This thesis grounds the design of learning technologies in cognitive learning theory to explore deeper formative measurement of the learning process. This work implements Graspable Math (GM; Ottmar, Landy, Weitnauer, Goldstone, 2015), a dynamic learning technology that has been designed using perceptual-motor learning theory, which has been shown to have a strong connection to mathematical reasoning (Kirshner, 1989; Kellman, Massey, & Son, 2010; Goldstone, Landy, & Son, 2010). With this dynamic mathematics learning technology, we can measure the algebraic problem solving process in ways that are not possible with pencil and paper or other more traditional learning technologies. By collecting this data, this research will explore how to move beyond traditional correctness-based assessment and design more formative measures of the learning process. This work provides a rich perspective on the evolution of research on mathematical proficiency, how this research is applied in practice, and an in-depth example of how one technology-based learning environment has been developed to measure mathematical proficiency. This work has three main objectives: 1) develop a theoretical framework to assess mathematical proficiency within GM, 2) explore GM-based measures of mathematical proficiency across K-12 populations, and 3) design GM-based tools that are grounded in theory on mathematical proficiency. This work first presents a conceptual model that maps student behavior data measured through GM onto the five theoretical strands of mathematical proficiency as defined by the National Research Council’s 2001 publication, Adding it Up. The first study reveals underlying constructs in Elementary student data and suggests there is an added benefit of including these formative measures within predictive models. Above and beyond background characteristics and summative measures of knowledge, formative measures of the learning process revealed subtle interactions based on student behaviors and prior knowledge. These constructs also show potential in mapping onto certain strands of mathematical proficiency. The second study compares underlying constructs within Elementary data to High School data using exploratory factor analysis and finds similar factors across both populations. These results suggest that certain constructs may underlie different age groups and have the potential to be used as measures of mathematical proficiency. While the first two sections describe the definition and measurement of mathematical proficiency within GM, the final section explores the implementation of these measures within the design process of new GM-based activities for students and tools for teachers. Ultimately, the goal of this work is to serve as an example method for other researchers, educators, and designers to move beyond summative measures of assessment and enhance the formative assessment capabilities of learning technologies by grounding measures in theories of learning.

<p> This study investigated the perceptions of teachers of grades three, four, and five regarding differentiated instruction in conjunction with Standards-Based Report Card as aligned to the Common Core State Standards. The purpose of this study was specifically seeking teacher perceptions on how these phenomenon interact, as well as teacher to parent communication, student awareness of standards, and reassessment practices. </p><p> The sample (n = 140) consisted of regular education teachers, grades three, four, and five from districts in both Illinois and Missouri. These districts used a Standards-Based Report Card at one or more of these intermediate grade levels. The participants completed a survey designed to determine teacher perceptions of the effect of differentiated instruction on the Standards-Based Report Card in conjunction with the Common Core State Standards. This survey was developed to answer the six research questions. </p><p> The researcher analyzed the data descriptively and inferentially. The researcher concluded that districts need more training and need to promote teacher buy-in. The descriptive results demonstrated teacher perceptions about communication, student awareness, and reassessment. Overall, teachers do not perceive that they are communicating more due to the Standards-Based Report Card. Teachers tend to agree that students are aware of their progress as a result of the Standards-Based Report Card and that they are reassessing in math and ELA. The researcher concluded the study by suggesting recommendations for further research in the area of Standards-Based Report Cards at the intermediate level.</p><p>

Thesis (Ed.M.)--Boston University

<p> The focus of the research is to explore how organizational and self-regulatory skills support student academic achievement in math class. The project is a mixed-methods study by taking a close look at the use of graphic organizers as a dimension of organizational and self-regulatory skills. The data sources include an online questionnaire, observation notes, individual interviews, and student semester grades. Participants completed a questionnaire about their organizational and self-regulatory skills, including how they have been using graphic organizers and taking notes. The author reported three focal interviews to grasp further how their organizational and self-regulatory skills surface in different settings, including home, school, work, and other routine areas. This document includes the details of data analyses for any associations between students&rsquo; skills and academic achievements. This research concludes (a) participating students carry sufficient social-emotional competencies. However, there is a disconnection between transferring their &ldquo;cultural&rdquo; knowledge into &ldquo;domain&rdquo; knowledge about self-awareness skills, social awareness skills, and responsible decision-making skills. (b) Both Advanced Algebra and Geometry students demonstrate very similar organizational skills, but (c) lower-classmen seem to have relatively higher self-regulatory skills. (d) The greater self-awareness and social awareness skills and better decision-making skills, higher academic achievement in math classes. The author concluded this paper had potential limitations of the findings and implications for future teaching practices. The results of this study may provide instruction insights about how social-emotional competencies affect student academic achievement in secondary math education.</p><p>

<p> Educators are now charged with instructing students who are growing up in a digital environment (Hsin, Li &amp; Tsai, 2014). Students need access to 21st century learning environments that incorporates technology use, especially in mathematics (Darling-Hammond, Wilhoit &amp; Pittenger, 2014). Unfortunately studies show that technology integration is happening least in mathematics compared to other subject areas (Howard, Chan, &amp; Caputi, 2015a; Howard, Chan, Mozejko &amp; Caputi, 2015b; Howard, Chan, and Caputi, 2014). Moeller and Reitzes (2011) found that according to a National Center for Education Statistics study, only 23% of K-12 teachers feel prepared to integrate technology into instruction. </p><p> The purpose of this sequential explanatory mixed methods study was to investigate and explore teacher perceptions regarding technology knowledge, content knowledge, pedagogy, and preparedness to implement technology integration in mathematics instruction in elementary teachers in an urban ring district in a northeast state. </p><p> This study addressed the following research questions: 1. How do elementary teachers rate their perceived knowledge of teaching and technology in mathematics on the following components of the Technological Pedagogical and Content Knowledge (TPACK) framework: technological knowledge (TK), content knowledge (CK), pedagogical knowledge (PK), pedagogical content knowledge (PCK), technological content knowledge (TCK), technological pedagogical knowledge (TPK), technological pedagogical content knowledge (TPACK), and models of TPACK related to preparedness? 2. Is there a significant difference in how elementary teachers rate their perceived knowledge of teaching and technology in mathematics on the components of the Technological Pedagogical and Content Knowledge (TPACK) framework by the following demographics: gender, age and years of teaching experience? 3. How do elementary teachers describe their perceived technology knowledge, content knowledge, pedagogical knowledge, and preparedness to implement technology integration as they relate to mathematics instruction? </p><p> The major themes that emerged from this study included limited teacher mathematics knowledge because mathematics instruction and expectations for understanding are different today than in the past; and teachers did not feel like they were supported or prepared well to integrate technology into mathematics instruction. Administration and teacher educators may benefit from knowing teachers feel a need to be supported in mathematics conceptual knowledge, problem solving and technology integration.</p><p>

The ubiquity of mobile devices together with their potential to bridge classroom learning to real-world settings has added a new perspective to contextualising mathematics learning, but this needs further exploration. The aim of this thesis is to examine the effects of using mobile technologies on students’ attitudes, engagement and achievement in mathematics. The study starts with a systematic review of maths and mobile learning studies followed by three iterations of data collection. The three studies were mixed-methods studies guided by the micro, meso, macro (M3) Evaluation Framework. The studies included eight mobile learning sessions spread over three months covering topics on geometry and information handling. These sessions were conducted as collaborative learning activities in indoor and outdoor settings. Participants were Primary 6 and 7 students from three different schools in Scotland. In Study 1 (a single-group design, n=24), students had positive evaluations of mobile learning but some technical problems experienced lessened their initially positive views. There was a small effect in student self-confidence (ES=.20) and a significant positive difference between pre and post-test achievement scores. Breakdowns identified via the critical incident analysis in Study 1 informed the activity design of Study 2. In Study 2 (a quasi-experimental design, n=52), students had more positive perceptions about the use of mobile technology. The experimental group had higher gain scores on the maths test than the control group. In Study 3, a randomised controlled trial over six weeks (n=74), students also had positive evaluations of the mobile learning activities but this varied by gender. Analysis of the maths test scores with pre-test as covariate showed both groups had significantly improved their scores, but no significant treatment effect was found. For items relating to common student misconceptions on angles, students in the experimental group had significantly higher gains than the control group. The overall results from the three studies provide some evidence that students can have positive perceptions about the use of mobile technologies and that these can be effective in supporting students’ engagement and performance in mathematics, especially when learning takes place outside the classroom. It also showed that the success of a mobile learning intervention is dependent on various factors, such as student and teacher characteristics, stability of the technology and content compatibility, among other factors. There were several limitations including sample size, length of intervention, and programme fidelity. Implications for practice and future researchers are discussed.

<p> Elementary mathematics teachers in Maryland are required to teach according to the Maryland College and Career-Ready Standards (MCCRS). Implementation of these standards requires teachers to understand and implement instructional shifts that are unlike the way most of them were taught mathematics in elementary school. Consequently, educator preparation programs in Maryland must ensure candidates are adequately prepared to teach elementary mathematics according to the Maryland standards and the necessary instructional shifts. </p><p> This study describes the preparedness of teacher candidates and first-year teachers from Maryland educator preparation programs to teach according to the elementary mathematics MCCRS. Preparedness is described from the perspective of mentor teachers who work with interns and mathematics instructional leaders (MILs) who work with first year teachers from Maryland preparation programs. The descriptions of the preparedness of these interns and first-year teachers provide multiple perspectives on both the strengths and needs of preservice teachers and recent graduates. </p><p> Mentors from five different school systems in Maryland and MILs from four school systems in Maryland completed a survey with both quantitative and qualitative questions. Nineteen mentors and 22 MILs participated in the survey. Ten of the participants volunteered for and participated in a follow-up interview. The participants reported on the interns or first-year teachers they worked with during the 2016&ndash;2017 school year. </p><p> Mentors and MILs described the teachers they work with as having strengths in implementing technology into instruction and described the teachers as willing to use manipulatives during instruction. Additionally, they perceived educator preparation programs as being well-aligned to their school system goals and priorities. Participants described needs of the teachers they work with, including the following: understanding the standards, understanding mathematics on a conceptual level, differentiating instruction, promoting mathematical discourse, and problem solving into instruction. These recommendations provide a basis for educator preparation programs when examining the preparedness of their candidates and graduates to teach according to the MCCRS for elementary mathematics.</p><p>

<p> This study used the TIMSS 2011 International Database to investigate predictors of 8th-grade mathematics achievement across three countries that represent a wide range of cultures and levels of mathematics achievement: Chinese Taipei, Ghana, and the United States. A review of literature on predictors of mathematics achievement yielded variables in four major contexts of learning&mdash;a student&rsquo;s home, beliefs, school, and classroom. The variables of home that were investigated are home possessions for learning, parent education, and parents&rsquo; expectations and involvement in their children&rsquo;s education. The variables of student beliefs were self-confidence in mathematics and the value of mathematics. The variables of school were school climate, school resources, administrator leadership, and school socioeconomic status. Finally, the variables of the classroom are access and equity, curriculum, tools and technology, assessment, and teacher professionalism.</p><p> A 2-level hierarchical linear model was used to investigate relationships between the predictors for learning mathematics and 8th-grade mathematics achievement. Level 1 represented the relationships among the student-level variables, and Level 2 represented the school-level variables.</p><p> In Chinese Taipei, statistically significant predictors of mathematics achievement in the final model included variables from the domains of home resources, student beliefs, school climate, and school socioeconomic status. In Ghana, both student-beliefs variables had statistically significant relationships with mathematics achievement, and one school climate and one school socioeconomic status variable each was found statistically significant. The U.S. had statistically significant predictors in the domains of home resources, student beliefs, school socioeconomic status, classroom-level access and equity, classroom assessment, and teacher professionalism.</p><p> This study extends previous research in several ways. It includes a review of classic and recent literature regarding predictors of mathematics achievement; 17 scales using the Rasch partial credit model were developed to measure predictors of mathematics achievement; and the results of this study may be used to examine the relationships between the independent variables of this study and middle-grades mathematics achievement in countries similar to the 3 in this study to reinforce and support variables that contribute to student achievement.</p>

<p> For most American High School students, taking algebra in high school has always been a rite of passage. Traditionally, Algebra I has long been a ninth-grade student's first experience with higher-level mathematics. To maintain a competitive edge in a global economy, numerous school districts in the United States have rearranged mathematics curricula to relocate algebra down to the middle school. Placement in eighth grade algebra provides students with an opportunity for rigor and higher levels of attainment in mathematics coursework by the completion of grade twelve. The effectiveness of moving algebra from grade nine to grade eight has become a highly debated topic amongst educators and lawmakers. Policymakers and administrators that favor moving Algebra I into the eighth grade believe doing so will assist in closing the achievement gap currently in existence for gender, race and socioeconomic status. To achieve this, substantial sums of money must be invested in the implementation of algebra programs in middle school. Proponents of grade eight algebra strongly advocate for algebra placement prior to high school as an intervention to reduce the gap between American students and their global counterparts. "The U.S. also needs to do a better job of identifying and nurturing its mathematically talented youth, regardless of their gender, race, or national origin. Doing so is vital to the future of the U.S. Economy" (Hyde, Mertz, &amp; Scheckman, 2009). In contrast, researchers such as Nomi (2012) have argued that early algebra placement is not beneficial for every child. Researchers such as Levy (2012) and Shearing (2016) agree that Black and Hispanic students, particularly of low socioeconomic status are victims of an achievement gap. "Students who are eligible for free and reduced lunch tend to be approximately two years behind that of students of the "average better-off student of the same age" (McKinsey &amp; Company, 2009, p. 6). While there has been agreement among the experts regarding the existence of the gap, their suggested solutions conflict. </p><p> The research conducted by this researcher will contribute to the existing literature on Algebra I placement. The purpose of this study was to examine both the proportionality of student placement in grade eight Algebra I by gender, ethnicity and socioeconomic status, and the impact of grade eight Algebra I participation on academic performance on mathematics in a large, urban, New Jersey Public School District. This impact was measured based on the outcomes of Algebra I and Geometry final grades, Algebra I and Geometry PARCC scores, and tenth-grade mathematics PSAT/NMSQT scores. This study examined the relationships between academic outcomes for eighth-grade Algebra exposure and academic outcomes as described.</p><p>

Using fonts as a context, we will analyze symmetry of fi gures. Diff erent letters and numbers will be measured, and participants will describe items that possess vertical, horizontal, and rotational symmetry. Our discussion and activity will focus on the mathematics of fonts and the presence and absence of symmetry in their design.