I just finished doing the 2010 edition of Math 1 (91pages) today. Now begins the synthesizing and summarizing, which I will put into blog posts.

Math 1 is an Algebra 1 course that includes an incredibly deep coverage of proportional reasoning, in addition to the usual linear, quadratic, and exponential function topics.

I did Math 1 because most of our incoming students are incredibly bright and hard-working but they were not the math monsters in their middle schools. They have many of the typical middle school gaps, but they are much more sophisticated than most 9th grade Algebra 1 students. So the fact that Math 1 is a REALLY TOUGH course that dives very deep into Algebra 1 material is a great thing because it will give my students the deep rich course they deserve, even though they are placed into Algebra 1 based on their current skill level.

My Algebra 1 learners find themselves stuck in a ZPD no-man's-land: their ZPD as math learners is nowhere near their ZPD as readers.

This presents a huge problem in the classroom. The math in CPM Algebra 1, for example, is rich and interesting, but the text is written for reluctant readers, discouraged readers, and English Language Learners, which is a huge turn-off for the vast majority of my enthusiastic and highly capable readers.

They feel insulted by it, and they are not shy about expressing these feelings. So my student population tends to dismiss it and resist it, even if they really do need to learn the content. This raises the question of how best to serve a population of learners who need to be challenged with greater nuance in textual interpretation and presentation in an introductory high school math class.

For all of these reasons, Math 1 is going to form a terrific problem-based “spine” for my Algebra 1 classes. The problem sequences are rich and interesting and engaging with sophisticated contexts, though they start from first principles. They develop to a point where even a mathematically sophisticated adult will find them very challenging.

To get started, I printed all pages of the problem sets, answer keys, and commentaries and created a binder with the following sections:

1 - Problem Sets plus glossary at the end

2 - Commentaries

3 - My Worked Solutions (for each page of problems, I have one stapled cluster of my worked solution pages)

4 - Answer Keys

I did all of my work on three-hole binder paper, with each new page from the problem set being its own stapled packet (or "blob") in the Worked Solutions section.

Whatever problem set I was working on I would take out of the binder along with the relevant answer key page. That way I could work on binder paper without having to carry the whole damn binder around all the time. Much of this work was done on a lap desk with my iPhone/Desmos for graphing, my TI-83-plus (sorry, Eli) for computation, and my monkey pencil case including my mechanical pencil, my ProRadian protractor, and my colored pencils.

A lot of people have asked me why I started at the end and worked from the end forwards, about 10 pages at a time. The answer has two parts: (1) whenever I started from the beginning, I bogged down or got sidetracked; and (2) it enabled me to see where we were going and where students would end up. By seeing where they would land at the end of the course, I could better understand how things worked from the beginning.

More thoughts coming soon, but I wanted to capture these ideas right away. If you have specific questions you'd like to discuss, please put them into the comments section below.

... so these are students whose reading is well above their math? Are you separating the math problems from the problematic reading?

ReplyDeleteWe're a magnet school and pretty much everybody is reading well above grade level. But most of the texts for kids who are *at* grade level in math are differentiated to include the weakest readers. But we don't *have* a lot of weak or reluctant readers, so that kind of text (such as CPM) is a turn-off to kids who read fearlessly and all the time. So Exeter seemed like a good choice to me because like ours, their students are strong readers but may not have been exposed to a lot of advanced math yet. That makes them sophisticated customers of the reading material, which needs to challenge them as much as the math does. Does this make any sense?

DeleteThanks for commenting.

- Elizabeth (@cheesemonkeysf)

Yup! And as somebody who has always excelled at figuring out math verbally, simplifying the language would annoy and insult me and make it harder to learn.

DeleteI've seen the SF Unified classwork packets and they use a mixture of Math shell tasks, CPM lessons, and some I believe connected math. It seems to be a mixed variety which in some ways can be better than solely CPM. I assume you feel it's a bit disjointed and doesn't flow which is why you are investigating this new curriculum. Did you buy it yourself, download it? I'm not familiar with it.

ReplyDeleteMy accelerated students disliked the CPM algebra 1, I think it spends too little time on some topics, not enough practice. Also, some of the lessons are a bit boring. None of them really get at students asking questions and investigating them a la 3 act tasks.

There is no perfect curriculum but I am curious about this one based on it's potential to shore up misunderstandings in proportional reasoning, something students are EXPECTED to master coming out of middle school, which we know is hard to guarantee especially when students are passed along to the next class no matter what grade they achieved, and it's of course hard to say what that grade represents depending on how much assessments are worth.

I'm teaching both of our 8th grade algebra (non honors) classes next year. It's made of kids that were in 7th Accelerated (1/2 of 7th and all of 8th) and didn't do well enough to go into honors algebra, but are still hard workers. I've been trying to figure out what to use as I DO NOT want to pilot the Big Ideas Algebra book with them. I was looking at EngageNY material, but maybe I should look at Exeter a Math 1??

ReplyDeleteI would definitely recommend looking at it. It starts from first principles but quickly accelerates into something very rich and interesting. One of the nice things is that it is a very rich, deep course in proportional reasoning that invites careful thinking with basic tools. That means these students will develop great confidence, subtlety, and courage in the courses to follow, where they may even end up kicking the butts of the honors kids, if you know what I mean. ;) Kind of a tortoise-and-hare leveler.

Delete- Elizabeth (@cheesemonkeysf)