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Topic: Reflection mathematics

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Hyperbolic geometry

Symmetry

Typhoon

Glide reflection

	Protfolio Guideline: Mathematics Education Graduate Programs, School of Education, Indiana University at Bloomington
		The qualifying portfolio is intended to assess the student’s understanding of major concepts and issues in mathematics education as well the breadth and depth of her or his preparation in the field.
		The reflection should include a discussion of how each sample in the portfolio is indicative of the student's professional growth and development, especially with respect to competence in designing and conducting empirical research or other forms of scholarly inquiry in the field, or in developing curricular or pedagogical innovations built on sound principles.
		The reflection should conclude with a discussion of the student's professional plans and intended contributions to the field of mathematics education.
	www.indiana.edu /~mathed/Portfolio.html (1413 words)

	Reflection (mathematics) - Wikipedia, the free encyclopedia
		In order to reflect a planar figure one needs the "mirror" to be a line ("axis of reflection"), while for reflections in the three-dimensional space one would use a plane for a mirror.
		A reflection does not move the points which are on the mirror, and the dimension of the mirror is by one smaller than the dimension of the space in which the reflection takes places.
		These observations allow one to formalize the definition of reflection: a reflection is an involutive isometry of an Euclidean space whose set of fixed points is an affine subspace of codimension 1.
	en.wikipedia.org /wiki/Reflection_(mathematics) (420 words)

	Reflection - Wikipedia, the free encyclopedia
		In mathematics, reflection is a transformation of a space.
		In electricity, reflection is reflected voltage in an electrical signal due to an impedance change.
		In psychology, reflection is a process of thoughtful meditation or rumination: see introspection.
	en.wikipedia.org /wiki/Reflection (208 words)

	Metamathematics Summary
		Mathematics about mathematics was originally differentiated from ordinary mathematics in the 19th century to focus on what was then called the foundational crisis of mathematics.
		Many issues regarding the foundations of mathematics (there is no longer necessarily considered to be any one "problem") and the philosophy of mathematics touch on or use ideas from metamathematics.
		Metamathematics is intimately connected to mathematical logic, so that the histories of the two fields largely overlap.
	www.bookrags.com /Metamathematics (816 words)

	Sheaf (mathematics) Encyclopedia
		In mathematics, a sheaf is the basic tool for expressing relationships between small regions of a space and large regions.
		It is still common in some areas of mathematics such as mathematical analysis.
		At this point sheaves had become a mainstream part of mathematics, with use by no means restricted to algebraic topology.
	www.hallencyclopedia.com /topic/Sheaf_(mathematics).html (6078 words)

	Reflection 2D
		The standard equation is used with N, L and R for, respectively, the surface normal, normalized direction to a light source, and normalized reflection of L off of a surface.
		The 2D Reflection applet was developed for use in an undergraduate computer graphics programming course and is appropriate chiefly for computer science students and other students who need to calculate light reflection.
		This affects the reflection vector (yellow) and the orientation of the surface (gradated arc).
	www.cs.brown.edu /exploratories/freeSoftware/repository/edu/brown/cs/exploratories/applets/reflection2D/reflection_2d_guide.html (187 words)

	Theory Into Practice: No time like the present: reflecting on equity in school mathematics
		Further, the mathematics achievement gap was slowly closing between White students and students of color (i.e., African American and Hispanic students) on assessments of basic skills.
		Reflection within the social reconstructionist tradition focuses specifically on the implications of practice for equity and justice.
		While reflection that is social reconstructionist may greatly improve the likelihood of positive learning environments in school mathematics, we concede that the development of this kind of reflective practice is by no means an easy task.
	www.findarticles.com /p/articles/mi_m0NQM/is_3_42/ai_108442648 (1333 words)

	NCTM e-resources – Reflections
		The site’s components are designed to assist teachers in reflecting on the mathematics they teach, and as a tool to systematically observe, analyze, critique, and improve classroom practices.
		Reflection can be facilitated by a video record and by individual and collegial analysis and discussion of such matters as the mathematics being taught, the mathematical tasks being used, the classroom discourse that occurs, the student learning that ensues, and the teaching decisions that are made.
		Reflections is designed to honor these beliefs and to help you improve practice – whether you are a teacher, a prospective teacher, a teacher educator, or a supervisor.
	my.nctm.org /eresources/reflections/about.htm (615 words)

	Bibliographies/Reflection in Education (1998)
		Reflection is a key aspect of the practicum experience for preservice teachers at the University of Central Queensland (Australia).
		Reflective journal writing focusing on descriptive, analytical, and affective levels of reflection was on-going throughout the internship.
		The document focuses on the researcher as a reflective coach, on themes emerging from and inherent to university/school relationships, and on the process of challenging traditional myths (beliefs) and metaphors associated with educational research and educational researchers.
	www.geocities.com /bibliographies/ReflectioninEducatio.html (16253 words)

	Agassiz World: Mathematics
		Mathematics learning is a lifelong process that begins and continues in the home and extends to the school and community settings.
		Mathematics is a language to be learned, with its own vocabulary, syntax, and rules of translation from language to symbol (and vice-versa).
		Mathematical tasks reflecting sound and significant mathematics should generate active classroom talk, promote the development of conjectures, and lead to an understanding of the necessity for mathematical reasoning.
	boston.k12.ma.us /agassiz/awmath.html (4102 words)

	The Methodology of Mathematics
		One aspect of this reflection is that it leads to the notion of value judgement, again a facility which humans have which is not apparently shared by other animals, or at least not in a way in which we can communicate, by and large.
		Reflection on an activity is, generally, a useful way of increasing its effectiveness, as we are able to analyse what is essential, what is important, and how the activity can be done avoiding the easiest of mistakes in method.
		Mathematics is about the study of pattern and structure, and the logical analysis and calculation with patterns and structures.
	www.bangor.ac.uk /~mas010/methmat.html (6518 words)

	The Methodology of Mathematics
		One aspect of this reflection is that it leads to the notion of value judgement, again a facility which humans have which is not apparently shared by other animals, or at least not in a way in which we can communicate, by and large.
		Reflection on an activity is, generally, a useful way of increasing its effectiveness, as we are able to analyse what is essential, what is important, and how the activity can be done avoiding the easiest of mistakes in method.
		Currently, the mathematics of category theory, a theory of mathematical structures, is being used to give new insights into future logics and algebras for the design of the next generation of programs and software.
	www.popmath.org.uk /centre/pagescpm/methmat.html (6519 words)

	Articulation and Reflection - Emerging Perspectives on Learning, Teaching and Technology
		The idea of Reflection in education first emerged in the writings of John Dewey, who defined Reflection in 1933 as "active, persistent and careful consideration of any belief or supposed form of knowledge in the light of the grounds that support it and the further conclusion to which it tends" (Dewey, 1933, p.
		Dewey divided the Reflection process into five stages, the first of which is "the indeterminate situation", during which routine ways of doing things fail to meet the needs of the problem solver (Miettinen, 2000, p.66).
		Her students must keep a journal and reflect and react to the actual piece of legislation as well the opinions they see and hear from the newspaper and television reports.
	projects.coe.uga.edu /epltt/index.php?title=Articulation_and_Reflection (3891 words)

	RUMEonline! - Periodic Publications in Mathematics Education
		Reflects both the variety of research concerns within mathematics education as well as the range of methods used to study them.
		Published under the auspices of the Canadian Mathematics Education Study Group, FLM aims to stimulate reflection on mathematics education at all levels, and promote study of its practices and its theories: to generate productive discussion; to encourage enquiry and research; to promote criticism and evaluation of ideas and procedures current in the field.
		Contributions are welcomed from teachers and users of mathematics at all levels on the contents of syllabi and methods of presentation; mathematical models arising from real situations, the use of computers, new teaching aids and techniques.
	www.maa.org /sigmaa/arume/journals.html (1580 words)

	Mathematics
		Through mathematics we can extrapolate from the experience that is the essence of the human mind to what life and conscious experience may evolve into.
		The capacity for subtle self reflection is a defining characteristic of human consciousness.
		In mathematics it is common to measure the power of a mathematical system by the level of self reflection or iteration that is definable within the system.
	www.mtnmath.com /expth/node6.html (326 words)

	reflection - Definitions from Dictionary.com
		The verb reflect is recorded from 1412, originally "to turn aside;" meaning "to turn back" an image or light rays is from 1530; sense of "to turn one's thoughts (back) to" is first attested 1605.
		Reflected waves remain in their original medium rather than entering the medium they encounter.
		the angle of reflection of a reflected wave is equal to its angle of incidence.
	dictionary.reference.com /browse/reflection (641 words)

	Agassiz World: Mathematics
		Mathematics learning is a lifelong process that begins and continues in the home and extends to the school and community settings.
		Mathematics is a language to be learned, with its own vocabulary, syntax, and rules of translation from language to symbol (and vice-versa).
		Mathematical tasks reflecting sound and significant mathematics should generate active classroom talk, promote the development of conjectures, and lead to an understanding of the necessity for mathematical reasoning.
	www.boston.k12.ma.us /agassiz/awmath.html (4102 words)

	CI5980S03 (Site not responding. Last check: 2007-10-22)
		The National Council of Teachers of Mathematics (NCTM) [ http://www.nctm.org/ ] is the national mathematics education organization dedicated to improving the teaching and learning of mathematics.
		It is a recognized leader in efforts to ensure an excellent mathematics education for all students and an opportunity for every mathematics teacher to grow professionally.
		Your reflections can include ideas about the reading that you are doing, about the work we do during class and implications for your mathematical learning, as well as something that occurs in your classroom related to your content understanding.
	www.appstate.edu /~schrampw/CI5980S03.html (1368 words)

	Polishing the Mirror: Reflection on Practice in Middle Grades Mathematics (Delaware Exemplary Math Curriculum ... (Site not responding. Last check: 2007-10-22)
		This year she was the eighth grade mathematics teacher in her urban middle school, a school which is home to what is often reputed to be one of the most challenging student populations in Delaware.
		But, as she noted, there was a lot of good mathematics going on and she did not want to interrupt it.
		I think the same might be said for Jenni's rethinking of the mathematical content and Sarah's careful attention to the various components of her lesson.
	lsc-net.terc.edu /do.cfm/report/7119/show/use_set-rf_case_study (3324 words)

	Reflective Gear (Site not responding. Last check: 2007-10-22)
		Surface reflectance may be subdivided into diffuse or Lambertian reflectance and specular, or Phong reflectance.
		The apparent reflectance for an ideal Lambertian surface is independent of the observer.
		"Reflections" is also the name of a hit song recorded by Diana Ross & The Supremes in 1967.
	www.blownspeakers.com /pages3/74/reflective-gear.html (353 words)

	Light Reflection
		The angle between the reflected ray and the normal is called the angle of reflection, or the reflected angle.
		Notice that the angle of incidence is equal to the angle of reflection.
		The reflection of light is often discussed using phrases such as "a ray of light bounces off of a mirror." This is because when a light ray reflects at the surface of a mirror it follows a path similar in behavior to a pool ball bouncing off of a cushion on a pool table.
	id.mind.net /~zona/mstm/physics/light/rayOptics/reflection/reflection1.html (354 words)

	Mathematics Tutorials and Problems (with applets)
		Interactive Geometry Tutorials and Problems on topics such as reflection across a line, sine and cosine laws, central and inscribed angles, perpendicular bisector, medians and circumcircle of a triangle are also included.
		Examples related to the applications of mathematics in physics and engineering such as the projectile problem, distance-time-rate problems and cycloid are included.
		Several java applets to describe the mathematical properties ofAntennas are also included.
	www.analyzemath.com (452 words)

	Reflection (mathematics) -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-22)
		Note that this applies to more than just (Geometry based on Euclid's axioms: e.g., only one line can be drawn through a point parallel to another line) Euclidean geometry.
		Reflections in (The geometery of affine transformations) affine geometry with respect to a given (Click link for more info and facts about hyperplane) hyperplane is not unique, for example.
		Also, an (Turning upside down; setting on end) inversion in (Click link for more info and facts about inversive geometry) inversive geometry is considered a reflection by this definition.
	www.absoluteastronomy.com /encyclopedia/r/re/reflection_(mathematics).htm (184 words)

	NH K-3 Math Curriculum Addendum - Evaluation and Assessment (Site not responding. Last check: 2007-10-22)
		Open-endedness: mathematics tasks can range considerably in how open they are; assessment, like instruction, should enable students to demonstrate what they can do both with single-answer, closed items, as well as tasks which allow for much more divergence of solution.
		Teachers of mathematics are experimenting with a range of new assessment strategies, and various sources are available to explain these approaches.
		Portfolios for mathematics are being used by a number of elementary school teachers, in New Hampshire and beyond.
	www.plymouth.edu /psc/math/curricula/k3metass.html (1243 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		Reading Reflections (40 points — 4 points for each reflection) Due: Each class beginning A 1-2 page reading reflection is required for 10 sets of reading assignments and is due at the beginning of each class meeting.
		Teacher Interview Reflection (20 points) Due: Monday, September 23 This assignment will provide you the opportunity to interview an elementary classroom teacher as to his or her goals and methods for establishing an effective classroom culture for learning mathematics.
		The purpose of this activity is to help you learn how to design effective mathematical activities, to provide you with an opportunity to begin compiling mathematical resources, and to provide an opportunity for you to practice teaching mathematics.
	lynx.csusm.edu /coe/archive/fall2002/EDMS.543.01.doc (3623 words)

	Reflection - TheBestLinks.com - Reflective, 1998, Reflection (mathematics), Reflection (computer science), ...
		In mathematics, reflection is the transformation of a space.
		In computer science, reflection is a programming language feature for metaprogramming.
		In electricity, reflection is reflected voltage in an electrical signal due to an impedance change.
	www.thebestlinks.com /Reflective.html (154 words)

	Masters Degree
		This module is intended to foster reflection on mathematics and its relation to the aims and nature of the mathematics curriculum and assessment, and to critically evaluate curriculum developments in mathematics.
		All of the mathematics education modules address issues relevant to both the primary and secondary phases of education, and course members may choose a topic of study for their dissertation to suit their own professional situation and phase of teaching.
		The module provides an opportunity for specialists in mathematics to reflect on the nature and philosophy of their chosen subject, its role in education and society, and its important part in promoting and hindering equal opportunities.
	webdoc.sub.gwdg.de /edoc/e/pome/masters.htm (12704 words)

	Ontario-Montclair School District: AB 466 Mathematics Institute - Practicum Requirements (Site not responding. Last check: 2007-10-22)
		AB 466 Mathematics (Year 1) log forms are in Microsoft Word and Adobe PDF format.
		Using the form provided, a lesson reflection may describe a successful lesson or a lesson that still needs to be improved.
		The purpose of the follow-up component of the AB 466 professional development requirement is to provide teachers an opportunity to transfer the learning (from the 40 hour training) into their daily practice in order to improve student achievement.
	www.omsd.k12.ca.us /persdiv/ab466math.html (988 words)

	Middle School Education Programs
		Personal Mathematics and Reflection: Each class participant will write a narrative reflection on her/his own mathematics "history," including positive and negative teaching/learning experiences, problem areas, and self-analysis of current status of mathematics understanding.
		Paulos, J.A. Innumeracy: Mathematical Illiteracy and Its Consequences.
		Students in schools of education throughout the Commonwealth are expected to engage in development of a portfolio to document their growth during the period of their professional preparation.
	www.lesley.edu /soe/middleschool/ur/ur_pro_esped6105.html (2036 words)

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