Category: classroom practice

Getting real about the challenges of differentiation

I thoroughly enjoyed reading this post by   (@ablinstein) about a challenging class she is teaching. I love a post that begins with a real challenge, a problem that needs to be solved. She writes about a high school class that includes multiple grades, skill levels, and previous experiences with math. While typically successful in focusing her classroom around collaborative group work (using Thinking Classrooms), this class challenges her. She notices that the kids are disengaging from group work, and hears complaints that the class is moving both too fast and too slow.

Anyone who has taught has faced this challenge. This challenge is particularly common when we teach based on lectures, but that is not the case here- Anna has designed her classroom around best practices of group work and rich tasks. Other classes are working with a range of learners, but this one is not. While she is not writing specifically about students with disabilities, this post is a test case of the “good teaching is good teaching” myth. I believe that both “students need to be tracked, students with disabilities need different math” and “just put them together, good teaching is good teaching” belie how challenging it is to teach a wide range of learners.

So what does she do? According to this post, she does a tremendous amount, some of which is supported by already existing research, and some of which is innovative and should be researched. She writes

Some suggestions that I implemented that seemed to make a difference:

  • Taking a break from random groups to help students regain their trust that the class would meet their needs; doing some work in pairs designed to foster productive collaboration; allowing students choice as to who to work with while also asking them to work with different students at times; being explicit when the goal of a task was to build collaborative skills

I love that she writes here about trust, knowing that her job is to gain the trust of kids, not just in her as a teacher, but in her ability to organize a class that will work for them. She offers more options for engagement for kids in this class, individual, pair, and group, offering additional choice in whom they work with. She makes it clear that goals are not always content-focused. If this sounds a lot like UDL (Universal Design for Learning), you are right. She is building flexibility and choice into her classroom.

Structuring activities so there was time at the start for individual exploration before asking students to share their thinking with others thus giving more processing time for students who worked more slowly; circulating and helping some students get started; building more optional challenge into tasks for students who worked very quickly or who had already had prior experience with a topic; creating tasks that could be approached with a greater variety of methods and building more writing into tasks so that different ways of thinking mathematically could be valued

This paragraph is a master class in creating an inclusive classroom in math. Thinking time is super important, particularly as for many neurodiverse learners, processing time is perhaps the fundamental difference from their peers. If class rushes past them, they don’t have the time to engage to their potential. Building in an optional challenge is a great way to engage students who don’t need that time- I think we should spend more time talking about how to do that so that students who work faster are offered opportunities to think deeply, not just move on to the next topic. She writes about creating rich, multi-leveled tasks, and basically notes that she had to be more careful about the tasks being multi-leveled as her class was more heterogeneous in terms of skill level. She looks to her tasks, rather than to deficits in the kids, as a point of change.

Meeting students where they were to regain trust and buy-in; this included at times splitting the class into two groups (students chose which group to join) – a more free-form exploratory group with more open and challenging problems and a more structured group where students would get some problems to activate prior knowledge and smaller, more concrete problems that would build over time to greater generalization and abstraction and more teacher guidance and reassurance that they were on the right track

This is a great strategy, and very UDL, as it is focused on students making the choices about how they learn, rather than a teacher doing the categorizing and sorting into differentiation groups. I would love to hear more about how these groups worked, and how students responded to them. Also, did students always pick the same groups? Did it vary by topic?

Noticing struggling students’ successes and highlighting them publicly; selecting which students would share their thinking to make sure that different voices could be heard over time

Here we see the important insights from Complex Instruction about status treatments, particularly important when working to establish status for kids with less status in heterogeneous environments.

Make sure to leave time for synthesis and practice problems (at different levels) during class – this helped address student concerns that they were leaving class with lots of questions and feeling unsettled about the concepts they had explored that day

Giving students more feedback during class about their understanding of a topic rather than relying more heavily on groupwork and self-assessment for students to know how they were doing and what might be helpful next steps

Here, she attends to making sure that students leave the class feeling secure in new knowledge. She attends to synthesis. Feedback is a critical element of learning, with kind of an unfortunate name that suggests a computational model of learning. But feedback is really getting human interaction around your work, to see what you think mirrored in another, and can be particularly important when coming from the teacher, since our kids (mostly!) value what we think about what they think. It makes our kids feel valued.

Providing more problems at different levels and helping students navigate which problems might be more helpful for them to do during/after a particular lesson – here is an example of a tiered homework problem set.

I love this example of a tiered homework problem set. It begins by laying out the essentials, then gives problems that are Important, Interesting, and Challenging. I love that these are not reducible to Easy, Medium and For The Smart Kids. The first set is Important, which is why you should do them.

This post helps us build on the important work of Complex Instruction, layering in practices that allow kids to learn in their Zone of Proximal Development, making choices about their own learning, which leads to increased meta-cognition.

Yes, as Anna notes, this is an unsustainable amount of work.  Yes, this is a tremendous amount of work, but the structures that you put into place are repeatable. That lovely homework, for example, is now made! Can departments, can the #MTBOS share these kinds of differentiated assignments?  UDL is meant to solve problems, and then to help save you work, to build flexible supports into classrooms as a key aspect of design, not afterthought.

And this post is a perfect example of UDL in action. Here, she views curriculum and pedagogy as the problem, not the kids. She takes up a problem-solving attitude, working to redesign the classroom around the edges. This classroom redesign is not about the mythical middle, but working to make the class work for those who are on the edges, both needing more time and less, etc. The redesign builds in choice and flexibility as the primary tool to accomplish that.

 

 

Counting Collections and Inclusion

I love Counting Collections. As a classroom teacher, I would always have my students count everything in the classroom, differentiating based on what number set they needed. We would work on representing numbers, and we would use charts to represent groups of ten, pushing understanding of place value. We didn’t call it Counting Collections, but a similar practice. I always saw it as a great activity for a class where kids were learning to count very different number sets, since I could easily differentiate within the context of counting. But now I don’t have to write that post, since Heidi Fessenden () recently wrote the best one ever. It is a beautiful post about her work with counting collections and students with disabilities and inclusion. Read it! It is beautiful!

Counting Collections: One Nearly-Perfect Answer to Inclusion

Her post highlights several critical features of great mathematics teaching for inclusion. First, throughout the piece, she frames her own work as a problem-solver, not as a expert, not as someone who has already figured it out. Heidi writes how difficult it has been to figure out how to include students with autism, who need additional scaffolds and support, into a general education mathematics routine. That attitude, having a problem-solver approach, is how she IS able to include all children in beautiful, collaborative learning. She tries, and if she fails, she thinks, she problem-solves, and she tries again. She provides kids with partners, and understands that both partners will learn, not just the child with the disability. Heidi incorporates collaboration, broadening the concept of learning beyond the individual. She provides scaffolds, like a visual schedule for the counting collection. I also love how she learned to not micromanage! Students with disabilities, particularly autism, are often micromanaged to within an inch of their lives. They are offered very little space to think, to grow, and to make choices. Heidi gave them space, gave them scaffolds, and let them count!

 

 

Developing meaningful mathematics goals for IEPs

In the last few months, several educators have asked me some variant of the following question:

How do we shift students’ IEP goals from rote memorization to meaningful mathematics?

IEP goals are the heart of instruction for students with disabilities. In my experience, a narrow goal can contribute to all sorts of unintended consequences for a child’s mathematics. Continue reading “Developing meaningful mathematics goals for IEPs”

Concrete Representational Abstract (CRA) in mathematics

In response to a Twitter inquiry, I decided to write up some longstanding thoughts on the Concrete Representational Abstract (CRA) sequence that is popular particularly in designing instruction for learners with disabilities. First, what is CRA? Here, from a researcher who done several studies on CRA with students with disabilities in mathematics: Continue reading “Concrete Representational Abstract (CRA) in mathematics”

CGI and special education

As I read the conference program for the CGI (Cognitively Guided Instruction) Conference  coming up this weekend in LA, I was reminded that while math education typically doesn’t include kids with disabilities, CGI has always been an exception. There are several great presentations this week that focus on kids with disabilities doing mathematics, including ones by Jeannie Behrend and Lio Moscardini whose research is discussed below. Here is a quick round-up of CGI research articles that included kids with disabilities (all these articles seem to focus on learning disabilities, which means that we need more work on CGI with other disability categories). Continue reading “CGI and special education”

Universal Design for Learning (UDL)

Universal Design for Learning (CAST, 2011) was inspired by Universal Design in architecture.  If you design for people with disabilities before you built the house, it can be more accessible, less expensive, and more beautiful.  UDL applies that theory to learning.  Beginning with the premise that variability is what all learners share, curriculum should be designed to work for the widest variety of learners possible.  Continue reading “Universal Design for Learning (UDL)”

Mindset

A great introduction to mindset from Jo Boaler.

Mindset is incredibly important for kids with disabilities in mathematics.  Too often, kids with disabilities are given the impression that they lack the ability to do complex mathematics.  And, perversely, when kids are labeled LD, they are often told that they are “smart” but their brains are not “wired” to read easily, or do mathematics easily.  In this sense, we are constructing fixed mindsets for kids.  We tell them that kids with LD are smart, and that their abilities in some areas are fixed at a high level, and their abilities in other areas are fixed at a low level. When we know how destructive fixed ability mindsets can be, why do we purposely create them in kids with LD? Continue reading “Mindset”