To answer your question directly, I believe that self-paced learning keeps cropping up as a solution because:

1. It's (kind of) a good idea. It tries to address one of the most obvious problems in conventional math education, which is that kids are forced to move on to the next topic even when they have not mastered the previous topic, which creates holes in their knowledge. Sal Khan has written about this eloquently.

2. It's easy to build. It does not require creating any new curriculum. However, it is NOT easy to implement, since it requires that teachers track and manage kids who are at different points in the curriculum. That's why it keeps failing. (Side note: English classes already allow a degree of self-pacing by allowing kids to read books at their own level, supported by a children's literature with reading-level-graded books. So it IS possible to allow self-pacing and still have the benefits of group interaction.)

3. It's easy to sell. This I think is the biggest reason this keeps coming up. I think that deeper solutions like group projects, group discussion of hard meaningful problems, etc. are far more important than just adding a variable speed knob to the assembly line, but these sorts of reforms directly challenge conventional ways of teaching math, and create a lot of resistance among teachers and administrators. So the easiest thing to sell is "let's do exactly the same thing, but allow variable pacing."

4. BUT it doesn't actually fix the problem. In the long run, doing the same thing faster is exactly what gets our society into trouble, whether we're talking about math education, energy use, global warming, or income disparity. One way or another we do need to do things very differently.

SO, I consider that the challenge for us math revolutionaries is to find ways to sell a deeper better solution in a way that it gets adopted and absorbed, not diluted and rejected.

The follow-on questions to your question are then:

Why do math reform efforts keep failing?

I've lived through New Math, Back to Basics, and Common Core, and all three have big obvious flaws in their conception or execution. The net result is mass PTSD around math education reform.

How can we create a successful math reform movement?

This is what interests me, and I infer, interests you.

Thanks for your leadership. I'm going to start a substack where I write about these issues directly.

The problem with maths eduction is it has to submit to a syllabus. I’m teaching myself and I use a non linear approach using hyperlinks.

This means that I’ll embark on a maths journey say Bayes Theorem and I’ll use a book on that subject and when I hit a brick wall (an area of maths I’ve forgotten or not familiar with) I backtrack, learn what needs to be learned and then move on.

I try to stay in the real world and apply what I’ve learned to pragmatic problems as soon as possible. Some websites use a form of hyperlink such as Maths Is Fun. I think hyperlinking could be used more extensively where at every step the student is presented with various options which take them on different routes. These routes can also be tailored to the desired outcomes of the student.

Unfortunately this type of study only works for the individual as opposed to the one-size-fits-all classroom education which is dependent on whatever syllabus demands of it. Also formal maths education is often divorced from reality to a large extent and only appeals to those type of students that enjoy theory as opposed to application in the real world. I suspect the formal classroom way of education does not encourage those that approach maths in a different way which may be a loss ot mathematics.

Hi Dan - my name is Rob, I'm a former high-school math teacher, and I co-founded the Modern Classrooms Project. I actually did that because I wanted to help other educators teach like you... I LOVED 3-Act Math as a teacher and found self-pacing enhanced those and other inquiry-based tasks. I also found that the MCP approach enhanced human interaction and connection in my classroom, and made my own role as a teacher even more essential.

Anyways, I'd love to speak with you sometime if you're up for it. I'm hesitant to share my personal email on a public forum, but if you email info@modernclassrooms.org, it will get to me. (I'm also reaching out on LinkedIn and Twitter, so please excuse the repeat notifications.) Whether we speak or not, I'm a big fan of your work... and I hope we'll be able to connect soon!

And those who read your post and don't understand the faults in such an approach probably don't see the importance of having a qualified teacher in a classroom.

Good math instruction comes from properly trained math teachers. Let's not forget, the main goal in teaching upper level math is to teach students how to think and not only HOW to get a solution.

To answer your question directly, I believe that self-paced learning keeps cropping up as a solution because:

1. It's (kind of) a good idea. It tries to address one of the most obvious problems in conventional math education, which is that kids are forced to move on to the next topic even when they have not mastered the previous topic, which creates holes in their knowledge. Sal Khan has written about this eloquently.

2. It's easy to build. It does not require creating any new curriculum. However, it is NOT easy to implement, since it requires that teachers track and manage kids who are at different points in the curriculum. That's why it keeps failing. (Side note: English classes already allow a degree of self-pacing by allowing kids to read books at their own level, supported by a children's literature with reading-level-graded books. So it IS possible to allow self-pacing and still have the benefits of group interaction.)

3. It's easy to sell. This I think is the biggest reason this keeps coming up. I think that deeper solutions like group projects, group discussion of hard meaningful problems, etc. are far more important than just adding a variable speed knob to the assembly line, but these sorts of reforms directly challenge conventional ways of teaching math, and create a lot of resistance among teachers and administrators. So the easiest thing to sell is "let's do exactly the same thing, but allow variable pacing."

4. BUT it doesn't actually fix the problem. In the long run, doing the same thing faster is exactly what gets our society into trouble, whether we're talking about math education, energy use, global warming, or income disparity. One way or another we do need to do things very differently.

SO, I consider that the challenge for us math revolutionaries is to find ways to sell a deeper better solution in a way that it gets adopted and absorbed, not diluted and rejected.

The follow-on questions to your question are then:

Why do math reform efforts keep failing?

I've lived through New Math, Back to Basics, and Common Core, and all three have big obvious flaws in their conception or execution. The net result is mass PTSD around math education reform.

How can we create a successful math reform movement?

This is what interests me, and I infer, interests you.

Thanks for your leadership. I'm going to start a substack where I write about these issues directly.

The problem with maths eduction is it has to submit to a syllabus. I’m teaching myself and I use a non linear approach using hyperlinks.

This means that I’ll embark on a maths journey say Bayes Theorem and I’ll use a book on that subject and when I hit a brick wall (an area of maths I’ve forgotten or not familiar with) I backtrack, learn what needs to be learned and then move on.

I try to stay in the real world and apply what I’ve learned to pragmatic problems as soon as possible. Some websites use a form of hyperlink such as Maths Is Fun. I think hyperlinking could be used more extensively where at every step the student is presented with various options which take them on different routes. These routes can also be tailored to the desired outcomes of the student.

Unfortunately this type of study only works for the individual as opposed to the one-size-fits-all classroom education which is dependent on whatever syllabus demands of it. Also formal maths education is often divorced from reality to a large extent and only appeals to those type of students that enjoy theory as opposed to application in the real world. I suspect the formal classroom way of education does not encourage those that approach maths in a different way which may be a loss ot mathematics.

edited Jan 18, 2023Hi Dan - my name is Rob, I'm a former high-school math teacher, and I co-founded the Modern Classrooms Project. I actually did that because I wanted to help other educators teach like you... I LOVED 3-Act Math as a teacher and found self-pacing enhanced those and other inquiry-based tasks. I also found that the MCP approach enhanced human interaction and connection in my classroom, and made my own role as a teacher even more essential.

Anyways, I'd love to speak with you sometime if you're up for it. I'm hesitant to share my personal email on a public forum, but if you email info@modernclassrooms.org, it will get to me. (I'm also reaching out on LinkedIn and Twitter, so please excuse the repeat notifications.) Whether we speak or not, I'm a big fan of your work... and I hope we'll be able to connect soon!

And those who read your post and don't understand the faults in such an approach probably don't see the importance of having a qualified teacher in a classroom.

Good math instruction comes from properly trained math teachers. Let's not forget, the main goal in teaching upper level math is to teach students how to think and not only HOW to get a solution.