Since the mid-20th century in the United States, there have been several reform movements within mathematics education; each movement has been subject to its own unique socio-cultural and -political forces. The National Council of Teachers of Mathematics’ (NCTM) Standards documents—Curriculum and Evaluation Standards for School Mathematics (1989), Professional Standards for Teaching Mathematics (1991), Assessment Standards for School Mathematics (1995), and Principles and Standards for School Mathematics (2000)—not only represent the most recent of these reform movements but also the most enduring. Collectively, these documents have formed a discourse (cf. Foucault, 1969/1972)—Standards-based mathematics education—that has guided mathematics education through the 1990s and beyond. This study uses Foucaultian archaeological and genealogical methods (cf. Foucault, 1969/1972, 1975/1995) to explore Standards-based mathematics education as a “discursive formation” (Foucault, 1969/1972) and the complex power relations (cf. Foucault, 1976/1990) that made it possible for the formation to become The discourse of school mathematics, making others impossible. Data for the exploration includes the Standards documents, earlier histories of the NCTM Standards moment, scholarly and policy literature surrounding the NCTM documents, and oral history interviews with several of the writers of the NCTM documents. The study presents a historical narrative of mathematics education in the 20th century that both contextualizes Standards-based mathematics education and problematizes NCTM’s efforts; a key focus is the strategy that NCTM deployed to maintain the viability of Standards-based mathematics education as a discourse. Foucault’s (1984) “author function” is used to address the ways that the writers, externalities, and NCTM as an organization “authored” the Standards documents. The study concludes arguing that perpetuating the discursive formation of Standards-based mathematics education is neither good nor bad but only dangerous; therefore, it requires mathematics educators to maintain a sense of pessimistic activism related to present and future reform efforts (cf. Foucault, 1983/1997).

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Doctor of Philosophy / Department of Secondary Education / Jacqueline D. Spears / Moses & Cobb (2001) argue that algebra is a “civil right” and assert that limited algebraic understanding has an unfavorable impact on African American students’ entry into post-secondary education. Gay (2000) outlines six pedagogical methods, known as culturally responsive teaching (CRT), which emphasize the importance of teachers creating learning environments that relate to the personal experiences and cultural perspectives of minority students. The National Council of Teachers of Mathematics (NCTM) prescribes five process standards (communication, problem solving, connections, representation, and reasoning and proof) and the Equity Principle (includes setting high expectations, responding to the needs of culturally and linguistically diverse students, and providing support) for effective mathematics instruction. CRT, the NCTM Process Standards, and the NCTM Equity Principle served as the conceptual framework for this mixed-method study. Thirty-four teachers from two elementary and two middle schools in one school district in the Midwest responded to The Powell Teaching Mathematics Index (PTMI), a five-option Likert survey that explored teachers’ current “use” and “desire” to use CRT methods, NCTM process standards, NCTM Equity Principle, and teachers’ personal efficacy in learning and teaching mathematics in general and in algebra. Results from the PTMI revealed that teachers had a “desire” to use CRT in mathematics with AA students (M=4.41, SD=0.70); and although there was more variance among respondents, teachers also reported a “desire” to use process standards in algebra with AA students (M=3.94, SD=1.03). One bivariate correlation revealed a relationship between “use” of process standards in general and “efficacy” (r =0.681, p[less than or equal to]0.01). Eight volunteer teachers participated in a professional development workshop on CRT and integrated one of the six pedagogical methods into their classrooms for one month. Teachers reported “strengths” from the implementation phase as: increased student engagement, transition from teacher-directed to student-directed learning and an increase in student confidence in mathematics. Implementation “strains” were reported as: a time consuming process, difficulty in providing individual attention and an increase in classroom noise level. Findings have implications for teacher education programs, local school district and teacher networks.

Syftet med denna studie var att undersöka i vilken utsträckning de tre kursplanerna för matematik 1 (1a, 1b och 1c) samt den tillhörande ämnesplanen gick att tolka i form av kompetenser. Vidare jämfördes även kompetensfördelningen mellan matematik 1 och matematik A. Studien grundade sig främst i ramverket MCRF (Mathematical Competency Research Framework) som presenterar sex matematiska kompetenser, men vi tog även hänsyn till ytterligare sex kompetenser som återfinns i NCTM (The National Council of Teachers of Mathematics), KOM-projektet (Competencies and the Learning of Mathematics project) samt Adding It Up. Kursplanerna och ämnesplanen har granskats med hjälp av en kvantitativ textanalys där innehållet delats upp och kategoriserats till de olika kompetenserna enligt kompetensernas definitioner. Utifrån resultaten kan man säga att förekomsten av de totalt tolv kompetenserna är relativt jämnt fördelade inom matematik 1a, 1b och 1c. Bland de sex kompetenserna i MCRF förekom kompetensen procedurhantering i högst utsträckning medan begreppsförståelse var vanligast bland de sex övriga kompetenserna. Vidare kunde man, bland de sex kompetenserna inom MCRF, se att matematik 1a innehöll betydligt mindre sambandskompetens än 1b och 1c. Matematik 1a innehöll dessutom en större del procedurhanteringskompeten medan matematik 1b innehöll en större andel representationskompetens. Vid jämförelse mellan matematik 1 och matematik A är det inte lika vanligt förekommande att innehållet i matematik 1 går att tolka till någon kompetens inom MCRF, detta gäller både ämnesplanen och kursplanerna. En likhet är dock att kompetenserna förekom i högre grad i kursplansavsnitten betygskriterier/kunskapskrav än i mål att uppnå/centralt innehåll i både matematik A och matematik 1.

Doctor of Philosophy / Curriculum and Instruction Programs / Margaret G. Shroyer / This study was designed to investigate teaching practices of mathematics teachers in rural high schools in Kansas in the context of the NCTM Principles and Standards. National reports advocate for change in the mathematics classroom while state assessments force teachers to focus on test scores. This study investigated the extent to which teachers whose students experienced repeated success on state assessments integrated the NCTM Process and Content Standards into the mathematics classroom. Those data were then compared with the teaching practices in schools whose students repeatedly did poorly on state assessments. This two-phase study used both quantitative and qualitative data from four main sources: survey, interview, observation, and collection of artifacts. Phase I surveyed all mathematics teachers in high performing and low performing rural high schools throughout the state of Kansas. Data collected in Phase I were used to examine differences and similarities in teaching practices of teachers from high and low performing schools. During Phase II qualitative data were collected and analyzed to further explore any existing patterns among high performing and low performing schools. Results from teachers in high and low performing schools were compared and contrasted to determine if there were differences between the teaching practices that were demonstrated by each group of teachers. Results of surveys, interviews, observations, and artifacts revealed teachers in high performing schools used a variety of different representations to teach and assess a topic while those teachers from low performing schools used one or two representations. Students from high performing schools had more frequent opportunities to communicate with the teacher to gain additional assistance in learning the mathematics content. Teachers in high performing schools also used formal assessment strategies as part of the learning process more consistently than their counterparts from low performing schools. Results from interviews, observations, and artifacts reveal that teachers in high and low performing schools implement teaching practices aligned with the algebra content standards in a very similar manner.

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Title from second page of PDF document. Includes bibliographical references (p. 91-98).

The purpose of this study was to determine the extent to which a preschool program followed the recommendations outlined by the National Association for the Education of Young Children (NAEYC) and the National Council of Teachers of Mathematics (NCTM) in their joint position statement "Early Childhood Mathematics: Promoting Good Beginnings." Six teachers were randomly selected from three of the preschool program's six locations that are situated in an urban city in North Texas. Two parts of this program's approach to mathematics were investigated: the teachers' instructional practices and the program's curricular materials. Data came from observations using the Classroom Observation of Early Mathematics-Environment and Teaching (COEMET) protocol and field notes. Each teacher participated in three interviews over the course of this research. Analyses of these sources provided insights into teachers' instructional practices for mathematics. Reviews of curricular documents and lesson plans for mathematics instruction provided information pertaining to the math curriculum used at this preschool program. All of these data sources were analyzed using the framework presented in NAEYC and NCTM's position statement. Analysis of the data indicated that, although teachers did not have any knowledge of these guidelines, teachers followed some of these recommendations; such as presenting children with daily developmentally appropriate mathematics activities and connecting mathematics to classroom routines. Other practices did not align with NAEYC and NCTM's suggestions, such as offering children few opportunities to engage in problem-solving situations and providing an inconsistent integration of mathematics into meaningful activities related to other content areas. Several possible factors may have influenced teachers' use of these recommendations. Teachers' prior educational opportunities, the program's curriculum materials, and the teachers' prior experiences with mathematics all may have contributed to the teachers' understandings of high quality mathematics instructional practices. Results from this research help to provide the foundation for future investigations of how teachers of young children follow NAEYC and NCTM's recommendations.

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