Pre-Service Teachers’ Mathematics Language and Reflection in the Context of an Early Childhood Mathematics Methods Course

Thesis (Ph.D.)--University of Washington, 2016-06

Learning mathematics in a classroom community of inquiry

This article considers the question of what specific actions a teacher might take to create a culture of inquiry in a secondary school mathematics classroom. Sociocultural theories of learning provide the framework for examining teaching and learning practices in a single classroom over a two-year period. The notion of the zone of proximal development (ZPD) is invoked as a fundamental framework for explaining learning as increasing participation in a community of practice characterized by mathematical inquiry. The analysis draws on classroom observation and interviews with students and the teacher to show how the teacher established norms and practices that emphasized mathematical sense-making and justification of ideas and arguments and to illustrate the learning practices that students developed in response to these expectations.

Understanding technology integration in secondary mathematics: Theorising the role of the teacher

Previous research on computers and graphics calculators in mathematics education has examined effects on curriculum content and students’ mathematical achievement and attitudes while less attention has been given to the relationship between technology use and issues of pedagogy, in particular the impact on teachers’ professional learning in specific classroom and school environments. This observation is critical in the current context of educational policy making, where it is assumed – often incorrectly – that supplying schools with hardware and software will increase teachers’ use of technology and encourage more innovative teaching approaches. This paper reports on a research program that aimed to develop better understanding of how and under what conditions Australian secondary school mathematics teachers learn to effectively integrate technology into their practice. The research adapted Valsiner’s concepts of the Zone of Proximal Development, Zone of Free Movement and Zone of Promoted Action to devise a theoretical framework for analysing relationships between factors influencing teachers’ use of technology in mathematics classrooms. This paper illustrates how the framework may be used by analysing case studies of a novice teacher and an experienced teacher in different school settings.

Comparison of Linear Functions in Middle Grades Textbooks from Singapore and the United States

Many U.S. students do not perform well on mathematics assessments with respect to algebra topics such as linear functions, a building-block for other functions. Poor achievement of U.S. middle school students in this topic is a problem. U.S. eighth graders have had average mathematics scores on international comparison tests such as Third International Mathematics Science Study, later known as Trends in Mathematics and Science Study, (TIMSS)-1995, -99, -03, while Singapore students have had highest average scores. U.S. eighth grade average mathematics scores improved on TIMMS-2007 and held steady onTIMMS-2011. Results from national assessments, PISA 2009 and 2012 and National Assessment of Educational Progress of 2007, 2009, and 2013, showed a lack of proficiency in algebra. Results of curriculum studies involving nations in TIMSS suggest that elementary textbooks in high-scoring countries were different than elementary textbooks and middle grades texts were different with respect to general features in the U.S. The purpose of this study was to compare treatments of linear functions in Singapore and U.S. middle grades mathematics textbooks. Results revealed features currently in textbooks. Findings should be valuable to constituencies who wish to improve U.S. mathematics achievement. Portions of eight Singapore and nine U.S. middle school student texts pertaining to linear functions were compared with respect to 22 features in three categories: (a) background features, (b) general features of problems, and (c) specific characterizations of problem practices, problem-solving competency types, and transfer of representation. Features were coded using a codebook developed by the researcher. Tallies and percentages were reported. Welch's t-tests and chi-square tests were used, respectively, to determine whether texts differed significantly for the features and if codes were independent of country. U.S. and Singapore textbooks differed in page appearance and number of pages, problems, and images. Texts were similar in problem appearance. Differences in problems related to assessment of conceptual learning. U.S. texts contained more problems requiring (a) use of definitions, (b) single computation, (c) interpreting, and (d) multiple responses. These differences may stem from cultural differences seen in attitudes toward education. Future studies should focus on density of page, spiral approach, and multiple response problems.

THE EFFECT OF PURPOSEFUL MATHEMATICS DISCOURSE IN THE CLASSROOM ON STUDENTS’ MATHEMATICS LANGUAGE IN THE CONTEXT OF PROBLEM SOLVING

This study examines how one secondary school teacher’s use of purposeful oral mathematics language impacted her students’ language use and overall communication in written solutions while working with word problems in a grade nine academic mathematics class. Mathematics is often described as a distinct language. As with all languages, students must develop a sense for oral language before developing social practices such as listening, respecting others ideas, and writing. Effective writing is often seen by students that have strong oral language skills. Classroom observations, teacher and student interviews, and collected student work served as evidence to demonstrate the nature of both the teacher’s and the students’ use of oral mathematical language in the classroom, as well as the effect the discourse and language use had on students’ individual written solutions while working on word problems. Inductive coding for themes revealed that the teacher’s purposeful use of oral mathematical language had a positive impact on students’ written solutions. The teacher’s development of a mathematical discourse community created a space for the students to explore mathematical language and concepts that facilitated a deeper level of conceptual understanding of the learned material. The teacher’s oral language appeared to transfer into students written work albeit not with the same complexity of use of the teacher’s oral expression of the mathematical register. Students that learn mathematical language and concepts better appear to have a growth mindset, feel they have ownership over their learning, use reorganizational strategies, and help develop a discourse community.

Mathematically Able but Yet Underachieving in School Mathematics

Teacher observation has shown that some pupils achieve very high on the Kangaroo Competition test (KC) but very low on the Swedish National test in Mathematics (SNM). This study will investigate the number of pupils who have high achievement scores on the KC (top 10%) but low achievement scores on the SNM (bottom 50%). Individual results on the SNM given in grade 6 (age 12) will be compared to results on the KC given in grade 7; concerning approximately 700 individuals. Results will give an example of the quantity of mathematically able pupils who underachieve in School Mathematics in Sweden. Data interpretation will connect this study to international research concerning mathematical abilities and mathematical achievement among mathematically able pupils.

Biliteracy effects on phonological awareness, oral language proficiency and reading skills in Taiwanese Mandarin-English bilingual children

The present study examined the effect of learning to read a heritage language on Taiwanese Mandarin-English bilingual children’s Chinese and English phonological awareness, Chinese and English oral language proficiency, and English reading skills. Participants were 40 Taiwanese Mandarin-English bilingual children and 20 English monolingual children in the U.S. Based on their performance on a Chinese character reading test, the bilingual participants were divided into two groups: the Chinese Beginning Reader and Chinese Nonreader groups. A single child categorized as a Chinese Advanced Reader also participated. Children received phonological awareness tasks, produced oral narrative samples from a wordless picture book, and took standardized English reading subtests. The bilingual participants received measures in both English and Chinese, whereas English monolingual children received only English measures. Additional demographic information was collected from a language background survey filled out by parents. Results of two MANOVAs indicated that the Chinese Beginning Reader group outperformed the Chinese Nonreader and English Monolingual groups on some phonological awareness measures and the English nonword reading test. In an oral narrative production task in English, the English Monolingual group produced a greater total number of words (TNW) and more different words (NDW) than the Chinese Nonreader group. Multiple regression analyses were conducted to determine whether bilingual children’s Chinese character reading ability would still account for a unique amount of variance in certain outcome variables, independent of nonverbal IQ and other potential demographic or performance variables and to clarify the direction of causality for bilingual children’s performance in the three domains. These results suggested that learning to read in a heritage language directly or indirectly enhances bilingual children’s ability in phonological awareness and certain English reading skills. It also appears that greater oral language proficiency in Chinese promotes early reading in the heritage language. Advanced heritage reading may produce even larger gains. Practical implications of learning a heritage language in the U.S. are discussed.

The influence of initial teacher training in future teachers' perceptions about mathematics teaching and learning

ICEMST 2014 INTERNATIONAL CONFERENCE ON EDUCATION IN MATHEMATICS, SCIENCE & TECHNOLOGY PROCEEDING BOOK (pp.865-869). Disponível em http://www.2014.icemst.com/

Gender issues in elementary mathematics teaching materials: a comparative study between China and Australia

International Association for the Evaluation of Educational Achievement (IEA) cross-national studies (FIMS, SIMS and TIMSS) show that gender differences in mathematical achievements and attitudes have decreased considerably over thirty years (Hanna, 2000), however, mathematics is still historically stereotyped as a male domain with crucial evidence supporting this belief (Forgasz, Leder, & Kloosterman, 2009). Previous research showed that gender differences in mathematics participation,performance and achievement existed widely in the majority of English speaking countries, specifically favouring boys (Forgasz, 1992; Hyde, Fennema, & Lamon, 1990; Tiedemann, 2000). Hyde, Lindberg, Linn, Ellis and Williams (2008) pointed out that the stereotype that females lack mathematical ability persists and is widely held by parents and teachers.Mathematics teaching materials play an important role in mathematics teaching and learning. The contents within mathematical teaching materials are rational, and deliver both explicit and implicit information. The explicit information refers to mathematics knowledge that students can learn from textbooks, while the latter one, also named as hidden curriculum, contains social and cultural messages. Hidden curriculum is a side effect of education. It has deep and long-term influences on students’ construction of math-gender stereotype that impact their future mathematicallearning (Zhang & Zhou, 2008). Therefore, this study will investigate Chinese andAustralian elementary mathematics teaching materials to explore the messages of gender equity and inequity delivered through hidden curriculum including names, images and problem-solving contexts. Based on the findings, practical implications concerning the promotion of equitable gender environments within elementary mathematics teaching materials from a cross-cultural perspective will be discussed.

Knowledge and writing in school mathematics : a communicational approach

This thesis is about young students’ writing in school mathematics and the ways in which this writing is designed, interpreted and understood. Students’ communication can act as a source from which teachers can make inferences regarding students’ mathematical knowledge and understanding. In mathematics education previous research indicates that teachers assume that the process of interpreting and judging students’ writing is unproblematic. The relationship between what students’ write, and what they know or understand, is theoretical as well as empirical. In an era of increased focus on assessment and measurement in education it is necessary for teachers to know more about the relationship between communication and achievement. To add to this knowledge, the thesis has adopted a broad approach, and the thesis consists of four studies. The aim of these studies is to reach a deep understanding of writing in school mathematics. Such an understanding is dependent on examining different aspects of writing. The four studies together examine how the concept of communication is described in authoritative texts, how students’ writing is viewed by teachers and how students make use of different communicational resources in their writing. The results of the four studies indicate that students’ writing is more complex than is acknowledged by teachers and authoritative texts in mathematics education. Results point to a sophistication in students’ approach to the merging of the two functions of writing, writing for oneself and writing for others. Results also suggest that students attend, to various extents, to questions regarding how, what and for whom they are writing in school mathematics. The relationship between writing and achievement is dependent on students’ ability to have their writing reflect their knowledge and on teachers’ thorough knowledge of the different features of writing and their awareness of its complexity. From a communicational perspective the ability to communicate [in writing] in mathematics can and should be distinguished from other mathematical abilities. By acknowledging that mathematical communication integrates mathematical language and natural language, teachers have an opportunity to turn writing in mathematics into an object of learning. This offers teachers the potential to add to their assessment literacy and offers students the potential to develop their communicational ability in order to write in a way that better reflects their mathematical knowledge.

Tools for enhancing oral proficiency and cultural understanding in teaching Arabic online to non-native speakers

One of the main challenges learners of Arabic as a foreign language face in Australia is the lack of opportunities to practice the language with native speakers of Arabic outside the classroom boundaries to enhance their language skills in general and their oral proficiency in particular. Learners have so little exposure to Arabic outside the classroom. This restriction in L2 exposure in the formal academic framework is due to the limited face-to-face learning time and, more significantly, is compounded by lack of exposure to the language’s authentic use settings. Students are often isolated from the target language’s authentic discourse communities and native speakers. This situation is exacerbated for Cloud (online) students studying in relative isolation. All of these factors make developing communicative oral fluency in Modern Standard Arabic (MSA) more difficult and challenging for many learners, particularly for Cloud learners. Deakin University is the only university in Australia that offers Arabic in both Campus and Cloud modes of delivery. This paper discusses an innovative approach used at Deakin University to enable online learners of Arabic to practice their developing skills by listening, practicing, and experiencing directly how the language is used outside the classroom boundaries. In addition to providing Cloud learners with an Arabic online environment rich with interactive opportunities to practice the language, it was also necessary to provide the learners with tools such as the virtual classrooms, chat rooms, discussion forums and social media language partner programs, to practice their oral fluency and enrich their learning experience.

Constructive development of the solutions of linear equations in introductory ordinary differential equations

The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.

Integrating Engineering Experiences within the Elementary Mathematics Curriculum

Engineering education for elementary school students is a new and increasingly important domain of research by mathematics, science, technology, and engineering educators. Recent research has raised questions about the context of engineering problems that are meaningful, engaging, and inspiring for young students. In the present study an environmental engineering activity was implemented in two classes of 11-year-old students in Cyprus. The problem required students to use the data to develop a procedure for selecting among alternative countries from which to buy water. Students created a range of models that adequately solved the problem although not all models took into account all of the data provided. The models varied in the number of problem factors taken into consideration and also in the different approaches adopted in dealing with the problem factors. At least two groups of students integrated into their models the environmental aspect of the problem (energy consumption, water pollution) and further refined their models. Results provide evidence that engineering model-eliciting activities can be successfully integrated in the elementary mathematics curriculum. These activities provide rich opportunities for students to deal with engineering contexts and to apply their learning in mathematics and science to solving real-world engineering problems.

Introducing Engineering Education in the Middle School

This paper first describes a new three-year, longitudinal project that is implementing engineering education in three middle schools in Australia (grade levels 7-9). This important domain is untapped in Australia. Hence, as a starting point, we conducted a context analysis to help situate engineering education in a school system. We report on this analysis with respect to findings from one of two literature-based surveys that gathered middle-school student responses in mathematics (n=172) and science (n=166) towards understanding their dispositions for engineering education. ANOVA indicated gender differences for 3 out of 23 items in both mathematics and science. In addition, the majority of students agreed or strongly agreed with 17 of the 23 survey items, however, there were some differences between mathematics and science. We conclude the paper with some recommendations for establishing engineering education in schools, including the development of partnerships among engineering and education faculties, school systems, and industry to develop contemporary engineering resources to support school-level mathematics, science, and technology.

Integrating engineering education within the elementary and middle school mathematics curriculum

Many nations are experiencing a decline in the number of graduating engineers, an overall poor preparedness for engineering studies in tertiary institutions, and a lack of diversity in the field. Given the increasing importance of mathematics, science, engineering, and technology in our world, it is imperative that we foster an interest and drive to participate in engineering from an early age. This discussion paper argues for the integration of engineering education within the elementary and middle school mathematics curricula. In doing so, we offer a definition of engineering education and address its core goals; consider some perceptions of engineering and engineering education held by teachers and students; and offer one approach to promoting engineering education within the elementary and middle school mathematics curriculum, namely through mathematical modeling.