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Title: DEVELOPMENTAL CHANGES OF KNOWLEDGE OF MATHEMATICS FOR TEACHING OVER TIME THROUGH PROFESSIONAL DEVELOPMENT
Creator: Alahmadi, Reham Abdulrahman
Date: 2019
Description: In the past, the knowledge base for effective teaching was measured based on presage variables, methods of teaching, process-product research,...
Show moreIn the past, the knowledge base for effective teaching was measured based on presage variables, methods of teaching, process-product research, competency-based teacher education, and professional decision-making. In addition, teachers’ effectiveness has been measured indirectly using proxy measurement. For example, teachers were assessed based on their performance on certification exams, their course, mathematical courses taken, and various experiences. Furthermore, teachers were measured based on students’ achievement tests, and using a pre-test and post-test model with limited knowledge of their development. This study aims to understand teacher mathematical knowledge for teaching (MKT), its development over time, and how professional development influences their professional knowledge. Twenty middle school teachers (sixth through eighth grade) participated in content-based (algebra) professional development (PD) in Saudi Arabia. The selection pool of teachers targeted in the study is eighth (sixth grade) mathematics teachers that represented a variety of years of experience and PD experience. The results of this study found that teachers positively developed their MKT through the professional development program. In particular, based on the results of the pre-test, teachers had a low level of MKT before they participated in the PD program. Teachers’ developmental steps of their changes over time were captured during the PD via multiple interviews. These interviews revealed within-teacher themes, cross-teacher themes, and factors that impacted teachers’ changes. Furthermore, a paired sample t-test showed that there was a significant difference between the means of pre-test and post-test.
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Title: What student responses do middle school mathematics teachers anticipate for contextualized and decontextualized problems about linear relationships?
Creator: Rupe, Kathryn Mary
Date: 2019
Description: The recent transition to the Common Core State Standards for Mathematics is in line with current initiatives to improve mathematics teaching...
Show moreThe recent transition to the Common Core State Standards for Mathematics is in line with current initiatives to improve mathematics teaching and learning through the emphasis of conceptual understanding and mathematical reasoning. Much research has been done on how to develop conceptual understanding for students in kindergarten through twelfth grade. Stein, Engle, Smith, & Hughes (2008) highlighted the importance of orchestrating productive classroom discussions. They suggest that this goal can be attained through the process of five steps, each depending on the previous step. Teachers must anticipate student responses to a task that will be taught, monitor student thinking as they are engaged in the task, purposefully select students to present based on their choice of representations, sequence those representations in a purposeful way, and then make connections among the representations so that students are able to understand key concepts. The first step in this process, anticipating student responses (ASR), is an area where little research has been done. The literature suggests that teachers that engaged in professional learning related to the practice did so at varying levels (Empson et al., 2017), and could develop those skills over time with explicit feedback (Popovic, Morrissey, & Kartal, 2018). However, research on average middle school mathematics teachers, those that were not enrolled in any professional learning focused on ASR, was absent from the literature. This study aimed to understand middle school mathematics teachers’ anticipation of student responses. A sample of 19 eighth grade math teachers that represented a variety of years of experience and curriculum use (traditional, reform, and teacher-developed) participated in semi-structured interviews and completed four common eighth grade math problems focused on the content of linear relationships and systems. Teachers’ anticipated student strategies were categorized as showing robust, moderate, limited, or lacking evidence of ASR. Based on the results, all of the teachers fit into one of four categories: those that anticipated student responses at (1) consistently high levels, (2) mixed levels, (3) consistently low levels, and (4) inconsistent levels. The results of this study found teachers who anticipated student responses at consistently high levels were experienced (over 10 years of experience), had numerous student-centered professional development experiences, considered their teacher-role as that of a facilitator, and had high expectations for students. They differed with respect to the type of curriculum they used, the certification they held, and the level of detail in their planning practices. Several of the teachers inconsistently anticipated student responses, providing robust and limited evidence for at least one problem. This speaks to the specialized knowledge that teachers have, what Hill and Charalambous (2012a) refer to as local mathematical knowledge for teaching. Among all of the variables considered, curriculum use did not appear to have an impact on teachers’ skills and knowledge related to anticipating student responses, although teachers used their curriculum materials in very different ways. Years of experience, secondary licensure, a student-centered philosophy of teaching, and teachers that described their role as that of a facilitator related to evidence of anticipating student responses. Understanding the variables that may impact teachers’ abilities to anticipate student responses, the first of five steps outlined by Stein et al. (2008), is important for supporting teachers as they orchestrate productive classroom discussions around important concepts.
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Title: THE EFFECT OF INTENTIONAL, PERSISTENT SMALL-GROUP LEARNING ON COLLEGE STUDENT ACHIEVEMENT AND RETENTION IN THE PRE-CALCULUS CLASSROOM
Creator: Peterson, Christy Lee
Date: 2019
Description: Various research studies have established that nearly half of all students who decide to pursuit a math, science, or engineering field change...
Show moreVarious research studies have established that nearly half of all students who decide to pursuit a math, science, or engineering field change their mind and seek a different major. The National Center for Education Statistics shows a decrease in the number of degrees in engineering and related fields from 36,900 degrees in the 2003 – 2004 academic year to 31,800 degrees in 2013 – 2014, a 13.8% decline. Not surprising, a report by the President’s Council of Advisors on Science and Technology in 2012 predicted that the United States workforce would see a deficit of one million college graduates in science, technology, engineering and math over the next decade. This study was designed to help answer the question, Is there a difference in achievement or retention for students participating in intentional, persistent small-group learning compared with randomly assigned small-groups in a college level pre-calculus course? This study compared the pre-calculus achievement scores, course pass rates and retention rates between two types of small-group membership, persistent and random. The study also compared students’ study habits throughout the semester and students’ experiences working in a small-group learning environment. Initial examination of the data showed that students participating in intentional, persistent small-groups had better course pass rates and consistently scored higher on unit exams and the final exam than students who participated in randomly assigned small-groups. The course pass rates for both types of small-group membership were similar to the pass rates for students in all other sections of pre-calculus offered at the college. The retention rate for the two courses was similar. However, when compared to the retention rate for all sections of pre-calculus offered at the college, retention was statistically higher in the two sections utilizing small-groups in this study. Given that retention is one of the challenges for pre-calculus, utilizing small-group learning might be a way to improve student retention in college pre-calculus. There were no significant findings for differences in students’ study skills or students’ experiences working in small-group learning environments. However, it was interesting to see that students in randomly assigned small-groups had stronger agreement on items related to working with multiple peers while students in the intentional, persistent small-groups had stronger agreement on items related to developing relationships. The results indicate there might be value to student achievement in utilizing persistent group membership over randomly assigned group membership or even whole-class lecture. Furthermore, the results of this study indicate that utilizing small-group learning in pre-calculus benefits the student retention rate.
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Title: Identity and Self-Efficacy Among Mathematically Successful African American Single Mothers in Urban Community College Contexts
Creator: Devi, Shavila
Date: 2019
Description: This dissertation is a phenomenological, multi-case study of 13 mathematically successful African American single mothers from two urban...
Show moreThis dissertation is a phenomenological, multi-case study of 13 mathematically successful African American single mothers from two urban community colleges in Chicago. While a number of recent studies have focused on Black girls and women in K-12 and university contexts, the community college context remains understudied despite the presence of large numbers of Black women. Moreover, there has been a tendency in mainstream research contexts to normalize failure, and focus on problematic aspects of being a Black single mother or being a Black mathematics learner. Bringing together considerations of identity (racial, mathematics, single mother) and mathematics self-efficacy, this study will be the first to focus on mathematically successful African American single mothers in the community college context. The following research questions guided the research for this dissertation:1. How do African American single mothers, who return to study mathematics at the community college and are successful in their courses, narrate their identities and life experiences around race, gender, mathematics learning, and being a mother?2. How do these women score on the Mathematics Self-Efficacy Scale (MSES) and what sources of and influences on their self-efficacy are reported by these women via interviews? 3. What other factors (intrapersonal and beyond) do these women report as being particularly salient in their mathematics success?Multiple forms of data–semi-structured interviews, pre-and-post responses to a widely-used mathematics self-efficacy survey, and mathematics artifacts–were collected to address the research questions. A cross-case analysis of the data revealed four themes that emerged across the 13 participants. Within-case analyses of three participants reveals how the themes play out in-depth for these women. The four themes are (1) strong counter-narratives of being a single mother that resisted dominant and deficit-oriented discourses; (2) education as a key tool and resource to manage and mitigate risks associated with single motherhood; (3) multifaceted stories of resilience to achieve success in mathematics and life; and (4) positive, success-oriented mathematics identities and positive math self-efficacy. This study contributes to an emerging success-oriented literature on Black women and mathematics, and a growing research literature on identity in mathematics education. In surfacing how the participants narrate and negotiate race, gender, and class, this dissertation also contributes to an emerging literature on intersectionality in mathematics education. Results from this study can inform community college administrators and faculty in crafting practice and policy to support African American single mothers in mathematics.
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Title: SIMILARITIES AND DIFFERENCES BETWEEN ACTUAL SCIENCE INSTRUCTION ENACTED IN THE HIGH SCHOOL CLASSROOM AND COLLEGE SCIENCE TEACHERS’ PERCEPTIONS OF STUDENTS’ KNOWLEDGE AND ABILITIES NECESSARY FOR ACADEMIC SUCCESS
Creator: Kedvesh, James
Date: 2019
Description: The enacted curriculum and classroom artifacts of a full unit of instruction from three subject areas (biology, chemistry, and physics) at two...
Show moreThe enacted curriculum and classroom artifacts of a full unit of instruction from three subject areas (biology, chemistry, and physics) at two levels of instruction (regular and advanced) were analyzed for the presence and degree of mathematics and critical thinking. These characteristics were selected from a review of the literature on college science faculty’s views of best student preparation. Classes were grouped and compared by subject area and by level of science class. Varying degrees of critical thinking and mathematics were found to be present in the six observed classes, but both characteristics were found in all of the observed units of instruction. Comparisons of the statistical and practical differences found the greatest differences when comparing mathematics by subject area. These differences were not due to within subject area differences. Comparisons found the greatest similarities when comparing critical thinking by level of instruction. It was found that classroom pedagogy was a more important factor than subject area or level of instruction in determining the degree of alignment of classroom instruction with respect to the presence and inclusion of mathematics and critical thinking. Overall, there was a common lack of explicit instruction in both mathematics and critical thinking among all observed units of instruction. These findings support the need for more explicit mathematics and critical thinking instruction within science classes. Also, it is recommended that pre-service and practicing science teachers are prepared with the knowledge and methods of best mathematics instruction to better incorporate these strategies within and alongside their science instruction.
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Title: A MULTIPLE CASE STUDY OF COLLEGE MATHEMATICS INSTRUCTORS’ TECHNOLOGICAL PEDAGOGICAL CONTENT KNOWLEDGE (TPACK) AND ITS RELATIONSHIP TO THE INTEGRATION OF INFORMATION AND COMMUNICATIONS TECHNOLOGY (ICT) IN THEIR TEACHING PRACTICES AND STUDENTS’ LEARNING
Creator: Alhejoj, Kawkab
Date: 2020
Description: This multiple-case study aimed to investigate the following essential aspects of instructors’ ICT integration in higher education: self...
Show moreThis multiple-case study aimed to investigate the following essential aspects of instructors’ ICT integration in higher education: self-reported technological pedagogical content knowledge (TPACK), level of ICT integration, and motivations-challenges to integrate specific ICT tools to teach particular mathematics concepts. Four college math instructors were selected purposefully from four community colleges. The TPACK conceptual framework was adopted through the use of the TPACK-M self-assessment survey to understand the perceived TPACK knowledge of the instructors. The model of Niess et al (2009), which describes the teacher’s level of practical ICT integration in the light of their TPACK, assisted in exploring the way college math instructors used ICT. Data collection involved surveys, semi-structured interviews, and direct classroom observations. Quantitative data was analyzed using descriptive statistics, while Atlas.ti software was applied for qualitative data. The findings showed that the total TPACK-M was rated high, with TPK the lowest among all the constructs. In terms of the ICT integration model, one instructor fitted into the recognizing level, another into the adapting level, and two others into the accepting level. There was a misalignment between the self-reported TPACK knowledge and the in-class level of ICT integration. Instructors need more support in developing practical TPACK abilities via effective PD and activating the “teacher model” to help college math instructors integrate ICT in creative and successful practice. Also, more research in higher education is recommended using a larger sample in the area of designing a TPACK instrument for college math instructors to help capture their perceptions and recognize any gap between what they know and what they do in higher education contexts.
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Title: IMPLEMENTING ASYNCHRONOUS DISCUSSION AS AN INSTRUCTIONAL STRATEGY IN THE DEVELOPMENTAL MATHEMATICS COURSES TO SUPPORT STUDENT LEARNING
Creator: Zenati, Lynda
Date: 2020
Description: Remedial known as developmental coursework are designed to get under-prepared students ready for college. Ninety one percent of colleges offer...
Show moreRemedial known as developmental coursework are designed to get under-prepared students ready for college. Ninety one percent of colleges offer remedial courses in mathematics and English (Seo, 2014). Evidence suggests that traditional teaching methods do not enable all students to engage with the types of academic literacy constitutive to higher education (Lea and Street, 2006). The popularity of online discussion has been made possible through their availability in most LMS which are widely used in higher education (Dahlstrom, Brooks, & Bichsel, 2014). This study aimed at examining the use of asynchronous discussion (AD) as an instructional strategy to help alleviate some of the difficulties developmental math students make in different topics. Participants were 15 students enrolled in Summer, 2019 semester at a Community College. Results showed that students’ performance increased from pretest to posttest for students’ who participated in AD. Comparison was made with two other sections of the same course at the same college taught by two different instructors. Controlling for prior academic ability, results showed a statistically significant difference between students’ performance in the posttest in the section that utilized the AD but not the other two sections. Content analysis of students' posts showed the use of AD at least temporarily corrected students’ misconceptions when they were active and Consistent. Results were mixed for the lurker and the passive students. Moreover, correlation analysis showed no relationship for the frequency of interaction; however, a significant relationship was found for the quality of participation and students’ performance as measured by the final exam. Furthermore; no relationship between the CoI presences and students’ performance. Students’ reflections indicated that students valued the online experience. Benefits were related to students’ engagement and collaborative learning. Obstacles included students’ behavior, timing and the structure of the AD. This may imply that using structured AD may help in building a community of learners. Also, instructor presence and facilitation were necessary to promote deep learning. Future research can build on this finding by replicating the study using a bigger sample size and a longer period to allow students to reflect and discuss any conflict with their peers.
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Title: High School Mathematics Teachers’ Conceptions of Nature of Mathematics (NOM) and How Prior Learning Environments Affect These Conceptions
Creator: Elefteriou, Katherine
Date: 2023
Description: Literature shows that the Nature of Mathematics Knowledge (NOMK) dates back to the era of Plato and Aristotle (Dossey, 1992). It suggests that...
Show moreLiterature shows that the Nature of Mathematics Knowledge (NOMK) dates back to the era of Plato and Aristotle (Dossey, 1992). It suggests that mathematics teachers’ beliefs, views, conceptions, and preferences about NOM influence the way in which they teach mathematics. It is important to understand how these conceptions are formed, which may evolve consciously or unconsciously from their experiences. Teachers’ experiences as students of mathematics, their family, school environment, cultural, and social experiences influence their behavior including their decisions, actions, class organization, learning activities, and students’ achievement (Beswick, 2012; Ernest, 2008; Thompson1984). Yet, there is no NCTM standard on NOM (Gfeller, 1999).The purpose of the present study was to assess high school mathematics teachers’ NOMK conceptions, and to explore how these conceptions have been influenced by their personal and educational experiences as students in learning mathematics. Another objective of this study was to explore whether the teachers’ years of mathematics teaching experience, and their level of education have any influence on their NOMK beliefs. The sample consisted of 52 high school mathematics teachers, who were certified to teach secondary mathematics, and who had at least three years of mathematics teaching experience. Two instruments were used to collect the data, 1) the VNOM D instrument to assess the teachers’ beliefs regarding the NOMK aspects, and 2) the demographics instrument to collect information on the teachers’ demographics, and on their experiences as students of mathematics. Interviews were also used to enhance the findings. Results showed that participants had strong beliefs regarding their NOMK, and that their years of experience, and level of education influenced their NOMK beliefs.
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Title: WHAT IMPACT DO NUMBER TALKS HAVE ON ELEMENTARY CLASSROOM MATHEMATICAL DISCOURSE AND STUDENT AND TEACHER ATTITUDES TOWARD MATHEMATICS?
Creator: Sleezer, Meghan V
Date: 2021
Description: Number Talks, created in the early 1990s by Ruth Parker and Kathy Richardson, have gained popularity in the mathematics education community...
Show moreNumber Talks, created in the early 1990s by Ruth Parker and Kathy Richardson, have gained popularity in the mathematics education community over the past decade with the publication of the book series Number Talks (Parrish, 2010, 2014), and especially since the publication of Making Number Talks Matter (Humphreys & Parker, 2015). All in all, the authors contend Number Talks can bring joy into the classroom (Humphreys and Parker, 2015, p. 6), improving student attitudes about mathematics and ultimately allowing for a more productive disposition. The characteristic that separates Number Talks from other pedagogical tools is the disconnectedness from the rest of the lesson: Number Talks need not build up to or build upon the day’s objective. Thus, what the authors argue is that the activity of Number Talks itself – albeit disconnected from the day’s objective – improves all of the aforementioned skills, regardless of what occurs during the remainder of each class session.Eight teachers from five different Chicago-area private grade schools implemented Number Talks in their 3rd-5th grade classrooms for four to six weeks in the early part of the year 2020. Student attitudes toward mathematics and toward mathematical discourse were assessed by way of survey and classroom observation before and after implementation. Classroom interactions and levels of mathematical discourse during the normal class time (outside of the Number Talk session) were assessed before and during implementation. No significant changes (positive or negative) relating to any measure were found. Teachers noticed that students who enjoyed math before the implementation also enjoyed Number Talks, while students who struggled with math were mostly disenchanted with Number Talks. Future research includes exploring whether tailoring Number Talks to relate to the upcoming lesson improves the positive effects advertised by the authors. Teacher professional development related to ambitious teaching practices (NCTM, 2017) and growth mindset (Boaler, 2016b) may complement the use of Number Talks to result in improved attitudes and discourse.
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Title: Case Study: A Comparison of Pedagogical Content Knowledge Between Coaches and Coaches/Mentees
Creator: Barone, Ana MargaritaSalinas
Date: 2024
Description: This multiple case study dissertation aimed to examine one of the domains of pedagogical content knowledge, knowledge of content and students,...
Show moreThis multiple case study dissertation aimed to examine one of the domains of pedagogical content knowledge, knowledge of content and students, between different types of elementary coaches and between coach and their respective collaborating teachers. It also investigated the impact a coaches’ background experiences have on the dynamic between coaches and teachers and the perceptions' teacher have on the effectiveness of coaching. The theoretical framework used in this qualitative study was Ball, Thames, and Phelps’ (2008) definition of PCK. Data was collected from six coaches–four instructional coaches and two math coaches–and eleven k-5th grade teachers. Data collection involved a survey, LMT assessment, and semi-structured interviews, and a thematic analysis method was conducted. The findings from the cross-case analysis resulted in ten themes, with the majority having multiple categories. One finding to one of the research questions was that there were no differences in knowledge of content and students between mathematics coaches and general instructional coaches, but other areas to further investigate emerged. Another finding was that coaches were either within the same capacity as their respective teachers or had extra knowledge of content and students. Although the majority of the coaches’ knowledge of content and students was at a higher level according to their LMT score, it does not necessarily mean that coaches are working with teachers in improving knowledge of content and students. In addition, more research is recommended in creating a pedagogical content knowledge instrument that is specific for coaches.
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Title: A Limited Case Study: Perspectives of Students, High School Teachers, and College Instructors About Advanced Placement Mathematics Courses
Creator: Joseph, DeJuana V.
Date: 2023
Description: ABSTRACTBackground. The underrepresentation of Black and Latinx students in STEM is highlighted due to structural impediments. Although AP...
Show moreABSTRACTBackground. The underrepresentation of Black and Latinx students in STEM is highlighted due to structural impediments. Although AP mathematics classes are being introduced as a solution, students from underprivileged schools continue to confront challenges. The study project seeks to investigate the obstacles associated with teaching AP mathematics courses in disadvantaged high schools and to gather perspectives from various stakeholders.Methodology. The study employs qualitative one-on-one interviews and an interpretive research paradigm. The sample comprises mathematics faculty, first-year college students, high school AP math teachers, and one high school student. Thematic analysis is used and ethical considerations are taken into account. Limitations include time and resource constraints, a small sample size, and potential inconsistencies in participant responses.Results and Findings. AP mathematics classes may inspire students to continue STEM in college, yet obstacles such as time constraints and knowledge gaps exist. Students' employment choices are influenced by their own interests and abilities. High school math teachers and college professors highlight algebraic skills as crucial for success in college mathematics, particularly in calculus classes.Discussion. The STEM enrollment problem does not only affect minority students; AP math can be a pathway for all kids. Improving AP math readiness for all students is critical for addressing the STEM professional shortage. It is essential to use extra measures to increase student interest in STEM. Strong foundational algebraic knowledge is required for success in higher education, necessitating stakeholders to focus on improving STEM enrollment and completion rates.
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