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This study explores the development and implementation of a five-day curriculum designed to enhance students' understanding of algebraic concepts through the integration of educational robotics and growth mindset principles. The study is structured around three research questions that investigate influences on decision-making in curriculum design, the alignment of teaching intents with practices, and the impact of self-study on integrating algebra, robotics, and growth mindset principles. Findings reveal themes focused on the importance of research and collaboration, using the Understanding by Design (UbD) framework, intentional curriculum creation, starting somewhere, personal growth and self-reflection, and experiencing and embodying constructivism in action. The study highlights the iterative nature of curriculum development, the importance of personal growth in the process, and contributes to the fields of mathematics education and educational robotics by offering a model for creating hands-on and engaging curricula that could promote both mathematical understanding and a growth mindset. By sharing these insights and practical applications, this study aims to inspire further innovation and refinement in curriculum design, particularly in the field of mathematics, ultimately enhancing the educational experiences and outcomes for students. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

While contemporary mathematics education literature argues that curricular resources, such as textbooks, play a significant role guiding mathematics teachers in what and how they teach, it also shows that these resources often do not do what they say they will do, nor adhere to the standards they claim to further. When it comes to the most utilized mathematics curricular resource in the United States, Eureka Math, there is a lack of scholarly literature investigating these types of claims made by the publisher. This study aimed to explore how the Eureka Math curricular resources are positioned within the context of the Common Core State Standards of Mathematical Practice (CCSS-MP) and mathematics education more broadly and, subsequently, how the content of the resources then positions it in relation to the constructivist-aligned practices of the CCSS-MP. Through a descriptive case study design, I first engaged in a critical discourse analysis of two webpages of the Eureka Math website to provide both a description and an interpretation of the text and images, followed by an explanation of a macro-level context of mathematical crisis that was revealed through the relevant literature. I then conducted a content analysis of tasks provided in a module of the Eureka Math curriculum using an adapted framework focused on three characteristics deemed essential for high-quality context-based tasks: type of context, type of information, and type of cognitive demand. Findings from the critical discourse analysis revealed that Eureka Math's online platform functions to convince consumers that their products provide a superior level of rigor, real-world problem solving, and conceptual understanding through its implementation. The content analysis showed that overall, few tasks (25%) throughout the module were context-based tasks, with very few (4%) being high-quality in the type of information provided, even fewer (3%) in the type of cognitive demand required, and none (0%) in the type of context featured. While this study focuses on the Eureka Math curriculum specifically, it aims to also inform broader discussions of mathematics curriculum and, more broadly, conversations about curriculum decision-making in all content areas. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

Despite the standardization of calculus education as a Calculus and Analytic Geometry course after the 1950s, curriculum updates have been slow to penetrate the undergraduate mathematics classroom practice, taking decades to manifest. Common struggles with the teaching and learning of calculus, such as relying on a procedural understanding of calculus topics, echoed those documented in the literature and highlight a common challenge for many students. The derivative, one of the central ideas of the calculus curriculum, remains difficult for some students to conceptualize due in part to its multifaceted nature and the manner in which mathematics is taught at the undergraduate level (e.g., a lecture model, which stands in contrast to more active learning models that are more familiar to students in secondary school settings). The Calculus Reform Movement of the early 1990s initiated various curriculum changes and promoted experimentation with active learning strategies, particularly those that place mathematical discourse at the forefront of the activities, to address these challenges. With the implementation of these discursive learning environments in mathematics classrooms across the country, this prompted my investigation into the derivative-based mathematics that students were learning and the ways in which they were learning such concepts in two specific discursive learning environments at a large research-intensive university in the southeastern United States. Resulting from a commognitive analysis, I present the cases of two highly different activities, fostering both explorative and performative routines among students which led them to draw upon varying aspects of mathematics to reason about the derivative concept. Implications highlight aspects of students' discourse of the derivative concept, such as leveraging only the productive and correct components of a metaphor to reason across contexts. Additionally, this research illuminates the role of documentative routines in discursive learning activities and suggests that instructors should be attentive to the affordances and constraints of such routines. Thus, curriculum designers should adhere to specific goals for discursive learning activities and incorporate routines that promote awareness of processes across the multifaceted classroom discourse and facilitate meaningful documentative routines which serve not only as an assessment but also as a tool to carefully attend to students' sense-making. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

In this portfolio, I reflect on my efforts to provide professional development targeted to support teachers during the launch phase of their mathematics teaching, to elicit and respond to student ideas and experiences. I grounded my study in research on ambitious teaching practices for launching complex mathematical tasks using problem-based learning. I incorporated the practical measures launch of a task surveys to capture student experiences, ideas, and reflections and then used this student feedback to help teachers shape their decisions in the math classroom. My artifacts provide a glimpse of my journey to achieve this goal. I analyzed launches in the Illustrative Mathematics curriculum, surveyed students about their role in math class and grounded my work in research to develop strategies to accomplish this goal. To address the problem, I designed a professional learning series to implement during Maplewood PLCs to help teachers bring the student voice into the classroom during the task launch. I followed up with coaching interventions focused on evidence-based practices (EBPs) for launching rich math tasks and practical measures student surveys to get students to engage in sense-making, thinking, and problem-solving. Professional learning was well attended, and teachers actively participated. I used an Innovation Configuration (IC), an observation tool to collect descriptions of teaching, to identify the differences between teacher and student-centered classrooms. Teachers reported seeing more diverse ways of thinking and an increase in participation. I recommend using the practical measures surveys at the School Success Center as a coaching tool, realizing we need more time to align surveys to the goals of our coaching partnership. In addition, I want to rethink our coaching model, namely our time within the classroom. We need to be more proactive and an integral part of the lesson. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

This work explores the complex cognitive processes students engage in when addressing contextual tasks requiring linear and exponential models. Grounded within Piagetian constructivism and the Knowledge in Pieces (KiP) epistemological perspective (diSessa, 1993, 2018), this empirical study in a clinical setting develops a Microgenetic Learning Analysis (MLA) of the reasoning of 14 students from an Algebra II course. It reveals the critical role of cognitive disequilibrium as an essential cognitive state for conceptual development and the process of reorganizing knowledge systems. The study uncovers the fluctuations in students' reasoning patterns and the significant impact on students' reasoning patterns of task-specific features, such as linguistic cues embedded in contextual tasks. The findings of the study underscore the importance of incorporating cognitive challenges and context-rich tasks into educational practices and advocate for instructional designs that promote metacognitive awareness and reflective thinking. This research contributes to our understanding of cognitive dynamics in learning mathematics and suggests implications for curriculum development, instructional design, and future educational research. Key insights and their far-reaching implications for enhancing mathematics learning are discussed. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

The National Council of Teachers of Mathematics (2000) emphasizes the importance of communication in mathematics and mathematics education. Effective mathematical communication is essential in mathematics instruction, as it is a collaborative and social activity between teachers and students (Moschkovich, 2002; Khairunnisa et al., 2020). This qualitative case study aimed to investigate how elementary school teachers facilitated meaningful mathematical discourse among English learners (ELs) with diverse backgrounds and how they used purposeful questioning strategies to accommodate students with varying levels of linguistic proficiency in culturally and linguistically diverse classrooms. The study also explored teachers' perceptions of supporting young ELs to enhance students' participation, conceptual understanding, and problem-solving abilities in advanced mathematics curricula. The study used socio-cultural theory (Vygotsky, 1978), including classroom observations, fieldnotes, semi-structured interviews, informal interviews, and classroom artifacts. Participants in the study consisted of four teachers from grades one and two who delivered an advanced mathematics curriculum to English learners in the BRIDGE program in a Northeastern state of America. After the data were collected and analyzed, the study discussed the results. The findings of this study revealed that teachers utilized various instructional and communication strategies to cultivate meaningful mathematical discourse among young ELs in their classrooms. They used various questioning techniques to improve students' mathematical skills and foster critical thinking and reasoning among ELs. Teachers recognized their pivotal role in creating a positive and supportive learning environment, particularly in the context of mathematics education for young ELs. They believed that with adequate support, ELs possess the capacity to excel in mathematics learning. They acknowledged their responsibility in facilitating the enhancement of students' proficiency in both mathematics and English. The implications of the findings for mathematics education and the instruction of ELs in culturally and linguistically diverse settings were discussed. This study is significant within the United States, where the population of English learners has dramatically increased, alongside the imperative demand for mathematical instruction and mathematics education reforms, particularly in the current era of accountability. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

Numerous states use research-based mathematics curricula as a teaching tool to enhance mathematics performance outcomes on state assessment scores. Despite implementation of the Eureka curriculum, students at the study site were still struggling to master Algebra 1 skills sufficiently to pass the Louisiana state exam. The aim of this basic qualitative study was to explore strategies teachers employed while implementing the Eureka curriculum to increase student achievement. The study was guided by Vygotsky's zone of proximal development (ZPD) theoretical framework and involved semi-structured interviews with 12 participants who had been teaching Algebra 1 with the Eureka curriculum for at least three years. The research question was focused on instructional strategies teachers used with Eureka to teach Algebra 1 students within their ZPD levels. Data analysis was conducted using open coding for review of themes and patterns. Identified themes included strategies to support Algebra 1 achievement, strategies that hinder student achievement, other factors influencing academic achievement, instructional strategies that were absent from the Eureka curriculum, and the necessity to enhance professional development. A professional development program was developed based on research findings to assist teachers in implementing effective strategies for the Eureka curriculum aimed at increasing students' academic performance in Algebra 1. This professional development initiative has the capacity to bring about positive social change by increasing teachers' facilitation of mathematics instruction with evidence-based strategies that increase student achievement in Algebra 1 concepts and skills. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

A Title I elementary school in New York City faced a challenge in supporting students in Grade 3 to Grade 5 who did not meet state proficiency standards in mathematics. The student body of approximately 300 was 80% Black and Brown students, with 40% of students identified as English language learners or students with disabilities. The assistant principal set out to decrease the percentage of students in testing grades who were not proficient in math by 10% by August 2024. The research is grounded in Gholson et al.'s stance on "Black Excellence." Using an improvement science approach, four primary drivers were identified: (a) improving students' familiarity with different strategies for solving math problems, (b) increasing the quality of student discussions in class, (c) instilling confidence in students and developing a positive attitude towards math, and (d) strengthening targeted support in math in testing grades. The primary change idea was to implement the Illustrative Mathematics curriculum that includes problem-solving strategies, instructional routines, and the use of culturally responsive pedagogy during instruction. Teachers engaged in professional learning supported by coaching and mentoring. The assistant principal engaged in structured leadership reflection using Drago-Severson's Pillars of Adult Learning Theory. The study generated four conclusions: (a) teachers need ongoing professional development, (b) it is critical to continue to engage in culturally responsive pedagogy and math professional learning, (c) it was effective to add an additional math period, and (d) it is important to provide adults with leadership roles and for educational leaders to mentor teachers and staff. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

Students who are affiliated with the United States Armed Forces will transition every two to four years depending on their parents' career. The students who move may have educational gaps in mathematics because of a United States Armed Forces move occurring in the middle of a school year. The problem of practice addresses the educational gaps that former students and teachers perceive occurring related to content knowledge and procedural fluency. The researcher used a mixed methods study to ask close-ended quantitative questions and open-ended qualitative questions. The research was conducted on the web-based platform of Facebook. The results of the research showed that while former students did not perceive mathematical gaps in specific mathematical needs, teachers could see mathematical gaps. This paper will explain the different parts of mathematical language, mathematical discrepancies in curriculum, and the five strands of mathematical learning to frame the research. The research will show the perceptions of former students and current teachers. The paper will discuss the results and recommendations for schools in both a military-affiliated community and a Department of Defense Education Activity [DoDEA] school. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

For the first time in 32 years, the national average scale score in mathematics dropped by seven points across the country in grades four and eight, according to the latest results of the National Assessment on Educational Progress (NAEP). The 2022 results in mathematics were staggering, in which "math performance fell for the first time in the history of the long-term trend assessments since its first administration in 1990 (Socol, 2022). This is an urgent reminder that education leaders must double down on and fully fund efforts to accelerate student learning" (Socol, 2022). For this Doctoral Capstone in School System Leadership, two researchers worked collectively on a Problem of Practice (PoP) related to mathematics and the challenges in student achievement. The PoP statement, in alignment with the persistent downward trend in Algebra I performance, states: "LMSD students are not meaningfully engaged in the Algebra I instructional classroom, resulting in a decrease of proficiency on state and district assessments". The researchers sought to answer two research questions: 1) Does the use of a student Algebra I Data-driven Protocol have an impact on teacher practice in engaging students in dialogue about Algebra I assessment data? 2) What are the teacher perceptions about the fidelity and use of a student Algebra I Data-driven Protocol? The researchers proposed the implementation of one change idea; the collaborative creation and implementation of a student data-driven protocol in a subset of Algebra I classrooms. The researchers tested the change idea with three Algebra I teachers in their classrooms within LMSD. The intention was to examine a particular theory of improvement: "if students are active participants in reviewing their own data from district-administered assessments, then they would gain a better understanding of Algebra I content." This exploratory research study utilized the Improvement Science Plan Do Study Act (PDSA) approach and the incorporation of a change idea (Algebra I Data-driven Protocol), intended to improve one aspect of teacher practice, greater preparedness in data literacy. This study found that even though at the beginning of the study, each of the three teachers felt that they were very comfortable reviewing data on their own and reviewing it with their students, all three teachers stated they felt even more comfortable in doing so after the study had concluded. This conclusion provided evidence for the researchers that the Aim Statement, "Teachers in select Algebra I classes will engage all students in a structured data participation activity, which will result in routine data discourse that was able to be documented as an outcome." Each participating teacher saw the need and benefit of incorporating this into their instructional practice on a regular basis and strengthening their data literacy. Five next steps were identified as a result: 1) the researchers will discuss these findings with the secondary mathematics curriculum office and propose the addition of a larger pilot group before adding the data protocol to the Algebra I curriculum, 2) the researchers will advocate for more innovative strategies to engage students in the Algebra I classroom to be added to current curriculum and instruction, 3) revise the protocol to ensure its inclusion as a differentiated strategy to use with a variety of student groups from various assessment types, 4) continue to conduct further large-scale studies in which the data protocol is utilized in other mathematics classrooms in other select middle and high school classrooms through an organized pilot over the span of an entire school year, and 5) devise a plan for how to measure student achievement over time with incorporation of the data protocol in piloted mathematics classrooms in order to revisit the original PoP and Aim statement. The plan of action for future development of the findings will include steps to measure student achievement data at incremental points throughout the school year to determine effectiveness of the protocol. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]