Teaching University-Level Mathematics Using Mathematica

This paper considers the use of the computer algebra system Mathematica for teaching university-level mathematics subjects. Outlined are basic Mathematica concepts, connected with different mathematics areas: algebra, linear algebra, geometry, calculus and analysis, complex functions, numerical analysis and scientific computing, probability and statistics. The course “Information technologies in mathematics”, which involves the use of Mathematica, is also presented - discussed are the syllabus, aims, approaches and outcomes.

Achievements and Problems in the In-service Teacher Education in Inquiry Based Style

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2015

An Approach for a more Objective Evaluation of Practical Projects, Used in the Training Process

Well–prepared, adaptive and sustainably developing specialists are an important competitive advantage, but also one of the main challenges for businesses. One option of the education system for creation and development of staff adequate to the needs is the development of pro jects with topics from real economy ("Practical Projects"). The objective assessment is an essential driver and motivator, and is based on a system of well-chosen, well-defined and specific criteria and indicators. An approach to a more objective evaluation of practical projects is finding more objective weights of the criteria. A natural and reasonable approach is the accumulation of opinions of proven experts and subsequent bringing out the weights from the accumulated data. The preparation and conduction of a survey among recognized experts in the field of project-based learning in mathematics, informatics and information technologies is described. The processing of the data accumulated by applying AHP, allowed us to objectively determine weights of evaluation criteria and hence to achieve the desired objectiveness. ACM Computing Classification System (1998): K.3.2.

Causal attributions for success or failure by passing and failing students in College Algebra

Success in mathematics has been identified as a predictor of baccalaureate degree completion. Within the coursework of college mathematics, College Algebra has been identified as a high-risk course due to its low success rates. ^ Research in the field of attribution theory and academic achievement suggests a relationship between a student's attributional style and achievement. Theorists and researchers contend that attributions influence individual reactions to success and failure. They also report that individuals use attributions to explain and justify their performance. Studies in mathematics education identify attribution theory as the theoretical orientation most suited to explain academic performance in mathematics. This study focused on the relationship among a high risk course, low success rates, and attribution by examining the difference in the attributions passing and failing students gave for their performance in College Algebra. ^ The methods for the study included a pilot administration of the Causal Dimension Scale (CDSII) which was used to conduct reliability and principal component analyses. Then, students (n = 410) self-reported their performance on an in-class test and attributed their performance along the dimensions of locus of causality, stability, personal controllability, and external controllability. They also provided open-ended attribution statements to explain the cause of their performance. The quantitative data compared the passing and failing groups and their attributions for performance on a test using One-Way ANOVA and Pearson chi square procedures. The open-ended attribution statements were coded in relation to ability, effort, task difficulty, and luck and compared using a Pearson chi square procedure. ^ The results of the quantitative data comparing passing and failing groups and their attributions along the dimensions measured by the CDSII indicated statistical significance in locus of causality, stability, and personal controllability. The results comparing the open-ended attribution statements indicated statistical significance in the categories of effort and task difficulty. ^

A comparison of content-based and context-based teaching on ninth-grade mathematics achievement

The purpose of this study was to determine if an experimental context-based delivery format for mathematics would be more effective than a traditional model for increasing the performance in mathematics of at-risk students in a public high school of choice, as evidenced by significant gains in achievement on the standards-based Mathematics subtest of the FCAT and final academic grades in Algebra I. The guiding rationale for this approach is captured in the Secretary's Commission on Achieving Necessary Skills (SCANS) report of 1992 that resulted in school-to-work initiatives (United States Department of Labor). Also, the charge for educational reform has been codified at the state level as Educational Accountability Act of 1971 (Florida Statutes, 1995) and at the national level as embodied in the No Child Left Behind Act of 2001. A particular focus of educational reform is low performing, at-risk students. ^ This dissertation explored the effects of a context-based curricular reform designed to enhance the content of Algebra I content utilizing a research design consisting of two delivery models: a traditional content-based course; and, a thematically structured, content-based course. In this case, the thematic element was business education as there are many advocates in career education who assert that this format engages students who are often otherwise disinterested in mathematics in a relevant, SCANS skills setting. The subjects in each supplementary course were ninth grade students who were both low performers in eighth grade mathematics and who had not passed the eighth grade administration of the standards-based FCAT Mathematics subtest. The sample size was limited to two groups of 25 students and two teachers. The site for this study was a public charter school. Student-generated performance data were analyzed using descriptive statistics. ^ Results indicated that contrary to the beliefs held by many, contextual presentation of content did not cause significant gains in either academic performance or test performance for those in the experimental treatment group. Further, results indicated that there was no meaningful difference in performance between the two groups. ^

Algebra I and other predictors of high school dropout

This study investigated the relation of several predictors to high school dropout. The data, composed of records from a cohort of students ( N = 10,100) who entered ninth grade in 2001, were analyzed via logistic regression. The predictor variables were: (a) Algebra I grade, (b) Florida Comprehensive Assessment Test (FCAT) level, (c) language proficiency, (d) gender, (e) race/ethnicity, (f) Exceptional Student Education program membership, and (g) socio-economic status. The criterion was graduation status: graduated or dropped out. Algebra I grades were an important predictor of whether students drop out or graduate; students who failed this course were 4.1 times more likely to drop out than those who passed the course. Other significant predictors of high school dropout were language proficiency, Florida Comprehensive Assessment Test (FCAT) level, gender, and socio-economic status. The main focus of the study was on Algebra I as a predictor, but the study was not designed to discover the specific factors related to or underlying success in this course. Nevertheless, because Algebra I may be considered an important prerequisite for other major facets of the curriculum and because of its high relationship to high school dropout, a recommendation emerging from these findings is that districts address the issue of preventing failure in this course. Adequate support mechanisms for improving retention include addressing the students' readiness for enrolling in mathematics courses as well as curriculum improvements that enhance student readiness through such processes as remediation. Assuring that mathematics instruction is monitored and improved and that remedial programs are in place to facilitate content learning in all subjects for all students, but especially for those having limited English proficiency, are critical educational responsibilities.

Development of a Game-Based Mathematics Curriculum for Preschool

America’s deficiency in mathematics can be benefitted by an emphasis in mathematics from an early age. An effective math curriculum for preschool should consist of the most important aspects of early childhood mathematics, including number writing and identification, one-to-one correspondence, cardinality, number comparison, ordinality, number sequence, and number bonds.

The effects of content-based ESOL instruction on the overall English proficiency of foreign -born college students

This study investigates the effects of content-based ESOL instruction on the overall English proficiency of foreign-born college students. Based on various psychological and social factors which affect second language acquisition, it is suggested that the techniques of content-based instruction, while focusing on subject matter, allow the learners to overcome the language barrier by neutralizing their subconscious defense mechanism, thus attaining greater proficiency.^ Two groups of Miami-Dade Community College ESOL students were chosen as subjects for this study: a control group composed of students from the North and Wolfson campuses, where the ESOL program is based predominantly on structural or structural-functional approach, and an experimental group of Medical Center campus students, where content-based instruction is incorporated into curriculum. Ethnicity, gender, age, and other differences in the population are discussed in the study.^ The students' English Placement Test (EPT) scores were used as covariate, and the scores on Multiple Assessment Programs and Services (MAPS) test as dependent variables. Multivariate analysis of variance (MANOVA) was applied to test significant difference between the means. The results of the analysis of data indicate that there is a consistent difference in the mean performance of the Medical Center campus ESOL students demonstrated by their scores on MAPS. Although neither ethnicity, nor gender of the subjects has affected the outcome, age had a contributing effect. The implications of these findings suggest that content-based instruction facilitates greater overall English proficiency in foreign-born college students. ^

The relationship between the secondary mathematics curriculum, college persistence, and success at an urban community college

According to Venezia, Kirst, and Antonio (2003) and Barth’s 2002 Thinking K16 Ticket to Nowhere report, the disconnect between K-12 and postsecondary education was a contributing factor to high attrition rates. Since mathematics emerged as a primary concern for college readiness, Barth (2002) called for improving student transitions from K-12 to postsecondary institutions through the use of state or local data. The purpose of the present study was to analyze mathematics course-taking patterns of secondary students in a local context and to evaluate high school characteristics in order to explore their relationships with Associate degree attainment or continuous enrollment at an urban community college. Also, this study extended a national study conducted by Clifford Adelman (The Toolbox Revisited, 2006) as it specifically focused on community college students that were not included his study. Furthermore, this study used the theoretical framework that human capital, social capital, and cultural capital influence habitus—an individual’s or a group’s learned inclination to behave within the parameters of the imposed prevailing culture and norms. Specifically, the school embedded culture as it relates to tracking worked as a reproduction tool of ultimate benefit for the privileged group (Oakes, 1994). ^ Using multilevel analysis, this ex post facto study examined non-causal relationships between math course-taking patterns and college persistence of public high school graduates who enrolled at the local community college for up to 6 years. One school-level variable (percent of racial/ethnic minorities) and 7 student-level variables (community college math proportion, remedial math attempts, race, gender, first-year credits earned, socioeconomic status, and summer credits earned) emerged as predictors for college persistence. Study results indicated that students who enter higher education at the community college may have had lower opportunities to learn and therefore needed higher levels of remediation, which was shown to detract students from degree completion. Community college leaders are called to partner with local high schools with high percentages of racial/ethnic minorities to design academic programs aimed at improving the academic preparation of high school students in mathematics and promote student engagement during the first year and summers of college. ^

The efficacy of an interactive computer system for teaching developmental mathematics to college students

Many students are entering colleges and universities in the United States underprepared in mathematics. National statistics indicate that only approximately one-third of students in developmental mathematics courses pass. When underprepared students repeatedly enroll in courses that do not count toward their degree, it costs them money and delays graduation. This study investigated a possible solution to this problem: Whether using a particular computer assisted learning strategy combined with using mastery learning techniques improved the overall performance of students in a developmental mathematics course. Participants received one of three teaching strategies: (a) group A was taught using traditional instruction with mastery learning supplemented with computer assisted instruction, (b) group B was taught using traditional instruction supplemented with computer assisted instruction in the absence of mastery learning and, (c) group C was taught using traditional instruction without mastery learning or computer assisted instruction. Participants were students in MAT1033, a developmental mathematics course at a large public 4-year college. An analysis of covariance using participants' pretest scores as the covariate tested the null hypothesis that there was no significant difference in the adjusted mean final examination scores among the three groups. Group A participants had significantly higher adjusted mean posttest score than did group C participants. A chi-square test tested the null hypothesis that there were no significant differences in the proportions of students who passed MAT1033 among the treatment groups. It was found that there was a significant difference in the proportion of students who passed among all three groups, with those in group A having the highest pass rate and those in group C the lowest. A discriminant factor analysis revealed that time on task correctly predicted the passing status of 89% of the participants. ^ It was concluded that the most efficacious strategy for teaching developmental mathematics was through the use of mastery learning supplemented by computer-assisted instruction. In addition, it was noted that time on task was a strong predictor of academic success over and above the predictive ability of a measure of previous knowledge of mathematics.^

Using blogs to enhance the capacity of mathematical communication in High School

The aim of this investigation is to analyze the use of the blog as an educational resource for the development of the mathematical communication in secondary education. With this aim, four aspects are analyzed: organization of mathematical thinking through communication; communication of mathematical thinking; analysis and evaluation of the strategies and mathematical thought of others; and expression of mathematical ideas using mathematical language. The research was conducted from a qualitative approach on an exploratory level, with the case study method of 4 classrooms of second grade of secondary education in a private school in Lima. The observational technique of 20 publications in the blog of the math class was applied; a study of a focal group with a sample of 9 students with different levels of academic performance; and an interview with the academic coordinator of the school was conducted. The results show that the organization of mathematical thinking through communication is carried out in the blog in a written, graphical and oral way through explanations, schemes and videos. Regarding communication of mathematical thinking, the blog is used to describe concepts, arguments and mathematical procedures with words and examples of the students. The analysis and evaluation of the strategies and mathematical thinking is performed through comments and debates about the publications. It was also noted that the blog does not facilitate the use of mathematical language to express mathematical ideas, since it does not allow direct writing of symbols nor graphic representation.

Correlation between anxiety and academic self-concept in interpreter trainees

This paper focuses on two basic issues: the anxiety-generating nature of the interpreting task and the relevance of interpreter trainees’ academic self-concept. The first has already been acknowledged, although not extensively researched, in several papers, and the second has only been mentioned briefly in interpreting literature. This study seeks to examine the relationship between the anxiety and academic self-concept constructs among interpreter trainees. An adapted version of the Foreign Language Anxiety Scale (Horwitz et al., 1986), the Academic Autoconcept Scale (Schmidt, Messoulam & Molina, 2008) and a background information questionnaire were used to collect data. Students’ t-Test analysis results indicated that female students reported experiencing significantly higher levels of anxiety than male students. No significant gender difference in self-concept levels was found. Correlation analysis results suggested, on the one hand, that younger would-be interpreters suffered from higher anxiety levels and students with higher marks tended to have lower anxiety levels; and, on the other hand, that younger students had lower self-concept levels and higher-ability students held higher self-concept levels. In addition, the results revealed that students with higher anxiety levels tended to have lower self-concept levels. Based on these findings, recommendations for interpreting pedagogy are discussed.

Motivation and Vocabulary Breadth in CLIL and EFL Contexts. Different age, Same Time of Exposure

Numerous studies have found a positive connection between learners’ motivation towards foreign language and foreign language achievement. The present study examines the role of motivation in receptive vocabulary breadth (size) of two groups of Spanish learners of different ages, but all with 734 hours of instruction in English as a Foreign Language (EFL): a CLIL (Content and Language Integrated Learning) group in primary education and a non-CLIL (or EFL) group in secondary education. Most students in both groups were found to be highly motivated. The primary CLIL group slightly overcame the secondary non-CLIL group with respect to the mean general motivation but this is a non-significant difference. The secondary group surpass significantly the primary group in receptive vocabulary size. No relationship between the receptive vocabulary knowledge and general motivation is found in the primary CLIL group. On the other hand, a positive significant connection, although a very small one, is identified for the secondary non-CLIL group. We will discuss on the type of test, the age of students and the type of instruction as variables that could be influencing the results.

The Impact of Global English in Xinjiang, China: Linguistic Capital and Identity Negotiation among the Ethnic Minority and Han Chinese Students

Thesis (Ph.D.)--University of Washington, 2016-08

Assessing the Role of Vocabulary Breadth and Depth in Reading Comprehension: A Quantitative Study of Finnish EFL Learners

In this MA thesis, Finnish learners of English were studied in order to examine the relationship between second language vocabulary size, vocabulary depth, and reading comprehension. In addition, given the well-established connection between vocabulary size and reading comprehension, the second aim of the study was to see whether assessing vocabulary depth could add another dimension in predicting and explaining reading comprehension proficiency. Two groups were studied: the first group consisted of 39 Finnish upper secondary school students (the TOKA group) whereas the second group consisted of 19 university students of English at the University of Turku (the YLI group). Thus, comparisons were made between the results of a less advanced and a very advanced group of English learners, which was the third aim of the study. The participants in both groups filled in a background information form and took three tests: a multiple-choice reading comprehension test, a multiple-choice vocabulary size test, and a test designed to elicit information on learners’ depth of vocabulary knowledge of certain English words. The data were analysed using statistical methods. The results of the study show that the scores on the three tests were positively correlated in both study groups as well as in the two groups together. However, the correlations were higher in the TOKA group and in the two groups in total than in the YLI group. When examining the variance in reading comprehension test scores explained by vocabulary size and vocabulary depth, the figures of explained variance were again higher in the TOKA group and in the two groups in total than in the YLI group. When it comes to the results of the YLI group, vocabulary depth did not indeed seem to add any explained variance into the explanation of reading comprehension test scores. Based on the results of the study, it seems that vocabulary size and depth have a less significant role in the reading comprehension skills of more advanced learners of English. When looking at the less advanced TOKA group, on the other hand, vocabulary size and depth seem to be clear indicators of reading proficiency. In addition, the test results of the YLI group were clearly more uniform than those of the TOKA group. The variance in the test results of the TOKA group was large.