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Cuisenaire Gattegno

Page history last edited by Joel Rosenberg 3 years, 8 months ago

Elementary Math

Manipulatives

Geometry

 

Cuisenaire & Gattegno

 

All the books: https://issuu.com/eswi

 

http://www.educationalsolutions.com/

http://www.educationalsolutions.com/about-visible-tangible-math/

Videos: https://www.youtube.com/user/EducationalSolutions/videos 

 

 

About Gattegno

https://en.wikipedia.org/wiki/Caleb_Gattegno

http://andromeda.rutgers.edu/~powellab/docs/articles/Powell(2007)Gattegno.pdf

https://www.revolvy.com/main/index.php?s=Caleb%20Gattegno

atm "Celebrating Gattegno" 2011 conference

 

http://www.arithmophobianomore.com/the-ultimate-cuisenaire-gattegno-resource-list/

http://www.arithmophobianomore.com/ultimate-cuisenaire-rods-list/

 

Thinking Afresh about Arithmetic (Gattegno article): http://www.jstor.org/stable/41184118?seq=1#page_scan_tab_contents

 

Math with rods: https://issuu.com/jmcuenca/docs/maths_with_rods

 

Playing with rods: http://marcialmiller.com/wordpress/2011/01/playing-with-cuisenaire-rods/

 

 

Gattengo Tens Chart -- https://nrich.maths.org/10314

https://www.tes.com/teaching-resource/place-value-through-gattegno-chart-7106481

https://nrich.maths.org/10741

http://mathsticks.com/my/2014/01/gattegno-chart/

from Visualizing Geometry: https://www.atm.org.uk/write/MediaUploads/Journals/MT205/Non-Member/ATM-MT205-04-05.pdf

 

 

Visible and Tangible Mathematics, Parts 1 & 2: Set of programs on 12 disks for an Apple microcomputer. Constitute an elementary mathematics course, from numeration to the four operations on the integers, and covers the material discussed in chapter 10 of this volume (From Science of Education part 2b: the awareness of mathematization).

https://books.google.com/books?id=9tG241_dx0oC&pg=PA176&lpg=PA176&dq=%22Visible+and+Tangible+Mathematics%22+apple&source=bl&ots=ZiAQO395CC&sig=FB-3X8bYY--LFVTruPzIMg7vLDQ&hl=en&sa=X&ved=0ahUKEwj9i7yZ19jWAhVgVWMKHcGACbkQ6AEIKzAB#v=onepage&q=%22Visible%20and%20Tangible%20Mathematics%22%20apple&f=false

 

Educational Solutions Newsletter, Vol XI, no 3-4, 1982: article about the first part of the microcomputer course: "Two of our breakthroughs" https://issuu.com/ESWI/docs/1128_-3----4-two-of-our-breakthroughs-february-apr

 

 

"Operaitons on Integers" Mathematics Teaching, 114 (1986): second part of the course, which is on 2 discs and which is devoted to the multiplication and division of integers. https://www.atm.org.uk/Mathematics-Teaching-Journal-Archive/44047

Also in the ATM book with Gattegno's articles

 

https://www.amazon.ca/Visible-Tangible-Math-Microcomputer-Program/dp/0878251820

ISBN-10: 0878251820

ISBN-13: 978-0878251827

 

 

Numicon Number Rod Trays 1-10 & 20: https://global.oup.com/education/product/9780198487128/?region=international

 

Rod track: http://www.rainbowresource.com/product/Cuisenaire+50-centimeter+Rod+Track/014565/1225921925-195635

 

Printable cards: https://forum.rpg.net/showthread.php?520369-Is-there-such-a-thing-as-printable-playing-cards

http://superiorpod.com/product/18-card-per-sheet---poker-individual-card-design#.WdpGsUpSx5M

 

Product cards: https://www.ncetm.org.uk/resources/24549

 

https://cuisenaire.wordpress.com/category/faq/why-algebra/

Product-Wallchart

 

Caroline Ainsworth's page

https://www.ncetm.org.uk/resources/28795 

 

Discussion: https://www.ncetm.org.uk/community/thread/31760 

 

 

Madeleine Goutard

 

An aspect of the teacher's role, Madeleine Goutard, 1968.

Mathematics teaching no. 44, (4) Autumn

 

Reviewed Work: Mathematics and Children by Madeleine Goutard

Review by: D. M. Kerslake

The Mathematical Gazette

Vol. 49, No. 369 (Oct., 1965), pp. 314-315

 http://www.jstor.org/stable/3612873?seq=1#page_scan_tab_contents

 

 

Ronit Bird: http://www.ronitbird.com/ebooks/ 

Ronit Bird's videos: https://www.youtube.com/watch?time_continue=160&v=2MTahFSEZDM

ebook for ipads, "Exploring Numbers Through Cuisenaire Rods" https://itunes.apple.com/us/book/exploring-numbers-through-cuisenaire-rods/id700219967?mt=11

 

 

 

Ian Benson, "The Primary Mathematics" book

 

 

Tizard Mission (at Stanford?) http://tizard.stanford.edu/users/ianbenson/ 

     http://tizard.stanford.edu/users/

     http://tizard.stanford.edu/users/rachaelrudge/

     http://tizard.stanford.edu/users/jennymcane/

 

 

"Functional relationships between patterns of Cuisenaire rods", Benson: http://tizard.stanford.edu/sandbox/users/ianbenson/weblog/fea8a/attachments/ed976/Introduction%20to%20Conceptual%20Maths.pdf?sessionID=ed063051ea608f80e207e4a2e712f83d92275c79

 

Benson, Cane, Spencer (2014): Early Algebra with Gattegno's Qualitative Arithmetic: Vocabulary and Grammar, Primary Mathematics

 

"Experiences with early algebra": http://tizard.stanford.edu/sandbox/users/ianbenson/weblog/87497/attachments/b3db0/PM%20May%202015%20Experiences.pdf?sessionID=ed063051ea608f80e207e4a2e712f83d92275c79

 

New South Wales Department of Education. (1969) Cuisenaire-Gattegno Arithmetic: A Correspondence Course.

 

Young, R. & Messum, P. (2011) How we learn and how we should be taught: An introduction to the work of Caleb Gattegno. Duo Flumina.

 

 

 

Simon Gregg: http://mathagogy.com/simon-gregg-how-i-teach-using-cuisenaire-rods/

 https://www.youtube.com/watch?v=E7tfXLT064E 

 

 

https://blog.learningresources.co.uk/numbers-in-colour-the-history-of-cuisenaire-rods/

http://www.froebelweb.org/web2026.html

60 years: http://cuisenaire.co.uk/index.php/home/60-years/pedagogical-articles

     http://cuisenaire.co.uk/index.php/home/60-years/60-years-of-cuisenaire-rods

 

 

Algebricks -- plastic, $50: http://www.educationalsolutions.com/algebricks/algebricks-rods

 

ESWI books: https://issuu.com/eswi

 

Gattegno bibliography: https://www.roslyn-young.fr/bibliographies/bibliography-of-gattegno-s-work/

 

Learning resources: https://www.learningresources.com/text/pdf/7536book.pdf

http://tizard.stanford.edu/sandbox/users/ianbenson/weblog/37b9a/attachments/abf31/IntroToCuisenaire.pdf 

 

Workbooks 1-6: http://shop.cuisenaire.co.uk/set-of-cuisenaire-workbooks-1-6/ 

Talks For Primary School Teachers: 

http://shop.cuisenaire.co.uk/talks-for-primary-school-teachers-b-stock/

 

Cuisenaire - from Early Years to Adult Paperback – 2017

by Association of Teachers of Mathematics (Author), Helen Williams, Simon Gregg, Mike Ollerton

     ebook: https://www.atm.org.uk/Shop/New-for-2017/Cuisenaire---from-Early-Years-to-Adult-e-book/ 

 

Idea Book, 1977

Patricia S. Davidson

 

Modern Mathematics Made Meaningful with Cuisenaire Rods Study Kit

 

 

De Geest, Els (2011). Gattegno’s mathematizing. In: Association of Teachers of Mathematics Conference 2011: Celebrating Gattegno, 18-21 April 2011, Wolverhampton, UK.

http://oro.open.ac.uk/30786/

     cites: 

Gattegno, C. (1987/2010) What we owe children. New York: Educational Solutions Worldwide.  First published 1987.  Reprinted 2010.

Gattegno, C. (1988) The Science of Education.  Part 2B: The awareness of mathematization. New York: Educational Solutions. 

Dawson, S. (1988) Words triggered by images: images triggered by words. In: John Chatley (ed)  Readings in Mathematica education: mathematical images. Derby: ATM

Collis, K. F.  (1975).  A Study of Concrete and Formal Operations in School Mathematics:  A  Piagetian  Viewpoint.   Victoria,  Australia:  Australian Council for Educational Research.

Jones, Ian (2008 A diagrammatic view of the equals sign: arithmetical equivalence as a means, not an end. Research in Mathematics Education 10:2, pp151 — 165

 

 

 

 

Animated Geometry by J.L. Nicolet

 http://shop.cuisenaire.co.uk/animated-geometry-by-j-l-nicolet/

http://www.worldcat.org/title/animated-geometry/oclc/875132744&referer=brief_results 

http://moodle.mce-fimem.it/pluginfile.php/2602/mod_resource/content/0/1966b%20Periodico%20di%20Matematiche%20IV%2C%20XLIV.pdf

 

 

See p178 of Science of Education 2b: Awareness of Mathematization

https://books.google.com/books?id=9tG241_dx0oC&pg=PA178&lpg=PA178&dq=%22L%27enseignement+des+mathe%CC%81matiques%22+nicolet&source=bl&ots=ZiAQO373AE&sig=5VM3o6daEG10wVuRTTWn7dIldog&hl=en&sa=X&ved=0ahUKEwiHzv_3ztjWAhVB8WMKHV8oBNUQ6AEIPTAE#v=onepage&q=%22L'enseignement%20des%20mathe%CC%81matiques%22%20nicolet&f=false

 

  • FTM 2: Articles on Nicolet films: https://issuu.com/eswi/docs/fttomv2webbook 
  •  
  • "L'esnseignment par le film mathematique" in Gattegno, La Material pour L'enseignement des Mathematiques, 1958
  • Animated Geometry series of films, produced by Gattegno:
    • Circles in the plane
    • Angles at the circumference
    • Common generaiton of conics
    • Two circles seen under equal angles
    • Poles and polars in the circle
    • Definitions of the right strophoid
    • Epi and hypo-cycloids
    • Pamphlet of notes, 1981
  • Folklore of Mathematics (see chapter 12), 5 parts, 4 min each, from Educational Solutions
  • Mathematics and Imagery, in Mathematics Teaching 33 (1965)
  • Educational Solutions Newsletter, Vol IX, #3, 1980
  • Foundations of Geometry, Gattegno 1979 film, 17 minutes, from Educational Solutions 

 

 

https://issuu.com/resonances22/docs/no10_ecole_primaire_1943 

 

E. Castelnuovo, "Jean Louis Nicolet e i suoi films di geometria"

Italian book pdf: http://moodle.mce-fimem.it/pluginfile.php/2602/mod_resource/content/0/1966b%20Periodico%20di%20Matematiche%20IV%2C%20XLIV.pdf

 


ATM 2007 film reflection: https://www.atm.org.uk/write/MediaUploads/Journals/MT205/Non-Member/ATM-MT205-02-03.pdf

 

nicolet "Intuition mathematique et dessins animes"

http://www.worldcat.org/title/intuition-mathematique-et-dessins-animes/oclc/491438064

https://www.amazon.fr/Intuition-math%C3%A9matique-dessins-anim%C3%A9s-p%C3%A9dagogique/dp/B0000DLOAB/ 

probably from  L'Enseignement des mathématiques. 2. Etude du matériel. 2e éd., pp. 63-80.

     http://www.worldcat.org/title/materiel-pour-lenseignement-des-mathematiques/oclc/84513767

 

 

The Method of Jean Louis Nicolet

Gattegno, Caleb

Mathematics Teaching Incorporating Micromath, n205 p42-43 Nov 2007

https://www.atm.org.uk/Mathematics-Teaching-Journal-Archive/3904 

     https://eric.ed.gov/?id=EJ781150

     cited by 1 https://scholar.google.com/scholar?cites=17486588141389125258&as_sdt=2005&sciodt=0,5&hl=en 

 

 

"The Foundations of Geometry" 

Caleb Gattegno and David Wheeler

For the Learning of Mathematics, Vol. 1, No. 1 (Jul., 1980), pp. 10-16

https://www.jstor.org/stable/40247695

 

Exploiting Mental Imagery with Computers in Mathematics Education (p.308 cites Nicolet, in Gattegno's 1958 version of "L'Enseignement des mathématiques.)

edited by Rosamund Sutherland, John Mason

https://books.google.com/books?id=Z6fxCAAAQBAJ&pg=PA141&lpg=PA141&dq=tahta+%22geometric+images%22&source=bl&ots=JiT8UtuT6o&sig=fUE-FgY62vA3kNmRCKGPN9cjwqk&hl=en&sa=X&ved=0ahUKEwjo2ej7vb_WAhWillQKHerCDVYQ6AEITDAL#v=onepage&q=tahta%20%22geometric%20images%22&f=false 

 

Unknown: https://www.youtube.com/watch?v=gum9kvxR9K8 

  1. Three points determine one circle
  2. Circles tangent to two concentric circles
  3. Contact point of parallel tangents to circles
  4. Subtended arc 
  5. A given line seen at a given angle
  6. Angles at the circumference
  7. Internal bisectors of a triangle
  8. External bisectors of a triangle
  9. The construction of the regular pentagon
  10. The golden section and the regular pentagon
  11. Triangle formed from sides of regular polygons: https://www.youtube.com/watch?v=4D3ttrC2Wdk 
  12. Hypocycloid motion with circles in a ratio of 1:2
  13. Two given circles seen under equal angles
  14. The strophoid and the golden section
  15. Poles and polars in the circle
  16. Generation of an ellipse I
  17. Locus of vertex of right angles tangent to an ellipse
  18. Generation of an ellipse II
  19. Generation of a hyperbola
  20. Generation of a parabola
  21. Anotehr generation of a parabola
  22. Common generation of conics

 

Some thoughts arising from the new Nicolet films

D Tahta - Mathematics Teaching, 1981

     cited by 37: https://scholar.google.com/scholar?cites=2098541424919867509

 

 

Gattengno's films:

Extensions of Pythagoras' Theoerm

Sections of the cube: https://www.youtube.com/watch?v=Rc8X1_1901Q 

Generation of some plane curves

Sections of the cone

 

 

Gattegno, C. (1980). ‘The Foundations of Geometry.’ In: For the learning of Mathematics 1 (1),

pp. 10-16. 

 

References Gattegno/Nicolet films: https://www.ncetm.org.uk/resources/24294 

 

Geoboard Geometry, 1971, later edition of "From Actions to Operations", 1958

 

Geometric Images, e-book 

Starting points for developing geometry through imagery

https://www.atm.org.uk/Shop/Geometric-Images---PDF/dnl019 

 

Foundations of Geometry - Notes on the Film: https://issuu.com/eswi/docs/1019_foundations-of-geometry---notes-on-the-film

https://www.jstor.org/stable/40247695?seq=1#page_scan_tab_contents

     https://dokumen.tips/documents/the-foundations-of-geometry-58831af267615.html 

 

Different author, but cites it: The History of the Geometry Curriculum in the United States (Research in Mathematics Education)

https://www.amazon.com/Geometry-Curriculum-Research-Mathematics-Education-ebook/dp/B01FNA2ZDQ

OR

History of Teaching Geometry, in Handbook on the History of Mathematics Education (Springer)

https://link.springer.com/chapter/10.1007/978-1-4614-9155-2_23

 

Dick Tahta: https://www.atm.org.uk/write/mediauploads/journals/mt202/non-member/atm-mt202-07-07.pdf 

     Images of Infinity (Leapfrogs team): https://www.tarquingroup.com/images-of-infinity.html

     http://www.open.edu/openlearn/ocw/pluginfile.php/632514/mod_resource/content/1/math_t9_28t_2.pdf 

     https://en.wikipedia.org/wiki/Dikran_Tahta 

     https://www.atm.org.uk/write/MediaUploads/Journals/MT205/Non-Member/ATM-MT205-02-03.pdf

 

Caroline Ainsworth Videos: http://cuisenaire.co.uk/index.php/home/videos/cuisenaire-rods-in-the-classroom/video/0 

     ppt: http://www.primarysupportteam.co.uk/files/caroline_ainsworth_workshop_presentation.pdf

 

 

http://www.mamaland.org/2011/02/gattegno-cuisenaire-rods-elementary.html

http://cuisenaire.co.uk/index.php/home/videos/gattegno-in-the-classroom

 

 

 

Handbook of Activities: http://www.arithmophobianomore.com/wp-content/downloads/BBL/Handbook-of-Activities-Textbook-for-the-Teaching-of-Mathematics-at-the-Elementary-School.pdf

 

 

 

http://www.jstor.org/stable/41184118?seq=1#page_scan_tab_contents

 

 

A Gattegno Anthology: https://www.atm.org.uk/Shop/Primary-Education/Primary-Education-Books/Books--PDF-Downloads/A-Gattegno-Anthology---PDF/dnl030

 

6 Foreword

  • 9 A farewell address, Easter, 1988

Occasions

  • 18 Mathematics teaching, MTl , 1955
  • 18 What matters most, MTI2, 1960
  • 21 Ten years ofMT, MT33, 1965
  • 22 21st anniversary, MT62, 1973
  • 23 30 years later, MTl00, 1982

Curriculum

  • 28 Functioning as a mathematician, MT39, 1967
  • 30 A prelude to the science of education, MT59, 1972
  • 33 Operations on integers, MT114, 1986
  • 38 Mathematics and imagery, MT33, 1965
  • 40 Algebra, MT105, 1983
  • 41 Roots, MT117, 1986
  • 42 Infinity, MT107, 1984

Learning

  • 46 Children and mathematics, MT94, 1981
  • 48 Parts and wholes, MT119, 1987
  • 49 Knowledge and experience, MTII0, 1985
  • 51 Notes on adolescence, MT108, 1984

Foundations

  • 56 Notes on a new epistemology, MT50, 1970
  • 59 Some books 

 

https://www.roslyn-young.fr/bibliographies/bibliography-of-gattegno-s-work/  

 

 

Newsletter on Software: https://issuu.com/eswi/docs/1128_-3----4-two-of-our-breakthroughs-february-apr

Computer and the mind: https://issuu.com/eswi/docs/1126_-1-the-computer-and-the-mind-september-1981

all newsletters: https://issuu.com/eswi/stacks/b74210f4d87a4257b9d390179be2a4c5

 

 

Gattegno Language Silent Way

http://www.saudicaves.com/silentway/

http://www.saudicaves.com/span/video.htm

https://www.youtube.com/watch?v=R302HvVAjIU

 

 

Homeschoolers

 

http://forums.welltrainedmind.com/topic/243744-cuisenaire-rods-for-dummies-please-direct-me/

 

http://nurturedbylove.blogspot.com/2008/12/cuisenaire-discovery-book.html

 

 

 

The Use of Coloured Rods in Teaching Primary Numberwork.

Vancouver Public Schools, WA. 1964

A review of research literature

https://eric.ed.gov/?q=ED028823&id=ED028823

 

 

John Trivett: https://eric.ed.gov/?q=john+trivett

 

 ...And so on : new designs for teaching mathematics [1980]

Trivett, John V.  (at stanford)

https://www.worldcat.org/title/and-so-on-new-designs-for-teaching-mathematics/oclc/425709761&referer=brief_results 

     Activities and problems are interspersed with commentary in this book on the learning and teaching of mathematics. The emphasis is on helping students to enjoy mathematics through an awareness of structure and patterns. The chapter titles are as follows: (1) "My Three Sons--A Game"; (2) "The Tower Game"; (3) "Mathematical Games on a Different Planet"; (4) "Computation as a Language Art"; (5) "Some Beginnings of Computation"; (6) "The Addition Table--Its Patterns"; (7) "Addition and Subtraction Without Borrowing"; (8) "The Multiplication Table Revisited"; (9) "Factors and Multiples--An Alternative Look at Previous Work"; (10) "Multiplication of Large Numbers"; (11) "Division--Another Creative Activity"; (12) "Fractions Are Not Parts of Wholes"; (13) "Operations on Fractions, When Representing Rational Numbers"; (14) "Decimals--Number Names Using Dots"; (15) "Per Dozens, Per Kilometers, Per Cents"; (16) "Exponents--Small Number Names Up High"; and (17) "The Problem of Problems." (MNS)

 

 

Introducing geoboards : activity cards.

Author: John V Trivett; Cuisenaire Company of America.

Publisher: New Rochelle : Cuisenaire Co. of America, ©1973

https://www.worldcat.org/title/introducing-geoboards-activity-cards/oclc/3775422&referer=brief_results

 

Fly Your Own Kite article, cited by: https://link.springer.com/article/10.1007/BF00311177

 

 

 

 

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