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03 de mar de 2010

A presentation made at All Nations University, Koforidua on 12/3/10 to mark Ghana\'s National Math Day

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- 1. ICT TOOLS IN MATHEMATICS INSTRUCTION<br />BY MIRACULE DANIEL GAVOR<br />
- 2. 'Calculators and computers are reshaping the mathematical landscape, and school mathematics should reflect those changes. Students can learn more mathematics more deeply with the appropriate and responsible use of technology. They can make and test conjectures. They can work at higher levels of generalization or abstraction. In the mathematics classrooms envisioned in Principles and Standards, every student has access to technology to facilitate his or her mathematics learning.' (National Council of Teachers of Mathematics / Overview of Principles and Standards for School Mathematics : 2006) <br />
- 3. When we look at Trends in Mathematics Education (WWWTools for Education: February 21, 2005), it was mentioned in the Post Script that 'there are lots of interesting Webtools for teachers and students to use in Mathematics Education, but they really deserve a dedicated newsletter - maybe next time...' Well here we are, finally, to deliver on that noncore promise. In the intervening period, many new resources and collections have appeared online, and ideas continue to mature - perhaps it was as well to wait. <br />
- 4. Among reasons for deciding that the topic's time has come: <br /> . the recent survey of readers' preferences indicated a degree of interest.<br /> . a subsequent watch on current content yielded a steady trickle of new material. <br /> . August is Australia's National Mathematics Month , featuring Literacy and Numeracy Week<br />
- 5. Mathematics is one of the key STEM disciplines , even underlying many areas where it's not the obvious focus - see examples from Projects at Mathematics Across the College Curriculum ... and anyway, how else could we pass on some good ideas on New Shapes for Soccer Balls (Roland Piquepaille / Emerging Technology Trends: July 10, 2006).<br />
- 6. Roles for ICTs in Mathematics Education. <br />Not so long back, Maths teachers were generally seen to be securely ensconced in a relatively stable core discipline, with a clearly defined pedagogy and established curricula - many were in no hurry to let new technology disturb the natural order. However, a few brave souls have indicated that there may be room for improvement in the way Mathematics is taught - see for example AmbjornNaeve's PPT presentation on Design Patterns in Mathematics Education (Royal Institute of Technology, Stockholm); in particular: <br />Slide 4: Structure of Today's Math Education System. <br />
- 7. Slide 5: Problems... doesn't stimulate interest, promote understanding, support personalisation, support transition between layers, integrate abstractions with applications or with human culture. <br />Slide 6: Improving Math Education... using ICT to visualise concepts, interact with formulae, personalise presentation, rout questions to live resources. <br />
- 8. Expanding on the theme: <br />Technology Helps Ratchet Up Math Instruction (Corey Murray / eSchool News : February 13, 2006) - an American perspective. See also21st Century Teaching; Mapping the Connections between ICT Literacy Skills, Technology Tools, and the Learning Goals of Core Subject Areas.<br />
- 9. (Ed Hazell / Access Learning: March 2005) - the section on 21st Century Math promotes the use of the Math ICT Literacy Map to identify ways in which technology can be used to enhance mathematical learning outcomes. <br />IT-Using Mathematic Educators (Oregon Technology in Education Council) links to topics such as: Brain Science and Computer Technology in Math Education and Virtual Manipulatives.<br />
- 10. ICT and Mathematics Education - a Dutch site presenting information and resources regarding the activities of the ICT Freudenthal Institute and research on Mathematics Education; links to popular Dutch websites and a glossary of ICT terms. <br />ICT – Bringing Maths to Life and Vice Versa (Adrian Oldknow / 2005) - reports on initiatives and learning resources in the UK. See also What's New(ish) in ICT and Mathematics at Adrian Oldknow's Home Page<br />
- 11. Curriculum and Instruction (CARET, a project of the International Society for Technology in Education) - how can technology be used to improve mathematics and problem solving skills? Cites research from a study of the PLATO learning system.<br />
- 12. Motivational Maths.<br />The Millennium Mathematics Project - the University of Cambridge initiative for ages 5-N, and recipient of the Queen's Anniversary Prize for Higher and Further Education. Emphasises enrichment and extension activities beyond the school curriculum. Activities include:<br />NRICH , offering free enrichment resources for ages 5-19; staff will also visit schools to run workshops. <br />
- 13. Plus Magazine - aimed at ages 15+, featuring articles on mathematics and applications to science, art and society; interviews, reviews and news; a digital careers library. <br />the Hands-On Maths Roadshow, promoting enjoyable mathematics at schools and public events. <br />the Enigma Schools Project's workshops, exploring cryptography. <br />
- 14. How Maths Can Be Great Fun (SoutikBiswas / BBC News: July 24, 2006) - an account of HeyMath's success in India. HeyMath! is an E-learning system for students in Grades 5-12 and their teachers; sample lesson and free trial. <br />
- 15. COMPASS - a project promoting the improvement of secondary school mathematics learning outcomes, offering a choice from 5 proven curricula :<br />Mathematics: Modeling Our World uses contextual questions about the real world and life in it to motivate mathematical investigation. <br />Contemporary Mathematics in Context - extends the informal knowledge of data, shape, change, and chance to situations and problems. <br />
- 16. Interactive Mathematics Program - a problem-based approach. <br />MATH Connections: a Secondary Mathematics Core Curriculum - a topical approach emphasising real-world applications and problems from the sciences, humanities, business and industry. <br />SIMMS Integrated Mathematics: A Modeling Approach Using Technology - designed to replace most grade 9 - 12 mathematics courses. <br />
- 17. Concerning Hardware.<br />On the Use of Handheld Technology in Math Instruction (Lars Jakobsson / Malmo University, 2001) - a calculated prediction: 'There are many reasons to believe that the use of ICT in mathematics will be concentrated on handheld technology'.<br />Making Math Interesting: All It Takes Is a Laptop (K-12 Computing Blueprint: February 01, 2006) - as reported from Seymour Papert's seminar on ' Mathematics Education for the Future' at Liberty School, Maine. <br />Using Technology to Enhance Math Learning (Math Forum @ Drexel: May 17, 2005) - questioning the focus on the use of calculators. <br />
- 18. Why Do Teachers Recommend Graphing Calculators? - Texas Instruments answers: research shows that graphing calculators can help students understand math. See also links to Classroom Activities and Professional Development.<br />The Educational Use of the Graphic Calculators TI-82 and TI-83 (Texas Instruments / MathsNet.com) <br />Graphics Calculators and School Mathematics (Australian Association of Mathematics Teachers) - a very positive recommendation.<br />
- 19. Some Useful Software.<br />A Taxonomy of Software for Mathematics Instruction (Terri L. Kurz, James A. Middleton and H. BahadirYanik / 2005) identifies 5 categories of tool-based mathematics education software, and considers affordances and constraints of each type. How well do the following examples fit? <br />Math Blaster (Knowledge Adventure) - the current version of a veteran product. <br />
- 20. Pattern Block Program (JacoboBulaevsky) - explore patterns using shapes. Designed to complement No Matter What Shape Your Fractions are In (Cynthia Lanius, 2004) <br />InspireData: Giving Students the Power to Visualize, Investigate, and Understand Data (TERC / July 10, 2006) - a review. See also the Inspiration website to see examples of classroom use, download a free trial version, find information on related products. <br />
- 21. Maple 10 - Maplesoft's analytical tool. <br />Mathematica 5.2 (Wolfram Research)- 'the tool of choice at the frontiers of scientific research, in engineering analysis and modeling, in technical education'<br />Scientific Workplace 5.5 (MacKichan Software) - create, edit, and typeset mathematical and scientific text. At the same site see also companion products Scientific Word Version 5.5 and Scientific Notebook Version 5.5.<br />The Calculation Management Suite (Mathsoft) - also lists Math Resources . <br />
- 22. TI InterActive (Texas Instruments) - extensive Features Summary; download the free 30 day trial version. <br />Tinkerplots Dynamic Data Exploration - a software construction set of basic operations; especially useful in teaching data analysis. <br />MathsPOWER Software Tutoring Programs for K-12 - Australian Government endorsement, try before you buy. <br />Riverdeep Products & Offerings > Math - large range of K-12 products. <br />
- 23. Cabri 3D 1.2.1 (CABRILOG SAS) - interactive computer-based geometry. Download a free trial version and work through the Mathematical Association's introduction at The 3rd Dimension - The Changing Shape Of Geometry<br />Math-Software.net (Merit Software) carries software reviews, articles, and lists of Recommended Resources<br />
- 24. Chartwell-Yorke'sAdvice for Teachers on using Software for Mathematics Education.. . lists recommended software, categorised as Dynamic Interactive Geometry (including free Cabri resources), Data Handling, Numbers and Algebra. <br />Beatrice C. Babbitt's 10 Tips for Software Selection for Math Instruction (LD OnLine) may take some of the pain out of decisionmaking.<br />
- 25. Lessons and Activities.<br />Mathematics Lessons that are Fun (Cynthia Lanius) - English / Spanish language options. <br />Go Figure! Math Challenge (MATHCOUNTS) - progressively harder questions. <br />Lesson Plans (Thirteen Ed Online) - developed by teachers for grades 3-12 <br />National Library of Virtual Manipulatives for Interactive Mathematics (Utah State University) - Pre-K to 12 activities covering: number and operations; algebra; geometry; measurement; data anaysis & probability. <br />
- 26. Math Teachers Activities and Ideas Page for Calculator Activities (Austintown Local Schools) for Grades 7-12. <br />More Mathematics and Theoretical Computer Science Video Lectures (PeterisKrumins / Free Science and Video Lectures Online: June 26, 2006) <br />Math Activities Online for Kids(Syvum) <br />
- 27. TI InterActive! in the Classroom (Tor Jan Aarstad et al / Teachers Teaching with Technology ) - activities for learning mathematics and science; units consist of a number of files, which are connected by hyperlinks - download all files of one unit to the the same folder on disk C. <br />Years 7-9 Rich Task #7: Pi in the Sky (Queensland Department of Education and the Arts) - provides access to a range of resources supporting the study of ancient Greek mathematics. <br />Teacher Resources: Browseable Lesson Plan Index (MarcoPolo) - search on Mathematics/all - 3300+ resources listed from most recent.<br />
- 28. For Students.<br />Elementary Math Club - Grades 3 - 6 (UT Austin) <br />Useful Online Resources for Students (Australian Association of Mathematics Teachers) <br />Students' Classroom (National Center for Education Statistics) <br />Australian CensusAtSchool: Student Area (Australian Bureau of Statistics, 2006) - enables students to take part in an Australia-wide data collection and analysis project. Relates to the Census of Population and Housing, to be held on August 08, 2006).<br />
- 29. Collections of Resources.<br />Math (Sites for Teachers) - categories: Lesson Plans; Ideas & Activities; Applications; Board Games; Puzzles & Problems; Organizations.<br />Teaching Resources for Mathematics (Standards Site, Primary National Strategy) - 193 teaching resources. <br />Years 1-10 Mathematics: Resource Links (Queensland Studies Authority / Last reviewed 12.09.2005) <br />
- 30. Mathematics Sites (Australian Association of Mathematics Teachers) <br />Collections at the P.L Duffy Resource Centre, Trinity College, Western Australia:<br />Assignment and Project Topics in Mathematics<br />Information and Communication Technology: ICT In Education<br />Mathematics Teaching <br />
- 31. Virtual Manipulatives for Math Teachers ( Virtual Training Center, Lane Education Service District / Last updated April 27, 2006) <br />Math Center (Education World) <br />Integrating Math and Technology (Manassas City Public Schools). <br />Illuminations (National Council of Teachers of Mathematics) - Activities, Lessons, Principles and Standards, Links. <br />
- 32. From the EdNA Online database: Mathematics AND Recently Added Resources - Category Mathematics <br />Mathematics and Mathematics Education Resources (Advanced Technology Council in Mathematics). <br />One-stop Mathematics Page : The Mathematics Department (Shambles) <br />A Selection of Mathematics Web Sites (Oundle School, Peterborough, UK) <br />
- 33. verwijzingen - a Dutch language Webliography. <br />Mathematics ( About, 2006) - see especially the sidebar links. <br />Technorati Tag: math - blog Posts tagged ' math': 9,281 posts in all languages; 6,530 posts in English. <br />S.O.S. Mathematics - for people who need to refresh their Maths. <br />techXtra Learning and Teaching Resources - search on 'mathematics' <br />Useful Links (Association of Teachers of Mathematics) <br />
- 34. Links (Queensland Association of Mathematics Teachers) <br />Blue Web'n Search Results for: Mathematics - 212 hits. <br />Math: Education: Teaching Resources (dmoz Open Directory Project) - lists 190 resources. <br />Math Ed Topics (Math Forum Internet Mathematics Library, Drexel University). See also a review of The Math Forum@ Drexel University in The Scout Report (July 28, 2006). <br />
- 35. maths online - a gallery of multimedia learning material for school and distant learning; German version also available. <br />Internet Places to Start! (Dave Wilson / Manchester Metropolitan University, 2004) <br />Technology Resources for Math (Linda Foote / Poway Unified School District, 2005) <br />
- 36. The Mathematical Sciences Digital Library(Mathematical Association of America) <br />Math Pathway (NSDL Middle School Portal) <br />TeachEngineering Resources for K-12 (NSDL Digital Library) <br />NEEDS (National Engineering Education Delivery System) - search on ' mathematics' <br />Math Resources (Kent School District)<br />
- 37. Toolbox.<br />Mathematical Toolkit, Release 2 (skool.co) - designed to support the teaching and learning of mathematics for UK pupils at Key Stage 3. <br />Experience Math and Science with Gizmos (ExploreLearning.com) - online simulations. <br />Online Graphing Calculator (Jiho Kim, 2006) <br />Graphing Calculator for Macintosh and Windows (Pacific Tech) <br />Wordsearch Applet - Numbers (Andrei Grigoriev)<br />
- 38. Professional Reading.<br />Using Technology to Enhance Mathematics Instruction ( Wikibooks) - many ways to use technology to enhance mathematics instruction. <br />Research Sampler (eds. Annie and John Selden / Mathematical Association of America, 2006) - brief expositions of research on undergraduate mathematics education. <br />Goals in Math Education (University of Oregon) <br />
- 39. Mathematics Teachers' Learning about and Incorporation of ICT into Classroom Practices (CosetteCrisan / Proceedings of the British Society for Research into Learning Mathematics , June 2004) <br />Mathematics Subject Designs (Interactive Education Project , University of Bristol) - ways to use ICT to enhance numeracy and mathematics learning. <br />ICT Enhanced Mathematics Education in the Framework of a Knowledge Manifold<br />(M. Nilsson, A. Naeve / 2004) - 'presents the Knowledge Manifold educational architecture and a number of tools which enable the construction of interactive mathematics learning environments'. <br />
- 40. BOOKS.<br />Technology-Supported Mathematics Learning Environments (Sixty-seventh Yearbook) (National Council of Teachers of Mathematics, 2005) Hardcover: $100.00 ISBN: 0-87353-569-3<br />- see also the Table of Contents, Preface, and direct purchase alternative at the NCTM's Catalog site <br />Exciting ICT in Maths (Alison Clark-Jeavons, Mary Pardoe, and Katherine Baxter / Network Educational Press, 2005)Paperback: $50.50 ISBN: 1855391910 <br />Teaching Mathematics Using ICT (Adrian Oldknow and Ron Taylor / Continuum International Publishing Group, 2004)Paperback, with a CD-ROM: $39.95 ISBN: 0826470599<br />

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