One of the missions of this blog is to take the work of the amazing online community of math teachers known as the MathTwitterBlogoSphere (MTBoS) and to show what modifications are made for students with disabilities. I call it the #MTBoS Mod(ification). You can read the first two editions here and here. This edition is about the lesson structure created by Dan Meyer known as a 3-Act Task.
#MTBoS MOD: 3-Act Edition
The 3-Act math task I chose was created by Graham Fletcher called It All Adds Up. I chose this because in our spring trimester we focus solely on financial literacy. As a teacher of students with disabilities we spend a great deal of time on the adaptive mathematics that is often over-looked or just simply considered a “real world context” in the classes of typically developing students. In the world of special education these tasks are known as Instrumental Activities of Daily Living (IADLs), which are complex skills needed to live independently. IADLs are not to be confused with the Activities of Daily Living, which are basic self-care tasks. At my school we call these skills the Mathematics for the Instrumental Activities of Daily Living.
As a pre-assessment for our “money unit” (as the students call it) I used “It All Adds Up.” The goal was to see how comfortable the students were with identifying coins and counting different combinations of coin denominations. I launched the task with three of my student groups. The task is great for students at different computation levels. At the simplest level the students can solve it by adding coins together to equal $1.00. At a more complex level students can look for patterns that can help them solve the problem more efficiently as well as reflect on the possibility of multiple solutions to the problem. I gave this task to groups of students with a variety of different needs and modes of processing. I’ve broken the three groups into the three stages of the Concrete-Representational-Abstract method of instruction.
Teaching is really only as valuable as the learning experiences and opportunities created for the students. Crafting and choosing which experiences and opportunities are available to students should be at the forefront of any teacher’s mindset when planning lessons or units. So let’s delve a little deeper into crafting and choosing learning experiences.
One of my classes has been using the geometric study of area in order to practice and apply multiplicative thinking. Crafting and choosing specifically rich tasks that engage the students has been one of my major goals for this unit. So I’d like to just investigate different iterations of reasonably similar tasks that apply multiplicative thinking in the geometric context of area.
You could just start and end your search with:
Draw a rectangle with an area of 56 units.
This certainly gets the job done. Students have to think about factors of 56 and which make the most sense. The great thing about this task and others like it (check out Open Middle for more) is that there are a multitude of correct answers. Having many “right answers” leads to deeper group work and richer class discussions. The drawbacks to this task are the lack of visual support and the separation from a concrete representation or real world context. Also the language processing comprehension of this task is high, so students who struggle in this area would require additional supports.
Ashli Black, over at Learning to Fold, recently posted this little bit of wit and whimsy. The post essentially recounts her experience in algebra classes and compares it to the experience of contestants on an extremely confusing, quite vague, and thus hilarious math game show. Ashli makes the point that, “As that kid without conceptual understanding in algebra, this skit is pretty much exactly what it was like in class for me. Confusing, almost no stated rules I understood, and at any moment the scene might change or I might be shoved in a box for not achieving Wangernumb.” Ashli considers the difference between teaching for conceptual understanding and teaching for procedural understanding in her post, but it got me thinking about my own students. I often think my students are holding their breath, waiting for me to tell them their answer was in fact “Numberwang.”
My goal as a special educator is to communicate the day’s lesson or task so the students will be able to access, understand, and apply the mathematical content. This often leads to accommodation, modification, and differentiation of everything for everyone. When one thinks of accommodations the first things that come to mind are standardized testing accommodations. The general list usually looks something like this:
Differentiation is a widely accepted (and debated) strategy for meeting the needs of a diverse range of learners, especially in special education classrooms. According to Carol Tomlinson, “a differentiated classroom provides different avenues to acquiring content, to processing or making sense of ideas, and to developing products so that each student can learn effectively.”
But what does it look like in practice?
First, let me describe our class setting to give you some background. I teach at a self-contained special education high school in Manhattan. The learners at our school range from students with learning disabilities or speech and language delays (which effect academic performance, but do not generally effect their physical appearance or how they react in social situations) to those with autism spectrum disorders or down syndrome (which effect socialization and communication as well as academic levels.) Our math classes are mixed grade (9th graders with 10th graders and 11th graders with 12th graders) in order to create groupings that can best meet each student’s academic and social/emotional needs. There are three concurrent math classes, which means our class groupings are no bigger than 8 students with a head teacher and an assistant teacher. This leads to collaborative in-class groups that can be as small as 4 students to 1 teacher.