**Mathematics**: The deductive study of shape, quantity, and dependence. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)

**Mathematical Concepts**: Numeric or quantitative entities, descriptions, properties, relationships, operations, and events.

**Models, Theoretical**: Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment.

**Mathematical Computing**: Computer-assisted interpretation and analysis of various mathematical functions related to a particular problem.

**Achievement**: Success in bringing an effort to the desired end; the degree or level of success attained in some specified area (esp. scholastic) or in general.

**Aptitude**: The ability to acquire general or special types of knowledge or skill.

**Algorithms**: A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task.

**Interdisciplinary Studies**: Programs of study which span the traditional boundaries of academic scholarship.

**Learning Disorders**: Conditions characterized by a significant discrepancy between an individual's perceived level of intellect and their ability to acquire new language and other cognitive skills. These disorders may result from organic or psychological conditions. Relatively common subtypes include DYSLEXIA, DYSCALCULIA, and DYSGRAPHIA.

**Test Taking Skills**: Skills and strategies, unrelated to the traits a test is intended to measure, that may increase test takers' scores -- may include the effects of coaching or experience in taking tests. (ERIC Thesaurus)

**Test Anxiety Scale**: A self-reporting test consisting of items concerning fear and worry about taking tests and physiological activity, such as heart rate, sweating, etc., before, during, and after tests.

**Engineering**: The practical application of physical, mechanical, and mathematical principles. (Stedman, 25th ed)

**Biology**: One of the BIOLOGICAL SCIENCE DISCIPLINES concerned with the origin, structure, development, growth, function, genetics, and reproduction of animals, plants, and microorganisms.

**Dyscalculia**: Impaired ability in numerical concepts. These inabilities arise as a result of primary neurological lesion, are syndromic (e.g., GERSTMANN SYNDROME ) or acquired due to brain damage.

**Underachievement**: Performance, usually in school work, poorer than that predicted from aptitude and/or intelligence testing.

**Problem Solving**: A learning situation involving more than one alternative from which a selection is made in order to attain a specific goal.

**Models, Biological**: Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment.

**Reading**

**Computer Simulation**: Computer-based representation of physical systems and phenomena such as chemical processes.

**Technology**: The application of scientific knowledge to practical purposes in any field. It includes methods, techniques, and instrumentation.

**Software**: Sequential operating programs and data which instruct the functioning of a digital computer.

**Science**: The study of natural phenomena by observation, measurement, and experimentation.

**Physics**: The study of those aspects of energy and matter in terms of elementary principles and laws. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)

**Educational Measurement**: The assessing of academic or educational achievement. It includes all aspects of testing and test construction.

**Knowledge**: The body of truths or facts accumulated in the course of time, the cumulated sum of information, its volume and nature, in any civilization, period, or country.

**Students**: Individuals enrolled in a school or formal educational program.

**Delaware**

**Intelligence**: The ability to learn and to deal with new situations and to deal effectively with tasks involving abstractions.

**Individuality**: Those psychological characteristics which differentiate individuals from one another.

**Dyslexia**: A cognitive disorder characterized by an impaired ability to comprehend written and printed words or phrases despite intact vision. This condition may be developmental or acquired. Developmental dyslexia is marked by reading achievement that falls substantially below that expected given the individual's chronological age, measured intelligence, and age-appropriate education. The disturbance in reading significantly interferes with academic achievement or with activities of daily living that require reading skills. (From DSM-IV)

**Aptitude Tests**: Primarily non-verbal tests designed to predict an individual's future learning ability or performance.

**Child Psychology**: The study of normal and abnormal behavior of children.

**Education of Hearing Disabled**: The teaching or training of those individuals with hearing disability or impairment.

**Child Development**: The continuous sequential physiological and psychological maturing of an individual from birth up to but not including ADOLESCENCE.

**Natural Science Disciplines**: The sciences dealing with processes observable in nature.

**Concept Formation**: A cognitive process involving the formation of ideas generalized from the knowledge of qualities, aspects, and relations of objects.

**Language Arts**: Skills in the use of language which lead to proficiency in written or spoken communication.

**Logic**: The science that investigates the principles governing correct or reliable inference and deals with the canons and criteria of validity in thought and demonstration. This system of reasoning is applicable to any branch of knowledge or study. (Random House Unabridged Dictionary, 2d ed & Sippl, Computer Dictionary, 4th ed)

**Teaching**: The educational process of instructing.

**Curriculum**: A course of study offered by an educational institution.

**Schools**: Educational institutions.

**Intelligence Tests**: Standardized tests that measure the present general ability or aptitude for intellectual performance.

**Intuition**: Knowing or understanding without conscious use of reasoning. (Thesaurus of ERIC Descriptors, 1994)

**Universities**: Educational institutions providing facilities for teaching and research and authorized to grant academic degrees.

**Comprehension**: The act or fact of grasping the meaning, nature, or importance of; understanding. (American Heritage Dictionary, 4th ed) Includes understanding by a patient or research subject of information disclosed orally or in writing.

**Early Intervention (Education)**: Procedures and programs that facilitate the development or skill acquisition in infants and young children who have disabilities, who are at risk for developing disabilities, or who are gifted. It includes programs that are designed to prevent handicapping conditions in infants and young children and family-centered programs designed to affect the functioning of infants and children with special needs. (From Journal of Early Intervention, Editorial, 1989, vol. 13, no. 1, p. 3; A Discursive Dictionary of Health Care, prepared for the U.S. House of Representatives Committee on Interstate and Foreign Commerce, 1976)

**Cognition**: Intellectual or mental process whereby an organism obtains knowledge.

**Educational Status**: Educational attainment or level of education of individuals.

**Learning**: Relatively permanent change in behavior that is the result of past experience or practice. The concept includes the acquisition of knowledge.

**Education, Special**: Education of the individual who markedly deviates intellectually, physically, socially, or emotionally from those considered to be normal, thus requiring special instruction.

**Genetic Pleiotropy**: A phenomenon in which multiple and diverse phenotypic outcomes are influenced by a single gene (or single gene product.)

**Education**: Acquisition of knowledge as a result of instruction in a formal course of study.

**Physiology**: The biological science concerned with the life-supporting properties, functions, and processes of living organisms or their parts.

**Language**: A verbal or nonverbal means of communicating ideas or feelings.

**Deafness**: A general term for the complete loss of the ability to hear from both ears.

**Research**: Critical and exhaustive investigation or experimentation, having for its aim the discovery of new facts and their correct interpretation, the revision of accepted conclusions, theories, or laws in the light of newly discovered facts, or the practical application of such new or revised conclusions, theories, or laws. (Webster, 3d ed)

**Models, Educational**: Theoretical models which propose methods of learning or teaching as a basis or adjunct to changes in attitude or behavior. These educational interventions are usually applied in the fields of health and patient education but are not restricted to patient care.

**Memory, Short-Term**: Remembrance of information for a few seconds to hours.

**Executive Function**: A set of cognitive functions that controls complex, goal-directed thought and behavior. Executive function involves multiple domains, such as CONCEPT FORMATION, goal management, cognitive flexibility, INHIBITION control, and WORKING MEMORY. Impaired executive function is seen in a range of disorders, e.g., SCHIZOPHRENIA; and ADHD.

**Language Development**: The gradual expansion in complexity and meaning of symbols and sounds as perceived and interpreted by the individual through a maturational and learning process. Stages in development include babbling, cooing, word imitation with cognition, and use of short sentences.

**Neuropsychological Tests**: Tests designed to assess neurological function associated with certain behaviors. They are used in diagnosing brain dysfunction or damage and central nervous system disorders or injury.

**Affective Symptoms**: Mood or emotional responses dissonant with or inappropriate to the behavior and/or stimulus.

**Adolescent Psychology**: Field of psychology concerned with the normal and abnormal behavior of adolescents. It includes mental processes as well as observable responses.

**Longitudinal Studies**: Studies in which variables relating to an individual or group of individuals are assessed over a period of time.

**Missouri**

**Task Performance and Analysis**: The detailed examination of observable activity or behavior associated with the execution or completion of a required function or unit of work.

**Cognition Disorders**: Disturbances in mental processes related to learning, thinking, reasoning, and judgment.

**Twins**: Two individuals derived from two FETUSES that were fertilized at or about the same time, developed in the UTERUS simultaneously, and born to the same mother. Twins are either monozygotic (TWINS, MONOZYGOTIC) or dizygotic (TWINS, DIZYGOTIC).

**Computational Biology**: A field of biology concerned with the development of techniques for the collection and manipulation of biological data, and the use of such data to make biological discoveries or predictions. This field encompasses all computational methods and theories for solving biological problems including manipulation of models and datasets.

**Systems Biology**: Comprehensive, methodical analysis of complex biological systems by monitoring responses to perturbations of biological processes. Large scale, computerized collection and analysis of the data are used to develop and test models of biological systems.

**History, 20th Century**: Time period from 1901 through 2000 of the common era.

**Statistics as Topic**: The science and art of collecting, summarizing, and analyzing data that are subject to random variation. The term is also applied to the data themselves and to the summarization of the data.

**Sex Factors**: Maleness or femaleness as a constituent element or influence contributing to the production of a result. It may be applicable to the cause or effect of a circumstance. It is used with human or animal concepts but should be differentiated from SEX CHARACTERISTICS, anatomical or physiological manifestations of sex, and from SEX DISTRIBUTION, the number of males and females in given circumstances.

**Models, Statistical**: Statistical formulations or analyses which, when applied to data and found to fit the data, are then used to verify the assumptions and parameters used in the analysis. Examples of statistical models are the linear model, binomial model, polynomial model, two-parameter model, etc.

**Nonlinear Dynamics**: The study of systems which respond disproportionately (nonlinearly) to initial conditions or perturbing stimuli. Nonlinear systems may exhibit "chaos" which is classically characterized as sensitive dependence on initial conditions. Chaotic systems, while distinguished from more ordered periodic systems, are not random. When their behavior over time is appropriately displayed (in "phase space"), constraints are evident which are described by "strange attractors". Phase space representations of chaotic systems, or strange attractors, usually reveal fractal (FRACTALS) self-similarity across time scales. Natural, including biological, systems often display nonlinear dynamics and chaos.

**Attention Deficit Disorder with Hyperactivity**: A behavior disorder originating in childhood in which the essential features are signs of developmentally inappropriate inattention, impulsivity, and hyperactivity. Although most individuals have symptoms of both inattention and hyperactivity-impulsivity, one or the other pattern may be predominant. The disorder is more frequent in males than females. Onset is in childhood. Symptoms often attenuate during late adolescence although a minority experience the full complement of symptoms into mid-adulthood. (From DSM-V)

**Attention**: Focusing on certain aspects of current experience to the exclusion of others. It is the act of heeding or taking notice or concentrating.

**Models, Genetic**: Theoretical representations that simulate the behavior or activity of genetic processes or phenomena. They include the use of mathematical equations, computers, and other electronic equipment.

**Data Interpretation, Statistical**: Application of statistical procedures to analyze specific observed or assumed facts from a particular study.

**Sex Characteristics**: Those characteristics that distinguish one SEX from the other. The primary sex characteristics are the OVARIES and TESTES and their related hormones. Secondary sex characteristics are those which are masculine or feminine but not directly related to reproduction.

**Anxiety**: Feeling or emotion of dread, apprehension, and impending disaster but not disabling as with ANXIETY DISORDERS.

**Program Evaluation**: Studies designed to assess the efficacy of programs. They may include the evaluation of cost-effectiveness, the extent to which objectives are met, or impact.

Grillet, Pierre Antoine (2007). Abstract

**algebra**. Graduate texts in**mathematics**. 242 (2 ed.). Springer. ISBN 978-0-387-71567-4. ... Lang, Serge (2002).**Algebra**. Graduate Texts in**Mathematics**. Springer. ISBN 0-387-95385-X.. ... In**mathematics**, especially group theory, the elements of any group may be partitioned into conjugacy classes; members of the ... Dummit, David S.; Foote, Richard M. (2004). Abstract**Algebra**(3rd ed.). John Wiley & Sons. ISBN 0-471-43334-9.. ...In

**mathematics**, and more specifically in homological**algebra**, a resolution (or left resolution; dually a coresolution or right ... Graded modules and**algebras**[edit]. Let M be a graded module over a graded**algebra**, which is generated over a field by its ... Eisenbud, David (1995), Commutative**algebra**. With a view toward algebraic geometry, Graduate Texts in**Mathematics**, 150, Berlin ... Weibel, Charles A. (1994). An introduction to homological**algebra**. Cambridge Studies in Advanced**Mathematics**. 38. Cambridge ...Bourbaki, Nicolas (1998), Elements of

**Mathematics**:**Algebra**I Chapters 1-3, Berlin, New York: Springer-Verlag, ISBN 978-3-540- ...**Algebras**over fields[edit]. Main articles:**Algebra**over a field and Lie**algebra**... The tensor**algebra**T(V) is a formal way of adding products to any vector space V to obtain an**algebra**.[72] As a vector space, ... Lang, Serge (2002),**Algebra**, Graduate Texts in**Mathematics**, 211 (Revised third ed.), New York: Springer-Verlag, ISBN 978-0-387- ...Islamic

**mathematics**covered**algebra**, geometry and arithmetic.**Algebra**was mainly used for recreation: it had few practical ... Main article:**Mathematics**in medieval Islam. Islamic mathematicians gathered, organised and clarified the**mathematics**they ... Maher, P. (1998). From Al-Jabr to**Algebra**.**Mathematics**in School, 27(4), 14-15. ... Hogendijk, Jan P.; Berggren, J. L. (1989). "Episodes in the**Mathematics**of Medieval Islam by J. Lennart Berggren". Journal of ...Whitney, H. (1933). "Characteristic Functions and the

**Algebra**of Logic". Annals of**Mathematics**. 34: 405-414. doi:10.2307/ ... Wallis, John (1685). A treatise of**algebra**. London: John Playford.. *^ Dedekind, Richard (1888). Was sind und was sollen die ... In**mathematics**, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, allows for multiple ... Burgin, Mark (2004). "Unified Foundations of**Mathematics**". arXiv:math/0403186.. *^ Burgin, Mark (2011). Theory of Named Sets. ...Graduate Texts in

**Mathematics**. 156. Springer. ISBN 0-387-94374-9. Kuratowski, K. (1966). Topology Vol. I. Academic Press. ISBN ... ISBN 3-7643-2428-7. CS1 maint: Multiple names: authors list (link) Arveson, William (1981). An Invitation to C*-**Algebras**. ... Graduate Texts in**Mathematics**. Springer-Verlag. ISBN 978-0-387-98412-4. Retrieved 2008-12-04. Ambrosio, L., Gigli, N. & Savaré ... Graduate Texts in**Mathematics**. 39. New York: Springer-Verlag. ISBN 0-387-90176-0. Bourbaki, Nicolas (1966). Elements of ...After some

**algebra**, this becomes M. v. 1. =. 2. λ. 1. u. 1. +. 0. M. T. u. 1. =. 0. +. 2. λ. 2. v. 1. {\displaystyle {\begin{ ... Journal of the Society for Industrial and Applied**Mathematics**. 6 (1): 51-90. doi:10.1137/0106005. JSTOR 2098862. MR 0092215.. ... In linear**algebra**, the singular-value decomposition (SVD) is a factorization of a real or complex matrix. It is the ... In numerical linear**algebra**the singular values can be used to determine the effective rank of a matrix, as rounding error may ...Nathan, M. J. (2002).

**Mathematics**Learning:**Algebra**. In James W. Guthrie (Ed.) Encyclopedia of Education, Second Edition (Vol. ... Nathan, M. J., and Koedinger, K. R. (2000). Moving beyond teachers' intuitive beliefs about**algebra**learning.**Mathematics**... Nathan, M. J., Kintsch, W., & Young, E. (1992). A theory of**algebra**word problem comprehension and its implications for the ... Evidence from an early**algebra**lesson. In Goldman, R., Pea, R., Barron, B. J., and Derry, S. (Eds.) Video Research in the ...1130-1180

**Mathematics**: Al-Samawal. An important member of al-Karaji's school of**algebra**. Gave this definition of**algebra**: "[it ... Rashed, R (1994). The development of Arabic**mathematics**: between arithmetic and**algebra**. London, England.. ... 1135**Mathematics**: Sharaf al-Dīn al-Ṭūsī. Follows al-Khayyam's application of**algebra**of geometry, rather than follow the ...**Mathematics**: Ibn al-Banna and al-Qalasadi used symbols for**mathematics**"and, although we do not know exactly when their use ...If the underlying term ring is a differential

**algebra**, then the**algebra**of formal power series is also a differential**algebra**, ... Wikimedia Commons has media related to Series (**mathematics**).. *. "Series", Encyclopedia of**Mathematics**, EMS Press, 2001 [1994] ... In this case the**algebra**of formal power series is the total**algebra**of the monoid of natural numbers over the underlying term ... Nicolas Bourbaki (1989),**Algebra**, Springer. : §III.2.11. *^ O'Connor, J.J. & Robertson, E.F. (February 1996). "A history of ..."Matrix", Encyclopedia of

**Mathematics**, EMS Press, 2001 [1994]. *. Kaw, Autar K., Introduction to Matrix**Algebra**, ISBN 978-0-615- ... Lang, Serge (2002),**Algebra**, Graduate Texts in**Mathematics**, 211 (Revised third ed.), New York: Springer-Verlag, ISBN 978-0-387- ... Greub, Werner Hildbert (1975), Linear**algebra**, Graduate Texts in**Mathematics**, Berlin, DE; New York, NY: Springer-Verlag, ISBN ... Schneider, Hans; Barker, George Phillip (2012), Matrices and Linear**Algebra**, Dover Books on**Mathematics**, Courier Dover ...2012). "S. N. Chernikov and the development of infinite group theory".

**Algebra**and Discrete**Mathematics**. 13 (2): 169-208. ... In**mathematics**, in the field of group theory, a locally finite group is a type of group that can be studied in ways analogous ... 256-262 Dixon, Martyn R. (1994), Sylow theory, formations and Fitting classes in locally finite groups, Series in**Algebra**, 2, ... Curtis, Charles; Reiner, Irving (1962), Representation Theory of Finite Groups and Associated**Algebras**, John Wiley & Sons, pp. ...2012). "S. N. Chernikov and the development of infinite group theory".

**Algebra**and Discrete**Mathematics**. 13 (2): 169-208. ... Palmer (2001). Banach**algebras**and the general theory of *-**algebras**. p. 1283. For the term, compare Engel's theorem, also on ... ISBN 0-387-90518-9. Palmer, Theodore W. (1994). Banach**algebras**and the general theory of *-**algebras**. Cambridge, UK: Cambridge ... Hungerford (1974).**Algebra**. p. 100. Zassenhaus (1999). The theory of groups. p. 143. Zassenhaus (1999). Theorem 11. p. 143. ...**Algebra**and Discrete

**Mathematics**. 13 (2): 169-208. Plotkin, Boris. "Sergei Nikolaevich Chernikov. Memoirs" (PDF).

**Algebra**and ... Journal

**Algebra**Discrete Math. M. Kurosh A.G., Chernikov S.N. (1947) Soluble and nilpotent groups. Uspekhi Math. Nauk 2, number ... Until November 1931 he taught

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**Mathematics**and Statistics. Retrieved 7 July 2016. Ershov, Y.L.; et al. (1988). "Sergei ...

Tian JP (2008). Evolution

**Algebras**and their Applications. Lecture Notes in**Mathematics**. 1921. Berlin; New York: Springer. doi: ... Interdisciplinary Applied**Mathematics**. 27 (2nd ed.). New York: Springer-Verlag. ISBN 0-387-20191-2. . LCCN 2003065728. OCLC ... The**mathematics**of genetic drift depend on the effective population size, but it is not clear how this is related to the actual ... genetic drift has no direction and is guided only by the**mathematics**of chance.[28] As a result, drift acts upon the genotypic ...... and their

**Algebra**course was designated one of five exemplary curricula for K-12**mathematics**educated by the US Department of ... "Middle School**Mathematics**intervention report: Cognitive Tutor®**Algebra**I" (PDF). What Works Clearinghouse. whatworks.ed.gov. ...**algebra**and geometry". PACT's most successful product was the Cognitive Tutor**Algebra**course. Originally created in the early ... Further, in 2005, Carnegie Learning released Bridge to**Algebra**, a product intended for middle schools that was piloted in over ...Examples of courses include

**mathematics**(split from grade 7 into**algebra**, geometry and physics), visual arts, Russian language ... For instance,**algebra**and geometry are taught instead of "**mathematics**." In the second preparatory phase, students study science ...**mathematics**, science/physics/chemistry), but also on a series of skills completed during the last year and on oral examinations ... which includes**Mathematics**, Literature and English. The maximum score for each test is 10, with the first two subjects (called ...Lang, Serge (2002).

**Algebra**. Graduate Texts in**Mathematics**. 211. Berlin; New York: Springer-Verlag. doi:10.1007/978-1-4613-0041 ... Faticoni, Theodore G. (2012). The**Mathematics**of Infinity: A Guide to Great Ideas. Pure and Applied**Mathematics**: A Wiley Series ... Eisenbud, David (1995). Commutative**Algebra**. Graduate Texts in**Mathematics**. 150. Berlin; New York: Springer-Verlag. Section 3.3 ... Stillwell, John (2010).**Mathematics**and Its History. Undergraduate Texts in**Mathematics**(3rd ed.). Springer. p. 40. ISBN 978-1- ...AP European History

**Mathematics**:**Algebra**I; Geometry;**Algebra**II;**Algebra**II BC; Precalculus/Trigonometry; Precaclulus/ ...**Mathematics**- Grade 7 take Elementary

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**mathematics**through**Algebra**II and Trigonometry; 3 years of science that must include Physics, Chemistry, and Biology (Hackley ... Finite**Mathematics**, Statistics, Organic Chemistry, Marine Biology, Ecology, Etymology, Computer Science, Electronic Publishing ...Fundamental structures of

**algebra**and discrete**mathematics**. p. 128. Pierre Antoine Grillet (2007). Abstract**algebra**. p. 124. ... In abstract**algebra**, the field of fractions of an integral domain is the smallest field in which it can be embedded. The ... Ėrnest Borisovich Vinberg (2003). A course in**algebra**. p. 131. Stephan Foldes (1994). ... Rings, Modules, and Linear**Algebra**: Hartley, B & Hawkes, T.O. 1970. ...It describes the maximal subgroups of the symmetric groups.[citation needed] Linear

**Algebra**(= Eagle**Mathematics**Series. vol. ... Michael O'Nan at the**Mathematics**Genealogy Project Michael E. O'Nan (1976). "Some evidence for the existence of a new simple ...Foldes, Stephan (1994). Fundamental Structures of

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