EXPLORING STUDENTS' COGNITIVE PROCESSES IN SOLVING NUMERACY TASK OF GEOMETRY AND MEASUREMENT REVIEWED BY MATHEMATICAL ABILITY

This study aims to analyze how the cognitive processes of high school students in terms of their mathematical abilities in solving the Minimum Competency Assessment Numeracy problems related to Geometry and Measurement. Problems were given to three 10th science students with categories of high, medium, and low mathematical ability. Data on the results of the subject's work were analyzed based on the cognitive processes stage, namely the stage of Comprehending linguistic and numerical information in the problem; 2)  Translating and transforming that information into mathematical notations, algorithms, and equations; 3) Observing relationships among the elements of the problem; 4) Formulating a plan to solve the problem; 5) Predicting outcome; 6) Regulating the solution path as it is executed; 7) Detecting and correcting errors during problem solution which is then followed by in-depth interviews. The results showed that students with high mathematical abilities went through all stages of the cognitive process quite coherently and completely. While students with moderate abilities went through the stage of understanding information to the calculation stage of planning, but there were some errors and corrections in finding solutions. Meanwhile, students with low abilities had not been able to show the stages of cognitive processes in a coherent manner so that many stages were interrupted and had to return to the stage of understanding the problem. Based on these results, it is hoped that learning for the preparation of the Minimum Competency Assessment for Geometry and Measurement material can be emphasized more and so that the understanding of information on students' problems can continue the completion stage according to the solution plan that they have made. Keywords: Cognitive Processes, Numeracy, Geometry and Measurement

A Creative Thinking Process of Junior High School Students in Solving Story Problems Viewed from Field Dependent – Field Independent Cognitive Style

Giving math subjects is very important in life. This is in line with content standards in Permendiknas No. 22 of 2006 that mathematics subjects need to be given to train and teach thinking skills, one of which is creative thinking. The purpose of this study was to describe the creative thinking processes of junior high school students with field dependent and field independent cognitive styles in solving problems on the material surface area of geometric figures. The subjects in this study were one student each with field dependent and field independent cognitive styles who had high and equal mathematical abilities and were male. The research instruments used were GEFT sheets to classify cognitive styles, Mathematical Ability Test (MAT) sheets to classify students' mathematical abilities, Problem Solving Task sheets (PST) and interview guidelines to find out in detail the students' creative thinking processes. Based on the results of the research conducted, the creative thinking process of students with field dependent cognitive style at the preparatory stage read the questions twice to understand the questions, at the incubation stage field dependent students needed 15 minutes to get out of this stage. At the illumination stage, field dependent students were not fluent in solving problems and only had one solution idea. At the verification stage, field dependent students are unsure of their answers and have no other solution ideas. The thinking process of students with field independent cognitive styles in the preparation stage of field independent students read the questions twice to understand the questions. At the incubation stage, independent field students managed to get out of this stage and found ideas to solve questions for 5-10 minutes. In the illumination stage, field independent students smoothly solve problems and have several ideas for solving them. At the verification stage, field independent students are very confident with their answers and have other solutions

Investigating Emotions in Creative Design

A wealth of research has suggested that emotions play a significant role in the creative problem solving process, but less work has focused on investigating the role of emotions in the design process. This is surprising given that creative problem solving lies at the heart of the design processes. In an exploratory study we interviewed 9 expert designers about their emotions during the design process. The content analysis allowed us to identify the various types of emotions relevant in the design process and to extend Wallas’ model of creative problem solving with emotional components for each of its stages. In addition, we identified two important roles of emotions in design and several ways in which expert designers regulate their emotions. We discussed the theoretical and practical applications of our work

Cognitive apprenticeship : teaching the craft of reading, writing, and mathtematics

Includes bibliographical references (p. 25-27)This research was supported by the National Institute of Education under Contract no. US-NIE-C-400-81-0030 and the Office of Naval Research under Contract No. N00014-85-C-002

Understanding requirements engineering process: a challenge for practice and education

Reviews of the state of the professional practice in Requirements Engineering (RE) stress that the RE process is both complex and hard to describe, and suggest there is a significant difference between competent and "approved" practice. "Approved" practice is reflected by (in all likelihood, in fact, has its genesis in) RE education, so that the knowledge and skills taught to students do not match the knowledge and skills required and applied by competent practitioners. A new understanding of the RE process has emerged from our recent study. RE is revealed as inherently creative, involving cycles of building and major reconstruction of the models developed, significantly different from the systematic and smoothly incremental process generally described in the literature. The process is better characterised as highly creative, opportunistic and insight driven. This mismatch between approved and actual practice provides a challenge to RE education - RE requires insight and creativity as well as technical knowledge. Traditional learning models applied to RE focus, however, on notation and prescribed processes acquired through repetition. We argue that traditional learning models fail to support the learning required for RE and propose both a new model based on cognitive flexibility and a framework for RE education to support this model

Geosciences for Elementary Educators: A Course Assessment

Geosciences for Elementary Educators engages future elementary teachers in a hands-on investigation of topics aligned with the third and fifth grade Earth/Space Science and Scientific Inquiry benchmarks of the Oregon Content Standards. The course was designed to develop the content background of elementary teachers within the framework of the science described in the content standards, to provide an opportunity for future teachers to explore the content area in relation to what takes place in the classrooms of elementary schools, and to initiate a community of learners focused on teaching science to elementary students. The course focused on four themes: the classroom teacher as an activity and curriculum developer using diverse resources to keep the content current and alive; the classroom teacher as educator dealing with the diverse backgrounds of students in a developmentally appropriate manner; the classroom teacher as reflective practitioner exploring the links among pedagogy, content, and student learning; and, the classroom teacher as citizen staying current with emerging policy issues and debates that impact education. In a course where process is extremely important, participants are assessed on what they can do with content and process knowledge through preparing lesson plans, presenting lessons in a simulated classroom environment, and developing a portfolio and journal. Lesson plans demonstrate participant understanding of inquiry, using models, deductive and inductive approaches, links between communication skills and content knowledge, and effective use of technology, including the Internet. For each topic, the mixture of demonstration, experimentation, inquiry, and lecture models are explored through investigation, discovery, and analysis

Symbols and the bifurcation between procedural and conceptual thinking

Symbols occupy a pivotal position between processes to be carried out and concepts to be thought about. They allow us both to d o mathematical problems and to think about mathematical relationships. In this presentation we consider the discontinuities that occur in the learning path taken by different students, leading to a divergence between conceptual and procedural thinking. Evidence will be given from several different contexts in the development of symbols through arithmetic, algebra and calculus, then on to the formalism of axiomatic mathematics. This is taken from a number of research studies recently performed for doctoral dissertations at the University of Warwick by students from the USA, Malaysia, Cyprus and Brazil, with data collected in the USA, Malaysia and the United Kingdom. All the studies form part of a broad investigation into why some students succeed yet others fail