Designing for mathematical abstraction

Our focus is on the design of systems (pedagogical, technical, social) that encourage mathematical abstraction, a process we refer to as designing for abstraction. In this paper, we draw on detailed design experiments from our research on children's understanding about chance and distribution to re-present this work as a case study in designing for abstraction. Through the case study, we elaborate a number of design heuristics that we claim are also identifiable in the broader literature on designing for mathematical abstraction. Our previous work on the micro-evolution of mathematical knowledge indicated that new mathematical abstractions are routinely forged in activity with available tools and representations, coordinated with relatively naïve unstructured knowledge. In this paper, we identify the role of design in steering the micro-evolution of knowledge towards the focus of the designer's aspirations. A significant finding from the current analysis is the identification of a heuristic in designing for abstraction that requires the intentional blurring of the key mathematical concepts with the tools whose use might foster the construction of that abstraction. It is commonly recognized that meaningful design constructs emerge from careful analysis of children's activity in relation to the designer's own framework for mathematical abstraction. The case study in this paper emphasizes the insufficiency of such a model for the relationship between epistemology and design. In fact, the case study characterises the dialectic relationship between epistemological analysis and design, in which the theoretical foundations of designing for abstraction and for the micro-evolution of mathematical knowledge can co-emerge. © 2010 Springer Science+Business Media B.V

The Use Of Props As To Increase Interest And Understanding Mathematics Concepts Ability Elementary School Students

This Researched study is a mixed methods (Mixed Method) type “Embedded Design” with an experimental type of study design shaped models with pretest-posttest control group design, which aims to conduct studies that focus on the use of teaching props that could be expected to improve the understanding of mathematical concepts and their impact on student interest in Elementary School. Instruments used in this research are to test the ability to understand mathematical concepts, students’ interest questionnaire with the Likert scale, observation sheets, and interviews. Based on data analysis we concluded that (1) The ability to understand mathematical concepts of superior and low students who use props better than the ability to understand mathematical concepts of superior and low students who obtain conventional learning, (2) The ability to understand mathematical concepts of the superior and low students using props by cooperative learning type. (3) There is a significant correlation between students' understanding of mathematics and students' interest in learning mathematics

The Use Of Props As To Increase Interest And Understanding Mathematics Concepts Ability Elementary School Students

This Researched study is a mixed methods (Mixed Method) type “Embedded Design” with an experimental type of study design shaped models with pretest-posttest control group design, which aims to conduct studies that focus on the use of teaching props that could be expected to improve the understanding of mathematical concepts and their impact on student interest in Elementary School. Instruments used in this research are to test the ability to understand mathematical concepts, students’ interest questionnaire with the Likert scale, observation sheets, and interviews. Based on data analysis we concluded that (1) The ability to understand mathematical concepts of superior and low students who use props better than the ability to understand mathematical concepts of superior and low students who obtain conventional learning, (2) The ability to understand mathematical concepts of the superior and low students using props by cooperative learning type. (3) There is a significant correlation between students' understanding of mathematics and students' interest in learning mathematics

Ability to Understand Mathematic Concepts: The Effect of The Hermeneutic Model Assisted by Gamification Teaching Materials

The ability to understand mathematical concepts in learning mathematics needs to be mastered by students to support the learning process and solve various mathematical problems. This study aims to determine the effect of the Hermeneutics-Assisted learning model of gamification teaching materials on the ability to understand mathematical concepts of students. This research is a type of Quasy Experimental Design research with a 3×1 factorial research design. The data collection technique in this study was a test of the ability to understand mathematical concepts. The data analysis techniques used are normality test, homogeneity test, and one-way analysis of variance. Based on the results of the study, it was concluded that there was an effect of applying the Hermeneutics learning model assisted by gamification teaching materials on the ability to understand students' mathematical concepts. Hermeneutics learning model assisted by gamification teaching materials has a significant influence on the ability to understand mathematical concepts of students

A Cognitive Theory Driven New Orientation of Indonesian Lessons

The main focus of this design research was on students\u27 mathematical thinking and skills and on their understanding of mathematical concepts and methods. The mathematical content our project starts with is the introduction of integers. For this content new learning environments have been developed, implemented and evaluated. An important question for the design of teaching and learning activities is how to establish appropriate models of mathematical concepts and methods for students and how they operate in students\u27 minds. In the lecture the use of those methodological concepts and theories in our approach will be explained and justified. The results indicate that the means and methods used in our project have a positive influence on the quality of teaching and learning processes in the class and on students\u27 mathematical thinking and skills

Control design variable linking for optimization of structural/control systems

A method is presented to integrate the design space of structural/control system optimization problems in the case of linear state feedback control. Conventional structural sizing variables and elements of the feedback gain matrix are both treated as strictly independent design variables in optimization by extending design variable linking concepts to the control gains. Several approximation concepts including new control design variable linking schemes are used to formulate the integrated structural/control optimization problem as a sequence of explicit nonlinear mathematical programming problems. Examples which involve a variety of behavior constraints, including constraints on dynamic stability, damped frequencies, control effort, peak transient displacement, acceleration, and control force limits, are effectively solved by using the method presented

PENGARUH MODEL PROBLEM BASED LEARNING (PBL) BERBANTUAN MEDIA VIDEO PEMBELAJARAN TERHADAP PEMAHAMAN KONSEP MATEMATIKA SISWA KELAS V SDN TAMBAHMULYO 01

This study aims to analyze the effect of the Problem Based Learning (PBL) learning model assisted by learning video media on understanding mathematical concepts. The research method used in this study is a quantitative method in the form of Quasy Experimental Design (pseudo-experimental). The design used in this study was a nonrandomized pretest-posttest control group design. The sample of this study was class V SD Tambahmulyo 01, namely class VA and VC. The data collection technique was test and non-test, the test technique used understanding of mathematical concepts while the non-test technique used observation and documentation. Data analysis techniques using normality test, homogeneity, and t test. The results of data analysis concluded that there was an influence of the PBL learning model assisted by video learning media on the ability to understand mathematical concepts of fifth grade students at SDN Tambahmulyo 01. This is evident from the results of the paired sample t-test, the results obtained were 0.03 <0.05 meaning H0 was rejected, meaning that the PBL model assisted by learning video media has an effect on the understanding of mathematical concepts of fifth grade students at SDN Tambahmulyo 01.Keywords: PBL Model, Understanding Mathematical Concepts, Learning Video

THE USE OF PAIR CHECKS LEARNING MODEL ON UNDERSTANDING ABILITY OF MATHEMATICAL CONCEPTS OF CLASS X HIGH SCHOOL STUDENTS

This research is based on the low understanding of mathematical concepts of students in SMA Negeri 1 Pasir Penyu because of the low ability to comprehend mathematical concepts of students, students' activeness in following the lesson is still low, student learning outcomes are still low. The purpose of this study is to know the understanding of mathematical concepts of students by using learning models pair checks. The research design used is Randomized Subjects Posttest Only Control Group Design. The population in this study is class XI IPS. Samples are randomly selected, the classes selected to be experimental class are XI IPS 1 class, and class XI IPS 4 becomes the control class. Data analysis technique in this test using normality test, homogeneity and hypothesis test that is t-test. Based on the results of the study can be concluded the ability of understanding mathematical concepts with the use of Pair Checks learning model is better than the understanding of mathematical concepts with the use of conventional learning model

PENGARUH PENERAPAN MODEL PEMBELAJARAN THINK PAIR SHARE TERHADAP PEMAHAMAN KONSEP MATEMATIS SISWA KELAS X DPIB SMK NEGERI 5 PADANG

This research is motivated by students' understanding of mathematical concepts is still low. The purpose of this study was to find out whether students' understanding of mathematical concepts by applying the Think Pair Share learning model is better than students' understanding of mathematical concepts by conventional learning in class X DPIB students of SMK Negeri 5 Padang. This research is a quasi-experimental research with a quasi-experimental design with a posttest only control group design with total sampling as research subjects. The sample of this research is class X students of SMK Negeri 5 Padang. This study used a final test instrument in the form of a description item with reliability = 0.54. The data analysis technique used is the t-test. Based on data collection techniques and data analysis performed tcount=2.28 and ttable=1.67 because tcount > ttable then the hypothesis is accepted, thus it can be concluded that student learning outcomes on students' understanding of mathematical concepts by applying the Think Pair Share learning model are better than student learning outcomes on students' understanding of mathematical concepts by applying conventional learning models