The development of a semantic model for the interpretation of mathematics including the use of technology

The semantic model developed in this research was in response to the difficulty a group of mathematics learners had with conventional mathematical language and their interpretation of mathematical constructs. In order to develop the model ideas from linguistics, psycholinguistics, cognitive psychology, formal languages and natural language processing were investigated. This investigation led to the identification of four main processes: the parsing process, syntactic processing, semantic processing and conceptual processing. The model showed the complex interdependency between these four processes and provided a theoretical framework in which the behaviour of the mathematics learner could be analysed. The model was then extended to include the use of technological artefacts into the learning process. To facilitate this aspect of the research, the theory of instrumentation was incorporated into the semantic model. The conclusion of this research was that although the cognitive processes were interdependent, they could develop at different rates until mastery of a topic was achieved. It also found that the introduction of a technological artefact into the learning environment introduced another layer of complexity, both in terms of the learning process and the underlying relationship between the four cognitive processes.

Undergraduate Students' Experiences of Their Mathematical Identity

This research study explored how undergraduate mathematics students perceive themselves as capable mathematics learners and whether gender differences exist in the undergraduates students' perceptions. The research was framed by three approaches of understanding identity: self-efficacy, environment, and four faces of learner's identity. A mixed methods approach to the study was used where data were collected from interviews and an online questionnaire. Data analysis revealed that undergraduate mathematics students' perceptions of their mathematical identity as capable mathematics learners are influenced by their perceptions of their experiences such as: (a) perceptions of having previous knowledge of the course, (b) being able teach others and others understand it, (c) being recognized by their professors, (d) contributing and fitting in, (e) having opportunities to interact with their peers, and (f) being able to fit in with their image of a capable mathematics learner.

Teaching Mathematics in English to Swedish Speaking Students : A systematic review of strategies for teaching mathematics to second language learners

The Swedish government has authorised the teaching of mathematics in English to Swedish speaking students. Much of that teaching is performed by foreign trained native English speaking teachers lacking training in second language learners. This systematic review summarises international studies from the last ten years that deal with the teaching of mathematics to second language learners. The review shows that second language students working in a bilingual environment achieve higher rates of content and language knowledge than learners in a monolingual environment. This study also summarises some of the teacher practices that are effective for teaching mathematics in English to second language learners.

An investigation of mathematics and science instruction in English and Spanish for English language learners

The contextual demands of language in content area are difficult for ELLS. Content in the native language furthers students' academic development and native language skills, while they are learning English. Content in English integrates pedagogical strategies for English acquisition with subject area instruction. The following models of curriculum content are provided in most Miami Dade County Public Schools: (a) mathematics instruction in the native language with science instruction in English or (b) science instruction in the native language with mathematics instruction in English. The purpose of this study was to investigate which model of instruction is more contextually supportive for mathematics and science achievement. ^ A pretest and posttest, nonequivalent group design was used with 94 fifth grade ELLs who received instruction in curriculum model (a) or (b). This allowed for statistical analysis that detected a difference in the means of .5 standard deviations with a power of .80 at the .05 level of significance. Pretreatment and post-treatment assessments of mathematics, reading, and science achievement were obtained through the administration of Aprenda-Segunda Edición and the Florida Comprehensive Achievement Test. ^ The results indicated that students receiving mathematics in English and Science in Spanish scored higher on achievement tests in both Mathematics and Science than the students who received Mathematics in Spanish and Science in English. In addition, the mean score of students on the FCAT mathematics examination was higher than their mean score on the FCAT science examination regardless of the language of instruction. ^

Developing Young Learners’ Logical/Deductive Thinking Skills and Second Language Skills through a CLIL approach

Trabalho de Projecto apresentado para cumprimento dos requisitos necessários à obtenção do grau de Mestre em Teaching English as a Second / Foreign Language.

Early Childhood Mathematics Education: Research, Curriculum and Educational Practice

This article reviews data obtained through research into early childhood mathematics education in Spain. It analyses the current curricular directions in mathematics education with early learners. It also provides an overview of mathematical practices in early childhood education classrooms to analyse the commonalities and differences between research, curriculum and educational practice. A review of the research presented at SEIEM symposia from 1997 until 2012 demonstrates: a) very little research has been done, a trend that is repeated in other areas, such as the JCR-Social Sciences Edition or the PME; b) the first steps have been taken to create a more and more cohesive body of research, although until now there has not been enough data to outline the curricular directions; and c) some discrepancies still exist between the mathematical practices in early childhood education classrooms and the official guidelines

Teaching Mathematics in English to Swedish Speaking Students : The Use of Second Language Teaching Practices in the Teaching of Mathematics in English to Swedish Speaking Students in Lower Secondary School

Over 20,000 Swedish lower high school students are currently learning mathematics in English but little research has been conducted in this area. This study looks into the question of how much second language learner training teachers teaching mathematics in English to Swedish speaking students have acquired and how many of those teachers are using effective teaching practices for second language learners. The study confirms earlier findings that report few teachers receive training in second language learning but indicates that some of the teaching practices shown to be effective with second language learners are being used in some Swedish schools

Bad Medicine: Homework or Headache? Responsibility and Accountability for Middle Level Mathematics Students

In this action research study of my 5th grade mathematics class, I investigated the issue of homework and its relationship with students and parents. I made some interesting observations and discovered that the majority of students and parents felt that the math homework that was given was fairly easy, yet issues of incomplete assignments and failing homework quizzes were notorious for some individuals. Comments were also made to make homework even easier and have shortened assignments despite the already indicated ease of the work. As a result of this research, I plan to look more closely at the history and development of homework, as well as the psychological implications and “hereditary” issues involving homework, which I believe are passed from one generation of learners to the next. My intent is to continue to study this phenomenon in future school years, trying to develop methods of instilling successful, intrinsic motivational skills to aid students in their homework endeavors. Finally, I will take a close inventory of my own beliefs and understandings toward homework: What is the purpose of having students do work away from the classroom, and how can homework serve as a proactive service for all who are involved?

The Role of Manipulatives in the Eighth Grade Mathematics Classroom

In this action research study of my classroom of eighth grade mathematics, I investigated the use of manipulatives and its impact on student attitude and understanding. I discovered that overall, students enjoy using manipulatives, not necessarily for the benefit of learning, but because it actively engages them in each lesson. I also found that students did perform better on exams when students were asked to solve problems using manipulatives in place of formal written representations of situations. In the course of this investigation, I also uncovered that student attitude toward mathematics improved when greater manipulative use was infused into the lessons. Students felt more confident that they understood the material, which translated into a better attitude regarding math class. As a result of this research, I plan to find ways to implement manipulatives in my teaching on a more regular basis. I intend to create lessons with manipulatives that will engage both hands and minds for the learners.

Supporting Whole-Class Collaborative Inquiry in a Secondary Mathematics Classroom

Recent mathematics education reform efforts call for the instantiation of mathematics classroom environments where students have opportunities to reason and construct their understandings as part of a community of learners. Despite some successes, traditional models of instruction still dominate the educational landscape. This limited success can be attributed, in part, to an underdeveloped understanding of the roles teachers must enact to successfully organize and participate in collaborative classroom practices. Towards this end, an in-depth longitudinal case study of a collaborative high school mathematics classroom was undertaken guided by the following two questions: What roles do these collaborative practices require of teacher and students? How does the community’s capacity to engage in collaborative practices develop over time? The analyses produced two conceptual models: one of the teacher’s role, along with specific instructional strategies the teacher used to organize a collaborative learning environment, and the second of the process by which the class’s capacity to participate in collaborative inquiry practices developed over time.

Use of Start Pages for Building a Mashup Personal Learning Environment to Support Self-Organized Learners

The paper explores the functionalities of eight start pages and considers their usefulness when used as a mashable platform for deployment of personal learning environments (PLE) for self-organized learners. The Web 2.0 effects and eLearning 2.0 strategies are examined from the point of view of how they influence the methods of gathering and capturing data, information and knowledge, and the learning process. Mashup technology is studied in order to see what kind of components can be used in PLE realization. A model of a PLE for self-organized learners is developed and it is used to prototype a personal learning and research environment in the start pages Netvibes, Pageflakes and iGoogle.

English Language Learners: A Correlational Study of the Relationship Between A Proficiency Level Assessment and End of Course Test Scores at one Georgia High School

Understanding the language of one’s cultural environment is important for effective communication and function. As such, students entering U.S. schools from foreign countries are given access to English to Speakers of Other Languages (ESOL) programs and they are referred to as English Language Learner (ELL) students. This dissertation examined the correlation of ELL ACCESS Composite Performance Level (CPL) score to the End of Course tests (EOCTs) and the Georgia High School Graduation Tests (GHSGTs) in the four content courses (language arts, mathematics, science, and social studies). A premise of this study was that English language proficiency is critical in meeting or exceeding state and county assessment standards. A quantitative descriptive research design was conducted using Cross-sectional archival data from a secondary source. There were 148 participants from school years 2011-2012 to 2013- 2014 from Grades 9-12. A Pearson product moment correlation was run to assess the relationship between the ACCESS CPL (independent variable) and the EOCT scores and the GHSGT scores (dependent variables). The findings showed that there was a positive correlation between ACCESS CPL scores and the EOCT scores where language arts showed a strong positive correlation and mathematics showed a positive weak correlation. Also, there was a positive correlation between ACCESS CPL scores and GHSGT scores where language arts showed a weak positive correlation. The results of this study indicated that that there is a relationship between the stated variables, ACCESS CPL, EOCT and GHSGT. Also, the results of this study showed that there were positive correlations at varying degrees for each grade levels. While the null hypothesis for Research Question 1 and Research Question 2 were rejected, there was a slight relationship between the variables.

Number of options in a movement sequence affects learners' behavior in a self-controlled practice condition

Self controlling practice implies a process of decision making which suggests that the options in a self controlled practice condition could affect learners The number of task components with no fixed position in a movement sequence may affect the (Nay learners self control their practice A 200 cm coincident timing track with 90 light emitting diodes (LEDs)-the first and the last LEDs being the warning and the target lights respectively was set so that the apparent speed of the light along the track was 1 33 m/sec Participants were required to touch six sensors sequentially the last one coincidently with the lighting of the tar get light (timing task) Group 1 (n=55) had only one constraint and were instructed to touch the sensors in any order except for the last sensor which had to be the one positioned close to the target light Group 2 (n=53) had three constraints the first two and the last sensor to be touched Both groups practiced the task until timing error was less than 30 msec on three consecutive trials There were no statistically significant differences between groups in the number of trials needed to reach the performance criterion but (a) participants in Group 2 created fewer sequences corn pared to Group 1 and (b) were more likely to use the same sequence throughout the learning process The number of options for a movement sequence affected the way learners self-controlled their practice but had no effect on the amount of practice to reach criterion performance.

Task Complexity and Variation in L2 Learner’s Oral Discourse

There are many factors which affect the L2 learner’s performance at the levels of phonology, morphology and syntax. Consequently when L2 learners attempt to communicate in the target language, their language production will show systematic variability across the above mentioned linguistic domains. This variation can be attributed to some factors such as interlocutors, topic familiarity, prior knowledge, task condition, planning time and tasks types. This paper reports the results of an on going research investigating the issue of variability attributed to the task type. It is hypothesized that the particular type of task learners are required to perform will result in variation in their performance. Results of the statistical analyses of this study investigating the issue of variation in the performance of twenty L2 learners at the English department of Tabriz University provided evidence in support of the hypothesis that performance of L2 learners show systematic variability attributed to task.

Subject/Object Asymmetry in the Comprehension of English Relative Clauses by Japanese Learners of English

While a number of studies have shown that object-extracted relative clauses are more difficult to understand than subject-extracted counterparts for second language (L2) English learners (e.g., Izumi, 2003), less is known about why this is the case and how they process these complex sentences. This exploratory study examines the potential applicability of Gibson's (1998, 2000) Syntactic Prediction Locality Theory (SPLT), a theory proposed to predict first language (L1) processing difficulty, to L2 processing and considers whether the theory might also account for the processing difficulties of subject- and object-extracted relative clauses encountered by L2 learners. Results of a self-paced reading time experiment from 15 Japanese learners of English are mainly consistent with the reading time profile predicted by the SPLT and thus suggest that the L1 processing theory might also be able to account for L2 processing difficulty.