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. What kind of mathematics instruction might a child receive whose IEP goal states,
Given a set of numbers, STUDENT will solve two digit addition problems without regrouping with 80% accuracy in 4/5 trials.
In this case, it would then appear to be the civil right of the child to receive endless worksheets in addition without regrouping to prepare them to master this goal. Then when they mastered that sub-skill, they could be taught addition with regrouping in a separate set of worksheets. This kind of instruction will create mathematical habits in children that we should not be encouraging: in this case, we are teaching the child that mathematics means applying memorized procedures when they are told to by the teacher, and does not include sense making or struggle. This creates children who, when you actually give them a meaty mathematical problem, ask you “but what is the operation?” We create that kind of learned helplessness in mathematics by oversimplifying and underchallenging children. So, in the endless cycle of educational unintended consequences, by following the child’s IEP, we provide instruction and assessment based towards a goal that will create a misunderstanding. Whew.
IEP goals need to be specific, measurable, achievable, relevant and time-bound, and that structure contributes to overly prescriptive mathematical goals. When I first began work as a special educator, I saw some very non-specific IEP goals such as
STUDENT will learn multiplication.
I am not kidding.
So this movement towards more relevant IEP goals, goals that actually can be assessed, IS a civil right for a child with a disability. IEP goals are tools to ensure that a child with a disability is being educated, rather than ignored. They should be taken seriously, and designed carefully for the good of that child.
But who will protect the children from overly-rote IEP math goals?
Here is a post called Developing Mathematics IEP Goals and Objectives that Work!, that documents the work of a group of educators in Maryland who collaboratively redesigned IEP math goals to better align with standards-based mathematics,
The result of the collaboration was a tool that guides special educators through the development of student goals and objective that focus on a student’s long-term mathematics learning. The focus on learning behaviors is shifting our special educator’s thoughts about supporting mathematics instruction. Instead of mathematics views as a disconnected set of skills to be memorized, our teachers are viewing problems as puzzles with multiple solution paths and high levels of critical thinking. Additionally, our teachers are reporting that the scaffolding of the behaviors helps determine exactly where student skill levels lie and how to adjust instruction to advance their mathematical abilities. So, for the first time, IEP goals and objectives are aligned to the everyday instruction meaning that our students are pulled out of first instruction far less frequently. (
Because the mathematics goals were better aligned to the standards-based mathematics in the general education classrooms, this shift in IEP goals allowed students with disabilities to be pulled out of math class “far less frequently.”
Clearly, for us to rethink mathematics IEP goals, we need to design collaborations between general and special educators. In the case of these educators from Maryland, a team approach mattered. What also mattered was shifting the focus of IEP goals from computation to the Standards for Mathematical Practice. I might suggest that a learner could benefit from two mathematics IEP goals: one SMP goal, and one content goal.
Let’s think through an IEP goal based on the first Standard for Mathematical Practice:
MP1. Make sense of problems and persevere in solving them.
The first SMP is a critical goal for all kids, and particularly for any kid who either doesn’t fully invest themselves in mathematical work, or who tends to apply procedures without thinking through the problem. So how can we make this goal specific, measurable, achievable, relevant and time-bound?
As I write this goal, I think of a student I once had, let’s call him Joe. Joe was in a special education classroom with traditional mathematics instruction until 3rd grade, when he was placed in a general education classroom. Joe was a quiet, thoughtful child who found mathematics difficult, and would often sit with a math problem for long periods of time without starting. Because Joe had lots of practice in math following teacher procedures, and very little practice solving independently, he needed additional support to be able to begin and solve those problems. What about this goal for his IEP, inspired by SMP1, but with different wording?
When given a CGI story problem, Joe will use strategies such as representing the problem with drawings or manipulatives, reaching a solution in 4 out of 5 classroom sessions, documented by teacher observation and/or student work.
To assess IEP goals, special educators make sure it is SMART (Specific, Measurable, Achievable, Relevant and Time-bound). Is this goal specific enough that we could assess it? It specifies the kind of problem that we will assess, not just any math work, but CGI story problems. We would be looking for BOTH Joe using strategies such as drawing, but also him reaching a solution (no mention of whether it was correct or not). We should be able to see him using these strategies, or direct-modeling the problem, as we observe him in class, and in his student work. It is only slightly time-bound, that he must reach a solution during a classroom session. Adding additional time pressure, I believe, would be highly counter-productive. Most importantly, it is relevant. If Joe was able to develop this new habit of making sense of mathematics, he would be able to tackle increasingly more challenging work.
The Standards for Mathematical Practices are made to be general, to cover many situations. Using them as IEP goals means that they need to be made specific to the curriculum of the child’s classroom and the child’s particular needs.
A good IEP goal is also tied to instructional strategies. In this goal, a teacher would need to conference with Joe, coaching him strategically. How can we begin to solve a problem? We can visualize the problem, we can represent it in a drawing, and we can represent the problem using manipulatives. The first objective might be:
When given a CGI story problem and a teacher prompt, Joe will use strategies such as representing the problem with drawings or manipulatives, reaching a solution 4 out of 5 classroom sessions, documented by teacher observation and/or student work.
Goals for other students using SMP 1 might look very different, depending on the child and the curriculum.
What can a group of educators work on to delve deeper into the mathematical IEP goals of their students? First, you could begin by picking focus students, writing MPS IEP goals for them, and then carefully assessing their progress. To get started, you could analyze the mathematical goals in a goal bank (here is one developed in Oregon and appears to be in use in NYC). What is the cognitive demand of these goals? Which are tied to the MPS? How will you assess the student’s developing of reasoning? Of mathematical critique? You could track their participation in small group and whole group discussion.