Fascinating topic. I spent the past two years as an instructional coach in my district (moving back to the classroom this fall), and was surprised by how few teachers understood the district’s math plan, beyond what they were teaching in their classroom. For example, I sat in on meetings with 6th grade teachers, who were surprised to learn that students had a number of opportunities to move to honors-level courses through high school, and the various avenues students had to reach calculus or statistics, if this was their goal. The teachers reported that this helped them with their parent conference, as they now saw what they were doing as part of a bigger system, rather than just an isolated grade-level experience. Based on this, I would suggest that all math teachers, along with counselors. should understand how what they teach fits into a student’s learning experience. Math departments should craft their mission so that it is clearly communicaed to all stake-holders, and work with students and parents to discuss plan not only grade to grade, but from grade 6 to graduation.

Just like we talk about math problems having multiple entry points, studends should have multiple opportunities to re-craft their math plan. The idea that you must take courses A, B, C and D or else you will never get to course E is antiquated. The fault-tolerant school provides opportunities, and encourages students to pursue them, rather than maintaining artificial obstacles.

There’s a lot here. Very interested to see where this goes.

[This comment is probably more political than what you were looking for.]
Although I have a lot of problems with Geoffrey Canada (especially some his math!), the Harlem Children’s Zone is a model for addressing the needs of high-poverty students. The issue is never as simple as determining the right pathway through mathematics, or to provide remediation and support to bring a student up to grade level – ask anyone who has taught in a high-need school (Example: the student who is habitually late/absent/falling asleep in class because they are babysitting their younger siblings/cousins/neighbors because the adults in the house work at night, or the student who is absent because her baby is sick). I am not absolving schools of the responsibility of finding ways to keep these students on track, but the task is almost Sisyphian in many cases. In areas where poverty is the rule, a school needs to be a community center, providing health-care related services, afterschool opportunities, and family programming; many students need this range of services in order to stay in school. Academic support beyond the school day could be made available in this type of setting as well, providing the tutoring that struggling students from more affluent families may receive privately. We can talk about engagement, perseverance, and productive struggle all day long, but truthfully, there is a HUGE block of students for which these issues are completely secondary to surviving their circumstances. Rather than tolerating the faults, we need to address them societally.

What about a fault-tolerant curriculum? I hear so much talk of “mastery by grade x” that I’m sure it can’t all be possible. I saw a panel presentation by Les Steffe and his former grad students in Philadelphia which presented research which indicates that few children show evidence of being capable of achieving the mastery goals set by the Common Core for fractions in 5th grade. The CCSS may not be as broad as others before it, but it is ambitious and far less cyclical and spiraling, in a Bruner sense. Have a bad year in 7th grade because you were ill or your parents divorced? Or maybe your brain was not ready to think multiplicatively until 9th grade. Sorry. Algebra may never make sense to you.
A fault-tolerant school is still a local phenomenon- what if the whole system, like an airplane or a fleet of commercial planes were fault-tolerant? Less ambitious and more tolerant?

One of the problems is that there are students who change schools often. There are many schools that require all sections of a particular math class to proceed in lock-step with each other, and there is only one starting time: the beginning of the academic year.

This brings to mind some questions.

Question #1: Does Algebra II class (for example) have to start in September and end in June? Why not have a section that starts in January or March (and perhaps spans an academic year)?

Question #2: Can a year’s curriculum be divided into independent modules, taught in different orders by different teachers? Students who come into a school mid-year could have more entry points.

We just moved cross-country, dealing with major fault tolerance issues at the moment, ones that have really altered the track of my kids full careers — and that’s just based on differences on what grades indicate about competency level in the two school systems (Our old school was an early Common Core implementation where district test scores went up as in-class grades went down; my kids arrived at the new school with worse grades and better skills than most students — guess which of those criteria was used for placement?)

One big struggle in higher education is we know meaningful experience is integrative, and we’ve bought into the idea of meaningfully tying together courses over the course of a career to prevent the fracturing of student experience. At the same time, students are increasingly itinerant, with most students receiving at least some portion of their education somewhere else. I work at a branch university, for example, where most of our students come out of the community college system, and some will try to get upper credits by taking online classes from some other institution. Additionally, terms like “3rd-year student” are increasingly ridiculous in a world where normal student experience encompasses both a three-year push to degree and a six-year slog.

The attendance patterns push us towards stricter articulatable outcomes, the pedagogy pushes us somewhere else. I think broad adoption of portfolio based assessment, where portfolios transcend individual universities, is a solution — it pushes the student to see and reflect on the integration of different parts their student career while not requiring too-tight integration of programs.

It does remind me that when I talk about the idea of a national student portfolio system supported by the government people look at me like I’m crazy, but somehow inBloom is normal. Ugh.

I think you’re assuming that my portfolio comment linked to the local issue I’m having with my school system – and that I’m arguing that portfolios could be a key piece of course/outcomes articulation between systems.

That’s not the point for me — on that front I agree with others above: get the national curriculum in place. Simplest solution, and has a whole bunch of other benefits in terms of community and sharing.

Where portfolios come into play in higher education (and perhaps high school) is student sense-making in a time of fractured “un-bundled” experience. We used to try to create coherent sequences of courses in multiple disciplines that were meant to mean something (we failed, but we tried). In a world where 50% of students that start at a university don’t finish there this clean idea of a progression plus a capstone becomes quaint at best.

What inter-institutional portfolios would do would be to allow the student to reflect on their experience across a career. And I mean portfolios very broadly here. My favorite form of “portfolio” is a blog + storage. When I say “portfolio-based assessment” I’m referring not to transfer credits, but students in a class pulling from work they’ve done in multiple places besides the class showing how they meet that standard, or reflecting on how they’ve progressed on dimension over a college career. My ideal portfolio system looks like UMWBlogs, just national — a permanent place of student presence where they can make a narrative out of their experience, in much the same way my blog has helped me integrate the experience of four jobs I’ve had since I started it.

Does that make more sense? Or less? The best model I’d argue is probably something like A Domain of One’s Own: http://umwdomains.com/