Searching "Donovan A. Johnson" on the broadly interdisciplinary Google Scholar yields 112 references to the book, on teaching math. The 37 page pamphlet is readily available on the Internet Archive (2 versions) looking for Donovan A Johnson ( at https://ia801300.us.archive.org/22/items/ERIC_ED077711/ERIC_ED077711.pdf
But searching Donovan A. Johnson on Google scholar, for example, leads to other interesting papers Title: A history of folding in mathematics http://gen.lib.rus.ec/book/index.php?md5=8BC61D7731DCC46DDA1A8A74D79DCEFF Author(s): Friedman.; Friedman, Michael; Goob Publisher: Birkhauser,Springer International Publishing Year: 2018 430 pages Table of contents : Content: Introduction. - From the 16th Century Onwards: Folding Polyhedra. - New Epistemological Horizons?. - Prolog to the 19th Century: Accepting Folding as a Method of Inference. - The 19th Century - What Can and Cannot be (Re)presented: On Models and Kindergartens. - Towards the Axiomatization, Operationalization and Algebraization of the Fold. - The Axiomatization(s) of the Fold. - Appendix I: Margherita Beloch Piazzolla: "Alcune applicazioni del metodo del ripiegamento della carta di Sundara Row". - Appendix II: Deleuze, Leibniz and the Unmathematical Fold. - Bibliography. - List of Figures. and to the later and smaller version Title: A History of Folding in Mathematics: Mathematizing the Margins Volume: http://gen.lib.rus.ec/book/index.php?md5=1964A01DCFCC4E0412A41B9D49AF1CD0 Author(s): Michael Friedman Series: Science Networks. Historical Studies Publisher: Birkhäuser Year: 2018 Edition: 1st ed. 2018 "While it is well known that the Delian problems are impossible to solve with a straightedge and compass – for example, it is impossible to construct a segment whose length is ?2 with these instruments – the Italian mathematician Margherita Beloch Piazzolla's discovery in 1934 that one can in fact construct a segment of length [square root] of 2 with a single paper fold was completely ignored (till the end of the 1980s). This comes as no surprise, since with few exceptions paper folding was seldom considered as a mathematical practice, let alone as a mathematical procedure of inference or proof that could prompt novel mathematical discoveries. A few question immediately arise: Why did paper folding become a non-instrument? What caused the marginalisation of this technique? And how was the mathematical knowledge, which was nevertheless transmitted and prompted by paper folding, later treated and conceptualised? Aiming to answer these questions, this volume provides, for the first time, an extensive historical study on the history of folding in mathematics, spanning from the 16th century to the 20th century, and offers a general study on the ways mathematical knowledge is marginalised, disappears, is ignored or becomes obsolete. In doing so, it makes a valuable contribution to the field of history and philosophy of science, particularly the history and philosophy of mathematics and is highly recommended for anyone interested in these topics." ========== An Investigation Of The Effect Of Origami-Based Instruction On Elementary Students’ Spatial Ability In Mathematics A Thesis Submitted To The Graduate School Of Social Sciences Of Middle East Technical University By Sedanur Çakmak 133 pages http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.633.1841&rep=rep1&type=pdf and Origami On Computer David Fisher 75 pages http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.74.8461&rep=rep1&type=pdf (The PDF excludes any illustrations) ------------- A History of Folding in Mathematics by Michal Friedman Individial chapters are on the Springer publisher site The chapter Coda First Online: 26 May 2018 has had 903 Downloads There are two versions of of the book on Library Genesis: 5.6 Mbytes and 10.4 Mbytes PDFs Friedman M. (2018) Coda: 1989—The Axiomatization(s) of the Fold. In: A History of Folding in Mathematics. Science Networks. Historical Studies, vol 59. Birkhäuser, Cham The DOI should get you lots of related items from Library Genesis and Sci-hub DOI https://doi.org/10.1007/978-3-319-72487-4_6 Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Setting the Scene: Which Instrument Is Stronger? . . . . . . . . . . . . . 1 1.2 Marginalization and Its Epistemological Consequences . . . . . . . . . 5 1.3 Marginalization and the Medium: Or—Why Did Marginalization Occur? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 The Economy of Excess and Lack . . . . . . . . . . . . . . . . . . . . . . . . 15 1.5 Historiographical Perspectives and an Overview . . . . . . . . . . . . . . 19 1.5.1 Marginalized Traditions . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.5.2 The Historical Research to Date and Overview . . . . . . . . . 22 1.5.3 Argument and Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2 From the Sixteenth Century Onwards: Folding Polyhedra—New Epistemological Horizons? . . . . . . 29 2.1 Dürer’s Nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.1.1 Underweysung der Messung and the Unfolded Nets . . . . . . 32 2.1.2 Folded Tiles and Folds of Drapery . . . . . . . . . . . . . . . . . . 39 2.1.3 Dürer’s Folding: An Epistemological Offer? . . . . . . . . . . . 44 2.2 Dürer’s Unfolded Polyhedra: Context and Ramifications . . . . . . . . 48 2.2.1 Pacioli and Bovelles, Paper Instruments and Folded Books: Encounters of Folding and Geometry . . 49 2.2.1.1 Paper Instruments: Folding for Science . . . . . . . . 53 2.2.1.2 A Historical Detour: Bat Books and Imposition of the Book—The Standardization of Folding . . . 59 2.2.2 Dürer’s Followers Fold a Net . . . . . . . . . . . . . . . . . . . . . . 66 2.2.2.1 Stevin’s and Cowley’s Impossible Nets . . . . . . . . 76 2.2.2.2 Nets of Polyhedra: A Mathematical Stagnation? . . 80 2.3 Ignoring Folding as a Method of Proof in Mathematics . . . . . . . . . 83 2.3.1 Folding and Geometry: A Forgotten Beginning—Pacioli Folds a Gnomon . . . . . . . . . . . . . 83 2.3.2 Folding and Geometry: A Problematic Beginning . . . . . . . 86 3 Prolog to the Nineteenth Century: Accepting Folding as a Method of Inference . . . . . . . . . . . . 93 3.1 Folding and the Parallel Postulate . . . . . . . . . . . . . . . . . . . . . . . . 94 3.1.1 Folding and Parallel Line: An Implicit Encounter During the Arabic Middle Ages . . . . . . . . . 94 3.1.2 Folding and Parallel Line: An Explicit Encounter During the Eighteenth Century . . . . . . . . . 96 3.2 Folding in Proofs: Suzanne and Francoeur . . . . . . . . . . . . . . . . . . 98 3.2.1 Symmetry and Folding Diderot and Symmetry in Francoeur’s Cours Complet . . . . . . . . . . . . . 100 3.3 Lardner, Wright, Henrici: Symmetry with Folding in Great Britain . . . . . . . . . . . . . . . . 104 4 The Nineteenth Century: What Can and Cannot Be (Re)presented—On Models and Kindergartens . . . . . . . 113 4.1 On Models in General and Folded Models in Particular . . . . . . . . . 114 4.1.1 Mathematical Models During the Eighteenth and Nineteenth Centuries . . . . . . . . . 115 4.1.2 Folded Models in Mathematics: Dupin, Schlegel, Beltrami, Schwarz and the Two Wieners . . . 126 4.1.2.1 Louis Dupin and Victor Schlegel: How to Fold Nets in the Nineteenth Century . . . . . . 126 4.1.2.2 Eugenio Beltrami and Models in Italy . . . . . . . . . 141 4.1.2.3 Schwarz, Peano and Christian Wiener . . . . . . . . . 152 4.1.2.4 Hermann Wiener . . . . . . . . . . . . . . . . . . . . . . . . 165 4.1.3 A Detour into the Realm of Chemistry: The Folded Models of Van ’t Hoff and Sachse . . . . . 180 4.1.3.1 Van ’t Hoff Folds a Letter . . . . . . . . . . . . . . . . . 181 4.1.3.2 Hermann Sachse’s Three Equations . . . . . . . . . . . 194 4.1.3.3 Folded Models in Chemistry and Mathematics: A Failed Encounter . . . . . . 200 4.1.4 Modeling with the Fold: A Minority Inside a Vanished Tradition . . . . . . . . . . 203 4.2 Folding in Kindergarten: How Children’s Play Entered the Mathematical Scene . . . . . . . . 206 4.2.1 Fröbel’s Folds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 4.2.1.1 Fröbel and Mathematics . . . . . . . . . . . . . . . . . . . 209 4.2.1.2 Fröbel Folds . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 4.2.1.3 Fröbel’s Influence and the Vanishing of Folding-Based Mathematics from Kindergarten . . . . 227 4.2.2 From Great Britain to India . . . . . . . . . . . . . . . . . . . . . . . 247 4.2.2.1 First Lessons in Geometry: Bhimanakunte Hanumantha Rao’s Book. . . . . . . . . . . . . . 250 4.2.2.2 The Books of Tandalam Sundara Row . . . . . . . . . 254 4.2.3 Folding in Kindergartens: A Successful Marginalization . . . 268 5 The Twentieth Century: Towards the Axiomatization, Operationalization and Algebraization of the Fold . 271 5.1 The Influence of Row’s Book. . . . . . . . . . . . . . . . . . . . . . . . . . . 272 5.1.1 First Steps Towards Operative Axiomatization: Ahrens, Hurwitz, Rupp . . . . . . . . . . . . 273 5.1.1.1 Anhrens’s Fundamental Folding Constructions . . . 274 5.1.1.2 The Basic Operations of Adolf Hurwitz . . . . . . . . 278 5.1.1.3 Lotka and Rupp: Creases as Envelopes . . . . . . . . 282 5.1.2 The Distinction Between Axioms and Operations: A Book by Young and Young . . . . . . . . . . . . 285 5.1.2.1 The Youngs’s The First Book of Geometry . . . . . 286 5.1.2.2 Translations and Acceptance . . . . . . . . . . . . . . . . 293 5.1.3 A Detour: How Does One Fold a Pentagon? . . . . . . . . . . . 295 5.1.3.1 The Construction of Euclid . . . . . . . . . . . . . . . . . 296 5.1.3.2 How Does One Fold a Regular Pentagon? . . . . . . 297 5.1.3.3 How Does One Knot a Regular Pentagon? . . . . . . 305 5.2 An Algebraic Entwinement of Theory and Praxis: Beloch’s Fold. . . . . . . . . . . . . . . . . . 318 5.2.1 Vacca’s 1930 Manuscript . . . . . . . . . . . . . . . . . . . . . . . . . 319 5.2.2 Beloch’s 1934 Discoveries . . . . . . . . . . . . . . . . . . . . . . . . 323 5.2.3 After 1934: Further Development and Reception . . . . . . . . 327 5.2.3.1 Lill’s Method of Solving Any Equation . . . . . . . . 330 5.2.3.2 A Fall Towards Oblivion? . . . . . . . . . . . . . . . . . 336 5.3 Epilog for the Twentieth Century: The Folding of Algebraic Symbols . . . . . . . . . . . . . . . . 340 5.3.1 The Faltung of Bilinear Forms . . . . . . . . . . . . . . . . . . . . . 341 5.3.2 Convolution as Faltung . . . . . . . . . . . . . . . . . . . . . . . . . . 350 6 Coda: 1989—The Axiomatization(s) of the Fold . . . . . . . . . . . . . . . . 355 6.1 The Operations of Humiaki Huzita . . . . . . . . . . . . . . . . . . . . . . . . 358 6.2 The Operations of Jacques Justin . . . . . . . . . . . . . . . . . . . . . . . . . 363 6.3 Conclusion: Too-Much, Too-Little—Unfolding an Epistemological Non-equilibrium . . . . . . . . 368 Appendix A: Margherita Beloch Piazzolla: “Alcune applicazioni del metodo del ripiegamento della carta di Sundara Row” . 377 Appendix B: Deleuze, Leibniz and the Unmathematical Fold . . . . . . . . . 381 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 And the footnotes should prove interesting https://link.springer.com/chapter/10.1007/978-3-319-72487-4_6 ----------- Also interesting are the 104 footnotes of the Australian paper mentioning Johnson. "Origami as a Teaching Tool for Indigenous Mathematics Education" by Michael Assis and Michael Donovan Jonathan M. Borwein Commemorative Conference JBCC 2017: From Analysis to Visualization pp 171-188 As usual the DOI can be plugged into Sci-Hub or Library Genesis to get the full paper Sci-hub and LIB-GEN are very useful if you can the the DOI of any paper. DOI https://doi.org/10.1007/978-3-030-36568-4_12 with references to ZbMath (Zentralblatt Math ) as well Google Scholar and MathScinet on each link to the abstracts if not the source papers
