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This research aims to help blind pupils in the fourth grade learn construction geometry (CG). For that purpose, some special geometrical tools were created from Egyptian environmental materials to help blind pupils learn CG. The effectiveness of these tools was measured after being implemented on a sample of blind pupils (N=5) in fourth grade. Some recommendations of the research were included. [ABSTRACT FROM AUTHOR]

Geometric habits of mind include several ways of thinking that can be used in the learning and teaching of geometry as well as the reasoning ability in the process of solving the geometry problem. Based on this framework, revealing students' geometric reasoning process can shed light to researchers and teachers in the selection and design of methods and materials. This study is aimed to investigate the geometric problem-solving processes of elementary school students based on the GHoM. In this qualitative study case study design was adopted. The participants of the study consisted of six elementary school students. In the interviews the students can easily use reasoning with the relationship GHoM in all tasks. Generalizing and investigating invariants habits can be seen in some of the tasks. However balancing exploration and reflection habits were appeared rare when compared to other GHoMs. It can be suggested that to reveal the ways of reasoning of the students, non-routine and open-ended geometry tasks similar to those designed for this research can be utilized in mathematics classes. [ABSTRACT FROM AUTHOR]

The tripartite function of faculty members in higher education includes instruction, research, and extension. Built-in into this function was to produce of instructional materials for students' and teachers' consumption. The objective of this study was to evaluate computergenerated instructional materials (CGIMs) used in college geometry courses. To attain this, the researchers used descriptive-evaluative design. The respondents were the twenty (20) teachers teaching Geometry and Curriculum Development. The instruments used were the worktext and multimedia efficiency rating scale, usefulness, accuracy, completeness, and appropriateness rating scale. The result shows that in terms of physical attributes, objectives, content, exercises, and evaluation, the worktext has a "very high" efficiency level while in terms of content, physical attributes, and visual clarity the multimedia presentation achieved a "very high" efficiency level. It was also found that in terms of usefulness, accuracy, completeness, and appropriateness, the developed CGIM has attained a "very high" level. This means that the developed CGIM achieved an excellent level of instructional material development. CGIM is recommended as a way to improve the achievement, mental habits, and problem-solving skills of Geometry students. [ABSTRACT FROM AUTHOR]

İn this study; we examined the influence of concept cartoons on academic achievement in the 5th grade geometry class. Quantitave research method is used in the research. Randomized paired control-group pretest-posttest design from experimental research methods was used in the research. Experimental study was carried out with 24 fifth grade students studying in Aşağı Göndelen Secondary School in Ereğli Country of Konya Province. Experts have examined the materials of Geometry Achievement Test, have been tested for reliability and validity, and as a result the "Geometry Achievement Test" has been established to be reliable and valid. GBT was applied to a group of 24 students. Based on the results of the results of the pre-test GBT, the experimental group with 12 member, in which the geometry was tough with concept cartoons, and the control group with 12 member, in which the geometry was tough with traditional teaching was established so that the successes of students would be homogeneous. In the analysis of the data obtained from the experimental study; Independent samples t-test was used. As a result of the experimental research, it was seen that the students of the experimental group using the concept cartoons had higher geometry achievements than the geometric achievement of the control group students who were taught traditional geometry. [ABSTRACT FROM AUTHOR]

In this study, the mathematical thinking processes of a gifted 4th grade student regarding geometry were examined. Based on the thought that the geometric thinking level of the student will affect his mathematical thinking skills, it was determined that his geometric thinking level is the second level. While studying mathematical thinking processes, the theoretical framework of the three worlds of mathematics was used. According to this theoretical framework, mathematical thinking is divided into three levels: the conceptual embodied world, the perceptual symbolic world and the axiomatic formal world. While examining the mathematical thinking processes of this student named Alp, two semi-structured interviews were conducted. In the first, his prior knowledge of geometry was questioned and a verbal expression of triangle inequality was presented. In the second interview, an activity that is expected to create knowledge structures about triangle inequality was presented. As a result of the research, it was seen that Alp was able to carry out a thinking process towards proof processes, even at a simple level. His thinking skills are generally limited to the conceptual embodied world dimension. [ABSTRACT FROM AUTHOR]

The article presents some examples of plane geometric variance of an area with the use of computer technology. These tools can offer teachers opportunities for adaptation and preparation of pedagogical presentations which will help students along the process of fruitful conjectures formation and eventually construction of formal deductive proofs. Some of the examples are original, and all are beautiful and insightful. The mathematical proofs of the selected examples are very simple and do not require the use of any "heavy" mathematical tools. All the examples have links to applets prepared in GeoGebra-Tube. The consequences of all the examples can be formulized as mathematical propositions, and vice versa, meaning any mathematical proposition might demonstrate a situation of variance and invariance properties. [ABSTRACT FROM AUTHOR]

The use of mobile learning offers new affordances to teaching and learning. In this study, students from two fourth grade classes used iPads in dyads and groups to learn about angle. Using a design-based research methodology, which included observations, video, researcher journals, and artefact collection, a local instruction theory was developed on how students can learn about angle concepts through mobile learning activities. The local instruction theory is comprised of two components: (a) a seven lesson curriculum for 4th grade students on developing an early understanding of angle utilizing a mobile learning approach, and (b) additions to the scholarly theories, by providing a revised set of indicator behaviours for van Hiele levels of geometric thinking in regards to angle. [ABSTRACT FROM AUTHOR]

Metaphors are regularly used by mathematics teachers to relate difficult or complex concepts in classrooms. A complex topic of concern in mathematics education, and most STEM-based education classes, is problem solving. This study identified how students and teachers contextualize mathematical problem solving through their choice of metaphors. Twenty-two high-school student and six teacher interviews demonstrated a rich foundation for these shared experiences by identifying the conceptual metaphors. This mixed-methods approach qualitatively identified conceptual metaphors via interpretive phenomenology and then quantitatively analyzed the frequency and popularity of the metaphors to explore whether a coherent metaphorical system exists with teachers and students. This study identified the existence of a set of metaphors that describe how multiple classrooms of geometry students and teachers make sense of mathematical problem solving. Moreover, this study determined that the most popular metaphors for problem solving were shared by both students and teachers. The existence of a coherent set of metaphors for problem solving creates a discursive space for teachers to converse with students about problem solving concretely. Moreover, the methodology provides a means to address other complex concepts in STEM education fields that revolve around experiential understanding. [ABSTRACT FROM AUTHOR]

We examined the effectiveness of (a) a working memory (WM) training program and (b) a combination program involving both WM training and direct instruction for students with geometry difficulties (GD). Four students with GD participated. A multiple-baseline design across participants was employed. During the Phase 1, students received six sessions of computerized WM training (Jaeggi et al., 2011); during Phase 2, they received six sessions of computerized WM training and six sessions of human-delivered direct instruction with Concrete - Representational - Abstract (CRA) representation sequence on triangle congruence. All four participants remarkably improved their WM, and enhanced their performance on the spatial rotation and general geometric problem-solving. However, the participants' performance on specific triangle-congruence tasks did not improve until direct instruction with CRA sequence was introduced. Practical recommendations were discussed. Practical recommendations of providing cognitive remediation combined with academic interventions were emphasized. [ABSTRACT FROM AUTHOR]

In this paper, we present the results of an experimental classroom activity, history-based with a phylogenetic approach, to achieve algebra properties through geometry. In particular, we used Euclidean propositions, processed them by a dynamic geometry system and translate them into algebraic special products. [ABSTRACT FROM PUBLISHER]

Prevalent characteristics of effective mathematical discourse in the literature include student autonomy, a positive social environment, and a degree of perceived mathematical competence. These characteristics are also found in Self-Determination Theory (SDT), which posits that actions are self-regulated when students' autonomy, competence, and social relatedness are fulfilled. Utilizing SDT as an additional lens for examining student engagement in whole class discussions, this study examined high school students' observed discourse actions and mathematical talk in the context of their self-reported psychological needs of autonomy, competence and relatedness. Results suggest that students' perceived needs correspond with their engagement in making mathematical statements in the context of classroom mathematical discussions. However, students who lack in one or more need can be supported by participation of peers with more fulfilled needs. [ABSTRACT FROM AUTHOR]

Although mathematical practice has traditionally valued two distinct kinds of mathematical work-referred to by Gowers () as theory building and problem solving-activity in classrooms appears to be organized largely around the latter, rather than the former. This study takes up the question of whether there is a customary role for theory building in the secondary geometry course and to what extent teachers of geometry hold students accountable for that disposition. We analyze records from study groups composed of experienced geometry teachers in the USA, and ask to what extent the disposition towards theory building is visible in those records, and how teachers react to the suggestion that it could play a larger role in their practice. Among our findings, we report that participants consistently attached a higher value to work organized around problem solving, rejecting the idea that they might hold their students accountable for theory building. [ABSTRACT FROM AUTHOR]

The purpose of this research is to investigate the phenomenon of online technology enhanced mathematics education. This is a mixed methods technology intervention action research case study on investigating the impact on secondary geometry and calculus students' academic achievement and affect when their face-to-face lessons are mirrored to the Cloud as lesson videos and note files for students to access outside of the classroom. The investigator discovered educational benefits from this intervention based on the results of a quantitative analysis of the students' assessment scores and a qualitative analysis of interview, questionnaire, and observational data collected during the intervention. This work is the result of an inquiry by the school's stakeholders on how to use online technologies to enhance mathematics education. [ABSTRACT FROM AUTHOR]

The article offers information on use of Tetris games in classroom activities for geometry students to enhance learning's in isometrics. It discusses use of mathematical notation by students from academic language for geometric transformations of rotations and translations in the game. It mentions writing moves sequences to identify line of isometric reflections. It also mentions several questions regarding geometry of online version of Tetris.

The article offers information on use of technology to solve triangle construction problems by geometry students from their knowledge points in concurrency, coordinate geometry, and transformational geometry. It discusses geometric assignments on numeric coordinates that develops students knowledge in coordinate geometry while maintain their algebra skills. It also mentions project which uses dynamic geometry software and Geometer's Sketchpad in finding coordinates of triangle vertices.

The article presents an open-ended geometry problem to illustrate the benefits of problem-based instruction to teachers and students. It highlights the circle problem and the opportunities that the exercise could offer to students, particularly in the evaluation and application of theorems that they previously studied. It notes that the said classroom activity could enhance the mathematical skills of students which include strategic competence, adaptive reasoning, and conceptual understanding.

Abstract: Statements conveying a degree of certainty or doubt, in the form of hedging, have been linked with logical inference in students’ talk (Rowland, 2000). Considering the current emphasis on increasing student autonomy for effective mathematical discourse, I posit a relationship between hedging and student autonomy. In the current study, high school Geometry students’ frequency of producing hedged mathematical statements were correlated with their perceived mathematical autonomy to determine if a relationship existed. Results found a strong and statistically significant correlation, providing support for a connection between students’ hedging and their perceived autonomy. However, additional analysis revealed that perceptions of mathematical competence and social relatedness were also influential to hedging. Implications of these results are discussed. [Copyright &y& Elsevier]

Abstract: We inspect the hypothesis that geometry students may be oriented toward how they expect that the teacher will evaluate them as students or otherwise oriented to how they expect that their work will give them opportunities to do mathematics. The results reported here are based on a mixed-methods analysis of twenty-two interviews with high school geometry students. In these interviews students respond to three different tasks that presented students with an opportunity to do a proof. Students’ responses are coded according to a scheme based on the hypothesis above. Interviews are also coded using a quantitative linguistic ratio that gauges how prominent the teacher was in the students’ opinions about the viability of these proof tasks. These scores were used in a cluster analysis that yielded three student profiles that we characterize using composite profiles. These profiles highlight the different ways that students can experience proof in the geometry classroom. [Copyright &y& Elsevier]

The article focuses on the types of problems present to students at various stages of their study of geometry course and the way their thinking develops in response. It discusses the problems that frequently encounter by the students on their first day class to offer them a real experience in conjecturing. It mentions that the Park School mathematics faculty's solution to the problems in teaching geometry by starting in the middle. It also explores the logical structure of an argument.

This article reports on a qualitative, interpretivist study that focused on the use of visualisation and analytic strategies by Grade 12 learners when working with problems based on transformation geometry. The research was conducted with 40 learners from a Grade 12 class at one high school in the north Durban area of Kwazulu-Natal. Participants completed a written task and a smaller sample of the participants engaged in investigative semi-structured interviews with the researchers. The framework for the study was based on transformations of semiotic representations as well as the visualiser/analyser model. The findings revealed that most learners performed treatments in the analytic mode when responding to the tasks, and showed limited movement across the two modes which are essential for a deepening of understanding. The study identified one learner, however, who was able to move flexibly between the modes and who displayed a deep understanding of the concepts. The article concludes by recommending that opportunities need to be created for learners to engage in transformation geometry activities which emphasise conversion. [ABSTRACT FROM AUTHOR]

The article discusses the different important aspects to consider when teaching geometry. It says that the teacher must sort out the most appropriate examples from all the materials and present them in the most effective way to the students. According to the author, the teacher should remember that the exercises will oblige the students to learn the terms they will encounter at the start of the systematic course and take in a series of geometric forms.

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We use Leibniz’s rule and the cotangent function to evaluate the following infinite series. [ABSTRACT FROM PUBLISHER]

To make optimal use of computational environments, one must understand how students interact with the environments and how students' mathematical thinking is reflected and affected by their use of the environments. Similarly, to make sense of research on students' thinking and learning, one must understand how the environments and contexts used in the research may affect the conclusions one derives. The research on students' learning of functions has approached the topic in terms of symbols and graphs (see, for example, Leinhardt et al. (1990) for a review of work up to that point; Harel and Dubinsky (1992) for a collection of research; and Dugdale et. al. (1995), for some recent thinking about implications for curriculum reform using technology). Dynamic geometry environments (DGEs) like Cabri Geometry or Geometer's Sketchpad, offer us an opportunity to get a new perspective on these old and important issues. DGEs let students build geometrical constructions and then drag certain objects around the screen in a continuous manner while observing how the entire construction responds dynamically. In this way DGEs model functional relationships that are not specified by symbols or represented by graphs. Based on interviews with undergraduate mathematics majors, this paper presents preliminary observations that confirm some old results and raise some new questions about students' notions of function. [ABSTRACT FROM AUTHOR]

Several letters to the editor are presented including one responding to the article "Change Math Attitudes With Aviation" in the March 2013 issue, one discussing the difficulty among many students to convert kilometers to astronomical units (AUs) and one commenting on the use of a cartoon in teaching the computation of AUs to eighth-grade geometry students.

The article describes an activity program for eight-grade advanced mathematics class which asks students to discover the relationships between a pre-image and an image using handheld technology. INSET: A Brief Explanation of Transformations.

The article offers the author's insights on the use of the movie version of the book "Flatland: The Movie," by Edwin Abbott, in teaching geometry. The author says that the movie introduces the nondimensional Pointland, two dimensional Flatland, and one-dimensional Lineland. She says that the movie also provides the source of cross-disciplinary discussion and learning. She adds that the discussion gave students a chance to see the significance of mathematics.