Manuscripts submitted for publication

1. Diary of a graduate teaching assistant

   Authors: S. Hauk, M. Chamberlin, R. Cribari, A. B. Judd, R. Deon, A. Tisi, and H. Kakakhail.
   Current State: Synthesis of practice submitted for publication in a double-blind peer-reviewed journal.
   Abstract. Selected entries are presented from a mathematics graduate teaching assistant (GTA)'s journal across three years. The excerpts are followed by an explanation of both their source and purpose along with a discussion of current recommendations and resources for GTA development.

2. No Teacher Left Behind: Pedagogical content knowledge for in-service teacher professional development

   Authors: S. Hauk, R. Deon, A. B. Judd, J. Kreps, & J. Novak
   Current state: Research report submitted for publication in double-blind peer-reviewed journal.
   Abstract. The article provides results of a study of the pedagogical content knowledge (PCK) of middle school mathematics teachers enrolled in a professional development program. About one-third were already ``Highly Qualified'' according to No Child Left Behind (NCLB, 2000) criteria and two-thirds were not. Measures of PCK included sub-scores on content, syntactic, anticipatory, and classroom action knowledge from a task-based interview and on a written test based on national standardized tests for teachers. Results indicate that a truly ``Highly Qualified'' teacher, one with robust PCK, may need professional development aimed specifically at building and developing self-awareness of mathematically rich anticipatory and classroom action knowledge structures in addition to opportunities to enrich mathematical understandings.

3. Fostering college students' autonomy in written mathematical justification

   Authors: S. Hauk and M. Isom.
   Current State: Research report submitted for publication in a double-blind peer-reviewed journal.
   Abstract. The focus of this study is the influence of regular structured writing about college algebra topics (acronym PSOLVE) on locus of control, flexibility of articulation, and accuracy of student work on mildly non-routine problems. We analyze and compare the problem solutions offered by college algebra students who had written about mathematical content using PSOLVE with the work of those who had not. The writing assignments provided students a framework for expressing their thoughts about mathematical actions, processes, structures, and language. Augmenting traditional college algebra curriculum with the PSOLVE writing assignments produced a noticeable increase in students' ability to communicate their ideas. Because the students can clearly discuss what they think they know, PSOLVE assignments may help an instructor gain insight into students' primitive knowledge of mathematical concepts. We also discuss potential benefits of the PSOLVE augmentation for the development of college mathematics teaching research and practice.

4. Case study of an African American Ph.D. mathematician teaching college algebra

   Authors: S. Hauk, A. B. Judd, J.-J. Tsay, & M. K. Davis.
   Current State: Research report submitted for publication in double-blind peer-reviewed book series.
   Abstract. The case study is part of a larger research program. The primary participant in the study is a Ph.D. mathematician with twelve years college teaching experience (six years part-time while a graduate student, six years full-time after the Ph.D.). Every class meeting of each of his two college algebra courses for one semester were videotaped. These classes were two among 54 sections taught that semester at a large, western, Research I university. The data for this case study are the videotapes, the transcriptions of some of them, student written work, and interviews with the instructor. Interview data from students were not included in this study but will be considered in future work. The research is qualitative and grounded theoretical. The research questions are:

   1. What are the significant social cognitive factors for this instructor in the given environment (i.e., primary personal, behavioral, and environmental influences) as evidenced by interview and classroom videotape data?
   2. What are the significant educational factors for this instructor in the given environment? We investigate the intended, implemented, expected, and achieved curriculum, as evidenced by interview and classroom videotape data and student written work.
   3. How do these factors interact to support and/or undermine instructional self-efficacy for this mathematician in the given environment?
   Our primary interests in this study were describing the evolution of the discourse between students and teacher over the course of the semester and the relationships among curriculm intended, implemented, expected, and achieved. We identify several conflicts between intended curriculum and implemented curriculum at two levels: between the department and instructor and within the instructor himself. For example, the data indicate that confounding the issue of establishing and maintaining an efficacious classroom environment, was the department's mandate that all first year mathematics examinations, except for the final exam, take place outside of the classroom in a departmental testing center. Conflicts also arose between the instructor's implementation and the students' expectations. These were evidenced in the classroom through student and instructor behaviors and the evolution of the contract for behavior in the classroom. The social cognitive aspects of the conflicts between educational factors fell into the three categories proposed by Bandura's [Bandura, 1997] social cognitive theory: personal, behavioral, and environmental. For example, the larger environment established by the departmental course coordinators for college algebra was fraught with sudden changes in policy. Emergent from the data were a collection of strategy changes (by the instructor and by the students) in negotiation of social norms for self-regulation within the classroom milieu. Also clear from the semesters' videotapes were the evolution of what Yackel and Cobb [Cobb & Yackel, 1996] described (in a school setting) as socio-mathematical norms; we look at these through the lens of social cognitive theory, in particular, the sub-area of self-efficacy theory [Bandura, 1997]. This case study is aimed at providing a research foundation for practical efforts - such as might build on the work of Friedberg [Friedberg, et al., 2001]. Among the implications for teaching to be discussed are: possible foci for training of graduate students before they enter full-time college teaching; suggestions for structuring of course coordination efforts to minimize curricular values conflicts; potential action-research paradigms for instructors in similar circumstance to the case-study within their respective departments.

5. Impact of the web-based homework program WeBWorK on student performance in moderate enrollment college algebra courses.

   Authors: S. Hauk, R. A. Powers, A. Safer, A. Segalla.
   Current State: Research report submitted for publication in a double-blind peer-reviewed journal.
   Abstract. The study investigated differences in mathematics achievement between college students using web-based homework (WBH) and those doing traditional homework. Twelve of 19 college algebra classes used the WBH software WeBWorK and 7 used traditional paper and pencil homework (PPH). A test of algebra skills was administered pre- and post-course. Quantitative analyses revealed no significant differences in performance by ethnicity or instructor between the two homework treatments even when analysis controlled for previous mathematics achievement. However, women in WeBWorK classes had statistically significantly higher score gains than women in PPH sections. Results support the conjecture that WeBWorK is at least as effective as traditionally graded paper and pencil homework for students learning college algebra.