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"Mathematics Drawings."
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Drawing as a way of knowing in art and science
In recent history, the arts and sciences have often been considered opposing fields of study, but a growing trend in drawing research is beginning to bridge this divide. Gemma Anderson's Drawing as a Way of Knowing in Art and Science introduces tested ways in which drawing as a research practice can enhance morphological insight, specifically within the natural sciences, mathematics, and art. Inspired and informed by collaboration with contemporary scientists and Goethe's studies of morphology, as well as the work of artist Paul Klee, this book presents drawing as a means of developing and disseminating knowledge, and of understanding and engaging with the diversity of natural and theoretical forms, such as animal, vegetable, mineral, and four dimensional shapes. Anderson shows that drawing can offer a means of scientific discovery and can be integral to the creation of new knowledge in science as well as in the arts.--Google Books.
Book
Drawing as a way of knowing in art and science
In recent history, the arts and sciences have often considered opposing fields of study, but a growing trend in drawing research is beginning to bridge this divide. Gemma Anderson’s Drawing as a Way of Knowing in Art and Science introduces tested ways in which drawing as a research practice can enhance morphological insight, specifically within the natural sciences, mathematics and art. Inspired and informed by collaboration with contemporary scientists and Goethe’s studies of morphology, as well as the work of artist Paul Klee, this book presents drawing as a means of developing and disseminating knowledge, and of understanding and engaging with the diversity of natural and theoretical forms, such as animal, mineral and four-dimensional shapes. Anderson shows that drawing can offer a means of scientific discovery and can be integral to the creation of knowledge in science as well as in the arts.
eBook
Adolescents' Drawings about School and School Subjects: Perspectives of Youth from India Compared with Youth from Seven other Countries
Most studies of student-teacher relations and student achievement in reading and mathematics focus on test results and the opinions of school leaders, educationalists, and other experts. This study sought to understand the perspectives of 471 young adolescents as revealed in their drawings and written comments. The drawings of 50 young adolescents from India were compared with matched samples from the U.S.A, Mexico, South Africa, Ghana, Switzerland, Iceland, and Singapore. When compared to the young adolescents from seven countries, the young adolescents in India expressed more negative views of school and school subjects and depicted their classroom experiences as more unfriendly, irrelevant, and unpleasant. Similar findings were reported in the 2009 Programme for International Student Assessment surveys. School psychology and educational psychology are the branches of applied psychology that can address the negative views of young adolescent students and help with school improvement in India.
Journal Article
Graph partitioning and graph clustering : 10th DIMACS Implementation Challenge Workshop, February 13-14, 2012, Georgia Institute of Technology, Atlanta, GA
Graph partitioning and graph clustering are ubiquitous subtasks in many applications where graphs play an important role. Generally speaking, both techniques aim at the identification of vertex subsets with many internal and few external edges. To name only a few, problems addressed by graph partitioning and graph clustering algorithms are: li>What are the communities within an (online) social network?How do I speed up a numerical simulation by mapping it efficiently onto a parallel computer?How must components be organised on a computer chip such that they can communicate efficiently with each other?What are the segments of a digital image?Which functions are certain genes (most likely) responsible for?The 10th DIMACS Implementation Challenge Workshop was devoted to determining realistic performance of algorithms where worst case analysis is overly pessimistic and probabilistic models are too unrealistic. Articles in the volume describe and analyse various experimental data with the goal of getting insight into realistic algorithm performance in situations where analysis fails. This book is published in cooperation with the Center for Discrete Mathematics and Theoretical Computer Science.
eBook
DRAW TO UNDERSTAND
Students who make drawings about mathematical concepts think about mathematics. Those who trust their own thinking become problem solvers who play with ideas on paper. During the drawing process, they call to mind the knowledge that they have stored in memory. They compare drawings to numbers and equations and look at the whole problem as well as the details. These thinking strategies contribute well to the construction of mathematical ideas.
Journal Article
Draw yourself doing mathematics: developing an analytical tool to investigate the nature of young children’s attitudes towards mathematics
Understanding children’s attitudes towards mathematics provides insights into their lived mathematical experience and engagement. Despite the considerable amount of research into students’ attitudes toward mathematics, limited research has been conducted into young children’s attitudes toward mathematics (YCATM). Within this limited research, investigating YCATM has certain challenges. From a methodological perspective, limitations exist regarding the type of research techniques that can be employed to study the nuances of the issue. The foci of this paper are to present and evaluate a methodological approach that used children’s drawings (N = 106) and interview responses as the primary sources of data. Findings indicate that the strategy of “Draw yourself doing mathematics”, when used with other research methods, generated rich attitudinal data in the form of personal stories about YCATM.
Journal Article
A Quasi-Variational-Hemivariational Inequality for Incompressible Navier-Stokes System with Bingham Fluid
In this paper we examine a class of elliptic quasi-variational inequalities, which involve a constraint set and a set-valued map. First, we establish the existence of a solution and the compactness of the solution set. The approach is based on results for an elliptic variational inequality and the Kakutani-Ky Fan fixed point theorem. Next, we prove an existence and compactness result for a quasi-variational-hemivariational inequality. The latter involves a locally Lipschitz continuous functional and a convex potential. Finally, we present an application to the stationary incompressible Navier-Stokes equation with mixed boundary conditions which model a generalized Newtonian fluid of Bingham type.
Journal Article
Make a drawing. Effects of strategic knowledge, drawing accuracy, and type of drawing on students' mathematical modelling performance
Drawing strategies are widely used as a powerful tool for promoting students' learning and problem solving. In this article, we report the results of an inferential mediation analysis that was applied to investigate the roles that strategic knowledge about drawing and the accuracy of different types of drawings play in mathematical modelling performance. Sixty-one students were asked to create a drawing of the situation described in a task (situational drawing) and a drawing of the mathematical model described in the task (mathematical drawing) before solving modelling problems. A path analysis showed that strategic knowledge about drawing was positively related to students' modelling performance. This relation was mediated by the type and accuracy of the drawings that were generated. The accuracy of situational drawing was related only indirectly to performance. The accuracy of mathematical drawings, however, was strongly related to students' performance. We complemented the quantitative approach with a qualitative in-depth analysis of students' drawings in order to explain the relations found in our study. Implications for teaching practices and future research are discussed.
Journal Article
Depicting classroom social climate: Using drawings to examine primary students’ perceptions of geometry teaching and learning practices
Climate conducive to learning is one of criteria of good teaching. Even though current pedagogies argue for contemporary type of instruction, mathematics instruction may still be dominated by traditional type of instruction. The present study examined participant-produced drawings of 250 primary grade students regarding geometry teaching and learning practices. Not only different aspects of traditional type of instruction, such as the teacher standing in front of the classroom and delivering the content while students sit at their desks and passively listen to the teacher with little student-student communication were reported, but also some aspects typical for contemporary type of instruction, such as learning through teacher-student discussions, and the use of teaching materials and tools. Still, the aspects of traditional type of instruction prevailed. The results offer potential opportunities for reconsidering the current teacher education as well as policy that would reflect the teaching practices conducive to contemporary geometry instruction.
Journal Article
The Use of a Bar Model Drawing to Teach Word Problem Solving to Students With Mathematics Difficulties
For students with mathematics difficulties (MD), math word problem solving is especially challenging. The purpose of this study was to examine the effects of a problem-solving strategy, bar model drawing, on the mathematical problem-solving skills of students with MD. The study extended previous research that suggested that schematic-based instruction (SBI) and cognitive strategy instruction (CSI) delivered within an explicit instruction framework can be effective in teaching various math skills related to word problem solving. A multiple-baseline design replicated across groups was used to evaluate the effects of the intervention of bar model drawing on math problem-solving performance of students with MD. Student achievement was measured in terms of increased correct use of cognitive strategies and overall accuracy of math word problem solving. Results showed that bar modeling drawing is an effective strategy for increasing elementary students' accuracy in solving math word problems and their ability to use cognitive strategies to solve the problems.
Journal Article