Extractions: Courseware for Elementary and Middle Grade Teachers San Diego State University This project was a research-based curriculum development project, focused on the development of courseware and instructional materials for mathematics courses for prospective elementary and middle school teachers, and for the professional development of practicing teachers. Our goal was to provide instructional materials for mathematics courses for prospective and practicing elementary and middle school that will help these teachers to reconceptualize One obstacle to preparing teachers to understand mathematics at a depth that will allow them to teach it to others is their narrow view about what mathematics is. All too often We have attempted to do more than simply reorganize the usual content of mathematics courses for elementary and middle grade teachers. We have selected and developed topics and problems that exemplify mathematical reasoning and problem solving, make mathematical connections clear, clarify and overcome common misconceptions, provide opportunities to communicate mathematically, and promote greater confidence in one's ability to deal with mathematics (all thrusts of NCTM's Principles and Standards for School Mathematics
Math Sciences Information The relationships between mathematics and computer science make an ability in Certification to teach mathematics at the secondary level is available http://www.math.cmu.edu/~rw1k/undergrad/content.htm
Extractions: INTRODUCTION TO THE DEPARTMENT The Mathematical Sciences Department at Carnegie Mellon offers outstanding opportunities for anyone seeking an undergraduate education that will open doors to exciting careers and graduate school opportunities. Described here are five major concentrations, the placements of our recent graduates, a sample of Summer opportunities that are available, and descriptions of special opportunities within the Department. In addition, the Department offers a Bachelors degree in Computational Finance as a joint program with the Heinz School. Our students benefit from the opportunity to work with outstanding research faculty in areas such as applied analysis, logic, discrete mathematics, and mathematical finance. Mathematical Sciences Faculty For additional information: rw1k+@andrew.cmu.edu MATHEMATICS This is the traditional major in mathematics providing a sound background in analysis and algebra. It permits a flexible choice of mathematics courses and can include three computer science courses as part of the major. Graduates from this program have gone to outstanding graduate schools and can also be found in exciting jobs in software and finance.
7-12 ELA Programs Basic computation skills continue to be needed in grades 912, When students notice that operations seem to have particular properties, http://www.dodea.edu/instruction/curriculum/math/MathMatters/Math_Matter_FreqQA.
Extractions: NCTM's Answers to Frequently Asked Questions Answers to Frequently Asked Questions Q. Are the traditional basics still important? Answer: Absolutely! A major goal in the early grades pre kindergarten through grade 5 is the development of computational fluency with whole numbers. In grades 6-8, students should acquire computational fluency with fractions, decimals, and integers. Basic computation skills continue to be needed in grades 9-12, in which students should develop fluency in operations with real numbers, vectors, and matrices. Even in complex calculations in which calculators or technology are being used, students need to understand the mathematics. In today's world, students' basic arithmetic skills must include the ability to choose what numbers to use and what operation is appropriate for carrying out the computation, to decide whether the results make sense, and then to make a decision about what to do next. Q. What mathematics beyond the traditional basics should all students learn?
Careers The areas of applied math which need people include computer science, operations Students interested in teaching mathematics in the public school system http://www.math.oakland.edu/Undergraduate/careers.html
Extractions: CAREERS IN THE MATHEMATICAL SCIENCES Click here for a neat poster about what you can do with a math degree. "For students with the necessary ability and training, many paths are open for satisfying and rewarding careers in mathematics and its applications. Periodic fluctuations in the economy will, of course, affect employment prospects in mathematics, as in all fields. However, even in the present period of relatively high unemployment, prospects in mathematics are above average among scientific fields. All indications are that because of the central role of mathematics in the physical and social sciences, in engineering, and in business, the demand for people trained in mathematics will continue to grow. Qualified secondary school teachers of mathematics are in demand, as are people to work as applied mathematicians in Industry and Government. More statisticians and actuaries are needed. Both of these fields require a basic preparation in mathematics. "To many persons, teaching is an attractive career with the opportunity it affords for working with young people and with the security given by permanent tenure and pension provisions. Teaching salaries, traditionally low, improved dramatically in the fifties and sixties, especially in mathematics and in the sciences, and are now considered adequate to good.
Graduate Programs At Northeastern Illinois University math 473 Advanced Topics in operations Research ScEd 410 Computers in the Teaching of Secondary School mathematics math 421 Modern Geometry http://www.neiu.edu/~gradcoll/programs/mathematics2.html
Extractions: M.S. Biology M.S. Chemistry M.S. Computer Science M.S. Earth Science ... M.S. Mathematics . Applied Mathematics . Secondary Education Mathematics M.S. Mathematics for Elementary School Teachers M.A. Music M.A. Political Science M.S.A. Accounting M.B.A. Business Administration M.A.T. Bilingual/Bicultural Education M.S.I. Bilingual/Bicultural Education M.A. Counseling . Community Counseling . School Counseling . Rehabilitation Counseling M.A. Educational Leadership
BC Education - Grade 6 - Number (Number Operations) Ask students to figure out a quick way to compute an answer mentally and to Teaching Tool; Machine Shop; mathematics From Many Cultures; Mental math in http://www.bced.gov.bc.ca/irp/mathk7/_6numno.htm
Extractions: Recommended Learning Resources It is expected that students will apply arithmetic operations on whole numbers and decimal fractions in solving problems. It is expected that students will: To view the prescribed learning outcomes for Number (Number Operations) in other grades click on an icon below. Students' number sense and estimation skills complement their abilities to compute accurately using appropriate strategies and tools such as mental computation, paper-and-pencil calculations, calculators, and computers. Allowing students the freedom to create and solve their own problems by using strategies that are intuitively obvious to them helps them feel more comfortable with the problem-solving process. Have students play the Maze game. Give each student a copy of the maze and a calculator. Each student begins by keying in 100 on the calculator. The goal is to choose a path that will give the player the largest value at the finish. Movement is unidirectional: players may not retrace a path or move upwards in the maze. For each segment moved along the maze, students key in the operation.
BC Education-Grades K To 1- Number (Number Operations) They should develop computational skills by doing meaningful tasks each day, Kids n Calculators How to Use the Calculator as a Teaching Tool; math http://www.bced.gov.bc.ca/irp/mathk7/k1numno.htm
Extractions: Recommended Learning Resources It is expected that students will demonstrate and use a variety of methods to show the processes of addition and subtraction on one-digit whole numbers It is expected that students will: To view the prescribed learning outcomes for Number (Number Operations) in other grades click on an icon below. Children need to make sense of the different ways that numbers are used so that they can develop an understanding of the relationship both within a number and between numbers. They should develop computational skills by doing meaningful tasks each day, both in school and at home. Their conceptual understanding of addition and subtraction begins with concrete experiences arising from problem situations. These experiences provide them with the opportunity to understand the purpose for their computations, as well as the opportunity to develop their arithmetic skills of adding and subtracting. Have students act out different classroom situations: Three people are going to the library, and two are going to use the computer lab. How many are going altogether?
Department Of Mathematics And Computer Science SECOND TEACHING FIELD COMPUTER SCIENCE Requirements 21 credits. CS 122 Introduction to Computer MA 328 Modeling and operations Research (3); or, http://www.nnu.edu/academics/catalogs/undergrad/healthscience/math.html
Research On The Teaching Of Math page 207 This scorn and ignorance of the art of computation by all but (2) He insisted upon a knowledge of number and the simplest operations, http://www.triviumpursuit.com/articles/research_on_teaching_math.htm
Extractions: Formal Arithmetic at Age Ten, Hurried or Delayed? Also read On Early Academics Provincialism is the word which we use to describe an opinion which is narrow and self-centered in perspective. Because the common practice in our culture in our day is to begin formal instruction in arithmetic as early as age four or five, many have questioned the suggestion that one may wait until age ten before beginning formal instruction in arithmetic. Waiting until age ten for formal instruction in arithmetic is often misnomered "late start" or "delayed academics." A History of Education in Antiquity , by Henri I. Marrou, translated by George Lamb, Sheed and Ward, London, 1956, page 158. At the universities little was done in mathematics before the middle of the 17th century . . . . During the reign of Queen Elizabeth, fresh statutes were given, excluding all mathematics from the course of undergraduates, presumably because this study pertained to practical life, and could, therefore, have no claim to attention in a university . . . . [page 207] This scorn and ignorance of the art of computation by all but commercial classes is seen in Germany as well as England.
Teaching Middle School Math With Technology - Home Designed for middle school math teachers (grades 48) who want to meet Teachers demonstrate a sound understanding of technology operations and concepts. http://www.uwstout.edu/soe/profdev/middlemath/
Extractions: Participants who complete the online course will be able to: Analyze current trends and research-based mathematics instructional strategies Analyze student responses to mathematical problems to detect typical error patterns and recommend specific approaches that address learning problems of middle grades math students to increase math achievement scores Apply the National Council for Teachers of Mathematics (NCTM) standards Analyze how to help students develop an understanding of math concepts using real-world and unit theme connections Apply interactive Web-based math resources Utilize technology to extend basic software applications such as word processing and spreadsheets, and graphic organizers with math instructional activities. Past participants' comments You will connect to learning modules via the World Wide Web and interact with other participants and the instructor through email and a private online class discussion board. Each module provides opportunities for participants to share ideas and participate in discussion with the instructor and peers. Participants may work with one other participant as a team.
Miami University: Academics computing, statistics, and operations research to solve problems in science, Mathematics education A license to teach mathematics in secondary http://www.miami.muohio.edu/academics/majorsminors/majors/mathematics_stats.cfm
Extractions: Advising The Miami Plan Core Curriculum Majors and ... University Offices UNDERGRADUATE MAJORS Accountancy American Studies Anthropology Architecture ======ART====== Art Education Graphic Design History of Art and Architecture Studio Art Athletic Training Biochemistry (See Chemistry) Biology (See Botany, Microbiology, Zoology) Black World Studies Botany Business-General Chemistry Classical Humanities Clinical Laboratory Science ======COMMUNICATION====== Mass Communication Speech Communication Strategic Communication Computer Science (See also System Analysis) Decision Sciences Dentistry (See Pre-Professional Study) Dietetics Diplomacy and Foreign Affairs ======ECONOMICS====== Business Economics Economics Quantitative Economics ======EDUCATION====== Adolescent/Young Adult Multi-aged Art (See Art) Music (See Music Education) ======ENGINEERING====== Chemical Engineering Computer Engineering Electrical Engineering Engineering (General) Engineering Management Engineering Physics Manufacturing Engineering Mechanical Engineering Paper Science and Engineering ======ENGLISH====== English/Creative Writing English/Literature English/Technical and Scientific Communication Linguistics (See also Journalism) Environmental Science Environmental Studies Exercise Science Family Studies Finance French Geography Geology German Gerontology (social) Graphic Design Greek Health Studies History History of Art and Architecture Interdisciplinary Studies Interior Design International Studies Italian Studies Journalism Latin Law (See Pre-Professional Study) Linguistics
217A Quantum Computation & Information Security math 217A (Winter quarter 2002). Topics in Applied mathematics equivalence between sets of operation elements for quantum operations http://math.ucsd.edu/~dmeyer/teaching/217A.html
Extractions: QUANTUM COMPUTATION AND INFORMATION SECURITY Instructor: David A. Meyer Course description Currently the most important applications of quantum information processing are to information security: Quantum key distribution has been demonstrated experimentally, and the security of cryptosystems based on the hardness of finding discrete logarithms or factoring is compromised, theoretically, by Shor's quantum algorithms. In this seminar we will use these applications to motivate an introduction to quantum computing. Basic concepts in quantum mechanics (superposition, measurement, entanglement, ...) will be introduced as we study quantum protocols for cryptographic primitives such as key distribution, bit commitment, coin flipping, etc. Appreciation for these results will require a parallel discussion of the importance of, and classical protocols for, these cryptographic primitives. Additional related topics will be determined by the students' interests and background, and may include quantum versions of game theory, secret sharing, communication complexity, algorithms, ... Some background in quantum mechanics, cryptography, complexity, coding, or game theory will be useful, but is not required. Although there is no text for this course, [
Teaching Math Computation And Problem Solving Skills Teaching math Computation and Problem Solving Skills (Students look to see what math operation to perform.) 2. Read the problem. http://deafed.department.tcnj.edu/math/computation.html
Extractions: Teaching Math Computation and Problem Solving Skills Phase 1: Pretest During this instructional phase, a pretest is administered to each student to determine whether instruction on a particular math skill (e.g., subtraction 10 to 18) is needed. If a student's score on the pretest is below the mastery criterion (i.e., 80%) and the student has the necessary prerequisite skills, then he or she is a good candidate for instruction on the pretested skill. Some teachers include students who score the mastery criterion, but take more than 4 or 5 minutes to complete the 20 problems on the pretest. These students benefit from the additional practice and become more fluent. Once the teacher has determined what instruction the students need, the teacher and students discuss the importance of learning the designated skill. The teacher attempts to get the student's commitment to learn. Written contracts help facilitate this process. Phase 2: Teach Concrete Application The concrete phase of instruction consists of Lessons 1 through 3. For each lesson, the books provide a suggested script to guide teachers through the instructional sequence, and a "Learning Sheet" designed to facilitate student practice of the skill. During these lessons, students learn to manipulate objects to solve the problems on their Learning Sheets. They also begin to solve word problems in which the numbers are vertically aligned, but blank spaces are provided after the numbers for students to write the name of the manipulative object used in the lesson. These concrete lessons act as a springboard for learning the skill at the representational and abstract levels.
Math Problem Solving Teaching math Problem Solving by Marilynn Magnani. NEXT. Dear Parents, In fact, children can carry out all kinds of computation without formal http://www.ncclschool.com/program/math1.htm
Extractions: by Marilynn Magnani NEXT Dear Parents, I want to share some observations I have made while listening to your children talk about their math. By listening to them explain their work I can better understand what sense they are making of our number system and how it works. I particularly want to talk about how your children make sense of computation and what supports sense making and what interferes with it. Many of us think that children aren't able to add, subtract, multiply or divide unless they are taught the standard algorithm or procedure for those operations. Therefore, we try to teach the procedures first before we let the children compute. Faced with a problem like 6 x $4.95, we feel compelled to teach the standard algorithm for multiplication. How else will a child be able to find the answer? In fact, children can carry out all kinds of computation without formal procedures and in so doing learn crucial information about our number system, information which allows them to make great sense out of their number work. An algorithm can be very useful as a short cut for recording computation on certain problems. But, because it is a short cut, an abbreviated or coded form of the operations, it is very abstract. Think about learning the algorithm for long division or where to put the zeroes as place holders in double digit multiplication. In most cases, the algorithms make very little sense to children and so they struggle to memorize them without thinking about the actual numbers they are computing.
Resource: Teaching Math: A Video Library, K-4 Teaching math K4 documents effective teaching and learning in many schools NCTM standards whole number computation, number sense and numeration, http://www.learner.org/resources/series32.html
Extractions: by Discipline Arts Education Education Reform Foreign Language Literature and Language Arts Mathematics Science Social Studies and History by Grade K - 2 College/Adult A video library for K-4 math teachers; 52 video programs (from 15 to 30 minutes in length) and guide See how the National Council of Teachers of Mathematics standards are used in elementary classrooms across America. Elementary teachers tap the excitement and energy of children from kindergarten through grade 4 as they solve problems, learn to make connections between concepts, and communicate and reason mathematically. Teaching Math K-4 documents effective teaching and learning in many schools: small, large, rural, suburban, and inner-city.
Teaching Discrete Mathematics Teaching Discrete Mathematics via Primary Historical Sources The next generation of computing equipment, the Electronic Discrete Variable Automatic http://www.math.nmsu.edu/hist_projects/
Extractions: dranjan@nmsu.edu Pedagogical Points of Departure General Benefits of Using Original Sources The Historical Projects Dissemination of the Projects ... Bibliography This site offers written curricular materials, based on primary historical sources, for beginning and advanced undergraduate courses in discrete mathematics and computer science. Such courses, which often cover combinatorics, deductive reasoning (logic) and algorithmic thought, draw a variety of majors, ranging from computer science, mathematics, the physical sciences and engineering to secondary education. Traditional methods of instruction follow ``The Modern American Discrete Mathematics Text,'' which although thorough and mathematically precise, present the material as a fast-paced news reel of facts and formulae, often memorized by the students, with the text itself offering only passing mention of the motivating problems and original work which eventually found resolution in modern concepts such as induction, recursion, or algorithm.
Kaisa Miettinen - Links Links Connected to Optimization, operations Research and Other Interesting Areas Computational Mathematics group at the University of Vienna, Austria http://www.mit.jyu.fi/miettine/lista.html
Extractions: Scientific Societies Journals Areas of Optimization Services in Operations Research ... Research Groups , and Homepages MPS (Mathematical Programming Society) SIAM (Society for Industrial and Applied Mathematics) IFORS (International Federation of Operational Research Societies) INFORMS (Institute for Operations Research and the Management Sciences) AMS (American Mathematical Society) INFORS Suomen Operaatiotutkimusseura ry, Finnish Operations Research Society EURO Association of European Operational Research Societies The Electronic International Journal - "Advanced Modeling and Optimization" Annals of Operations Research Applied Mathematics and Computation Online articles of future issues ... The Electronic Journal of the Argentine Society for Informatics and Operations Research (SADIO) Engineering Optimization European Journal of Operational Research Fuzzy Optimization and Decision Making
Metacognitive Strategies This site complements the instructional video model for Teaching math metacognitive strategies are simply memorable plans or approaches that students http://coe.jmu.edu/mathvidsr/metacognitive.htm
Extractions: Metacognitive Strategies by Math Concept Area Introduction Teaching Metacognitive Strategies, which you can access by clicking on the Instructional Strategies site found on the main navigational page. You can also access the video model by clicking on the icon entitled Metacognitive Strategies Video found in the section titled "How Do I Teach Them." return What Are They? Math metacognitive strategies are simply memorable plans or approaches that students use to problem-solve. These strategies include the students thinking as well as their physical actions (Lenz, Ellis, & Scanlon, 1996). Some of the most common metacognitive strategies come in the form of mnemonics, which are meaningful words where the letters in the word each stand for a step in a problem-solving process or for important pieces of information about a particular topic of interest. For example, you may remember the names of the Great Lakes through the mnemonic "HOMES:" H uron
CESA 6 Media Center Provides reinforcement materials for teaching early math concepts. Is a basic skills practice in the basic computational skills. http://www.cesa6.k12.wi.us/CMC/math/advancedmath.html
