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Modern Elementary Mathematics
Modern elementary mathematics is the theory and practice of teaching elementary mathematics according to contemporary research and thinking about learning. This can include pedagogical ideas, mathematics education research frameworks, and curricular material. In practicing modern elementary mathematics, teachers may use new and emerging media and technologies like social media and video games, as well as applying new teaching techniques based on the individualization of learning, in-depth study of the psychology of mathematics education, and integrating mathematics with science, technology, engineering and the arts. General practice Areas of mathematics Making all areas of mathematics accessible to young children is a key goal of modern elementary mathematics. Author and academic Liping Ma calls for "profound understanding of fundamental mathematics" by elementary teachers and parents of learners, as well as learners themselves. * Algebra: Early algebra covers the approach ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Mathematics
Elementary mathematics consists of mathematics topics frequently taught at the primary or secondary school levels. In the Canadian curriculum, there are six basic strands in Elementary Mathematics: Number, Algebra, Data, Spatial Sense, Financial Literacy, and Social emotional learning skills and math processes. These six strands are the focus of Mathematics education from grade 1 through grade 8. In secondary school, the main topics in elementary mathematics from grade nine until grade ten are: Number Sense and algebra, Linear Relations, Measurement and Geometry. Once students enter grade eleven and twelve students begin university and college preparation classes, which include: Functions, Calculus & Vectors, Advanced Functions, and Data Management. Strands of elementary mathematics Number Sense and Numeration Number Sense is an understanding of numbers and operations. In the 'Number Sense and Numeration' strand students develop an understanding of numbers by being taught ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Problem Solving
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields. The former is an example of simple problem solving (SPS) addressing one issue, whereas the latter is complex problem solving (CPS) with multiple interrelated obstacles. Another classification is into well-defined problems with specific obstacles and goals, and ill-defined problems in which the current situation is troublesome but it is not clear what kind of resolution to aim for. Similarly, one may distinguish formal or fact-based problems requiring psychometric intelligence, versus socio-emotional problems which depend on the changeable emotions of individuals or groups, such as tactful behavior, fashion, or gift choices. Solutions require sufficient resources and knowledge to attain the goal. Professionals such as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Learning Style
Learning styles refer to a range of theories that aim to account for differences in individuals' learning. Although there is ample evidence that individuals express personal preferences for how they prefer to receive information, few studies have found any validity in using learning styles in education. Many theories share the proposition that humans can be classified according to their "style" of learning, but differ in how the proposed styles should be defined, categorized and assessed. A common concept is that individuals differ in how they learn. The idea of individualized learning styles became popular in the 1970s, and has greatly influenced education despite the criticism that the idea has received from some researchers. Proponents recommend that teachers have to run a needs analysis to assess the learning styles of their students and adapt their classroom methods to best fit each student's learning style. Critics say there is no consistent evidence that identifying an indiv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expert System
In artificial intelligence, an expert system is a computer system emulating the decision-making ability of a human expert. Expert systems are designed to solve complex problems by reasoning through bodies of knowledge, represented mainly as if–then rules rather than through conventional procedural code. The first expert systems were created in the 1970s and then proliferated in the 1980s. Expert systems were among the first truly successful forms of artificial intelligence (AI) software. An expert system is divided into two subsystems: the inference engine and the knowledge base. The knowledge base represents facts and rules. The inference engine applies the rules to the known facts to deduce new facts. Inference engines can also include explanation and debugging abilities. History Early development Soon after the dawn of modern computers in the late 1940s and early 1950s, researchers started realizing the immense potential these machines had for modern society. One of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Cognition
Numerical cognition is a subdiscipline of cognitive science that studies the cognitive, developmental and neural bases of numbers and mathematics. As with many cognitive science endeavors, this is a highly interdisciplinary topic, and includes researchers in cognitive psychology, developmental psychology, neuroscience and cognitive linguistics. This discipline, although it may interact with questions in the philosophy of mathematics, is primarily concerned with empirical questions. Topics included in the domain of numerical cognition include: *How do non-human animals process numerosity? *How do infants acquire an understanding of numbers (and how much is inborn)? *How do humans associate linguistic symbols with numerical quantities? *How do these capacities underlie our ability to perform complex calculations? *What are the neural bases of these abilities, both in humans and in non-humans? *What metaphorical capacities and processes allow us to extend our numerical understandin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Embodied Cognition
Embodied cognition is the theory that many features of cognition, whether human or otherwise, are shaped by aspects of an organism's entire body. Sensory and motor systems are seen as fundamentally integrated with cognitive processing. The cognitive features include high-level mental constructs (such as concepts and Categorization, categories) and performance on various cognitive tasks (such as reasoning or judgment). The bodily aspects involve the motor system, the perceptual system, the bodily interactions with the environment (situatedness), and the assumptions about the world built into the organism's functional structure. The embodied mind thesis challenges other theories, such as Cognitivism (psychology), cognitivism, computationalism, and Dualism (philosophy of mind), Cartesian dualism. It is closely related to the extended mind thesis, situated cognition, and enactivism. The modern version depends on insights drawn from up to date research in psychology, linguistics, cogni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maria Montessori
Maria Tecla Artemisia Montessori ( , ; August 31, 1870 – May 6, 1952) was an Italian physician and educator best known for the philosophy of education that bears her name, and her writing on scientific pedagogy. At an early age, Montessori enrolled in classes at an all-boys technical school, with hopes of becoming an engineer. She soon had a change of heart and began medical school at the Sapienza University of Rome, becoming one of the first women to attend medical school in Italy; she graduated with honors in 1896. Her educational method is in use today in many public and private schools globally. Life and career Birth and family Montessori was born on August 31, 1870, in Chiaravalle, Italy. Her father, Alessandro Montessori, age 33, was an official of the Ministry of Finance working in the local state-run tobacco factory. Her mother, Renilde Stoppani, 25 years old, was well-educated for the times and was the great-niece of Italian geologist and paleontologist Antonio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Algorithms
In elementary arithmetic, a standard algorithm or method is a specific method of computation which is conventionally taught for solving particular mathematical problems. These methods vary somewhat by nation and time, but generally include exchanging, regrouping, long division, and long multiplication using a standard notation, and standard formulas for average, area, and volume. Similar methods also exist for procedures such as square root and even more sophisticated functions, but have fallen out of the general mathematics curriculum in favor of calculators (or tables and slide rules before them). The concepts of reform mathematics which the NCTM introduced in 1989 favors an alternative approach. It proposes a deeper understanding of the underlying theory instead of memorization of specific methods will allow students to develop individual methods which solve the same problems. Students' alternative algorithms are often just as correct, efficient, and generalizable as the stand ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spaced Repetition
Spaced repetition is an evidence-based learning technique that is usually performed with flashcards. Newly introduced and more difficult flashcards are shown more frequently, while older and less difficult flashcards are shown less frequently in order to exploit the psychological spacing effect. The use of spaced repetition has been proven to increase the rate of learning. Although the principle is useful in many contexts, spaced repetition is commonly applied in contexts in which a learner must acquire many items and retain them indefinitely in memory. It is, therefore, well suited for the problem of vocabulary acquisition in the course of second-language learning. A number of spaced repetition software programs have been developed to aid the learning process. It is also possible to perform spaced repetition with flashcards using the Leitner system. Alternative names for spaced repetition include spaced rehearsal, expanding rehearsal, graduated intervals, repetition spacing, r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mnemonic
A mnemonic ( ) device, or memory device, is any learning technique that aids information retention or retrieval (remembering) in the human memory for better understanding. Mnemonics make use of elaborative encoding, retrieval cues, and imagery as specific tools to encode information in a way that allows for efficient storage and retrieval. Mnemonics aid original information in becoming associated with something more accessible or meaningful—which, in turn, provides better retention of the information. Commonly encountered mnemonics are often used for lists and in auditory form, such as short poems, acronyms, initialisms, or memorable phrases, but mnemonics can also be used for other types of information and in visual or kinesthetic forms. Their use is based on the observation that the human mind more easily remembers spatial, personal, surprising, physical, sexual, humorous, or otherwise "relatable" information, rather than more abstract or impersonal forms of informa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constructivism (learning Theory)
Constructivism may refer to: Art and architecture * Constructivism (art), an early 20th-century artistic movement that extols art as a practice for social purposes * Constructivist architecture, an architectural movement in Russia in the 1920s and 1930s Education * Constructivism (philosophy of education), a theory about the nature of learning that focuses on how humans make meaning from their experiences * Constructivism in science education * Constructivist teaching methods, based on constructivist learning theory Mathematics * Constructivism (philosophy of mathematics), a logic for founding mathematics that accepts only objects that can be effectively constructed * Constructivist type theory Philosophy * Constructivism (philosophy of mathematics), a philosophical view that asserts the necessity of constructing a mathematical object to prove that it exists * Constructivism (philosophy of science), a philosophical view maintaining that science consists of mental constructs c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Anxiety
Mathematical anxiety, also known as math phobia, is anxiety about one's ability to do mathematics. Math Anxiety Mark H. Ashcraft defines math anxiety as "a feeling of tension, apprehension, or fear that interferes with math performance" (2002, p. 1). It is a phenomenon that is often considered when examining students' problems in mathematics. According to the American Psychological Association, mathematical anxiety is often linked to testing anxiety. This anxiety can cause distress and likely causes a dislike and avoidance of all math-related tasks. The academic study of math anxiety originates as early as the 1950s, where Mary Fides Gough introduced the term ''mathemaphobia'' to describe the phobia-like feelings of many towards mathematics. The first math anxiety measurement scale was developed by Richardson and Suinn in 1972. Since this development, several researchers have examined math anxiety in empirical studies. Hembree (1990) conducted a meta-analysis of 151 studies c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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