<p> The aim of the study is to examine high school mathematics teachers' lesson plan development and implementation practices used in the border region of Mexico and USA. The study also attempts to determine how a transition from Mexico (Ciudad Juarez, Chihuahua) to the U.S. (El Paso, TX) impacts high school mathematics teacher&rsquo;s lesson plan development practices incorporating the Borderland Pedagogy. The Borderland Pedagogy theoretical framework (Cline &amp; Necochea, 2006; Romo &amp; Chavez 2006; Fiume, 2005) was developed to explore educational experiences of teachers situated within border regions. The framework highlights key characteristics of Borderland Pedagogy that influence lesson plan development and implementation practices. The framework was used to design multiple case studies research to examine and understand teaching practices on both sides of the border in general, and pedagogical experiences of transitioning teachers in particular. Elbaz-Luwish (2007) and Sabar (2004) defined teacher transition as an adaptation of a teacher to a new language, culture, and new educational system. Scholars (Shimizu, 2008; Diazgranados et al., 2008; Lit and Lit, 2009) suggest that lesson plans are designed according to teachers&rsquo; experiences, knowledge about the subject matter, and beliefs about teaching, and learning. The study is built on understanding that teaching on the border impose unique requirements on lesson plan development practices reflecting flexibility, cultural and linguistic diversity. The research sample included two Mexican teachers, two US teachers, and one transitioning teacher. The design of the study is operationalized based on the following data sources: (1) teacher-developed lesson plans, (2) classroom observations, and (3) structured interviews. Data was analyzed using frequency-based initial and focus coding scheme. The key observation in lesson plan development among participating Mexican and US teachers revealed complexity and uniqueness of borderland teachers&rsquo; practices in recognizing, addressing, and implementing national/ state standards and curriculum (Secretar&iacute;a de Educaci&oacute;n P&uacute;blica, Texas Education Agency). Results of the study suggest that the Borderland Pedagogy could serve not only as a framework but also as an instrument to document and interpret transformative pedagogical practices of teachers teaching on the border.</p>

<p> The purpose of this study was to explore and analyze which fifth-grade teacher inputs were the most important predictors of future outcomes of eighth-grade math students. This quantitative study looked at mathematical achievement through the lens of an education production function. The three inputs that were analyzed were fifth-grade teachers&rsquo; background; perception of professional development; and instructional practices and the relationship of those practices to achievement in eighth-grade math. In order to find the relationship between the above variables and student achievement, descriptive statistics, multiple correlations, and multi-variable regression analysis were conducted to examine which predictors had a stronger relationship between eighth-grade math outcomes than others. Taken as a whole, fifth-grade teacher math inputs in this study seemed to explain a small part of the variance regarding eighth-grade math achievement. As a whole, the more frequently students wrote and spoke about math in fifth grade as well as used math tools effectively, the better the outcome in eighth grade.</p>

<p> The basis of this work is to lay the groundwork for relational thinking in mathematics by giving a general mathematical definition of relational thinking in mathematics that builds on the theory of relational thinking in arithmetic and then extends that theory to include all other mathematics subjects, especially algebra and geometry. The necessity to include all other mathematics subjects in relational thinking is predicated on the need for students at all levels to be able to think relationally. In an effort to further establish relational thinking in mathematics, this work attempts to merge mathematics and philosophy by examining Plato's <i>Meno</i> and Wittgenstein's <i>Philosophical Investigations</i> to show the importance of deductive reasoning, logic, and language in the use of relational thinking in mathematics. Further, this work also sets out to establish relations in a mathematical sense as a unifying concept in algebra and geometry. I therefore define relational thinking in mathematics as the skill and propensity to use deductive reasoning and logic in order to make connections between and among abstract mathematical concepts and specific instances thereof. This definition stems from mathematics being built on two pillars--that is, deductive reasoning and logic--and being of two different branches--that is, abstract mathematics and applied mathematics. </p>

<p> The purpose of this study was to investigate the effects of mathematical acceleration on gifted learners&rsquo; academic achievement. The study compared academic achievement and mathematical attitudes of accelerated and nonaccelerated first through third grade gifted students. The study was conducted using a causal-comparative, quantitative design with pre and post assessments from STAR Math for achievement and the Attitudes Toward Mathematics Inventory to evaluate change in attitudes toward the accelerated subject. Independent samples t-tests were used to analyze the differences in growth in the accelerated gifted groups&rsquo; and nonaccelerated gifted groups&rsquo; STAR Math achievement scores and attitudes on the Attitudes Toward Mathematics Inventory. Results indicated a slight increase for the accelerated gifted learners in the area of achievement. However, the differences in growth in mean scores for achievement was not statistically significant. In the area of attitudes, the domains of enjoyment and confidence reported statistically significant differences in the growth in mean scores for accelerated gifted learners. Nonaccelerated gifted learners showed the greatest growth in mean scores for the doain of motivation. However, the domain of value did not note statistically significant differences in the growth in mean scores for accelerated or nonaccelerated gifted learners.</p>

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<p> This study sought to provide a preliminary examination of the relationship between the implementation of Guided Math and student achievement in Title I schools as measured by the percentage of students who met or exceeded the standard for the Georgia Mathematics CRCT. The study examined data from thirty Title I elementary schools in one suburban Atlanta school district. The percentage of students who met or exceeded the standard on the Math CRCT increased from 2010 to 2011, after one year of Guided Math implementation, suggesting that Guided Math is working to close the achievement gap in the area of mathematics among African American and Hispanic/Latino students as well as economically disadvantaged students. However, there was not a statistically significant difference in the percentage of students who met or exceeded the standard from 2010 to 2011, p = 0.435, where significance occurs at p &lt; 0.05. Because this study was a preliminary study to determine the results of implementing a Guided Math program after one year of implementation, the cohorts used for this study should be followed for several more years to see if their academic achievement continues to increase. Also, similar studies should be conducted on larger scale over longer periods of time in order to obtain a global picture of the effects of Guided Math on mathematics achievement</p>

<p> It is a well-documented finding that high school students in schools across the nation, including California, fail to achieve at the proficient level in mathematics, based on standardized test scores. The purpose of this research study was to compare the findings of students taught using traditional instructional methodologies versus cooperative learning methodologies. The study was conducted in four ninth grade Algebra I classes on a South Los Angeles high school campus, which has 1,700 students. Of the student population, 110 students participated in the study. The researcher utilized descriptive statistical analysis as a means to review previous student standardized test scores to determine baseline performance. After the treatment, a district adopted assessment was administered and used as a post-test to gather quantitative data to compare the scores of students who were taught using cooperative learning methodologies versus those who were taught using traditional methodologies in Algebra I.</p>

<p> In a national context of high failure rates in freshman calculus courses, the purpose of this study was to understand who is struggling, and why. High failure rates are especially alarming given a local environment where students have access to a variety of academic, and personal, assistance. The sample consists of students at Colorado State University (CSU) who attended a course in freshman calculus from Fall 2007 to Fall 2012. An explanatory sequential mixed methods approach was used in this study. </p><p> Using data from CSU's Registrar's Office and Mathematics department, descriptive statistics highlighted several student attributes worth pursuing. Fall and spring cohorts have a different make up and different outcomes. Hence this study concentrated on the fall cohort, which comprises mainly of freshmen. The combination of attributes that produced the strongest prediction of student's final result in calculus were Colorado Commission on Higher Education index scores, CSU Mathematics department placement test scores, and calculus repeat status (<i>R²</i>=.30, <i>n</i>=1325). For Fall 2012, these attributes were combined with student motivation and student strategies constructs, measured using the MSLQ instrument. The combination giving the strongest prediction of student's first mid-term examination results (<i>R²</i>=.34, <i>n</i>=124) included CSU Mathematics department placement test scores, along with MSLQ constructs test anxiety, and self-efficacy for learning and performance. However, using logistic regression only 38.7% of the students who failed were correctly predicted to fail. </p><p> Former students of CSU's calculus course aimed at freshmen STEM students were interviewed or surveyed, in an attempt to probe how students experience this course. Several common elements emerged. Students were dedicating vast amounts of time to this course. There was a common belief this course could be passed if the student worked hard enough. The difference between those who succeeded and those who did not appeared to relate to how this study time was spent. Those who floundered often struggled to locate appropriate help, although they were quite aware they needed assistance. Many of those interviewed also avoided working with other students. Reasons cited ranged from claims of being individual learners, to frustration at finding a group who had the same study goals. Some non-traditional students were also alienated by the prospect of working with `teenagers'. </p><p> Two other results from the analysis of student interviews suggested reanalyzing the quantitative data and including student's prior history with mathematics, as well as if the student was non-traditional. The combination of attributes that gave the strongest relationship (<i>R²</i>=.40, <i> n</i>=101) were CSU Mathematics department placement test results, combined with MSLQ constructs test anxiety, self-efficacy for learning and performance, organization, as well as the student's own appraisal of the quality of mathematics teaching they received in high school. However, the ability to accurately predict if a student will fail was minimal. </p><p> Focusing on students who do fail, three groups of students of interest were isolated: those who have yet to declare their major, 'non-traditional' students, particularly those enrolled in the eight a.m. class, and, curiously, those students who choose to enroll in the ten a.m. class.</p>

<p> With more and more focus on accountability, algebra achievement has become a major focus of math curriculum developers. In many states, students are expected to pass standardized Algebra achievement tests in order to satisfy graduation requirements.</p><p> The purpose of this study was to identify teacher qualities and teaching qualities linked to teacher effectiveness in 7th-grade Algebra I Honors. This study examined two aspects of teachers, teacher quality and teaching quality. Teacher quality refers to the characteristics that teachers possess and teaching quality refers to what teachers do in the classroom to foster student learning. For this study, teacher quality included teacher professional preparation characteristics and teacher knowledge. Also, aspects of teaching quality that promote conceptual understanding in Algebra were examined.</p><p> In this mixed methods study, quantitative data were used to determine a relationship between teacher qualifications and student achievement. Qualitative data were used to gain an in-depth understanding of the characteristics of teaching quality.</p><p> Based on the findings of this study, in this group of teachers, there is a relationship between teacher quality and teaching effectiveness; however it is very limited and only based on participation in two specific workshops. The difference between more and less effective teachers in this study lies in teaching quality, what teachers do in the classroom, as opposed to teacher quality, what those teachers bring with them to the classroom.</p><p> The findings of this study indicate that elements of teaching quality are more indicative of teacher effectiveness than elements of teacher quality among teachers in the study. Although there was some evidence of a relationship between elements of teacher quality and teacher effectiveness, there were clear differences in teaching quality among more effective and less effective teachers in this study.</p>

<p> This study investigated elementary school teachers' conceptions of their beliefs and expectations of African American students, their pedagogical practices, and the rationale for choosing the pedagogical practices for grades 3 through at Star Maker Elementary. The researcher employed a mixed methodology. The Math Teacher of African American Students Inventory (MT-ABSI) served as the quantitative method. Frequency analysis was employed to analyze the survey. Qualitative methods included two focus group interviews and lesson plans analysis. The researcher employed thematic coding to analyze the qualitative methods. Although the results from the MT-ABSI indicated that teachers had low level beliefs and expectations of their African American elementary students' ability in mathematics, the teachers professed to have high beliefs and expectations and communicate them to their students by using real world experiences in their mathematics classes, providing extra help outside of the mathematics class, and expressing their expectations verbally and non verbally. Further results of the survey indicated that teachers professed to implement some best practices in mathematics classroom than other. These best practices included the use of manipulatives and informing students of state standards. Overall, this is in agreement with the focus group interviews and lesson plans with special emphasis on differentiating instruction, professional development, and lesson plans cycle. There rationale for choosing the pedagogical practices included building background, learners' preference, and reinforcement and advancement of skills.</p>