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Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allow machine learning, statistics, symbolic computation, data manipulation, network analysis, time series analysis, NLP, optimization, plotting functions and various types of data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other programming languages. It was conceived by Stephen Wolfram, and is developed by Wolfram Research of Champaign, Illinois. The Wolfram Language is the programming language used in Mathematica. Mathematica 1.0 was released on June 23, 1988 in Champaign, Illinois and Santa Clara, California.
A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The development of the computer algebra systems in the second half of the 20th century is part of the discipline of "computer algebra" or "symbolic computation", which has spurred work in algorithms over mathematical objects such as polynomials.
Bloom's taxonomy is a set of three hierarchical models used for classification of educational learning objectives into levels of complexity and specificity. The three lists cover the learning objectives in cognitive, affective and psychomotor domains. The cognitive domain list has been the primary focus of most traditional education and is frequently used to structure curriculum learning objectives, assessments and activities.
Instructional scaffolding is the support given to a student by an instructor throughout the learning process. This support is specifically tailored to each student; this instructional approach allows students to experience student-centered learning, which tends to facilitate more efficient learning than teacher-centered learning. This learning process promotes a deeper level of learning than many other common teaching strategies.
Critical thinking is the analysis of available facts, evidence, observations, and arguments to form a judgment. The subject is complex; several different definitions exist, which generally include the rational, skeptical, and unbiased analysis or evaluation of factual evidence. Critical thinking is self-directed, self-disciplined, self-monitored, and self-corrective thinking, and accordingly, a critical thinker is one who practices the skills of critical thinking or has been schooled in its disciplines. Richard W. Paul has suggested that the mind of a critical thinker engages both the intellectual abilities and personal traits necessary for critical thinking. Critical thinking presupposes assent to rigorous standards of excellence and mindful command of their use. It entails effective communication and problem-solving abilities as well as a commitment to overcome native egocentrism and sociocentrism.
In contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and carrying out scholarly research into the transfer of mathematical knowledge.
Andrea diSessa is an education researcher and author of the book Turtle Geometry about Logo. He has also written highly cited research papers on the epistemology of physics, educational experimentation, and constructivist analysis of knowledge. He also created, with Hal Abelson, the Boxer Programming Environment at the Massachusetts Institute of Technology.
Information and communications technology (ICT) is an extensional term for information technology (IT) that stresses the role of unified communications and the integration of telecommunications and computers, as well as necessary enterprise software, middleware, storage and audiovisual, that enable users to access, store, transmit, understand and manipulate information.
Cognitive apprenticeship is a theory that emphasizes the importance of the process in which a master of a skill teaches that skill to an apprentice.
Digital literacy refers to an individual's ability to find, evaluate, and communicate information through typing and other media on various digital platforms. It is evaluated by an individual's grammar, composition, typing skills and ability to produce text, images, audio and designs using technology. The American Library Association (ALA) defines digital literacy as "the ability to use information and communication technologies to find, evaluate, create, and communicate information, requiring both cognitive and technical skills." While digital literacy initially focused on digital skills and stand-alone computers, the advent of the internet and use of social media, has resulted in the shift in some of its focus to mobile devices. Similar to other expanding definitions of literacy that recognise cultural and historical ways of making meaning, digital literacy does not replace traditional forms of literacy, but instead builds upon and expands the skills that form the foundation of traditional forms of literacy. Digital literacy should be considered to be a part of the path to knowledge.
Reform mathematics is an approach to mathematics education, particularly in North America. It is based on principles explained in 1989 by the National Council of Teachers of Mathematics (NCTM). The NCTM document Curriculum and Evaluation Standards for School Mathematics (CESSM) set forth a vision for K–12 mathematics education in the United States and Canada. The CESSM recommendations were adopted by many local- and federal-level education agencies during the 1990s. In 2000, the NCTM revised its CESSM with the publication of Principles and Standards for School Mathematics (PSSM). Like those in the first publication, the updated recommendations became the basis for many states' mathematics standards, and the method in textbooks developed by many federally-funded projects. The CESSM de-emphasised manual arithmetic in favor of students developing their own conceptual thinking and problem solving. The PSSM presents a more balanced view, but still has the same emphases.
Futurekids, Inc. is a privately held internationally franchised K–12 educational software company headquartered in El Segundo, California, which focuses on technological literacy and computer literacy.
Computational thinking (CT) is the mental skill to apply concepts, methods, problem solving techniques, and logic reasoning, derived from computing and computer science, to solve problems in all areas, including our daily lives. In education, CT is a set of problem-solving methods that involve expressing problems and their solutions in ways that a computer could also execute. It involves automation of processes, but also using computing to explore, analyze, and understand processes.
Conrad Wolfram is a British technologist and businessman known for his work in information technology and mathematics education reform. In June 2020, Wolfram released his first book, The Math(s) Fix: An Education Blueprint for the AI Age.
Statistics education is the practice of teaching and learning of statistics, along with the associated scholarly research.
Computer-Based Math is an educational project started by Conrad Wolfram in 2010 to promote the idea that routine mathematical calculations should be done with a computer.
21st century skills comprise skills, abilities, and learning dispositions that have been identified as being required for success in 21st century society and workplaces by educators, business leaders, academics, and governmental agencies. This is part of a growing international movement focusing on the skills required for students to master in preparation for success in a rapidly changing, digital society. Many of these skills are also associated with deeper learning, which is based on mastering skills such as analytic reasoning, complex problem solving, and teamwork. These skills differ from traditional academic skills in that they are not primarily content knowledge-based.
The computational knowledge economy is an economy 'where value is derived from the automated generation of knowledge.
A notebook interface is a virtual notebook environment used for literate programming, a method of writing computer programs. Some notebooks are WYSIWYG environments including executable calculations embedded in formatted documents; others separate calculations and text into separate sections. Notebooks share some goals and features with spreadsheets and word processors but go beyond their limited data models.
References
- ↑ Conrad Wolfram on Computational Thinking, gettingsmart.com, Aug 5, 2020.
- ↑ Computational Literacy and the big picture. Journal of Mathematical Thinking and Learning Vol 20, 2018
- ↑ The Math(s) Fix p28. ISBN 9781579550295
- ↑ UK Parliamentary Education Committee
- ↑ Journal of Computer Science Integration, Vol 1, 2018
- ↑ Educational Development Center