I love what you said how curriculum is “a big collection of math problems.” Personally, that’s all I really need! I’m always hunting for good problems that are rigorous and make students think. I don’t need a strict lesson by lesson pacing guide, or the pressure to use the curriculum materials “with fidelity.” It’s too bad you’ve noticed a trend in districts requiring that, thankfully I’m in a district where we have that flexibility.
When I had my first teaching job back in 1999 (I was teaching in the 20th century, you young'uns!) there were few resources available for conceptual, creative teaching. All the textbooks I ever saw were pages of facts and examples, followed by long, long lists of problems. Any creative, student-centered ideas would have to come directly from the teacher themself. I held onto my Marilyn Burns tightly, and was overjoyed when I discovered MARS. But neither was particularly good at helping me with my Algebra II class directly.
The American curriculum was always faulted for being a mile wide and an inch deep. The textbooks were always too much, too big, too long. I heard it blamed on the various states: the book needed to cover these three topics that were required in Texas, and those four for California, and next thing you know there is 15 chapters and a teacher could only possibly cover six of them. This question of "not enough practice problems" was certainly not on the table -- practice problems were all we had.
So when you complain that the material is too tightly concentrated at grade level, and does not have enough practice problems, well, I have to take a moment to celebrate. For a teacher who wants to engage students using math, and mix conceptual work with fluency, this is a great step forward. It is easier to find a good scaffolding lesson (try last year's book, for example) or practice problems (IXL, Khan, etc) than it is to make up all the conceptual lessons and real-world examples on your own.
Really, I never thought we'd be here. I never thought that "not enough practice problems in the textbooks" would be the complaint. We've turned a corner. Although not everyone is in agreement about what math should look like, this is still a major milestone.
Next steps? I love your assessment here, that we need easier access to scaffolding lessons. That districts need to give teachers more leeway. (I would add: district also should provide teachers with the type of coaching that helps them see the value in the materials provided -- many don't). Overstuffed programs -- yeah, it's not new, but it's annoying too. Let's work on that as well. CMP and IMP provide interesting templates in that direction, having paved the way where the big publishers now take charge.
Thanks, as always, for sharing your insights, Dylan. Hope you enjoy the rest of your summer.
I think you're right that a lot of what we see today is a response to the issues of textbooks of the past, and it feels surprising that math ed managed to shake that status quo. I don't know exactly how that happened, would be interesting to learn about the forces behind the scenes.
Congrats! This is the best math blog comment thread Ive found in years!
I have left @tieandjeans fallow for almost a decade (running #makered chat from Korea on elementary recess duty was a serious conflict), but I do miss these things.
Do you mind if I chime in here? For #mtbos context:
Andrew
Years in classroom: 23
First Day Goals: Convince the first years what the class is. Learn names, see how relationships have changed since last year. Move their bodies in space. Check on everyone's device, for OS and Python version and international keyboard layout.
I now teach IB CS, so there are some domain specific needs. :)
Let me take a stab at 101qs inspired stab at proposing a rule
I think there are three main First Day Concern categories for a classroom teacher[^1]
- Routine
- Identity
- Community
and that, roughly speaking, I expect to see a rough correlation between years teaching and a preference for community and identity over routine. To disambiguate between those, I would like to ask questions about age of student and frequency of class meetings.
My first math classroom was 2002, and remember how my fondness for early CPM drove a legit wedge between my HS mentor teacher and myself.
My California math education was Dolciani Algebra, page 345 1-87 Every Other Odd homework and incandescent overhead projector modeled problems. The memorable math project for all of middle school was one construction paper polyhedra project that hung from the ceiling all year.
I hated math until my mentor snuck some contraband curiosity and fascination into the classroom, and I deviated into math.
CPM felt like a breath of fresh air. Diamond Problems were a legit revelation. I had a real degree in math, but I didn't come back into the classroom with any better ideas about how to TEACH this stuff than what I had seen.
But I've spent the last decade plus writing and critiquing CS and MakerEd curriculum, which show a similarl divide between "Are we describing a classroom practice or a curricular domain"?
Right there with you on CPM (and the diamond problems!) feeling like a breath of fresh air. Also love the student team emphasis from CPM. Desmos Algebra 1 also feels good. It was like a team of actual educators had already created, better, what I’d been trying to do for years with IM for my students.
I used Dolciani's "Modern Algebra: Structure and Method", 1962 edition for my classes. I purchased 30 copies when they were reasonably priced on Amazon and used those to supplant the official algebra textbook. I liked the sequence of topics and how they built on each other, and the word problems were very good. Yes, I had to supplement the word problems so there was enough scaffolding. And I didn't like that her worked examples always used the more complex problems so it was hard for students to follow. That aside, the book worked well for my students who have told me over the years when I run into them, that they were very well prepared for subsequent math courses in high school.
Thanks for sharing! I haven't compared the '62 edition from the ones I used in the 80s. I also find the Dolciani sequencing comfortable, but that may be my exposure bias.
Do you mean does Desmos do these things? I use a lot of their activities but I haven't looked extensively at their just-released curriculum. I would say the lack of practice is true for them. They don't have very much scaffolding but my impression is their recent release worked to remedy that. It's definitely not overstuffed like some other programs.
I love what you said how curriculum is “a big collection of math problems.” Personally, that’s all I really need! I’m always hunting for good problems that are rigorous and make students think. I don’t need a strict lesson by lesson pacing guide, or the pressure to use the curriculum materials “with fidelity.” It’s too bad you’ve noticed a trend in districts requiring that, thankfully I’m in a district where we have that flexibility.
Thanks for sharing, great post!
Woo hoo!!! I need to celebrate for a moment!
When I had my first teaching job back in 1999 (I was teaching in the 20th century, you young'uns!) there were few resources available for conceptual, creative teaching. All the textbooks I ever saw were pages of facts and examples, followed by long, long lists of problems. Any creative, student-centered ideas would have to come directly from the teacher themself. I held onto my Marilyn Burns tightly, and was overjoyed when I discovered MARS. But neither was particularly good at helping me with my Algebra II class directly.
The American curriculum was always faulted for being a mile wide and an inch deep. The textbooks were always too much, too big, too long. I heard it blamed on the various states: the book needed to cover these three topics that were required in Texas, and those four for California, and next thing you know there is 15 chapters and a teacher could only possibly cover six of them. This question of "not enough practice problems" was certainly not on the table -- practice problems were all we had.
So when you complain that the material is too tightly concentrated at grade level, and does not have enough practice problems, well, I have to take a moment to celebrate. For a teacher who wants to engage students using math, and mix conceptual work with fluency, this is a great step forward. It is easier to find a good scaffolding lesson (try last year's book, for example) or practice problems (IXL, Khan, etc) than it is to make up all the conceptual lessons and real-world examples on your own.
Really, I never thought we'd be here. I never thought that "not enough practice problems in the textbooks" would be the complaint. We've turned a corner. Although not everyone is in agreement about what math should look like, this is still a major milestone.
Next steps? I love your assessment here, that we need easier access to scaffolding lessons. That districts need to give teachers more leeway. (I would add: district also should provide teachers with the type of coaching that helps them see the value in the materials provided -- many don't). Overstuffed programs -- yeah, it's not new, but it's annoying too. Let's work on that as well. CMP and IMP provide interesting templates in that direction, having paved the way where the big publishers now take charge.
Thanks, as always, for sharing your insights, Dylan. Hope you enjoy the rest of your summer.
I think you're right that a lot of what we see today is a response to the issues of textbooks of the past, and it feels surprising that math ed managed to shake that status quo. I don't know exactly how that happened, would be interesting to learn about the forces behind the scenes.
Congrats! This is the best math blog comment thread Ive found in years!
I have left @tieandjeans fallow for almost a decade (running #makered chat from Korea on elementary recess duty was a serious conflict), but I do miss these things.
Do you mind if I chime in here? For #mtbos context:
Andrew
Years in classroom: 23
First Day Goals: Convince the first years what the class is. Learn names, see how relationships have changed since last year. Move their bodies in space. Check on everyone's device, for OS and Python version and international keyboard layout.
I now teach IB CS, so there are some domain specific needs. :)
Let me take a stab at 101qs inspired stab at proposing a rule
I think there are three main First Day Concern categories for a classroom teacher[^1]
- Routine
- Identity
- Community
and that, roughly speaking, I expect to see a rough correlation between years teaching and a preference for community and identity over routine. To disambiguate between those, I would like to ask questions about age of student and frequency of class meetings.
My first math classroom was 2002, and remember how my fondness for early CPM drove a legit wedge between my HS mentor teacher and myself.
My California math education was Dolciani Algebra, page 345 1-87 Every Other Odd homework and incandescent overhead projector modeled problems. The memorable math project for all of middle school was one construction paper polyhedra project that hung from the ceiling all year.
I hated math until my mentor snuck some contraband curiosity and fascination into the classroom, and I deviated into math.
CPM felt like a breath of fresh air. Diamond Problems were a legit revelation. I had a real degree in math, but I didn't come back into the classroom with any better ideas about how to TEACH this stuff than what I had seen.
But I've spent the last decade plus writing and critiquing CS and MakerEd curriculum, which show a similarl divide between "Are we describing a classroom practice or a curricular domain"?
Right there with you on CPM (and the diamond problems!) feeling like a breath of fresh air. Also love the student team emphasis from CPM. Desmos Algebra 1 also feels good. It was like a team of actual educators had already created, better, what I’d been trying to do for years with IM for my students.
I used Dolciani's "Modern Algebra: Structure and Method", 1962 edition for my classes. I purchased 30 copies when they were reasonably priced on Amazon and used those to supplant the official algebra textbook. I liked the sequence of topics and how they built on each other, and the word problems were very good. Yes, I had to supplement the word problems so there was enough scaffolding. And I didn't like that her worked examples always used the more complex problems so it was hard for students to follow. That aside, the book worked well for my students who have told me over the years when I run into them, that they were very well prepared for subsequent math courses in high school.
I need to check out Dolciani, never seen one myself
Thanks for sharing! I haven't compared the '62 edition from the ones I used in the 80s. I also find the Dolciani sequencing comfortable, but that may be my exposure bias.
Where is Desmos?
Do you mean does Desmos do these things? I use a lot of their activities but I haven't looked extensively at their just-released curriculum. I would say the lack of practice is true for them. They don't have very much scaffolding but my impression is their recent release worked to remedy that. It's definitely not overstuffed like some other programs.