From Inclusive Math Excellence Project

There was a lovely article that Seattle Public Schools put out at the end of the school year, sharing some of the work on a pilot project we ran with them this year. The first year of the project was incredibly promising. I think it deserves to be duplicated in other places.

The Vision: Depth over Acceleration

We were invited into this project by the district’s Department of Highly Capable Services. The standard brief of such departments is be to identify gifted/highly capable students and make sure they receive additional services to challenge them appropriately. One of the standard ways this happens is with acceleration: kids may be offered a spot in one of the hi-cap schools, and work 2 grades ahead.

We advocate for another approach. If a student isn’t being challenged by 2nd grade math, then 4th grade math may be an improvement, but there’s a HUGE missed opportunity here. The goal shouldn’t be to speed through math topics like we have somewhere else to be; we should take the opportunity to work deeper instead of quicker.

SIDENOTE: I was one of those kids who was accelerated through math classes quickly. I finished calculus in grade 9. I would have been bored doing math at grade level, and being accelerated was better than nothing. But racing through math classes doesn’t end with a prize; it was a race to nowhere.

I didn’t take any math classes in tenth grade. There weren’t any options.

What I needed – and what so many kids need – was deep, interesting work that involves creative problem solving.

(Perhaps a metaphor for this would be to point out that you’d learn more about ocean life by looking in tide pools rather than waterskiing. And looking at tide pools might lead you to want to snorkel or scuba dive to learn even more. Learning math deeply isn’t about rushing over the surface, but about taking the time to look, question, and understand. And there’s a ton to learn if you look deeply at elementary topics.)

The Ninth Math Practice

This perspective is reflected in a proposed “9th Math Practice” (an extension of the Eight Math Practices in Common Core) that came from the National Association for Gifted Children, working in tandem with NSCM and NCTM:

Math Practice 9

Solve problems in novel ways and pose new mathematical questions of interest to investigate.

The Vision: The Good Stuff is for Everyone

Once you accept that Math Practice 9 is important for gifted kids, it’s tempting to imagine how nice it would be if we could offer that kind of experience to all kids. Doesn’t everyone deserve the good stuff? We’d need to make sure we found accessible ways to do it, of course, but if we could… wouldn’t that make math class an amazing place for students to think and grow?

The Vision: Invest in Teachers and Impact gen-ed classrooms

Paula Montgomery, who heads the Hi-Cap Dept. in Seattle, set some far-sighted goals for this project:

1. Invest in teacher capacity
2. Provide challenging educational experiences for kids who get hi-cap services while they’re in their regular, general-ed classrooms, in a way that works for all the kids in the room.

And to achieve these goals, she partnered with us 🙂

The Design: Leverage Autonomy and Curiosity 

We met with 4th & 5th grade teachers from five schools for four lab sessions over the year, and with 6th grade teachers for four separate lab sessions.

We designed lessons based on rich tasks that were technically on grade level, and accessible to all the students in the room. But they were designed for depth sufficient to challenge kids ready to work above grade level, without relying on topics from higher grades. In particular, we included extra opportunities for student choice and autonomy, curiosity and mathematical argument.

And here’s the crazy thing: the lessons were nearly always successful with nearly all the kids in the classrooms we visited, and we almost never knew who actually qualified for gifted/hi-cap services. It was just kids getting curious, making conjectures, and trying to figure stuff out. Like in this wonderful moment where two sixth graders trying to figure out whether their conjecture about star polygons was true made a sign for their desk that said, “Do not disturb. We are working hard.”

The Design: Manipulatives make Deep Work more Accessible

One element of our secret sauce in this context was manipulatives. Using, for example, 21st Century Pattern Blocks to explore fractions gives a tactile/visual way in and makes the grade-level topic more accessible to students who don’t have a solid foundation for a topic yet. But there are much deeper questions that can be authentically motivated with the blocks.

For example, students had to follow (and generate) arguments to find the values of the pattern blocks given that the yellow hexagon was worth 1. For some blocks, this is straightforward, but for others, it’s nontrivial!

Once students had those values, they got to create their design with a target value, or just figure out the value of what they had created.

What’s striking about the work is how you can see a more robust understanding of fractions developing. Students are doing work that would likely feel too hard to most students if they had to do it on the page. Finding 5 + 3 1/2 + 4/3 + 4/3 + 20/6  is, on the page, difficult-looking. But students connect the fractional blocks to equations, and build understanding of the actual meaning of the fractions: six green triangles make a hexagon, which is 1 unit, which makes the green triangles 1/6. So 20 sixths equals 3 wholes with 2 sixths leftover, or 3 2/6 . And since 2 triangles is the same as one blue rhombus, which is a third, we could write  3 1/3.

Later, they designed tax systems that levied various taxes on collections of blocks (imagining them as currency), and argued about which tax was most fair.

What’s hard to communicate is just how powerful the project felt. My favorite feedback was from one of the sixth grade teachers: “students are doing math, not just learning math.”

The Future

We’re hoping to continue working with 4th and 5th grade teachers next year, and extend the lab sessions to grades 2 and 3 as well. (Hopefully we’ll have a good option for the 6th grade teachers too.)

There’s another element I’d like to see too, which is outreach to parents about what authentic mathematical challenge – and success – looks like. As a parent, it’s easy to get fixated on being “ahead” in math. If more parents knew what depth in math felt like and if more classroom teachers were equipped to offer it, I think families would get out of the business of wanting to move kids forward and want them moving deeper instead.

Paula and I are also planning to present at the WAETAG conference in Bellevue, WA this October to share more details about this project. A world where districts invest in their math teachers who in turn create opportunities in everyday classes for their students to be creative, be curious, and get challenged appropriately, regardless of who they are… I think it’s worth advocating for, and working toward.

The good stuff can be for everyone.