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Opportunity-to-learn context-based tasks provided by mathematics textbooks
Based on the findings of an error analysis revealing that Indonesian ninth-and tenth-graders had difficulties in solving context-based tasks, we investigated the opportunity-to-learn offered by Indonesian textbooks for solving context-based mathematics tasks and the relation of this opportunity-to-learn to students' difficulties in solving these tasks. An analysis framework was developed to investigate the characteristics of tasks in textbooks from four perspectives: the type of context used in tasks, the purpose of context-based tasks, the type of information provided in tasks, and the type of cognitive demands of tasks. With this framework, three Indonesian mathematics textbooks were analyzed. Our analysis showed that only about 10 % of the tasks in the textbooks are context-based tasks. Moreover, at least 85 % of these tasks provide exactly the information needed to solve them and do not leave room for students to select relevant information by themselves. Furthermore, of the context-based tasks, 45 % are reproduction tasks requiring performing routine mathematical procedures, 53 % are connection tasks requiring linking different mathematical curriculum strands, and only 2 % are reflection tasks, which are considered as tasks with the highest level of cognitive demand. A linkage between the findings of the error analysis and the textbook analysis suggests that the lacking opportunity-to-learn in Indonesian mathematics textbooks may cause Indonesian students' difficulties in solving context-based tasks. Based on the results of this study, recommendations are given for improving the opportunities-tolearn to solve context-based tasks as well as for doing further research on this topic.
Journal Article
Differential Equations
Differential Equations: A Modern Approach with Wavelets is the newest book from one of the most published authors in all of mathematics is an attempt to offer a new, more modern take on the Differential Equations course. The world is changing. Because of the theory of wavelets, Fourier analysis is ever more important and central. Plus, applications are a driving force behind much of mathematics.
This text presents a more balanced picture. It covers differential equations (both ordinary and partial), Fourier analysis, and applications in equal measure and with equal weight. The Riemann integral is used throughout. The author does not assume that the student knows any functional analysis. Likewise, he does not assume that the student has had a course in undergraduate real analysis. To make the book timely and exciting, a substantial chapter on basic properties of wavelets, with applications to signal processing and image processing, is included. This should give students and instructors alike a taste of what is happening in the subject today.
Features
Provides a new approach to the Differential Equations course from one of the most widely published authors in mathematics
There is not a textbook quite like this one; a similar approach is taken for the separate Partial Differential Equations course, but this is new to the subject
The book can be used for several courses in the advanced mathematics curriculum, while aimed at more prepared students
Features numerous problems and exercises throughout the text
eBook
Finite mathematics
Features step-by-step examples based on actual data and connects fundamental mathematical modeling skills and decision making concepts to everyday applicability Featuring key linear programming, matrix, and probability concepts, Finite Mathematics: Models and Applications emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences. In order to emphasize the main concepts of each chapter, Finite Mathematics: Models and Applications features plentiful pedagogical elements throughout such as special exercises, end notes, hints, select solutions, biographies of key mathematicians, boxed key principles, a glossary of important terms and topics, and an overview of use of technology. The book encourages the modeling of linear programs and their solutions and uses common computer software programs such as LINDO. In addition to extensive chapters on probability and statistics, principles and applications of matrices are included as well as topics for enrichment such as the Monte Carlo method, game theory, kinship matrices, and dynamic programming. Supplemented with online instructional support materials, the book features coverage including: Algebra Skills Mathematics of Finance Matrix Algebra Geometric Solutions Simplex Methods Application Models Set and Probability Relationships Random Variables and Probability Distributions Markov Chains Mathematical Statistics Enrichment in Finite Mathematics An ideal textbook, Finite Mathematics: Models and Applications is intended for students in fields from entrepreneurial and economic to environmental and social science, including many in the arts and
humanities.
eBook
Geometry and Discrete Mathematics
This two-volume set collects and presents many fundamentals of mathematics in an enjoyable and elaborating fashion.The idea behind the two books is to provide substantials for assessing more modern developments in mathematics and to present impressions which indicate that mathematics is a fascinating subject with many ties between the diverse.
eBook
Mapping research on Indonesia's government mathematics textbooks: current insights and potential directions
Education policy must prioritize research-driven mathematics textbook development to ensure rigorous alignment with curriculum reforms. The purpose of this study was to investigate research trends on Indonesian Government Provided (IGP) mathematics textbooks. This literature review examined the Science and Technology Index (SINTA), an Indonesian research database that includes researchers, institutions and journals in Indonesia. The use of several frameworks helped to capture the nature of research in this area. First, we classified textbooks based on their role as either research objects, dependent variables, or independent variables. Then, we applied content, theoretical, and problem analysis. In general, the number of studies on IGP mathematics textbooks has fluctuated from 2016 to 2024. Furthermore, they have focused on specific mathematics subjects and educational levels. Interestingly, the results also showed that all the studies on IGP mathematics textbooks treated them as a research subject. Their distribution in terms of content, theoretical and problem analysis varied considerably. The impact of this study is not just academic; it is a pragmatic step to ensure that research-driven textbook regulations translate into measurable improvements in learning materials.
Journal Article