SOME students and for SOME definition of "work." But that isn't their claim. Their claim isn't "this can work." Their claim is this works 4x faster than "a traditional math class." But traditional math classes aren't required to work for SOME students. They're required to provide a free and appropriate education to EVERY student. That's the fallacy here.
Most private schools offer "a traditional math class" too.
The selection bias in the examples you noted is key. And knowing how to get the derivative (procedural math) can be orthogonal from conceptual understanding, as you cleverly demonstrated with your kids. Anything worth learning takes work for the vast majority of learners.
While teaching them this little stupid mathy trick, I literally had the thought that "this is going to make actually understanding the derivative harder for them later."
I can see that! I also have a kiddo around your kids’ age. I haven’t taught them derivates yet :), but we’re learning multi-digit arithmetic through a concrete-pictorial-abstract method. I am the tutor, not AI. At this age, it’s so important to have human-led learning. I do see some of the merits of AI and apps down the road when they’re older—but I’m not planning to outsource this process right now! Plus I enjoy teaching math, so that helps.
"But on some level everyone knows you get the big results (in education) through selection effects. The only question is whether you are paid to not know this."
So true...and unfortunately "private" education is literally paid to not know this...and public education is under attack as it seeks to confront it...
🎯 Several commenters noted after the recent NAEP results that students in Catholic schools scored higher and at lower cost than students in public schools. I, someone who is not paid to not know what is going on, might suggest that selection effects are at play here. Others, paid to not know what is going on, have implied that we should turn over the education of our nation's kids to the US Conference of Catholic Bishops, who seem to have figured out the secret to better, more efficient education! C'mon, folks!
I've encountered this framing several times lately, so I want to understand the argument better. Is the point that "public education underperforms because it accepts everyone and so there's a high variance in the student population?"
Yes. Selective private schools (or public magnet schools) have academic requirements for admission, so their achievement data looks great. Is it because of the teachers? Or is it because their student population is already more likely to academically succeed? Clearly, in my view, the latter is the answer.
If they set a height requirement for admission to Harvard, they'd be able to brag about how tall their students were, but would that mean they had a meaningful impact on the height of their students? Not necessarily.
The single most important, mostly ignored, aspect of all education data is the impact of selection effects.
As a former board member of Vanderbilt Charter Academy in Holland, MI, I encouraged the board and leadership to engage in progress monitoring, rather than outcome monitoring...this I believe provides more accurate information. Economic and social factors of the student body also impact outcome measurements, ESL, family stability etc.
I always appreciate your insights. I suppose, before we have anyone trying to "redefine math learning" we should, most importantly, define math learning. The challenges associated with reading through your state's curricula, matching your learning objectives and assessments with the conceptual underpinnings of the math at hand and then clearly targeting your "state's goals" is difficult for an experienced teacher with ultimate control in their classroom and probably impossible for most inexperienced teachers. If we are going to "win at math", we will first need some better definitions, hopefully with the guidance of these experienced teachers.
When I homeschooled my boys for one year during Covid, one was in Algebra the other in Geometry. I knew Algebra had a state test and I wanted to make sure my son learned all he should. I used my state standards, but they were unclear. I used a state specific textbook (it was great and aligned well with state standards), I used "StudyIsland", it was good because teachers from each state had aligned it with state standards and I used a well known publisher's online platform (I had used this publishers college platform and LOVED it when I taught). The "well known publisher" had standards NO WHERE NEAR my states standards-the concepts labelled Algebra I for the state of PA included about 40% of the content slated for Algebra II here in PA. The amount of time I had to spend "picking and choosing" content made the online platform valueless-StudyIsland was 25x more helpful. Now, the best aligned product, StudyIsland, is no longer available for families or individuals so if your district doesn't adopt it, a teacher must "cobble together" a curriculum that might align with state standards or receive a stale set of guidelines created long ago.
We really could use a national set of standards that guarantee a certain level of math understanding for each grade. We should be in the habit of helping teachers and families understand the definition of "math learning" for a grade and working together to not only meet but exceed that goal. Until we define math learning, it will consistently be a victim of being undefined which will allow companies to constantly redefine the objectives to suit their desired results.
Thank you Dan for so clearly spelling out WHY NOT.
Complete neutral here as a non-user*, but did you try the site?
The blog seems to end abruptly without any kind of insight, opinion or conclusion etc?
*I have been following MA and engaging with users but not yet signed up.