Lesser has extensively written songs and lyrics for **mathematics** teaching (Lesser, 2014a; 2014b; 2015). He states that songs with lyrics can be a valuable vehicle for learning and engagement; and are popular amongst students of all ages. Furthermore, Lesser identifies the potential for lyrics to act as pedagogical tools in courses from higher education by discussing how they can enhance students’ learning in college-level **mathematics** and statistics classes. In this work I examine a special case of **arts**-integrated teaching in **mathematics** by investigating a piece of mathematical lyrics and related music entitled: “e is a magic number”. Through lyrics and music, the particular song under investigation was designed to inspire and explain some aspects of the number e (Moar, 1994). For this case study I offer backgrounding on: what inspired me to create the song; the educational design principles drawn upon; the technology employed to create the song; and how users interacted with the song after it was uploaded to YouTube.

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Integrated STEAM education in South Korea is an approach to preparing a quality STEM workforce and literate citizens for highly technology-based society by integrating science, technology, engineering, **arts** and **mathematics** in education. It is named differ- ently from STEM due to its emphasis on **arts** (fine **arts**, language **arts**, liberal **arts**, and physical **arts**) as an important component of integration. While the STEAM reform movement is in alignment with STEM reform in other countries, its added component, i.e., **arts**, was inspired by the concurrent social discourse on education for creativity and a well-rounded citizen in the twenty-first century (Baik et al., 2012). Also, the na- tional concern for students’ low confidence and interest in learning science regardless of high achievement (Organization for Economic Co-operation and Development, 2013) factored in promoting the integration of **arts** with STEM education for affective goals. A similar idea now can be found elsewhere (e.g., Henriksen, 2014; The STEAM journal, 2013). Since then, the South Korean government has allocated a substantial educational budget for promoting STEAM through various routes. With the idea of creating innovative thinkers by integrating ideas from STEAM fields, i.e., all subjects in schools, the term, ‘ convergence education ’ has been coined and used to refer to the in- tegrated STEAM education initiative. Convergence refers to creating new ideas or products formed by interdisciplinary or multidisciplinary thinking. Thus, the main goal of integrated STEAM education is to develop ‘talents in convergence’.

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Students may enroll in Bachelor of **Arts** in **Mathematics**, Bachelor of Science in **Mathematics** degree, Bachelor of **Arts** in **Mathematics** Edu- cation, or Bachelor of Science in **Mathematics** Education degrees. In addition, students can select **Mathematics** as an emphasis in the Inte- grated Studies Bachelor of Art or Bachelor of Science programs. The DSU **Mathematics** Department also offers all coursework necessary to obtain a Utah Secondary Education Math Endorsement. The Utah State Office of Education Educator Quality & Licensing information for Secondary **Mathematics** Endorsements can be found here: http:// www.schools.utah.gov/cert/Endorsements-ECE-License.aspx .

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high school. During the 2007-2008 academic year only 11 states met their ELL accountability endeavors under the No Child Left Behind Act (Zehr, 2011). A Texas study reported that 80% of ELLs did not graduate from high school (Echevarria & Short, 2010). Research states that ELLs that attend middle and high schools have become long term ELL. Their individual learning needs required for success in school are largely ignored, therefore creating an underperforming group of ELL students (Olsen, 2010). While studies of the schooling experience of emergent bilingual secondary students have been generated (Suárez-Orozco, Suárez-Orozco, & Todorova, 2008), research about these students remains limited overall, as studies of emergent bilinguals typically focus on elementary students. As a result, secondary emergent bilinguals have been deemed 'overlooked and underserved' both in research as well as in educational practices (Short & Fitzsimmons, 2007; Rance-Roney, 2009). Especially at the secondary level, wide disparities are apparent between Limited English Proficient students and others. For instance, these students are disproportionately represented in national rates of dropout, grade retention, and course failure (Menken, 2008). Research also reveals that a large number of ELLs reach an intermediate level of English proficiency after a few years, and then cease to make additional gains, meaning that they can engage in conversational English but falter in their ability to apply grammar, structures and specialized vocabularies of English that are required for grade level coursework. Therefore, these students continue to underperform on state tests in English language **arts**, **mathematics** and science (Clark, 2009).

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Table 7 illustrates the frequency and percentage distribution of the respondents according to present occupation. Aside from the five (5) or 23% of the most recent graduates of the BS **Mathematics** programs, the rest of the alumni of the course are employed in specific places of occupation as teachers which comprised four (4) or 18% of the participants, private company employees which numbered to twelve (12) or 55% of the respondents and one (1) 0r 4% being employees of the public sector. This only proves that the employability status of the BS **Mathematics** program of the College of **Arts** and Sciences of Batangas State University for AY 2014 – 2018 is commendable bearing the truth that most of the graduates of the program are active members of the workforce.

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With adoption of the Common Core State Standards for **Mathematics**, elementary students will learn fewer math concepts in each grade, but will study them in greater depth and detail in order to develop stronger foundational understandings. Starting in elementary school, these standards will provide greater focus, coherence, and rigor in **mathematics** learning than students have typically experienced in the past. Sometimes a concept will be taught at an earlier grade level. To help parents, teachers, school boards, legislators and other policy makers better understand the impact of the Common Core and the new multi-state assessments being developed, the Center for K-12 Assessment & Performance Management at ETS assembled a team of elementary level math experts to explore the ramifications of the new standards by looking closely at three tasks that illustrate important topics and features of the Common Core. The participants were:

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b For the Teachers Attitude to the Individualised Programme-Questionnaire The difference between the pre and post test scores of student 'Attitude towards mathematics' Y2 - Y1 for each [r]

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SL.4 ( FOCUS) Report on a topic or text, tell a story, or recount an experience in an organized manner, using appropriate facts and relevant descriptive details to support main[r]

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Paul Klee's Form Generation Paul elements; tone, texture, words such as and expression to visual surface area that stretches Sketchbook Sibyl define visual create a simple shape or confi[r]

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Do mathematics majors and nonmathematics majors differ significantly in their attitudes toward value of theories, value of applications, enjoyment of theories and enjoyment of applicatio[r]

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HYPOTHESIS 2 At all stages, there was no significant difference between mathematics majors and non-mathematics majors in their attitudes toward value of theories, value of applications, [r]

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The purpose of this study was to examine the predictive validity of the 2013 Oregon Kindergarten Assessment (OKA) early literacy and early math scores on 2016-2017 third-grade Smarter Balanced Assessment (SBAC) English language **arts**/literacy (ELA) and math scores in the Shepherd Public Schools (pseudonym). This study used a multiple linear regression model to examine the relationship between OKA scores and SBAC scores for the cohort of students who were kindergarteners in the Shepherd Public Schools during 2013-14 and third-graders in 2016- 2017. In addition, this study used a hierarchical regression model to examine the extent to which OKA scores interacted with students’ ethnicity, socioeconomic status (SES), English learner (EL) status, classification for special education services, and gender to predict their SBAC achievement scores. This chapter details the results of the data analyses. It includes information on the demographics of the sample, descriptive statistics, results of the analysis of missing data, results of the testing of assumptions associated with linear regression and hierarchical regression, and results of the linear and hierarchical regressions utilized to address the research questions. Sample Demographics

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Creative teaching is influenced by various components. The first component is related to basic pedagogical skills such as lesson planning, classroom management, communication, and evaluation. The second component refers to the domain specific expertise, creative techniques (Girl, 1998). This study utilizes techniques like “analogy, stories, origami, tangram, drawing, visualization, and brainstorming” within the framework of Teaching Math Creatively. Starko (2005) draws attention to creative activities like “drawing, thinking flexibly, trying multiple paths, looking at problems in more than one way, asking questions, and making hypotheses” which can be used in math classes. Fisher (1995) proposes techniques like stories, drawing, and brainstorming which can be used during the creative process. According to Fisher, stories can provide a rich stimulus for divergent thinking (Fisher, 1987; cited in Fisher, 1995). Drawing is a wonderful way of making thinking visible. A child may not find it easy to express thinking in words but can always attempt to express it visually and find it easier to understand something in visual terms. Brainstorming is a useful strategy for generating ideas with children of all ages. Brainstorming helps children to reveal and share the fund of knowledge they bring to the learning situation (Fisher, 1995). Further, Zimmerman (1999; cited in Meissner, 2006) defines creative problem solving in four steps as finding analogies, double representations (visual-perceptual/formal-logical), multiple classifications, and reducing complexity. Hirsh (2010) challenges traditional **mathematics** instruction and proposes creative practices like **arts** to be utilized in **mathematics** classes. These practices include drawing pictures to solve problems, presenting information visually, visual story problems, visual representation of math concepts, and spatial strategies (charts, tessellations, geometrical grids, graphs, logic puzzles, flip charts, origami, information tables, and games) (Wilson 2009; cited in Hirsh, 2010).

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The Mississippi State Board of Education, the Mississippi Department of Education, the Mississippi School for the **Arts**, the Mississippi School for the Blind, the Mississippi School for the Deaf, and the Mississippi School for **Mathematics** and Science do not discriminate on the basis of race, sex, color, religion, national origin, age, or disability in the provision of educational programs and services or employment opportunities and benefits. The following office has been designated to handle inquiries and complaints regarding the non-discrimination policies of the above mentioned entities:

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Standard Four: Knowledge of Content : The elementary teacher is knowledgeable, in addition to literacy and **mathematics** in the following content areas: civics, economics, foreign language, geography, history, science, music, visual **arts**, and physical education. Middle school and secondary content teachers shall be knowledgeable in literacy and **mathematics** and expert in their content endorsement area(s).

graduates). Of those in employment, the most common jobs included marketing, business, customer service and human resources. Overall, opportunities for this cohort were a little more concentrated in London than for other fields of study – 31.5% of **arts** and humanities graduates in graduate-level work started their careers in London, compared to 21.5% for graduates as a whole. Other popular locations included Manchester, Surrey, Birmingham, Kent, Hampshire, Leeds, Oxford, Bristol and Glasgow.

The study of art enhances visual perception, develops critical thinking and an understanding of complex processes. Yet art degrees aren’t just for art careers. Visual art studies complements liberal **arts** studies; any student may minor in Visual **Arts**. Visual **arts** majors may double major or minor in other subjects. The study of visual art contributes to a well-rounded, humanist education, defining a lifelong appreciation of beauty and the **arts**. It is of great relevance and enrichment to a variety of disciplines, including but not limited to communications, history, literature, education, theatrical studies, business studies and the sciences. Our visual **arts** alumni work in a variety of fields outside the **arts** including business, human resources, and teaching non-art subjects.

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Now, what is **mathematics**? Roundtable discussion of seven Fields Medallists in 1991 came up with the conclusion that there is no definition that can cover the wide aspects of **mathematics** (Casacuberta & Castellet 1991). In that book, the editors have remarked that **mathematics** is what mathematicians say that **mathematics** is. This remark reflects how difficult to construct an axiomatic system of **mathematics**. However, we can easily distinguish it from the other sciences particularly those included in normal science (Kuhn 1996). If, for example, biology, chemistry and physics are about the study of matter, **mathematics** has nothing to do with matter except when it is considered as a language. A detailed explanation is given by Alain Connes, a Fields Medallist in 1982 (see Casacuberta & Castellet 1991). He pointed out that **mathematics** has two aspects which make it difficult to explain and different from other sciences. The first aspect is that **mathematics** is, in many ways, used as a language in other sciences. More precisely, **mathematics** is reduced to a language in the sense that, if scientists use **mathematics** (say, in modelling), they do not use **mathematics** as mathematicians do.

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The use of context in **mathematics** test items is now accepted practice in many forms of national assessment in the UK, with, on occasion, as many as 50% of questions in a particular set of papers involving some mention of a context external to **mathematics**. Yet that the use of context is not entirely straightforward is borne out by research. For example, Silver, Shapiro & Deutsch (1993) researched the now famous ‘bus’ item, reporting how children, when asked to work out how many 36- seater buses would be required to transport 1128 soldiers, included fractions of a bus in their answers. Similarly, Verschaffel, De Corte & Lasure (1994) found that children can fail to apply realistic considerations to their solutions of word problems. In the UK, Cooper and Dunne (2000) studied National Curriculum test items for **mathematics** at Key Stage 2 (when pupils are 11) and, while they found a similar range of ‘misinterpretations’ as Silver et al and Verschaffel et al, they, interestingly, carried the analysis a stage further by looking at responses in relation to family social class. What they concluded was that the way children applied mathematical procedures was subject to class bias, implying, for Cooper and Dunne, that National Curriculum test items are unreliable. An alternative explanation might be that the test items analysed were flawed in the sense that the degree of realism brought to each item by those taking the tests invited a range of responses that were not taken sufficiently into account by the assessment mark schemes. This raises the issue of the nature and degree of ‘realism’ presented in assessment items and what influence this might have on the range of responses obtained. While this existing research seems relevant to the situation in A-level **mathematics**, in surveying the literature, no equivalent research appears to have been carried out in relation to the use of context in post-16 examinations.

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Both infinity and nothingness cause problems for algebra, often leading to what are known as “indeterminate forms,” expressions whose limits require further analysis to calculate (for example, how do you solve the equation: ∞ − ∞ = X?). If we are to take infinity and nothingness seriously in climate politics we must look beyond algebra to other branches of **mathematics**. One place we might start, which would allow us to maintain the threads with Adorno and Benjamin, is set theory. Set theory became popular in philosophy with Alain Badiou’s 1988 Being and Event. But it played a role, many decades prior, in the development of Benjamin’s theory of historical time. During his university studies, Benjamin had a keen interest in **mathematics**. In Bern, he attended Henoch Berliner’s seminars on number theory, one of which he described as “uncanny” (Fenves 2011: 113). Benjamin was also the nephew of prominent mathematician, Arthur Schoenflies, with whom he often met and whose work he would frequently consult. Schoenflies was an early proponent of set theory, describing it as a science that “undertook the division of infinite sets according to their power and showed, in particular, that algebraic numbers form a countable set, whereas the continuum is not countable” (quoted in Fenves 2011: 113). The influence of these ideas on Benjamin is evident in the diaries of his friend, Gershom Scholem. In August 1916, Benjamin began a conversation with Scholem by making a “difficult remark” about historical chronology. In Scholem’s recollection, the remark was that “years are countable, but in contrast to most countables, not numerable” (quoted in Fenves 2011: 256–258). For numerability, Scholem notes, would presuppose exchangeability, “and this applies neither to numbers nor to years: they are in no way exchangeable.”

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