TeacherA teacher, also called a schoolteacher or formally an educator, is a person who helps students to acquire knowledge, competence, or virtue, via the practice of teaching. Informally the role of teacher may be taken on by anyone (e.g. when showing a colleague how to perform a specific task). In some countries, teaching young people of school age may be carried out in an informal setting, such as within the family (homeschooling), rather than in a formal setting such as a school or college.
Vector spaceIn mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, may be added together and multiplied ("scaled") by numbers called scalars. Scalars are often real numbers, but can be complex numbers or, more generally, elements of any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. The terms real vector space and complex vector space are often used to specify the nature of the scalars: real coordinate space or complex coordinate space.
Active learning (machine learning)Active learning is a special case of machine learning in which a learning algorithm can interactively query a user (or some other information source) to label new data points with the desired outputs. In statistics literature, it is sometimes also called optimal experimental design. The information source is also called teacher or oracle. There are situations in which unlabeled data is abundant but manual labeling is expensive. In such a scenario, learning algorithms can actively query the user/teacher for labels.
Space (mathematics)In mathematics, a space is a set (sometimes called a universe) with some added structure. While modern mathematics uses many types of spaces, such as Euclidean spaces, linear spaces, topological spaces, Hilbert spaces, or probability spaces, it does not define the notion of "space" itself. A space consists of selected mathematical objects that are treated as points, and selected relationships between these points. The nature of the points can vary widely: for example, the points can be elements of a set, functions on another space, or subspaces of another space.
Learning theory (education)Learning theory describes how students receive, process, and retain knowledge during learning. Cognitive, emotional, and environmental influences, as well as prior experience, all play a part in how understanding, or a worldview, is acquired or changed and knowledge and skills retained. Behaviorists look at learning as an aspect of conditioning and advocate a system of rewards and targets in education.
Normed vector spaceIn mathematics, a normed vector space or normed space is a vector space over the real or complex numbers on which a norm is defined. A norm is a generalization of the intuitive notion of "length" in the physical world. If is a vector space over , where is a field equal to or to , then a norm on is a map , typically denoted by , satisfying the following four axioms: Non-negativity: for every ,. Positive definiteness: for every , if and only if is the zero vector.
Teacher educationTeacher education or teacher training refers to programs, policies, procedures, and provision designed to equip (prospective) teachers with the knowledge, attitudes, behaviors, approaches, methodologies and skills they require to perform their tasks effectively in the classroom, school, and wider community. The professionals who engage in training the prospective teachers are called teacher educators (or, in some contexts, teacher trainers). There is a longstanding and ongoing debate about the most appropriate term to describe these activities.
Social learning theorySocial learning is a theory of learning process social behavior which proposes that new behaviors can be acquired by observing and imitating others. It states that learning is a cognitive process that takes place in a social context and can occur purely through observation or direct instruction, even in the absence of motor reproduction or direct reinforcement. In addition to the observation of behavior, learning also occurs through the observation of rewards and punishments, a process known as vicarious reinforcement.
Observational learningObservational learning is learning that occurs through observing the behavior of others. It is a form of social learning which takes various forms, based on various processes. In humans, this form of learning seems to not need reinforcement to occur, but instead, requires a social model such as a parent, sibling, friend, or teacher with surroundings. Particularly in childhood, a model is someone of authority or higher status in an environment.
Secondary educationSecondary education or post-primary education covers two phases on the International Standard Classification of Education scale. Level 2 or lower secondary education (less commonly junior secondary education) is considered the second and final phase of basic education, and level 3 upper secondary education or senior secondary education is the stage before tertiary education. Every country aims to provide basic education, but the systems and terminology remain unique to them.
