Popular culture has had a great deal of impact on our social, cultural, and political worlds; it is portrayed through different mediums, in different forms, and connects the world to ideas, beliefs, and different perspectives. Though this dissertation is part of a larger body of work that examines the complex relationship between popular culture and mathematical identity, this study takes a different perspective by examining it through the lens of mathematical Internet memes. This study was conducted with 31 secondary school participants and used a two-tiered approach (in-depth focus groups and an individual meme activity) at each of the five school sites visited around New York City. Multiple sources of data were used to reveal that students are receiving messages about mathematics from memes in popular culture. In particular, participants described six core themes from the meme inventory: (1) stereotypical views of mathematics; (2) mathematics is too complicated; (3) no effort should be needed in mathematics; (4) mathematics is useless; (5) mathematics is not fun; and (6) sense of accomplishment from mathematics. Participants were also given free rein to create hypothetical mathematics memes. Findings demonstrate that not only are memes being used to depict mathematical stereotypes, thereby reinforcing negative messages, but also support social media practices (liking, commenting, sharing, and creating) that reify negative messages about mathematics with little to no resistance from opposing perspectives. In general, participants described mathematical memes in a specific manner that demonstrates them having influence over students’ mathematical identity but not entirely on the way one may think. Future research implications include explorations of the “new” online mathematical space students are utilizing; to wit, what makes these specific memes go viral? What are common misconceptions? Are commenters learning from their mistakes and other answer responses? Implications for practice include the creation of formal spaces within classrooms and communities for students to debrief their thoughts and sentiments about mathematics, as well as informal opportunities for educators, students, and community members to engage positively about mathematics: because without these interventions the messages found in memes, whether positive or negative, are potentially legitimized through popular culture’s presentations. Moreover, the results of this study also show that students are unaware of the processes and proficiencies of mathematical learning. More specifically, teachers and others must help students understand knowledge is not transmitted by copying notes or that teaching strategies need to account for students being apprehensive to ask questions in a mathematics classroom. Memes can also be used to explore mathematics content, through error analysis and explanation of concepts.

As the high failure rate in developmental mathematics remains a national concern (Bonham et al., 2011), community colleges have begun experimenting with alternative delivery and design for remedial mathematics sequences. One approach was to implement mathematical literacy in their program, focusing on quantitative reasoning. Mathematical Literacy is an individual’s ability to formulate situations and reason mathematically, employ mathematical tools, concepts and procedures as well as to explain, apply and evaluate mathematical results (OECD, 2017). The intent of this study was to observe and evaluate learner attitudes regarding mathematics in a community college mathematical literacy course. Two groups of students from two different courses were part of the study; one group was in a mathematical literacy course and another group in an elementary algebra course. To measure students’ growth in self-confidence and in the perceived value and usefulness of mathematics, quantitative data were collected with an anonymous pre- and post-mathematics attitudes survey from the mathematical literacy course and the elementary algebra course. In addition, qualitative data were gathered with an open-ended question administered to participants in the mathematical literacy sections during the last week of the semester to offer richer insights into the findings from the attitude survey. Findings from the quantitative data revealed statistically significant effects for participants in the mathematical literacy course compared to their counterparts in the elementary algebra course in the area of attitudes regarding the perceived value and usefulness of mathematics, real-world problems, working in groups, as well as using computers in mathematics courses. Qualitative data were aligned with the findings from the quantitative data and indicated participants’ positive views on working in groups, the usefulness of the mathematical literacy course, and improvement of their attitudes regarding mathematics thanks to the course. The study suggested further research to improve our understandings of mathematical literacy and its impact.

This study examined mathematics self-efficacy and the characteristics of flow in the context of performing mathematical tasks.  In particular, it explored the subjective experiences of 113 undergraduate students enrolled in a developmental mathematics course while they were independently solving certain mathematical problems.  This study supplemented the literature on the role of self-efficacy as a mediator of the effect of the challenge/skill ratio on flow by applying it to the context of mathematical problem solving. This study also expanded the discussion on how findings may indicate a direction for further research on mathematics anxiety.   Additionally, the relationship between mathematics self-efficacy and flow-like experiences as measured by the Flow Short Scale was considered.

本研究透過分析四十多份數學史教學實證研究，發現過往的研究較少以了解數學歷史演變及發展作為研究內容、亦鮮有對學生的數學觀進行分析。為了填補這些研究上的缺口，本研究從了解演變及發展的角度出發，在設計函數的課程時，以歷史角度及學重演法則，由接觸巴比倫列表，到不連續函數，探討在學習過程中加入數學史怎樣影響學生的數學觀，包括數學趣味、數學人性化量表、數學演變、對數學的看法。 / 本研究於一所中學內進行，以兩班數學成績相近的中四學生為測試對象，一班是實驗組，一班是參照組。實驗組使用的教材由研究者設計出來，參照組則使用教科書。 / 透過認知測試、問卷調查、訪談、概念圖、教師日誌等量化、質化的研究方法，探討是次在教學上使用數學史教學怎樣影響學生的數學觀及老師對是套教材的建議，例如：數學史如何影響學生的數學認知層面、又如何影響學生的數學態度、老師使用這套教材時的困難、老師認為是次數學史教學與平常的教學有何不同、任教老師有否對數學史觀感上的改變、老師會否把數學史在高中教學上使用等。 / 是次研究發現，數學史對不同數學能力學生產生不同層次的效用。在選取數學史材料時，需要注意學生的數學能力及興趣，教學時應作出適切的調整，才能讓不同數學能力的學生之數學觀獲得不同層次的擴展。 / This study, with an analysis of over 40 empirical researches about the history of mathematics teaching, discovered that only a few studies conducted research about the evolution and development of history of mathematics and they seldom analysed students’ mathematical beliefs. In order to fill the gap, this study is aimed to design the topic of function through the perspective of the evolution and development, namely from the Babylonian tables to discontinuous function. It also seeks to explore how that affects students' mathematical beliefs including math fun, math humane scale, mathematical evolution, and students’ views of mathematics. / The study was conducted among two classes of F.4 students who have the similar mathematics abilities in a local secondary school. One is the experimental group and another one is the reference group. The teaching materials developed by the researcher were used in the experimental group while the textbooks were used in the reference group. / Through cognitive tests, questionnaires, interviews, concept maps and teacher journals, the way in which the history of mathematics affects students’ mathematical beliefs is explored .The subsequent analysis of the data attempts to answer the following questions: How the history of mathematics affects students' mathematical cognitive level? How history of mathematics affects students' mathematics attitudes? What difficulties the teacher suffers when using this teaching material? Are there any differences between the normal teaching and history of mathematics teaching? Are there any changes in teacher’s mathematical belief? Is it appropriate to conduct history of mathematics teaching in senior form? / This study discovers that history of mathematics has different effects on students of various mathematical abilities. When selecting the material of history of mathematics, stakeholders need to pay attention to students’ mathematics abilities and interests as well as make appropriate adjustments to teaching, so that students of different mathematical ability canobtain different levels of expansion on their mathematical beliefs. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / 張慧珊. / Parallel title from added title page. / Thesis (Ed.D.) Chinese University of Hong Kong, 2014. / Includes bibliographical references (leaves 134-143). / Abstracts in English and Chinese. / Zhang Huishan.

The prevalence rate of autism spectrum disorder (ASD) among school aged children in the US has increased exponentially, compared to estimates from the year 2000. Increased numbers of elementary students with ASD are spending 80% or more of the school day in general education settings, which may pose challenges for both veteran and beginning elementary teachers. Furthermore, there are more rigorous mathematics and science standards that beginning teachers will be responsible for providing instruction to all students, including those with ASD. The transition of mathematics and science standards impacts both elementary teachers and special education teachers because many professional teaching organizations feel both types of instructors should have the proper knowledge in these subject areas for effective instruction. However, there is evidence that both special education and elementary education teachers may not feel efficacious to teach this content. Established and novel survey instruments were administered to a sample of 39 senior pre-service teachers majoring in special education and elementary education, to obtain data related to their field teaching experiences, personal experience interacting with individuals with ASD, and their reported undergraduate coursework. This study was designed to investigate and compare the self-efficacy beliefs of pre-service teachers majoring in special education and elementary education, which was focused on the following context-specific instructional situations: 1) mathematics instruction; 2) science instruction; 3) mathematics instruction to students with ASD; 4) science instruction to students with ASD; and 5) general instructional considerations for teaching students with ASD. Results of the study indicated elementary education pre-service teachers had lower teaching efficacy beliefs in teaching mathematics and science to students with ASD, compared to their mean teaching efficacy scores for the instruction with mathematics and science in general situations. Furthermore, elementary education majors scored significantly lower on teaching mathematics to students with ASD, teaching science to students with ASD, and teaching students with ASD in general, compared to their special education peers in the obtained sample. The new instruments measuring mathematics and science teaching efficacy were determined to have good reliability. Implications for teacher preparation programs and recommendations for future research are discussed. / A Dissertation submitted to the School of Teacher Education in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester 2019. / February 12, 2019. / Includes bibliographical references. / Mary Frances Hanline, Professor Directing Dissertation; Insu Paek, University Representative; Elizabeth M. Jakubowski, Committee Member; Kelly Whalon, Committee Member.

No description available.

Abstract not available

The purpose of this study was to determine if a teacher's knowledge of a sixth grade student's prior academic performance affects the teacher's grading of the student's work on math papers. This study attempted to isolate the singular characteristic of a teacher's prior knowledge of a student's academic performance as a possible source for grading discrepancies.Four math papers were developed following the guidelines from the Indiana Statewide Test of Educational Progress (ISTEP) in mathematics for sixth grade. Four selected report cards representing high academic performance and four representing low academic performance were attached to the four student papers along with the appropriate answer keys. One-third of the instruments had high academic performance attachments, one-third had low academic performance attachments, and one-third had no academic performance attachments. The instruments were randomly assigned to experienced teachers for grading.The analysis of the data indicated that the mean number grades for high academic performance papers when compared to the control group differed significantly at the .05 level of confidence. The mean of the letter and number grade scores assigned to low academic performance papers compared to the control group did not differ significantly.Based on the findings of this study, conclusions were drawn. Among the conclusions reported were:1. Teachers' grades on the same math papers were remarkably varied.2. Number grades assigned to the same math papers differed significantly for high academic performance.3. The range for letter and number grades for each paper was extremely broad over all independent variables.4. The scoring discrepancies for letter and number grades created a question regarding grading validity.

This article presents the findings of a research which concerned with primary level students’ understanding of arithmetic principles. The objectives of this research were to investigate primary students’ understanding of inverse relation between addition and subtraction and find the possible difficulties when students using inverse relation principle. In this research, “Understanding” involved two aspects: 1. Knowing the fact and here, the fact referred to the knowledge of the inverse relation between addition and subtraction; 2. Ability to identify the situation that related to inverse relation and ability to make use of the inverse relation principle properly in related situation. With this definition, our research not just only concerned the students’ knowledge base, but also concerned how the students analyzed different problems and how they used the principle in different situations. The different situations meant the inverse related questions with different complexity and they were categorized into transparent inverse problems and non-transparent inverse problems. According to the result, students partially understood the inverse principle because they obviously underused the inverse principle in the related problems and they preferred calculating step by step with using column form. We also discovered that their understanding varied among different grades because of their arithmetic experience and the type of the inverse related questions. Basically, students did better in transparent inverse questions than non-transparent inverse questions and higher grade of students had higher level of understanding and they could use the inverse principle properly more often. But, the primary 3 students surprisingly did worse in non-transparent five-term inverse problems than primary 2 students. It may because the students experience and the attitude of analyzing the questions. These findings gave us some insight of teaching arithmetic in primary levels. / published_or_final_version / Education / Master / Master of Education

Not available / text