1. Perspectives or Theoretical Framework:

Improving student achievement in mathematics and science has been a concern in the United States of America since the early 80s when international tests began showing U.S. students falling behind most developed countries in mathematics and science skills. Educators and policymakers have not always agreed about the reasons for such a failure. For some, many mathematics teachers lack mathematical content knowledge themselves, and thus are unable to teach their students to the highest level (Ahuja, 2006; Ginsburg, Cooke, Leinwand, Noell & Pollock, 2005).  Others (Darling-Hammond, 2007; National Science Board, 2006) in part relate such an educational failure not only to the lack of qualified teachers with solid content knowledge in STEM, but also to a profound lack of understanding of teaching and learning in grades K-12. For Brown and Borko (1992), and Ball and Bass (2000), content knowledge and understanding of the methods of inquiry in mathematics are at the core of effective teaching and learning.  

The use of inquiry-based approaches to instruction, in which students have opportunities to construct their own understanding of basic concepts, has been found to be most appropriate in developing studentsÕ understanding of mathematics concepts. Such approaches call for teachers to be able to engage students in critical, in-depth, higher-order thinking using manipulatives, cooperative learning and other pedagogy that enable them to construct mathematics concepts on their own through reasoning, verifying, comparing, synthesizing, interpreting, solving problems, making connections, communicating ideas and constructing arguments (Grouws & Shultz, 1996).  This approach departs in significant ways from what occurs in ÒtraditionalÓ classrooms. Helping teachers make this fundamental shift in practice requires more powerful approaches to professional development (PD).

One such approach is the process of inquiry through the Action Research (AR) cycle. In this approach, teachers are engaged in a process that does not cease, in asking questions and understanding problems, continually revisiting critical issues relative to teaching and learning, designing plans to resolve the issues, implementing the plans, and collecting and analyzing data to assess the effectiveness of the designed plans. As teachers improve their pedagogical skills, they increase their ability to explain terms and concepts to students, interpret studentsÕ statements and solutions, engage students in critical, in-depth, higher order thinking, and consequently leading to increased student achievement (Grouws & Shultz, 1996; National Council of Teachers of Mathematics [NCTM], 2000).

2. Methods, Techniques, or Modes of Inquiry:

The process of inquiry through AR is at the center of our three-year multi-dimensional NSF-funded PD program that had 33 certified mathematics teachers with 4-10 years of experience enrolled at the time of this study. As part of the program, participants took a two-part course series that focused on AR strategies. During the second part of the course series, they used mixed methods to complete and report on at least one AR investigation.  

In studying the extent to which the practice of AR leads to teachersÕ growth and student learning, we sought answers to the following research questions:

1)    What is the impact of the practice of AR on teachersÕ growth in pedagogical knowledge?

2)    To what extent does the practice of AR leads to studentsÕ gains in performance and change in attitudes?

Answers to the research questions were based on teachersÕ reflections from their AR reports, AR course blogs, open-ended and quantitative self-ratings from course evaluations, and the 29 action research projects developed by 23 of these teachers that involved 1017 students (639 HS and 378 MS students). For student performance, teachers considered student success in terms of attitudinal changes and motivation—as opposed to test scores and grades—and relied heavily on qualitative methods of data collection such as open-ended questions, review of student work samples, and interviews with individual students.

3. Results and/or Conclusions:

Most teachers identified growth in the related areas of becoming a more reflective teacher, being able to conduct an AR inquiry, and learning to pay greater attention to studentsÕ needs, prior knowledge, and understanding. Most rated themselves highly in their ability to identify and describe errors and misconceptions (78%), design activities to address these misconceptions (74%), collect and analyze student data (70%), and reflect upon the results of their classroom research (70%).

Fifty-two percent of student demonstrated a significant change in performance; 24% a significant change in performance in some areas of mathematics; 55% a significant change in their attitudes toward and understanding of mathematics; finally, 38% some evidence of change in attitudes toward and understanding of mathematics. Students were more engaged, gained more self-confidence, expressed themselves better mathematically, were slightly more open to word problems, and took more responsibility for their own learning.

4. Educational/Scientific Importance:

Teachers identify lack of motivation as the main barrier to student learning, especially in urban areas where a lack of engagement has been especially pronounced for adolescent minority students. High engagement through effective participation and willingness to collaborate are indications of intrinsic motivation. As a model of student-centered approach, AR has therefore the potential of having the greatest impact on higher student engagement and studentsÕ learning. Student engagement plays an essential role in the learning process and is a strong predictor of student learning (Seashore et al., 2010). Indeed, research shows that engaged students experience greater satisfaction with school experiences, which may in turn lead to greater school completion and lower incidences of acting-out behaviors and the overarching goal of student success.

Selected References

Ahuja, O.P. (2006).  World-class high quality mathematics education for all K-12

American students. The Montana Mathematics Enthusiast, 3(2), 223-248.  

Brown, C. & Borko, H. (1992): Becoming a mathematics teacher. In: D. Grouws

(Handbook of Research on Mathematics Teaching and Learning (pp. 209–239). New York: Macmillan.

Grouws, D.A. & Schultz, K.A. (1996). In Sikula, J. (ed.), Handbook of Research on

Teacher Education, 2nd Ed. New York: Macmillan.

Seashore, K. L. et al. (2010). Learning from leadership: Investigating the links to

improved student learning. Final Report of Research to the Wallace Foundation. University of Minnesota and University of Toronto.