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Math Teacher Twitter is considered by some to provide an important example of contemporary professional development that can take place within a virtual participatory media platform. This study investigated the phenomenon of Math Teacher Twitter by analyzing a dataset of 9881 tweets associated with 3133 profiles obtained by querying the Twitter API using a set of four key Math Education Twitter Hashtags (METHs), #mtbos, #iteachmath, #mathchat, and #math. Investigating the discourse features hashtags used, tweet content, discursive style, values expressed, profile content, and engagement, allowed a description of the Twitter discourse associated with Math Teacher Twitter to be developed. Particular patterns of hashtag use, discursive style and value expression were associated with a difference in engagement, topical relevance, and profile descriptions. The elements of this Twitter discourse were further analyzed from the perspectives of two models of situated learning: the affinity spaces and communities of practice. This analysis suggested that while the affinity space model provides helpful descriptions of particular features of Math Teacher Twitter, the critical perspective provided by the communities of practice model remains helpful in understanding the underlying dynamics of this phenomenon. The methodological and theoretical implications of these findings for researchers who wish to observe and understand Math Teacher Twitter are discussed, along with some practical implications for its participants.

Master of Science / Department of Mathematics / Andrew G. Bennett / The purpose of my research is to identify what features of a graph are important for college teachers with the intention of eventually developing a system by which a machine can recognize those features. In particular, I identify the features that college algebra teachers look at when grading graphs of lines and how much disagreement there is in the relative importance graders assign to each feature. In the process, eleven students from college algebra classes were interviewed and asked to graph six linear functions of varying difficulty. Eleven experienced college algebra graders were asked to grade the selected graphs, and interviewed to clarify what features of the graphs were important to them in grading. Altogether, a general grading rule appears to be: slope is worth 4 points, y-intercept is worth 4 points, labeling of intercepts, points and graph is worth 1 point. After that, add 1 point if everything is correct. All graders considered slope and y-intercept to be very important. Only some of them considered labeling to be important. Anything else was a matter of a single point adjustment. Furthermore, the graders judged slope and intercept from two points(the y-intercept and the first point to the right). Returning to the students’ work, I saw that the students also placed extra importance on points to the right of the y-axis. I conclude that this grading style may have a role in students’ learning to think only about two points in a line (but nothing else), and that replicating human grading may not be the best use of machine grading.

<p> The purpose of this qualitative multiple case study was to explore how five sixth grade female students navigated the process of project-based learning as they designed and implemented their own project centered on mathematics while using a social justice lens. The theoretical frameworks of Authentic Intellectual Work and Social Justice Mathematics are blended to support a proposed new pedagogy of Project Based Social Justice Mathematics (PB-SJM). </p><p> Five female participants contributed to the findings of this study, all sixth grade students attending a project-based learning, charter middle school called The Academy of Innovation and Creativity. Data collection occurred throughout the entirety of a four-week project-process, including extensive field notes, two interviews per participant, multiple physical artifacts from each participant, and formal presentations by each participant.</p><p> Adapted from Gutstein's (2006) work with 3 C's (Classical, Community, and Critical), four propositions served as the basis for analysis, also known as the four knowledge bases or the Four C's&mdash;Content Knowledge, Community Connections, Critical Inequity, and Change Agency. The major findings of the study centered on the Four C's, specifically producing nine total themes. Within Content Knowledge, three themes emerged, that of a) Learning Targets&mdash;Understanding and Application, b) Complex, Non-Algorithmic Thinking, and c) Humanization of Mathematics. Two themes emerged in Community Connections, that of d) Personalizing Context and e) Experts as Sources. Likewise, two themes emerged within Critical Inequity, specifically f) Developmental Readiness and g) Growing Understanding of Critical. Lastly, Change Agency also produced two themes of h) Belief&mdash;Personal Agency and i) Action&mdash;Voice is Power. Collectively, the Four C's and the nine themes represent the findings of this research study.</p>

<p> Science, technology, engineering, and mathematics education, or STEM, is an area that is currently growing in popularity with educators (Becker &amp; Park, 2011). A qualitative study consisting of interviews was conducted and data were gathered from three leaders in professional STEM organizations, four principals from elementary STEM schools, and six teachers from elementary STEM schools to gain their perceptions of elementary STEM schools in Missouri. The perceptions of leaders in professional STEM organizations regarding STEM education were consistently all positive, and each leader was a proponent of STEM education at the elementary level. The perceptions of principals and teachers were also similar in response to interview questions. Both principals and teachers reported STEM education has the ability to increase student engagement and student achievement. The principals provided information that showed a shift in teacher attitude toward STEM from hesitant to giving full support. The teachers offered answers to the interview questions that showed favor and support for continuing professional development in regards to STEM education. Results and conclusions from this study may assist schools in deciding if STEM education should be integrated within their curriculum.</p>

<p>The under-preparation in math at the high school and college levels, as well as the low participation of ethnically and linguistically diverse individuals in STEM fields are concerning because their preparation for work in these areas is essential for the U.S. to remain competitive in the innovative knowledge economy. While there is now a substantial body of research on this group of students, there remain unresolved questions around the role of linguistic factors, affective variables, and prior achievement. In light of this concern, the purpose of the study was two-fold. One was to examine the moderating role of first language (L1) proficiency on the effects of language minority (LM) status in English reading. The second was to investigate the mediating roles of English reading and math achievement in the relationship between such interaction and math self-efficacy. The study was a secondary analysis of the Education Longitudinal Study (ELS 2002, n =16,110). Using a multilevel SEM analysis the study did not find support for the moderating role of L1 proficiency. However, English reading and math achievement mediated the relationship between LM status and math self-efficacy. These findings provide further knowledge for the development of targeted interventions that aim at increasing the preparation and participation of linguistically and ethnically diverse students in STEM fields. </p>

<p> This quasi-experimental quantitative research study examined factors affecting students' decisions to drop out from developmental mathematics courses at a community college in California. Three major variables were utilized in this study: the independent variables of academic challenge, degree of dissatisfaction, and personal reasons; the covariates of age, ethnicity, gender, GPA, and marital status; and a dependent variable in the form of the dropout decision. The study sought to determine if the independent variables, along with the covariates, had predictive significance on student decisions to drop out from developmental mathematics courses at a community college in California. Data for this research was obtained by using a specially designed questionnaire of the National Center for Higher Education Management Systems (NCHEMS) Questionnaire for Non-returning Students (Bower &amp; Meyers, 1979). The data was collected during the Fall 2013, Summer 2013, and Spring 2013. semesters. A total of 560 students were surveyed from both the Lancaster and Palmdale campuses of Antelope Valley College. Out of this number, 338 were female and 221 were male.</p><p> The PAWS Statistics 18.0 statistical package was used for this study. The chi-square test, and analysis of variance (ANOVA) test were also utilized for bivariate analysis of the data. The logistic regression analysis method was the major multivariate analysis method utilized for the study. Results from the logistic regression analysis indicated that there was a statistically significant relationship between students' academic challenge and dropout decision (<i>X</i>² ( 5, 560) = 26.824, p = .003). The variable in the equation indicated that <i>inadequate study time </i> had a significant overall effect (Wald = 6.101, df = 1, p = .014); and the Exp (B) column indicated that the less time a student used for study the greater the chance the student would drop out from developmental mathematics; <i> course not challenging</i> also had a significant overall effect (Wald = 9.046, df= 1, p = .0003).</p><p> The results of the Omnibus Tests (<i>X</i>² (13, 560) = 29.454, and p = .006) also revealed a statistically significant relationship between dropout decision and students' <i>personal reasons </i>. These results showed that <i>personal reasons</i> was a significant predictor of dropout decision. Furthermore, examination of the Homers and Lemeshow Test (p = .099) supported the finding that the full model with <i>personal reasons</i> was a good fit and that personal reasons was a significant predictor of dropout decision. From the variable in the equation in, <i>study too time consuming</i> had a significant overall effect (Wald = 4.408, df = 1, p = .036).</p><p> No statistical relationship was found between students' degree of dissatisfaction and students' dropout decision, or between student characteristics such as age, ethnicity, gender, GPA, and marital status, and students' dropout decision. </p><p> The analysis, interpretation, and discussion of these results contributed to existing literature on students' dropout decision. The results of this research study also suggest the need for more research to be conducted on the subject of dropout decision from mathematics courses in community colleges. The study also revealed specific categories within the <i>academic challenge and personal reasons</i> scales that contributed most to the dropout models.</p>

<p> This study investigated the relationship between attention to student thinking during lesson planning and the level of cognitive demand at which tasks are implemented for six pre-service teachers enrolled in a teacher education program that focuses on attention to student thinking during planning and instruction. Lesson plans were examined for attention to student thinking using two coding schemes, and samples of student work were examined to assess the level of cognitive demand at which tasks (associated with the enacted lesson plans) were implemented during instruction. Other planning related data sources were qualitatively drawn upon to support the extent to which pre-service teachers focused on student thinking with regard to planning. </p><p> One of the lesson planning coding schemes provides numerical scores indicating different degrees of attention to six elements of student thinking. The level of cognitive demand of task implementation for each lesson was able to be coded as high or low. In particular, the quantitative analysis suggested a trend that as overall attention to student thinking during lesson planning increases the odds of high level task implementation become greater compared to the odds of low level task implementation. Given a small sample size the quantitative results need to be considered within their limitations.</p><p> Qualitative analysis examining attention to student thinking during planning and task implementation supports the quantitative trend. In particular, the qualitative analysis suggests three findings. The first finding is that the two pre-service teachers who demonstrated the most attention to student thinking with regard to planning were the only pre-service teachers who implemented all of their tasks at a high level of cognitive demand. The second finding is that when receiving specific planning based support for a lesson as part of a university assignment, all the pre-service teachers were able to implement the task at high level of cognitive demand. The third finding is that a large majority of lessons using tasks accompanied by detailed planning support sources were implemented at high levels of cognitive demand.</p>

This action research project examines the role classroom culture and discourse can play on student learning, with a focus on female students. A sixth grade science classroom was evaluated through analysis of two videotaped astronomy lessons. The classroom environment utilized qualitative methods to examine teacher and student interactions, student and student interactions, and classroom environment. The research project began in response to a previous research project which found that after completing an astronomy unit male students not only out preformed female students, but female students lost gains in several area. Findings suggested that there may be a connection between the classroom discourse and microculture and the girls’ low performance.

<p> This qualitative multiple case study sought to discover third-grade teacher perspectives of the strategies used when effectively implementing Cognitively Guided Instruction (CGI). Five exemplar third-grade teachers were purposefully selected based on recommendations from their principal and instructional coach. The purpose of the study was to learn how the implementation of the essential elements of CGI affected planning of mathematics lessons and how those elements were implemented into mathematics instructional practices. </p><p> The study utilized triangulation of data sources, including semi-structured interviews, observations, and document analysis. Based on the results from the first research question, planning for CGI lessons was found to be more difficult compared to planning for traditional mathematics lessons. The teachers spent more time developing word problems due to the lack of resources, because CGI is to be customized to meet the needs of the students. For the second research question, five themes emerged as strategies the teacher used for implementing CGI during class: 1) conceptualizing, 2) articulating, 3) using multiple strategies, 4) questioning, and 5) scaffolding. These strategies were employed by all teachers, but were differentiated by each teacher to best meet the needs of the students.</p>