Guess what? Poverty really sucks. It’s incredibly hard. All the lifespan studies going back to the 1920s show that poverty in youth is a very hard force. We need to build fault-tolerant schools and systems if we’re actually going to address equity. —Uri Treisman, Iris M. Carl Equity Address, NCTM 2013, at 35min, 10sec.

Every year at my school we try to improve the math program, and I think the quotation above captures what we’ve been going for. Our challenges:

#### Students in the wrong course

We do our best to place incoming freshmen from the information we have, but we’re finding that middle school grades don’t really communicate what students are able to do. So next year we’re hoping to up our game on intake, placing them from our own assessment within a week of their arrival. This also means offering, for freshmen, not only Algebra 1, but also an accelerated pre-algebra-plus-Algebra-1 course, as well as an Algebra 2.

#### Students below grade level

Next year we also hope to offer a couple options for kids to double up on their mathematics so they can catch up to a level that would allow them to take AP Stats, AP Calc or Pre-Calc before they graduate, even if they’ve previously gotten behind.

#### Intermittent attendance

This one is harder. Most of our courses are still structured around the expectation that every kid is there every day. That is a legitimate expectation to which to hold most of our students, but we don’t want their prospects to end if they miss some school. We’re all working on how to create structures to provide more individualized instruction to help fill gaps. A few of us have also been kicking around the idea of a master standards list spanning all four years (or at least three years), so students wouldn’t necessarily be tied to learning a particular blob of material in a particular 9-week term, but it’s unclear how to make this work without a lower student-faculty ratio.

#### Repeat repeaters

Fewer and fewer students are failing a course repeatedly. This is clearly a case where prevention is the best cure (see items above). Still, as long as the number of these students is more than zero, we need to find some way in that works for them.

#### Speeding up students’ applying new concepts

Throughout the program we’re increasing the amount of time that students spend solving problems alone and in groups, and articulating their solutions verbally and in writing. I’ve seen students’ abilities to think, write, speak, and critique improve dramatically. In my room, though, when students solve problems they tend to rely on concepts they are fluent in (like adding) and avoid concepts that are new to them (like exponentiation, or modeling with equations). Helping them master particular skills *and* provide copious opportunities for them to practice applying them in a meaningful context is an ongoing challenge.

#### The overall goal

We want to make sure that each student has a clear path to get from his or her current level of ability to, at a minimum, success in college coursework, and for most students, an AP or similar college-prep experience prior to graduation. We’re working to build a system where a student isn’t permanently derailed if something goes wrong for a while.

The true meaning of “no child left behind.”

The first two categories are ones we are especially sensitive to at our school. We have a large number of high school students who are new to our PK – 12 school and we have a large number of international students. We have some standardized tests that we have used in house for a number of years and we have a decent sense of what prospects there are for students based on their placement scores. What is trickier for us is how to deal with local and other domestic kids whose middle school transcripts just don’t line up with our expectations. We do offer/advise 9th grade algebra I kids to think about doubling up on algebra II and geometry the next year to help make up for lost opportunities at their old school.

I want to hear more/talk more about the standards thing. Some of my colleagues and I are writing objectives that are for all the math classes and then particular ones per course. The idea is that there will be a not-huge (n <=12) per subject and then some group of objectives students work on over all 4 years. I am hoping that through various problems, students will have a lot of opportunities to demonstrate fewer (more important/general) standards and that will help a lot for students who are absent more often.

Also, I'm thinking about (for Alg 1 in particular) instituting a "you're not done until you've completed/showed a problem at least two ways." In this way, if students like using logic instead of equations, that's legitimately great/important, and then they'll have to do an equation/graph/whatever too.

[…] Goldner has picked up the conversation where Treisman left it and I hope he continues it. His school has targeted five areas for fault tolerance ranging from […]

Thanks for this post- very interesting ideas for “fault tolerance”. Regarding number three, “intermittent attendance,” that sounds like a problem for which some kind of self-paced online program could be very helpful. If you were able to direct students who for some reason were on a more unique path to materials that allowed them to meet the “missing” standards in more of a individualized way, they might then be able to get back on track. Maybe some kind of a “learning lab” for this with one teacher in which all the students are working semi-independently?

[…] Building a fault-tolerant math program | Work in Pencil. […]

I won’t say we’re anywhere close to this goal, but at my school we’ve begun to face these challenges, and we’re getting more adept at grappling with the problems rather than blaming the problems.

Re:students below grade level – We created a smaller class (n<15) for these students, so that they would have more focused attention. I opted not to change the curriculum for them – mostly because I thought they could rise to the challenge. It did require a lot more scaffolding, but since I had such a great teacher to student ratio, I was able to provide that support. [I should note that this didn't actually accelerate their rate of credit accumulation, but it did ensure that those who were at a 5th grade math level passed Algebra 1 rather than compounding the problem.]

Re:intermittent attendance – We have an atrocious attendance rate. I've spent many a morning calling parents to wake them up (when the phone numbers listed actually worked), but eventually decided we had to do something in addition to trying to get kids there. [Actually, as part of our SIG, we also had funds for "attendance advocates" for the past 3 years, whose only job was to contact truant students/parents and encourage attendance. It helped, but we had to resort to other safety nets…] So, I started requiring after school tutoring not based on attendance, but based on mastery. If students weren't making it, regardless of the cause (though often the cause was attendance) I called home and made it sound mandatory that they attend after school tutoring with me. Of course, most parents I couldn't get ahold of, and more often than not students skipped out. So next, I started requiring Saturday School. I bought pizza as an incentive with amazing powers, and the greatest part was then I got administrative support for this intervention. If the student didn't come to Saturday School, they had in-team suspension for a week, which was a desk facing the wall in my classroom where they had my personal attention for an entire week, all day. The other teachers on my team were supposed to provide work for the student, just as we would for a suspended student. But if they didn't, which frequently happened, I got to catch them up on math muahahaha. We also had permission to count Saturday School time as absence recovery, so their attendance improved along with their skills. It is important to remember as we create checklists of attendance interventions, though, that almost nothing is more powerful than a concerned conversation with a teacher you truly trust who cares about you. "Hey Jesus, do you realize that you have 24 absences? Okay, listen I'm not trying to get in your business, but if you don't start making them up, you're going to have to take my class again next year. I know you love it, and would love to have me again;), but that's going to be really annoying. And it sounds like a lot, but if you stay after school 14 times, you'll be back down to 10, which gets you credit. You can stay for 2 weeks solid plus saturday school, or we can just do MWF for a few weeks. Which sounds better to you? Great… I'll have some snacks and we'll get your grade up too."

I wrote to Uri and he had some reports forwarded to me about relevant work. Some this was mentioned in his talk as well.

Studies on Math Course-Taking Patterns: The Center for the Future of Teaching & Learning at WestEd’s report, “College Bound in Middle and High School? How Math Course Sequences Matter,” follows up Steve Waterman’s smaller study of course-taking patterns from middle school to high school. The research team found that many students repeat algebra, but few repeaters achieve proficiency on their second attempt. The research team also found that school districts are keenly aware of poor student performance in mathematics, but less aware of the course-taking patterns and their implications for student learning. (From Sara Spiegel at the Noyce Foundation)

Programs at the Dana Center: Academic Youth Development and Intensified Algebra.

@Sammie: Sounds like we are seeing similar patterns. I’m hoping we can figure out how to get kids hooked in and help them make up for the time they lost, like you’ve done … ideally in a way that doesn’t require one teacher to do it all after school and on weekends. Your students are lucky to have you.

My ideas on attendance were to go ahead and create the standards (or use common core) and create shorter Problem Based Learning Units to meet the standards. Make say 5 8-week units for a year (yep extending school year or cal it summer school) or better yet up to 10 4-week units.

Some of the more advanced units would have prerequisites allowing students to build their way to a diploma. Badge systems and gamification of education could easily be tied into the system.

I can see a scheduling nightmare and obviously a rebuilding of curriculum, but I like the possibilities.

[…] find myself going back to Dan Goldner’s post on fault tolerant mathematics programs frequently (fun story: I forgot to bookmark his post initially and spent about 6 months googling […]