# Unscaffolding Math Problems

Several months ago, the new NPR show Invisibilia did a broadcast about expectations.  The main theme of the program was that the expectations others hold of an individual can effect the outcomes of that individual, either positively or negatively.  If you’d like to know more about this idea please listen to the radio show, its great!

I wanted to incorporate the show’s theme into a blog post about special education math classes, but was unsure how until Alex Overwijk, a teacher from Ottawa, sent me the following comment about my post about scaffolding

Expectations…

This led me to consider how the over-scaffolding of mathematical tasks and problems for special education students creates an atmosphere of lowered expectations.  Both Alex and I agreed that students with disabilities need a certain amount of scaffolding to be successful. What we didn’t know was to what degree and when this scaffolding should be provided.

Thinking more deeply about this question, I believe the degree to which scaffolding is provided to students with disabilities is a very individual, personalized process.  Great special ed teachers who understand their student’s learning pathways will be able to determine the appropriate level of scaffolding for them.  But the timing of when scaffolding is provided can show students what a teacher’s expectations are for them in math class.  If scaffolding is implemented too early in a lesson or unit, students may feel a sense of lowered expectations which according to Invisibilia would result in lowered outcomes as well.  You can’t get much earlier in a lesson or unit than the pre-assessment, so let’s start there.

Pre-assessments are an often over-looked, but vital instructional tool.  Teachers use them to figure out where their students are in the process of mastering a concept or skill.  Pre-assessments are an important aspect of popular pedagogical strategies like Backward Design and Differentiated Instruction.  Math teachers can also use mathematical problems or tasks as their pre-assessments.

Dylan William and Paul Black state, “… all those activities undertaken by teachers, and by their students in assessing themselves, which provide information to be used as feedback to modify the teaching and learning activities in which they are engaged. Such assessment becomes ‘formative assessment’ when the evidence is actually used to adapt the teaching work to meet the needs.”  Using mathematical problems and tasks as methods of formative pre-assessment will only be successful when they are not scaffolded.

The expectation for a student faced with a new problem or task should be that they will eventually complete it independently, regardless of disability, either initially or at the end of a lesson or unit.  Students with disabilities should be expected to demonstrate progress towards independence at their instructional level determined by pre-assessment data collected by the teacher.  Independent completion of a task or independently solving a problem would not be evident with any level of scaffolding in place.  Scaffolding (in the form of graphic organizers, modeling, prompting, etc.) should be provided after students initially attempt a problem or task in order to guide them towards their highest level of independence.

Students should be allowed to not be able to pick the apples, to see the need for the step stool.

When a student first encounters a math problem they internally decide where it falls in Vygotsky’s zones of proximal development.  The student will decide if they can complete it on their own (independent), whether they need help to complete it (aided), or whether they can’t complete it at all.  In a strengths based special education classroom the teacher may want the students to view all math problems as being able to be completed easily, but this will not create an atmosphere of heightened expectations.  In fact it may do the exact opposite.  This is why I use problems and tasks as pre-assessments and my goal is to keep them unscaffolded.

It is my belief that the use of mathematical problems and tasks as pre-assessments can set the level of expectations that a teacher holds for their students.  It is also my belief that these expectations, heightened or lowered, can effect student outcomes, either positively or negatively.  Students with disabilities can develop a growth mindset through heightened expectations and learning from mistakes.  Students won’t make those valuable mistakes if every task or problem is over-scaffolded from the outset.

So show your students that you have high expectations for them regardless of their disability! Unscaffold your math problems!