This session addresses the priority area of professional learning. It describes the movement of four special educators toward reform-based mathematics teaching and learning and identifies components within a professional development project affecting that movement.

Conceptual/Theoretical Perspective

Because of the widely held view that low achievers and students with learning disabilities cannot learn mathematics in a reform-based environment (e.g., Carnine, Dixon, & Silbert, 1998), programs that serve special-needs students typically focus on direct instruction rather than on using “inductive techniques that emphasize a reasoning and problem-solving approach” (Mastropieri & Scruggs, 2002, p. 162). As is common with general education teachers, the latter approach may not only challenge beliefs of special educators regarding mathematics teaching and learning but also may require deeper and more connected knowledge of mathematics content (Ma, 1999), pedagogy, and student development than they possess. Thus, in addition to facing the challenges related to acquiring the beliefs, knowledge, and practices associated with a reform-based perspective (Wood, Nelson, & Warfield, 2001) characterizing general education change, special educators may face other challenges embedded within a context that mitigates against reform.

The National Council of Teachers of Mathematics (NCTM) recommends that special educators participate in professional development in mathematics education:

Students with special learning needs in mathematics must be supported both by their classroom teachers and by special education staff. Special-needs educators responsible for mathematics instruction should participate in mathematics professional development, which will allow them to collaborate with classroom teachers in assessing and analyzing students’ work in order to plan instruction. (NCTM, 2000, p. 369)

This study seeks to describe special educators’ movement toward reform-based mathematics education and to identify factors within professional development impacting that movement. It is situated within a program that involved both special educators and general classroom teachers of grades 3-6 in a 2-year (18-credit-hour) sequence of coursework leading to a state elementary mathematics endorsement. The theoretical model—an Integrated Model of Teacher Change (IMTC) (_______, _______, & Wentworth, 2011)—guiding the program utilizes an integrated view of teaching and learning based upon four positions from which mathematics educators study that learning—content, pedagogy, student thinking, and student development (Wood, Nelson, and Warfield, 2001). The IMTC allows researchers to examine changes in teachers’ beliefs, knowledge, and practice from each of the four positions as well as from three additional positions representing the overlaps of the original four positions.     

Some experts in special education have provided specific strategies for teachers to use in inclusive classrooms (e.g., Mastropieri & Scruggs, 2007). However, little research is available to help teachers support special-needs learners in a reform-based mathematics environment (e.g., Baxter, Woodward, & Olson, 2001). Additionally, little is known about the nature of special educator change in the context of reform-based professional development. Our intent was to learn from the experience of four special educators involved alongside general educators in a professional development project.  

Research Questions and Design

The current study addresses two major research questions, with subquestions, as follows:

1.  What was the nature of the movement of four special educators toward reform-based mathematics education?

     In order to investigate this question, we asked the following subquestions.

a.  How did the richness of artifacts (including reflections) produced by these special educators change over the duration of the 2-year program?

b.  To what extent did the content of these artifacts indicate a general change toward a reform perspective?

c.  To what extent did the content of these artifacts reveal specific changes in the special educators’ beliefs, knowledge, and practices?

2.    What components of the professional development program appeared most salient in impacting movement toward reform-based mathematics education?

Four of the six special educators involved in the professional development program were purposefully selected (Patton, 2001) as study participants. They represented a range of school contexts regarding reform-based mathematics education, from reticence to consider reform to willingness to implement reform.

In this case study, which is primarily descriptive, multiple in-depth cases provided the data for pattern-matching both within and across cases, thus increasing the potential for robustness of findings (e.g., Yin, 1994).

Data Collection Techniques and Analyses

Reflective assignments and projects completed by the study participants over the 2-year program—general reflections, collaborative lesson studies, an action research project, a series of three student performance assessments, and numerous content assignments—served as the major artifacts for this study. These assignments were regularly contextualized within the day-to-day classroom responsibilities of the participants, and many included student work or reports of student work.

Data analysis is currently under way, with analysis of data for six major artifacts completed for each of the four participants. The co-researcher and research assistant, both well-versed in mathematics reform, worked together to analyze artifacts until consistency was established. They each analyzed the remaining data separately, then met together to reach consensual analysis.

Analyses associated with the first research question were conducted as shown below.

a.  Artifact richness was operationally defined as the number of distinct ideas within an artifact divided by number of pages (size) of that artifact. This definition of richness enabled comparisons across artifacts to show trends.

b.  The extent to which the artifacts evidenced a reform-based perspective was assessed holistically using a 4-point rubric, with predetermined indicators:

1- No evidence of a reform perspective

2- Slight evidence of a reform perspective

3- Some evidence of a reform perspective

4- Substantial evidence of a reform perspective

c.  A priori codes derived from the IMTC were used to code and categorize ideas within artifacts as being indicative of participants’ beliefs, knowledge, or practice.

Credibility was addressed through triangulation of data sources, analysis of data by researchers who were not involved as professional developers in the program, and referential adequacy (Lincoln & Guba, 1985).

Summary of Preliminary Findings

A prominent trend toward increased richness in artifacts over time was evidenced for each of the four participants.

The changes in the nature and content of artifacts examined indicate substantive changes in overall perspective toward reform-based mathematics as well as in specific beliefs, knowledge, and practices characterizing that perspective. Trend analyses enabled the creation of a unique learning trajectory for each participant; these analyses suggest that growth occurred in a broad, balanced manner across participants.

Timeline for Session

The lead speaker will provide a 10-minute overview presentation of the study. Then the speakers will participate in roundtable discussions with participants as described in the guidelines for Interactive Paper Sessions.

References

_______,_______, & Wentworth, N. M. (2011). An integrated model of teacher change: A theoretical framework for conceptualizing teacher learning in an era of mathematics reform.  Manuscript in preparation.

Baxter, J. A., Woodward, J., & Olson, D. (2001). Effects of reform-based mathematics instruction on low achievers in five third-grade classrooms. The Elementary School Journal, 101, 529-547.

Carnine, D., Dixon, R., & Silbert, J. (1998). Effective strategies for teaching mathematics. In E. Kameenui & D. Carnine (Eds.), Effective teaching strategies that accommodate diverse learners (pp. 93-112). Columbus, OH: Merrill.

Lincoln, Y., & Guba, E. (1985). Naturalistic inquiry. Beverly Hills, CA: Sage.

Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah, NJ: Erlbaum.

Mastropieri, M. A., & Scruggs, T. E. (2002). Effective instruction in special education (3rd ed.). Austin, TX: Pro-Ed.

Mastropieri, M. A., & Scruggs, T. E. (2007). The inclusive classroom: Strategies for effective instruction. Upper Saddle River, NJ: Pearson.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

Patton, M. Q. (2001). Qualitative research and evaluation methods (3rd ed.). Thousand Oaks, CA: Sage.

Wood, T., Nelson, B. S., & Warfield, J. (Eds.). (2001). Beyond classical pedagogy: Teaching elementary school mathematics. Mahwah, NJ: Lawrence Erlbaum.

Yin, R. (1994). Case study research: Design and methods (2nd ed.). Beverly Hills, CA: Sage Publishing.