Developing Learning Trajectory For Enhancing Students’ Relational Thinking

Algebra is part of Mathematics learning in Indonesian curriculum. It takes one half of the teaching hours in senior high school, and one third in junior high school. However, the learning trajectory of Algebra needs to be improved because teachers teach computational thinking by applying paper-and-pencil strategy combining with the concepts-operations-example-drilling approach. Mathematics textbooks do not give enough guidance for teachers to conduct good activities in the classroom to promote algebraic thinking especially in the primary schools. To reach Indonesian Mathematics teaching goals, teachers should develop learning trajectories based on pedagogical and theoretical backgrounds. Teachers need to have knowledge of student’s developmental progressions and understanding of mathematics concepts and students’ thinking. Research shows that teachers’ knowledge of student’s mathematical development is related to their students’ achievement. In fostering a greater emphasis on algebraic thinking, teachers and textbooks need to work more closely together to develop a clearer learning trajectory. Having this algebraic thinking, students developed not only their own character of learning and thinking but also their attitude, attention and discipline. Key Words: Learning Trajectory, Relational Thinkin

TLAD 2010 Proceedings:8th international workshop on teaching, learning and assesment of databases (TLAD)

This is the eighth in the series of highly successful international workshops on the Teaching, Learning and Assessment of Databases (TLAD 2010), which once again is held as a workshop of BNCOD 2010 - the 27th International Information Systems Conference. TLAD 2010 is held on the 28th June at the beautiful Dudhope Castle at the Abertay University, just before BNCOD, and hopes to be just as successful as its predecessors.The teaching of databases is central to all Computing Science, Software Engineering, Information Systems and Information Technology courses, and this year, the workshop aims to continue the tradition of bringing together both database teachers and researchers, in order to share good learning, teaching and assessment practice and experience, and further the growing community amongst database academics. As well as attracting academics from the UK community, the workshop has also been successful in attracting academics from the wider international community, through serving on the programme committee, and attending and presenting papers.This year, the workshop includes an invited talk given by Richard Cooper (of the University of Glasgow) who will present a discussion and some results from the Database Disciplinary Commons which was held in the UK over the academic year. Due to the healthy number of high quality submissions this year, the workshop will also present seven peer reviewed papers, and six refereed poster papers. Of the seven presented papers, three will be presented as full papers and four as short papers. These papers and posters cover a number of themes, including: approaches to teaching databases, e.g. group centered and problem based learning; use of novel case studies, e.g. forensics and XML data; techniques and approaches for improving teaching and student learning processes; assessment techniques, e.g. peer review; methods for improving students abilities to develop database queries and develop E-R diagrams; and e-learning platforms for supporting teaching and learning

TLAD 2010 Proceedings:8th international workshop on teaching, learning and assesment of databases (TLAD)

This is the eighth in the series of highly successful international workshops on the Teaching, Learning and Assessment of Databases (TLAD 2010), which once again is held as a workshop of BNCOD 2010 - the 27th International Information Systems Conference. TLAD 2010 is held on the 28th June at the beautiful Dudhope Castle at the Abertay University, just before BNCOD, and hopes to be just as successful as its predecessors.The teaching of databases is central to all Computing Science, Software Engineering, Information Systems and Information Technology courses, and this year, the workshop aims to continue the tradition of bringing together both database teachers and researchers, in order to share good learning, teaching and assessment practice and experience, and further the growing community amongst database academics. As well as attracting academics from the UK community, the workshop has also been successful in attracting academics from the wider international community, through serving on the programme committee, and attending and presenting papers.This year, the workshop includes an invited talk given by Richard Cooper (of the University of Glasgow) who will present a discussion and some results from the Database Disciplinary Commons which was held in the UK over the academic year. Due to the healthy number of high quality submissions this year, the workshop will also present seven peer reviewed papers, and six refereed poster papers. Of the seven presented papers, three will be presented as full papers and four as short papers. These papers and posters cover a number of themes, including: approaches to teaching databases, e.g. group centered and problem based learning; use of novel case studies, e.g. forensics and XML data; techniques and approaches for improving teaching and student learning processes; assessment techniques, e.g. peer review; methods for improving students abilities to develop database queries and develop E-R diagrams; and e-learning platforms for supporting teaching and learning

The Secondary-Tertiary Transition in Mathematics: What High School Teachers Do to PrepareStudents for Future Success in College-Level Calculus

Quantitative analysis of the Factors Influencing College Success in Mathematics (FICSMath) Survey data indicates that high school mathematics teachers’ abilities to teach for conceptual understanding is a significant and positive predictor of student performance in singlevariable college calculus. To explore these findings further, we gathered and analyzed interview data gained from a representative sample of high school precalculus teachers from across the U.S., identified by their students as requiring high levels of conceptual understanding (n=13). Seventeen themes were identified and then combined into five overarching phenomenological themes. These overarching themes suggest that teachers who teach for high conceptual understanding (a) support relational understanding during problem solving, (b) require students to learn how to study to build on prior knowledge and learn from mistakes, (c) use mathematical language and ask critical questions to support learning, (d) focus on content knowledge necessary to make connections, and (e) use technology to support learning concepts but limit calculator use. Comparison of these results to quantitative findings further illuminate that intentional development of disciplinary knowledge, cognition, and language are noteworthy points of intersection for teachers and researchers alike

A study of the impact of instructional approach on community college students’ problem solving and metacognitive abilities in the developmental mathematics course, Introductory Algebra

The purpose of this quasi-experimental study was to examine the cognitive, metacognitive, affective and instructional constructs that influence students’ problem solving development in a community college Introductory Algebra course. The study addressed the lack of success that developmental mathematics students in a community college have in the Introductory Algebra course and in subsequent curriculum mathematics courses. Research suggests that the prevalent procedural-oriented instructional methodology used in most mathematics classrooms may be contributing to the lack of student success. The community college students (N = 140) in this study were enrolled in an Introductory Algebra course. The study investigated the relationships among the constructs self-regulation, students’ problem solving development, and instructional methods used in the Introductory Algebra course. A correlational design established the quantitative relationships among the constructs. The aim of this study was to heighten the awareness of both the cognitive and non-cognitive aspects of adult student learning, as well as, the importance of attending to the students’ conceptual understanding of mathematics

A strategy for the modularization of courseware

In order to enable courseware reuse, learning platforms nowadays require the materials to be decomposed into small independent learning units. When trying to fulfill this need, authors face the problem of not knowing how to determine suitable learning objects in their content. What is the appropriate size of one such object? The rather general and abstract definitions for learning objects found in the literature are not very helpful for answering this question. What authors need is an operational definition, which can be directly applied to the learning materials. This paper proposes such a set of formal yet practical definitions by describing learning objects along their contents and resource type and shows how these definitions are used by our platform, SCORE

Equal or Not? An Exploration of Eighth-Grade Students\u27 Experience of Algebra

Over the past two decades, a considerable amount of algebra instruction nationwide has shifted from high school to middle school. In Georgia, all eighth-grade students have been required to take a course that is equivalent to about 80 percent of a traditional Algebra 1 course. The purpose of this qualitative study was to explore how a selected group of eighth-grade students in a suburban Georgia middle school experience algebra within the eighth grade mathematics curriculum. A qualitative research design was used to investigate students’ perceptions of algebra, the strategies employed by teachers to teach algebra, students’ difficulties with algebra, and students’ prior experiences with mathematics. Constructivism provided the theoretical framework for the study. As a theory of active knowing and learning, constructivism is a primary theoretical perspective on learning mathematics (Ernest, 1997). Purposeful sampling was used to select six eighth-grade participants for the study. Specifically, intensity sampling was used to identify students who had difficulty with algebra to a high, but not extreme, extent (Gall, Gall, & Borg, 2007). Data collection methods included student profiles, individual and focus group interviews, think-aloud interviews, and document analysis. Data were analyzed through the constant comparative method. Findings from this study indicate that the participants perceive algebra as being too difficult for eighth grade, especially in terms of the pace of instruction. While the participants indicated that it was important for all students to learn algebra, they noted that differentiated instructional strategies are necessary. Data from this study, however, reveal that teachers continue to rely on traditional teaching methods such as lecture and note taking. Participants further noted a benefit from cooperative learning strategies, as well as support and encouragement from teachers. It was also evident from the data that students are relying on memorization of rules or steps to solve algebra problems, rather than developing an understanding of the concepts. In addition, the participants reported feeling unprepared for the algebra they experienced in eighth grade, based on their previous math classes. These findings indicate opportunities for improving students’ experience of algebra in two major areas: curriculum and pedagogy

AFRICAN AMERICAN ADOLESCENTS’ PERCEPTIONS OF THEIR LEARNING, INSTRUCTIONAL, AND RELATIONAL EXPERIENCES

This study was conducted to examine African American adolescents’ perceptions of their learning, instructional, and relational experiences to provide additional insight into how to eliminate the achievement gap. Research investigating the pedagogical experiences of African American adolescents’ is limited. A review of the literature suggested that the theories of pedagogy, culture, and motivation might inform our understanding of their achievement. A multiple-case design and methodological triangulation procedures were used to collect data from a stratified purposive sample of 12 African American eighth-grade students from an urban school district. The sample consisted of four high, four average, and four low achievers. Students’ perceptions were assessed using (a) the Patterns of Adaptive Learning Scales; (b) semi-structured interview questions; and (c) questions related to focus group scenarios. Interpretational analysis was used to identify categories to describe students’ perceptions. Within-case analyses were used to document the students’ voices, and cross-case analyses were used to generate findings for high, average, and low achievement subgroups. The following major categories emerged: achievement goals, instructional preferences, academic press, affect-care and humor, and collaboration. The results of this study related to learning suggested that African American adolescents’ achievement goals (e.g., mastery or performance) are related to their achievement levels. High achievers had mastery goals; average achievers had mastery and performance goals; and low achievers were characterized by performance goals. All African American adolescents preferred communalism (group work) to promote understanding. The results of the study related to instruction suggested that high and average achievers perceived that their teachers communicated mastery goals in the classroom (e.g., goals focused on effort and understanding), and preferred instructional methods that promoted understanding. All high, average, and low- achieving students preferred diverse instructional methods. The results of the study suggested that high and average achievers perceived that their teachers pressed them to understand. The students also perceived that their teachers cared. High, average, and low achievers responded that humor, and collaboration were important. Additional research is needed with the low achievement subgroup to understand the attitude-achievement paradox they exhibited, and their preferred instructional and relational experiences. To capture the African American adolescents’ school experiences more effectively, the use of observations and student voice as methodologies is recommended

BEYOND THE DREAM: IMPROVING COLLEGE-READINESS OF UNDERPREPARED COMMUNITY COLLEGE STUDENTS

The majority of the nation’s first-year college students are not prepared to assume postsecondary level studies. Many are diverted to developmental education programs and most never attain postsecondary credentials. Educational reform is on the national agenda and challenges community colleges to address the growing lack of postsecondary achievement. The purpose of this instrumental multi-case study was to explore and analyze reformative strategies that effectively address college-readiness and achievement of underprepared community college students. A qualitative methodology was employed in analyzing strategies implemented at community colleges to improve college-readiness. A criterion-based selection process identified six community colleges recognized by the Achieving the Dream organization as Leader Colleges in improving student success and located within systems with statewide educational policy reform. In addition, purposeful sampling was used to design a focus group of field experts to examine effective strategies and best practice criteria. Data were collected via semi-structured interviews with Core Team Leaders who led implementation of reformative strategies at the six colleges. Collected demographic survey-data offered context and pertinent document reviews and focus group data contributed to the triangulation of evidence. The interviews yielded insight into 18 strategies designed to improve college-readiness. Findings include descriptions, evidence of impact, factors that supported effectiveness, perceived potential for wide-scale implementation, and recommended best practices. Cross-case analyses offered aggregated comparative analysis and a disaggregated examination of ten common strategies. Composite analyses revealed seven themes that underscore common purposes of the strategies and factors that improve effective implementation. Three common core purposes among the effective strategies include instructional reform, student engagement, and transition to college. Four thematic elements that support effective implementation of strategies include college culture, evidence of effectiveness, integrated systems, and committed leadership. A Relational Paradigm is offered that describes the multidimensional interplay between the core purposes of the strategies and the contextual factors that influence effective implementation. The Paradigm can be used to guide adaptation of strategies to fit unique college cultures. Implications for community colleges to improve college-readiness include the need for strong leadership with system-wide collaborations to create new instructional and organizational models that support student transition, engagement, and learning