A couple of years ago, James Sheldon and Kai Rand started a Working Group at the Psychology of Mathematics Education North America conference. This group, now called Critical Perspectives on Disability and Mathematics, is made up of mathematics education scholars who work at the intersections of disability and equity. We seek to create new discussions about disability and mathematics, discussions that move beyond deficit discourses. One of our projects was a special issue, which was just published in Investigations in Mathematics Learning. This special issue brings together scholars from mathematics education and disability studies in education. We are so pleased with the range of scholarship in this special issue. Check out the editor’s introduction here for a introduction to all the articles in special issue: Lambert, Tan, Hunt & Candela 2018
For over two years, I have had a word document on my computer entitled, “Myths in Teaching Mathematics for SwD.” I kept adding bits of writing, particularly when I encountered another myth. Imagine my excitement when Jo Boaler sent out a call for a special issue of Education Sciences on Myths in Mathematics Education. I am so proud to have a paper in this issue, which is amazing and available for free online. (I particularly recommend this amazing piece on dyscalculia by my colleagues Katherine Lewis and Dylan Lane)
My paper: http://www.mdpi.com/2227-7102/8/2/72
I decided to focus the paper on students with Learning Disabilities (or specific learning disabilities in reading, writing or math, otherwise known as dyslexia, dysgraphia or dyscalculia). While I wanted to write about a wider range of disabilities, the best research evidence was on this group of learners. I also picked two myths to focus on:
- Students with LD ONLY benefit from explicit or direct instruction.
- Students with LD cannot create their own strategies in math, and cannot handle multiple strategies.
The first is a major myth that I hear all the time, and the second is a kind of a sub-myth. The assumption that students with LD cannot construct strategies is so pernicious that I decided to include it as a separate myth.
I structured the paper around two things: first a quote written about students with disabilities. This was published in a prominent special education journal in 1998:
“The premise that secondary students with LD will construct their own knowledge about important mathematical concepts, skills, and relationships, or that in the absence of specific instruction or prompting they will learn how or when to apply what they have learned, is indefensible, illogical, and unsupported by empirical investigations.”.(Jones, Wilson, & Bhojwani, 1998, p. 161)
This quote still shocks me. Having known, taught, been a friend to and a family member or so many people with various permutations of LD, the idea that such learners cannot “construct knowledge” is exceptionally bigoted and wrong. This particular article described constructivism as “ideology” rather than a valid approach to teaching math. In the paper, I try to describe why these myths are themselves “indefensible, illogical and unsupported.” I do not ignore the strong empirical evidence from special education mathematics that students with LD can benefit from explicit instruction, but I present evidence that suggests inquiry instruction as also effective. We also need to consider why we teach mathematics- it is not just to make students into effective computers, but to help them develop life-long identities as mathematical thinkers and explorers. The myth emerges from the assumption that there exists sufficient evidence that inquiry mathematics is NOT effective for students with LD, or that explicit instruction is the only method that is evidence-based. As the National Mathematics Advisory Panel states, “it is important to note that there is no evidence supporting explicit instruction as the only mode of instruction for students [with LD]” (2008, p. 1229).
As I was writing this piece, I checked Twitter and found this tweet:
Thank you Abby. This tweet inspired me to keep writing, and keep poring through research. If you are more interested in understanding the research divide between math ed and special ed, I would check out another article I wrote with Paulo Tan in Education Sciences (http://www.mdpi.com/2227-7102/7/2/51).
- What myths still need to be unpacked?
- What kind of research would you like to see around students with disabilities and mathematics? What specific questions have emerged from your work?
One of the most important agents of change in special education is paraprofessionals. These dedicated professionals are often the mediators between classroom teachers and our students with disabilities. They help create access for the child to the curriculum. Unfortunately, paraprofessionals are almost never given planning time with teachers, and are not usually allowed access to professional development. In mathematics, this can mean that the paraprofessional and the mathematics teacher have different ideas about what and how the student should be engaged in mathematics.
Judy Storeygard (author of several excellent texts on mathematics teaching for students with learning differences and/or special education services (Count Me In and My Kids Can) has been working with colleagues on addressing the issue of access for paraprofessionals. Funded by the National Science Foundation, they have provided a pilot program for paraprofessionals in the Boston Public Schools, designed to increase access for paraprofessionals to high-quality professional development in mathematics. I would love to see more projects like this!
Check out this video: http://stemforall2018.videohall.com/presentations/1095
1) Paras need opportunities, over time, to immerse themselves in mathematics activities that help them to develop their mathematical thinking. Often, they have not had positive experiences learning math themselves, and so as part of this process, they are developing their math confidence. Many have become quite excited about doing math!
2) Our paras (and other paras we have spoken with) can identify the ways in which math instruction is quite different than what they experienced as students–but since many haven’t been involved in a teacher education program, they aren’t always sure about what it means to instruct with an inquiry-oriented curricula or resources. Understanding the goals of such curricula and experiencing inquiry approaches within their PD have been important to them. Also, they have been eager to learn and try out instructional strategies in their classrooms (e.g., how to listen for student thinking, asking questions that provide students with new challenges within an activity, asking students to re-tell the story problem), and then return to PD to debrief with each other and us.
3) Follow-up activities have also been helpful. Through our project, the paras have had opportunities to plan with their teachers and reflect on their students’ math learning and struggles.
4) And last, but not least, the paraeducators have created a math learning community where they provide each other with support, encouragement, and new ideas. They are incredible resources for each other!
Over one million para educators currently assist in classrooms, and another 100,000 are likely to be added in the next ten years. Para educators are often required to teach content, such as mathematics, but there are few efforts to provide them with the knowledge or supervision they need to be effective when working with a range of students, including those with disabilities and for whom English is a second language. While professional development will enable paras to make a greater difference in the classroom it may also increase their access to continuing education and workplace opportunities. Our project is designed to develop, pilot, study, and refine PD, that focuses on developing the confidence, mathematics knowledge, and teaching strategies of para educators, grades K-3 in the Boston Public Schools, as well as providing support for their collaborating teachers.
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”
As I read the conference program for the CGI (Cognitively Guided Instruction) Conference
#cgi2015la 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”
Zhang, D., Xin, Y. P., & Si, L. (2013). Transition from Intuitive to Advanced Strategies in Multiplicative Reasoning for Students with Math Difficulties. Journal of Special Education, 47(1), 50–64. I love this article because it uses constructivism to understand the development of three kids with disabilities in learning multiplication, particularly drawing from the work of Siegler on how kids use multiple strategies over their course of their development with a new mathematical operation. Take-away- kids only switched strategies from counting when the numbers got big enough. Lesson to be learned is to stop giving kids only easy problems, because such problems actually encourage them to continue using less sophisticated strategies. Continue reading “How to help kids use more complex strategies in multiplication? Give them harder problems.”
A recent post by my friend and colleague Andrew Benjamin Gael rightly critiqued the recent NCTM conference for omitting disability in current calls for equity. The recent Executive Summary of the Principles to Actions doesn’t mention disability or special education at all. Andrew asked why, and then went on to describe some recent, powerful work on meeting the needs of students with disabilities using the Mathematical Practices.
As a researcher and teacher educator in both special education and mathematics education, I am constantly confronted with the invisibility of kids with disabilities in mathematics education. Continue reading “Disability, invisibility, and equity in mathematics (part one)”