Supporting A Standards-based Teaching And Learning Environment A Case Study Of An Expert Middle School Mathematics Teacher

Although it has been more than 20 years since the publication of Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989) and 10 years since the second version of standards, Principles and Standards for School Mathematics (NCTM, 2000), the research underlines the lack of essential practices for standards-based teaching (Franke, Kazemi, & Battey, 2007). The literature also emphasizes the importance of planning in standards-based teaching, although few studies focus on the direct planning of the teacher (Kilpatrick, Swafford, & Findell, 2001). The aim of the current study was to conduct a case study to extract the planning and classroom practices of an expert seventh grade mathematics teacher. The extracted practices were interpreted using the teaching-in-context theory which is based on the beliefs, goals, and knowledge of the teacher. The case study was conducted in a design experiment environment where the instructional sequence was revised based on the classroom instruction. The data were collected through different resources including videotapes of classroom sessions, teacher notes, students‟ artifacts, audiotapes of daily teacher interviews, weekly teacher meetings and classroom small groups in five weeks. Transcripts were used to observe the action patterns of the teacher during both planning and classroom practices. By triangulating the data, planning practices were separated into five categories: preparation, reflection, anticipation, assessment, and revision. These practices were interrelated in an environment of collaboration. Classroom practices also were categorized into five groups, namely creating and sustaining social norms, facilitating genuine mathematical discourse, supporting the development of sociomathematical norms, capitalizing on students‟ imagery to create inscriptions and notation, and developing small groups as communities of learners. Similar to the planning practices, these iii were also highly interrelated with social norms playing a key role in application of all other practices. The results showed that the expert teacher used a diverse set of practices with each practice comprised of multiple actions to create and sustain a standards-based environment. The results also indicated that standards-based teaching requires a rich and connected body of knowledge about students, curriculum, content, and literature. It was found that the depth of the teacher‟s knowledge allowed her to develop practices that were consistent with her beliefs and goals. Finally, the planning and classroom practices were found to be highly interrelated. While effective planning practices facilitated the application of standards-based teaching, the classroom teaching practices equipped the teacher with the data necessary to perform effective planning practices

Improving The Quality Of Mathematics Teaching With Effective Planning Practices

Although it has been two decades since National Council of Teachers of Mathematics Standards were published, research underlines the lack of essential practices for quality reform teaching. The literature also emphasizes the importance of planning in reform teaching although few studies focus directly on the planning of the teacher. This study attempts to shed light on teacher planning through a particularistic case study within a design research experiment which was performed to improve the quality of teaching. In particular, this study aims to extract the planning practices of an expert seventh-grade mathematics teacher before and during instruction on integers. The extracted practices were interpreted through the teaching-in-context theory, which uses beliefs, goals, and knowledge as the backbone of the analysis. The results indicate that five core practices underlay the development of effective planning: preparation, reflection, anticipation, assessment, and revision. Each practice included multiple actions performed in an environment of collaboration. © 2013 Copyright Teacher Development

Chaos in hydrology: A case study in Konya Basin, Turkey

Every natural behaviour is non-linear, but not always is chaotic. This paper aims to investigate low dimensional chaotic behaviour of study area: Konya Basin by using non-linear time series techniques with three stages: i) Mutual Information, ii) False Nearest Neighbour ( FNN) algorithm, iii) Stretching Exponential. These techniques calculate the delay time, the embedding dimensions and the maximal positive Lyapunov exponent respectively. The data set consists of daily average flow rates of three stations in Konya Basin through the study period between 1968 and 2014. Analysed data implied that these time series have shown chaos. This information helps catchment manager to forecast future and the extreme flow rates such as droughts and floods

A Proposed Instructional Theory for Integer Addition and Subtraction

This article presents the results of a 7th-grade classroom teaching experiment that supported students' understanding of integer addition and subtraction. The experiment was conducted to test and revise a hypothetical learning trajectory so as to propose a potential instructional theory for integer addition and subtraction. The instructional sequence, which was based on a financial context, was designed using the Realistic Mathematics Education theory. Additionally, an empty, vertical number line (VNL) is posited as a potentially viable model to support students' organizing their addition and subtraction strategies. Particular emphasis is placed on the mathematical practices that were established in this setting. These practices indicate that students can successfully draw on their experiences with assets, debts, and net worths to create meaning for integer addition and subtraction

Dealing with the gray zones in the management of gastric cancer: The consensus statement of the Istanbul Group

The geographical location and differences in tumor biology significantly change the management of gastric cancer. The prevalence of gastric cancer ranks fifth and sixth among men and women, respectively, in Turkey. The international guidelines from the Eastern and Western countries fail to manage a considerable amount of inconclusive issues in the management of gastric cancer. The uncertainties lead to significant heterogeneities in clinical practice, lack of homogeneous data collection, and subsequently, diverse outcomes