<p> When applied to mathematics education, manipulatives help students to visualize mathematical concepts and apply them to everyday situations. Interest in mathematics instruction has increased dramatically over the past two decades with the introduction of virtual manipulatives, as opposed to the concrete manipulatives that have been employed for centuries. This quasi-experimental study proposed to explain the relationship between concrete and virtual manipulatives when used in a seventh-grade mathematics classroom. Using students' mathematics composite scores on standardized and teacher-created assessments, it compared the effectiveness of using concrete manipulatives alone versus using a combination of concrete and virtual manipulatives. The foundational theory of the study is that when students can visualize a mathematical concept in action, a deeper level of understanding occurs. </p><p> The results of this mixed methods study consisting of 44 seventh-grade students (22 in each group) indicated that coupling concrete manipulatives with virtual manipulatives led to a measureable change in mathematics composite scores. One recommendation is that mathematics educators incorporate both concrete manipulatives and virtual manipulatives into their mathematics curriculum. As the results of this year-long study indicated, the combination of these two types of manipulatives enabled the students in this group to accomplish a measureable change in tested mathematical ability. Educators need to offer their students lessons that are authentic and interesting in order to hold students' attention as they attempt to grasp the concepts. The different options also provide students with the needed differentiated instruction to suit their varied learning styles.</p>

<p> Recent curriculum recommendation call for mathematical argumentation to play a significantly greater role in U. S. mathematics instruction at all grade levels, including the elementary grades. To better understand how preservice elementary teachers (PTs) enrolled in a one-semester course emphasizing mathematical argumentation might become better prepared to implement this change, I interviewed five such PTs at two points in time, near the beginning of the course and shortly after they completed it. Both interviews focused on a problem set in which nine fictional elementary school students present arguments for their solutions to mathematical problems. Interviewees compared the arguments, decided which were convincing and which were not, and gave reasons for their choices. Using an interpretative, phenomenological approach, I analyzed their responses and found that they initially preferred arguments in which they perceived the arguer as knowing what to do, getting the correct answer, using a quick way to get it, showing how with numbers, and having the right attitude. In contrast, after they had completed the course, they focused on understanding the problem, finding answers that made sense, and explaining why with diagrams. They also viewed the arguer&rsquo;s attitude as a more complex issue than they had at the beginning of the course. These and other findings suggest that current research on PTs&rsquo; approaches to mathematical justification may: (a) overemphasize the formal aspects of mathematical arguments and undervalue their substance, (b) overemphasize the role of verification and undervalue explanation, (c) be too far removed from PTs&rsquo; perspectives, and therefore (d) fail to accurately reflect significant progress in PTs&rsquo; understandings.</p>

<p> The purpose of this study was to examine children's musical and mathematical behaviors as they participated in an interdisciplinary pre-K curriculum. Research questions were: 1. What connections&mdash;if any&mdash;do young children make between music learning and mathematics learning? 2. Is there a relationship between young children's emergent rhythm development and emergent numeracy development? </p><p> To address these questions, a concurrent embedded mixed-methods design was utilized. One intact class of 14 preschool children were observed at predetermined points throughout the Spring 2012 semester through participant observation and video footage of music classes, math activities, and other times where music was used in the curriculum. Interventions for classroom and music teachers were intended to foster developmentally appropriate practice in music and mathematics. Music aptitude and pre- and post-test measures of early music rhythm achievement and early numeracy achievement were correlated to embed a quantitative dimension. </p><p> Observed rhythm responses included movement such as (a) continuous, free-flowing motion during songs; (b) steady beat motions of bouncing, tapping, and clapping; and (c) rhythmic body motions of tapping or clapping rhythm patterns; chanted responses of (a) echoed rhythm patterns, (b) improvised rhythm patterns, and (c) parts of poems. Sung responses included singing with a light quality in initial singing range, as well as resting tone and tonal patterns. Mathematical responses included subitizing, one-to-one correspondence, counting fingers, forward and backward verbal counting, and using finger patterns to count on, and add and subtract numbers less than 10. </p><p> Limited, but supportive quantitative evidence was found regarding the relationship of early rhythm and early mathematics development. Emergent themes, <i> community of learning and sharing, expanded social conventions,</i> and <i> reinforcement of learning,</i> revolved around current thought that learning is both individually and socially constructed. That some children express themselves more readily through music and others through mathematics was supported; carefully selected song literature that meets both music learning and mathematics learning objectives can elicit observable musical and mathematical responses and may reinforce learning connections. Recommendations include replication with a design that addresses limitations of the present study and increased music and math pedagogy courses and professional development for pre-K classroom teachers.</p>

<p> The purpose of this qualitative phenomenological study was to explore and describe the practices of teacher leaders in a PLC content team along with the supports they received and needed as well as the challenges they encountered during implementation of the Common Core State Standards for high school mathematics in a Southern California school district. Because research shows most change initiatives require active leadership and yet are difficult to sustain there existed a need to study and describe the experiences of the teacher leaders during this curricular change to the Common Core State Standards. The experiences described by the seven teacher leaders participating in this study strengthen the practices of using collaborative content groups lead by teacher leaders. Common themes of teacher leader practices included having updated knowledge and skills about the reform through multiple trainings, honest and trusting relationships with their peers, sharing experiences and ideas, along with a shared vision and purpose, timelines and agendas. The supports received by the teacher leaders included the support of leadership through a TOSA or coach, the structure and time of the collaborative PLC content teams and on-going professional development. The challenges experienced by the teacher leaders were the need for more time and materials. </p><p> The conclusions confirm that teacher leaders are the experts in their subject who practice building relationships through sharing of experiences and focusing on the goals for student improvement. Nine conclusions from this study confirm that the important practices of teacher leaders are knowledge of the change in curriculum to provide a common vision and purpose for student learning, using norms, agendas and timelines to stay focused on the goals, building trusting relationships and an environment of trying new things and sharing experiences. The leadership supports required include the PLC team time and structure including stronger administrative direction at the beginning and more choice as the work continues, the support of a TOSA or coach who advocates for the teachers and teacher leaders through communication, direction and resources and the additional support through on-going and continual professional development. The needs and challenges of the teacher leaders include more time to development, assess, adjust and improve the curriculum and the need for materials for both the teachers and students.</p>

<p> The purpose of this study is to examine the relationship between exposure to the arts and performance in Science, Technology, Engineering, and Math (STEM) subjects. STEAM, an integration of arts-based instruction into science and math related fields, is viewed as an alternative to traditional STEM academies. The literature briefly examines the current state of STEM programs and the deficiencies in graduate quality and quantity and the call from employers for a more innovative workforce. Advocates for STEAM argue for arts as a means to improve creativity, collaboration, risk-taking and exploration. Arguments against arts in STEM are grounded in political opinions concerning arts funding and logistical complications of implementing STEAM. However, some schools and STEM programs have embraced the STEAM premise and have begun to integrate arts into the traditional curriculum. The 2009 National Assessment of Educational Progress (NAEP) dataset was utilized to determine a correlation between the number of arts credits earned and mathematics/science achievement. Results from the NAEP dataset indicated a correlation between the amount of arts credits and increased achievement scores in science and math. The same correlation was found when controlling for demographic factors such as gender, race, and socio-economic status (SES). Overall, the arts' greatest impact was on students identified as "at-risk" or underrepresented in STEM fields. Controlling for these variable groups, one can note the quantifiable differences in scores. Overall, findings of the study provide empirical support for the addition of arts in STEM.</p>

<p> The purpose of this study was to examine the differences between mathematics preparation and teachers' perception of self-efficacy for teaching mathematics at low- and high-performing schools. Bandura's theory of self-efficacy was the guiding theoretical framework. The study used a descriptive comparative method to obtain quantitative data regarding teacher backgrounds and teacher efficacy level. Self-reported data from the Mathematics Teacher Efficacy Belief Instrument was used to calculate two dimensions of teaching efficacy, personal mathematics teaching efficacy (PMTE) and mathematics teaching outcome expectancy (MTOE). Preparation was determined by individual calculations for successful completion of preservice mathematics coursework, completion of mathematics methodologies coursework as well as hours and types of teacher professional development completed. An analysis of 69 teachers, 33 from low-performing schools and 36 from high-performing schools, revealed statistically homogenous mathematics preparation and self-reported self-efficacy levels. Elementary mathematics teachers from high-performing schools demonstrated slightly higher level of preparation, PMTE and MTOE; however, differences were not statistically significant. Results were incongruent with prior research and indicate the need for future research supported by data collected from external sources, beyond self-reported data.</p>

<p> The ability to change is essential in the field of education and of great concern to teacher educators. While some change initiatives have succeeded, many others have failed to be transformative or sustainable. A need exists to better understand the process of behavioral change to inform the design and evaluation of change initiatives and assess progress using a common vocabulary. This study addresses this need by synthesizing change models from clinical psychology, advertising design, and social cultural learning to create a theoretical model for behavioral change. A temporal change model composed of stages has theoretical and practical significance for those promoting behavioral change in education and other professional fields. This new framework was applied to two groups of pre- and in-service teachers engaged in a change initiative around questioning behavior. Data analyses indicated that individuals entered the model at different entry points and moved sequentially through stages, with participants generating the lowest pre-intervention percentages of the target behavior making the most amount of relative change. Qualitative data revealed resistance to change due to personal attitudes and beliefs about roles in conjunction with the behavior. The utilization of behavioral change as the focus of this study necessitated the reconceptualization of behavior as scientific knowledge capable of being defined, modeled, and taught. Additional theoretical and practical significance is the positioning of other behaviors as knowledge, capable of being structured and generalized.</p>

<p> Developmental math currently poses a hurdle that many community college students are unable to overcome. Eighty percent of developmental math students do not successfully complete any college-level course within three years (Bailey, Jeong, &amp; Cho, as cited by Strother, Van Campen &amp; Grunow, 2013, p. 1). Despite numerous reform attempts, there has been a lack of consistent improvement and a lack of understanding regarding which methods are the most successful and the reasons why. Faculty need a new pedagogy to connect with developmental math students and effectively engage them in order to improve student learning outcomes. Proponents regard game-based learning as a way to leverage the intense engagement of video games in an educational context to increase engagement, increase the amount of time on task, and improve overall student success metrics. </p><p> The author has reviewed the studies and the evidence; weighed the value and legitimacy of the studies; synthesized the weight of the evidence of introducing a game-based learning pedagogy, and then examined the potential efficacy of game-based learning in the developmental math environment. The author has created an evidence-based implementation plan to incorporate game-based learning into developmental math education in a way that has the highest potential to improve student learning. </p><p> Key words: Game-based learning, gaming, serious games, developmental math, developmental education reform, innovation.</p>

<p> The perception of higher self-efficacy in young children has been determined to be a better predictor of intellectual and academic performance than simply the acquisition of skills alone. This empirical qualitative single-case study was conducted in order to explore the influence of self-efficacy instruction on perceptions toward and achievement in mathematics among a class of fourth grade students in rural Oregon. Pre- and post-intervention assessments of students' self-efficacy were employed using the Six Seconds Emotional Intelligence Assessment-Youth Version (SEI-YV). The SEI-YV was used to ascertain the status and possible growth in the three self-efficacy competencies of exercising optimism, enhancing emotional literacy, and engaging intrinsic motivation (Six Seconds, 2011). Student and parent pre-and post-intervention surveys, daily student journals, and field notes were used to triangulate and support outcomes. The Oregon Assessment of Knowledge and Skills (OAKS) was used to measure possible growth in mathematics skills. This case study was conducted for three months and involved students in lessons specifically designed for fourth graders. Student self-efficacy scores rose by an average of five points. Students' active participation in this intervention contributed to their academic success as evidenced by the OAKS and sample OAKS. The number of students passing the pre-intervention OAKS equaled five. The number of students passing the post-intervention sample OAKS was 13, more than double that of the pre-intervention number of students. This study may offer a basis from which to launch other researchers into investigating the use of self-efficacy at varying intervals for mathematics instruction with elementary level students. Adjustments to various conditions used in this research as well as the incorporation of additional variables not used here could provide valuable data and insights into the specifics of self-efficacy and, perhaps, the entire range of social emotional learning. It may be that the development of self-efficacy competencies in the earlier years of formalized schooling leads to greater academic success in mathematics than if done in later years. The social and academic changes possible through this type of mathematics coursework at the fourth-grade level has far-reaching and intriguing ramifications.</p>

Elementary school teachers teach a variety of subjects requiring a range of content and pedagogical knowledge, and substantial professional development to support this knowledge often is lacking (Clements & Sarama, 2008). Mentoring, an important aspect of professional development, is particularly useful for developing content and pedagogical knowledge. However, content mentoring, i.e., mentoring support in a specific content area such as mathematics, has received little attention in research on elementary teachers. To address this gap in the research, this study examines support in a master’s program that provides mentoring specifically in mathematics for elementary school teachers. Using a sequential explanatory design, this mixed methods study employs the Mentoring for Effective Mathematics Teaching (MEMT) survey with twenty-six (26) graduates of the program. The 34-item Likert scale survey reveals perceptions of their mathematics mentoring experience. In order to obtain a deeper understanding of the perceptions, four (4) of the teachers participated in semi-structured interviews. This last data source provides additional insights into the role of school context in mentoring. The results reveal qualities of mentors that inservice elementary mathematics teachers found to be important beyond mathematics content knowledge, specifically, differences in school contexts that impact elementary mathematics teachers’ mentoring experiences. The results suggest direction for future research on mentoring for elementary school teachers who teach mathematics.