Mathematics Curriculum Coaching and Elementary School Students’ Mathematics Achievement in a Northeast Tennessee School System

Educators and policymakers have demonstrated interest in finding ways to better equip mathematics teachers so they can help students achieve at a higher level. Academic coaching has been identified as an effective professional development activity for teachers. The purpose of this study was to investigate the difference between students’ achievement levels before and after a mathematics initiative in a Northeast Tennessee school district. In this study I analyzed grades 3 – 6 students’ Tennessee Comprehensive Assessment Program or TCAP scores in the year prior to the hiring of a mathematics coach and their respective scores 2 years after the placement of the mathematics coach. All statistical analyses were analyzed at a .05 level of significance. All null hypotheses under both research questions were analyzed with a pairsampled t-test using repeated-measures design. The results indicate significant difference in students’ TCAP scores prior to and after specialist. Scores after specialist were significantly higher than scores before specialists. The difference was present for students who attended Title I schools as well as for students who attended non-Title I schools. School administrators and school district leaders can benefit from such a study because it presents academic coaching as a viable means to equip teachers so they can help students increase their achievement in mathematics

Mapping the Road to Instructional Coach Effectiveness: Exploring the Relationship Between Instructional Coaching Efficacy, Practices, and Outcomes

Despite the presence and potential impact of instructional coaches, many schools are not experiencing significant improvements in teachers’ practices or student achievement. In gaining more insight into forces that impact instructional coach effectiveness, this study (a) explored the relationship between sources of instructional coaching efficacy and dimensions of instructional coaching efficacy [Mathematics Content & Mathematics-Specific Pedagogy (ME), Student Centered & General Pedagogy (SE), Interpersonal & Communication Coaching (IE), and Personal Coach Characteristics]; and (b) explored the relationship between dimensions of instructional coaching efficacy and instructional coach outcomes. Participants included teachers (n=144) and their instructional coaches (n=19), from elementary schools located within a large urban school district in the southeastern U.S. Teachers completed an adapted Coach Effectiveness Questionnaire (Yopp, Burroughs, & Sutton, 2010), which assessed their perceptions of coach outcomes. Coaches completed an adapted Coach Efficacy Questionnaire (Yopp, Burroughs, & Sutton, 2010), which assessed their perceptions of source information and dimensions of instructional coaching efficacy. Significant correlations were found between the source Degree Major (Math) and ME (r =.534). Moreover, canonical correlation analysis showed that dimensions of instructional coaching efficacy were significantly associated with instructional coach outcomes, F(45, 363.21) = 2.326, p \u3c .001. Particularly, regression analyses found IE to be predictive of instructional coach behavior (β =.395, t = 3.534, p \u3c .01); instructional coach impact (β =.343, t = 2.982, p \u3c .01); and teacher satisfaction (β =.264, t = 2.272, p = .025) with their instructional coach. Mathematics content & mathematics-specific coaching efficacy (ME) was also predictive of teacher satisfaction with their instructional coach (β =.181, t = 2.012, p = .046). These results were generally supportive of the theoretically expected relationships between instructional coaching efficacy and instructional coach outcomes. Lastly, context and individual instructional coach qualities accounted for a substantial amount of variance in instructional coach outcomes. These findings are consistent with previous research that link situational factors and individual differences to coach effectiveness (Horn, 2002)

A Study of the Teaching Beliefs of the Modern Post Secondary Science Instructor and Implications They May Hold for the Future of Science Education

It was the purpose of this study to examine the teaching beliefs of community college science instructors and discover whether their teaching beliefs were student oriented or instructor oriented. In addition, this study sought to examine demographic factors and find their relation, if any, to these teaching beliefs, as well as explore topics that may be useful in the future to helping community colleges science instructors’ curricula and beliefs come together and work in unison. To do this, the study built on the foundation laid by Sampson et al., in their creation of the Beliefs about Reformed Science Teaching and Learning (BARSTL) questionnaire. This study consisted of the BARSTL framework, together with six demographic questions and four short answer questions. Quantitative and qualitative methods were used to analyze the significance of the differences between the BARSTL score and the demographic groups created by the questions. Mean BARSTL scores and subscores for all 36 demographic groups created by the demographic and short answer questions were calculated. Homogeneity of variance between the groups created by the nine questions was calculated where the group size was sufficient to meet statistical requirements (one question had a single, overwhelming, common response). Eight ANOVAs were then used, along with post hoc tests where appropriate, to see if there was a significant difference between the BARSTL scores in the groups created by eight questions. Additionally, eight MANOVAs were used, along with post hoc tests where appropriate, to examine whether there was a significant difference between the BARSTL subscores in the groups created by eight questions. Further, one question lent itself to a t-test to examine the difference in the groups created by the two most common responses, and it was performed as well. Certain responses to the four short answer questions were also explored using qualitative means to further understand why community college science instructors responded in the manner in which they did and what implications their responses may have for community colleges and science beliefs

Math and Math-in-School: Changes in the Treatment of the Function Concept in Twentieth Century Secondary Algebra Textbooks

The exercises found in the chapters on function in five American textbooks (each taken from different twenty-year spans of the twentieth century) were analyzed using Mesa's (2000) coding scheme. Problems were analyzed based on the context, the operations needed to solve the problem, the representations used, and the control structures (or checks) available to the students. This analysis allowed for the identification of trends across time. These trends were compared to trends in the concept of function in the mathematics discipline and trends in recommendations for mathematics education. This analysis was undertaken to address three basic research questions. First, is there evidence of change in the treatment of function in school algebra across time? Second, how do any changes that exist in the texts correlate with recommendations for mathematics education? And third, how do changes in the texts correlate with the developments of the function concept in the mathematics discipline

Preservice Secondary School Mathematics Teachers\u27 Current Notions of Proof in Euclidean Geometry

Much research has been conducted in the past 25 years related to the teaching and learning of proof in Euclidean geometry. However, very little research has been done focused on preservice secondary school mathematics teachers’ notions of proof in Euclidean geometry. Thus, this qualitative study was exploratory in nature, consisting of four case studies focused on identifying preservice secondary school mathematics teachers’ current notions of proof in Euclidean geometry, a starting point for improving the teaching and learning of proof in Euclidean geometry. The unit of analysis (i.e., participant) in each case study was a preservice mathematics teacher. The case studies were parallel as each participant was presented with the same Euclidean geometry content in independent interview sessions. The content consisted of six Euclidean geometry statements and a Euclidean geometry problem appropriate for a secondary school Euclidean geometry course. For five of the six Euclidean geometry statements, three justifications for each statement were presented for discussion. For the sixth Euclidean geometry statement and the Euclidean geometry problem, participants constructed justifications for discussion. A case record for each case study was constructed from an analysis of data generated from interview sessions, including anecdotal notes from the playback of the recorded interviews, the review of the interview transcripts, document analyses of both previous geometry course documents and any documents generated by participants via assigned Euclidean geometry tasks, and participant emails. After the four case records were completed, a cross-case analysis was conducted to identify themes that traverse the individual cases. From the analyses, participants’ current notions of proof in Euclidean geometry were somewhat diverse, yet suggested that an integration of justifications consisting of empirical and deductive evidence for Euclidean geometry statements could improve both the teaching and learning of Euclidean geometry