I started teaching special education in 1970, prior to the Education for All Handicapped Children Act of 1975, or PL 94-142. I welcomed the enactment of that legislation, because it forced school districts and state education departments to provide a free and appropriate education for students with disabilities. Before its passage, children could be excluded from public school. PL 94-142 emphasized providing an education based on the individual child鈥檚 needs.
Then, in 2002, President George W. Bush signed the No Child Left Behind Act, a law reauthorizing the Elementary and Secondary Education Act of 1965. Before its implementation, administrators鈥� efforts in educating students with disabilities were focused on following the existing law and procedural safeguards in this field. Unlike many educators, I welcomed this new law, NCLB, because it forced educators to focus on student achievement, including that of students with disabilities. The impact of NCLB, I thought, would be that districts now would have a stake in how this group of students achieved, because their scores would be part of school accountability.
In , the current version of PL 94-142, and in the law鈥檚 subsequent regulations, an attempt was made to deal with some of the academic-achievement issues of special-needs students by requiring that learning goals be included in the individualized education program, or IEP; that they be connected to state standards; and that they be based on research as much as possible. The goals would have to be measurable, and progress monitored. They were still to be based on 鈥渋ndividual needs,鈥� but the legislation did not address how to determine what those needs are.
Despite all our efforts at legislating solutions to the achievement gap between students with disabilities and the general population, significant progress is not being made."
Several implementation issues specific to mathematics have proved to be problematic. Since math builds on previous knowledge, if there is too big a gap between a child鈥檚 current level of performance and the standards for his or her grade, it is a challenge to write learning goals that bridge that gap, that are useful for guiding instruction, that accelerate learning, and that meet federal requirements.
Because they are easier to assess, identify, and quantify, mathematics learning goals that are procedural, such as computation, or that address functional skills, such as counting change or telling time, are the norm in IEPs, rather than goals dealing with conceptual understanding. A random Web search for mathematics learning goals in IEPs will most often yield goals that emphasize computation, procedural skills, or functional skills. Typically, the goals comprise something similar to this: 鈥淕iven 10 problems involving some type of computation, the student will solve eight out of 10 accurately by such-and-such date.鈥�
So even though the intent of IDEA 2004 was to ensure that academic goals were included and student achievement was monitored, it has had mixed results, in that the path of least resistance in writing mathematics learning goals is to emphasize procedural knowledge and avoid goals for conceptual understanding. This is not surprising, because goals for conceptual understanding are difficult to write and to assess. When conceptual knowledge is not developed, however, the student will, at some point, find that math does not make sense, and his or her progress in achieving in higher mathematics courses such as algebra will be impaired.
Despite all our efforts at legislating solutions to the achievement gap between students with disabilities and the general population, significant progress is not being made. The proverbial elephant in the room is this: We say that the IEP鈥檚 learning goals are based on individual needs, but in math we still don鈥檛 have an adequate way to determine those needs.
In my view, we can accelerate achievement if we improve the process of writing learning goals in mathematics and provide targeted instruction based on those goals. In this way, we can fast-track student learning and narrow the achievement gap.
[T]he path of least resistance in writing mathematics learning goals is to emphasize procedural knowledge and avoid goals for conceptual understanding.鈥�
How should we approach that task? When looking at math learning goals, a few key questions need to be answered. First, who writes the goals and what is their expertise in deciding that these are appropriate goals for the individual student? Even experts need tools and resources to write good learning goals. We would not expect a doctor to make a diagnosis of a complicated case without access to diagnostic tools, such as blood-work results, diagnostic imaging, and so forth. Yet a beginning teacher is often asked to write learning goals without comparable resources. Even experienced teachers can have difficulty with this task. Certainly, the time they have to do research and to think about the problem in depth is nonexistent in a normal teacher鈥檚 day.
Second, what resources are available to determine the learning goals? Our educators are asked to write IEP math learning goals with very few, or no, resources. I believe the reason this happens is that we have the mistaken idea that the 鈥渋ndividual needs鈥� of a student cannot be preplanned. That underlying assumption keeps us from questioning our practice, and from asking whether we could individualize more if we had better diagnostic resources. In current practice, developing IEP mathematics learning goals seems to be a hit-or-miss activity without a strategic plan for improvement.
Quality learning goals would have several key elements:
鈥� They would be very specific and identify in detail the concepts and skills the students are missing, as well as take into consideration students鈥� strengths.
鈥� They would be based on research as much as possible, as well as exemplary practice, since the mathematics research we have available is sparse.
鈥� They would outline a learning trajectory for the student connected to grade-level standards that would help guide acceleration of student learning toward grade-level achievement.
鈥� They would include a strong emphasis on developing conceptual understanding as well as procedural fluency and functional skills.
鈥� They would take into consideration the student鈥檚 age or developmental level.
We also need to develop assessments correlated to the learning goals, so that we can objectively determine what the students need, rather than subjectively guess what they need. These assessments would not be the standardized tests states give for accountability. They should provide the detailed information regarding what the student knows, as well as what he or she doesn鈥檛 know that is holding him or her back from achieving.
Development of these resources for identifying appropriate learning goals is not a trivial job that one individual can do alone. I suggest a national initiative to develop the detailed mathematics learning goals and assessments we need鈥攇oals and assessments that follow a learning sequence that makes sense developmentally and mathematically, are based on research and exemplary practice, and are detailed and fine-tuned so that important landmarks in developing student understanding are not neglected.
Under a well-reasoned program to do this, all teachers, whether novices or experts, would have functional resources to help them identify what type of instruction the student needs to make progress. Then we could really have mathematics learning goals for students with disabilities based on individual needs.
Investment in such an effort would have benefits beyond the special-needs population. The resources developed and the research conducted could assist 鈥渞esponse to intervention,鈥� or RTI, efforts, and might even have applications in gifted education. Curriculum writers of regular education materials could ensure that important concepts are included at key points in their curricula, with explicit instructions for teachers for formative assessment in order to prevent gaps in student knowledge from developing. Finally, use of the resources by teachers would be a form of professional development, because it would improve their knowledge of the math all of their students need to learn.
