Since 2004, we work with my colleague Alex Volkov, on exploring didactical value of mathematics textbooks, old and modern ones. We look at conceptual approaches that authors represent in their books. Our latest publication for the ICME-12 is now awailable online: http://www.icme12.org/upload/UpFile2/TSG/0703.pdf
We look at fractions in the first Russian arithmetics textbook written by Magnitskii in the beginning of the 18th century. While some authors point at the origins of the book from earlier European medieval texts, others claim original didactical ideas of introducing concept of fraction. The paper belong to the TSG35 on the History of mathematics teaching and learning and there are other interesting contibutions on textbooks development.
Showing posts with label Interesting articles. Show all posts
Showing posts with label Interesting articles. Show all posts
Monday, May 28, 2012
Tuesday, May 22, 2012
Reading (Texts)
Hannah's Question, by Alan Block
Curriculum from the Back of the Bookstore, by Alan Block
You are a Mathematician, by Peter Appelbaum
pdf version of Chapter Three: "You are a Mathematician" - c.f., pp. 107-114
Embracing Mathematics, Prologue
Herbel-Eisenmann & Wagner on the ways a math textbook positions the reader
A method for doing genre analysis, by Susan Gerofsky
Guides by mathematicians:
MAA Website: Ashley Reiter, Maine School of Science and Mathematics, "Helping Undergraduates Learn to Read Mathematics"
Kevin Lee, Purdue-Calumet "Tips for Reading Mathematics"
Alet Roux, Univerity of Hull, "How to Read Mathematics"
College-Algebra.com, "Reading Mathematics"
Further reading:
Gutstein, Eric. 2006. Reading and writing the world with mathematics: Toward a pedagogy for social justice. Routledge.
Leaonard, Jacqueline. 2008. Culturally specific pedagogy in the mathematics classroom: Strategies for teachers and students. Routledge.
Social/Propaganda uses of Mathematics Textbooks
Example 1: Nazi Math Textbooks
Ethics in EducationFacing History and Ourselves
Christopher Wagner
Post Holocaust Science Education
Example 2: Numerist Propaganda
The Math SkepticExample 3: Selected Scans of Pages from Chinese Cultural Revolution
Propaganda or propaganda for anti-Maoists? (May 23 entry)Isn't everything propaganda/ideology???
Appelbaum, "Target: Number"Monday, May 21, 2012
More on the use of texts historically in math education
Rewriting the early history of mathematics education in North America - ("...published histories relating to the teaching and learning of mathematics in the North American colonies, and during the first 75 years of the United States of America, have over-emphasized the role of printed textbooks.")
A brief history of CEMREL - aesthetic education program in mathematics curriculum development
1910 Review of three studies of arithmetic: The teaching of Arithmetic by David Eugene Smith; Arithmetical Abilities and Some Factors Determining Them, by Cliff Winfield Stone; and Manual of Instruction for Giving and Scoring the Courtis Standard Tests in Arithmetifc, by S.A. Courtis. (Journal of Educational Psychology, 1 (10), 1910)
Eric Love & David Pimm, 'This is so' : a text on texts
Sunday, May 20, 2012
Curriculum Discourses (a canon?): Notes on Mathematics as …
· Aesthetic
Text
o
Sinclair, Aesthetic
Considerations in Mathematics
o
Sinclair, Pimm, Higginson, Mathematics
& the Aesthetic
(a) Judgements,
sentiments, taste
(b) Affective
domain
(c)
Critique of one’s own and others’ work, as part
of a broader set of traditions and breaking with traditions
·
Autobiographical
Text
o
Cook, Mariana, Mathematicians: An outer view of the inner
world (videos, sample chapters) [one
curious review]
Institutionalized Text
o
Gueudet, Ghislaine, Birgit Pepin & Luc
Trouche, From
‘Text’ to Lived Resources: Mathematics Curriculum Materials and Teacher
Development
o
Remillard, Janine & Martha Bryans, Teachers’
Orientations Toward Mathematics Curriculum Materials: Implications for Teacher
Learning
o
Gates, Peter, Markets, Marx, Modernity and Mathematics Education.
A Response to Michael Apple
o
Brown, Tony, Comforting Narratives of Compliance: Psychoanalytic
perspectives on new teacher responses to mathematics policy reform
(a) Less
experienced teachers tend to more fully implement packaged curriculum
materials?
(b) The
existence of text materials implies that they were developed by people “who
know”.
(c)
Texts “qualify” teachers and students in
Foucauldian senses, skilling and deskilling these participants in particular
ways, while establishing social and cultural norms at individual, group,
school, district, provincial, national, and other levels of analysis.
(d) Texts position readers and teacher-readers as
“needing a text” – i.e., as someone who cannot perform their role without a
text or without the assistance of a text.
·
International
Text
o
Which works are most useful here?
(a) On
the one hand, mathematics is commonly taken as a universal/transnational and
transcultural language.
(b) One
the other hand, ethnomathematical approaches help us see how (Western, Ameroeuropean)
mathematics is a form of global imperialism that denies indigenous forms of mathematics
while raping the cultural landscape for new mathematical concepts and models.
(c)
·
Phenomenological
& Cultural Text
o
Brown, Stephen I., and Marion Walter, The
Art of Problem Posing; Brown, Humanistic Mathematics: Personal Evolution and
Escavations
o
Mason, John, et al. Thinking
Mathematically
o
Kirshner, David, Exercises, Probes, Puzzles.
(a) Historical
trajectory toward the experience of mathematics as a “meta-subject” with transient
“location” or position, outside of the world of mathematics.
(b) Enculturation/acculturation
in/with/to communities of practice
David Kirshner on enculturation vs. acculturation
David Kirshner on enculturation vs. acculturation
·
Political
Text
o
Mellin-Olsen, Stieg, The
Politics of Mathematics Education
o
Knjinik, Gelsa, Ethnomathematics and the politics
of mathematics education: Reflections on a research-project developed with the
Brazilian Landless Movement
o
Skovsmose, Ole – which references of many are
relevant to mathematics “texts”?
o
Gutstein, Eric, Reading
and Writing the World with Mathematics
(a) Conceptions
of (critical) “competence” and relations of power
(b) Foregrounding
the question, “What knowledge is of most worth?”, and to corollaries, “Who gets
to decide? How does this matter/make a difference?”
(c)
Mathematics education as/for social justice
o
Appelbaum, Peter Embracing
Mathematics
o
Rotman, Brian, Becoming
besides ourselves: The alphabet, ghosts, and distributed being; [one
person’s seminar reading notes]
o
Video: Paul Ernest and Allan Tarp
(a) Mathematics
contributes to an understanding of no fixed selves, truths, mirroring of
reality, conceptions of knowledge, value, or moral codes; flux over stasis.
(b) Ethics
replaces morals in the interrogation of how mathematics and mathematics
education contributes to the establishment of ideological commitments and
institutional structures of social and cultural reproduction
(c)
Institutions work in strategies of maintenance;
forms of resistance and social change manifest themselves in tactics, poaching,
perruque
·
Theological
Text
o
Rotman, Brian,
Ad Infinitum: The Ghost in Turing’s
Machine
o
Pickover, Clifford, The
Loom of Mathematics: Tapestries of Mathematics and Mysticism
o
Davis, Phillip, A Brief
Look at Mathematics and Theology
(a) Platonic
mathematics might be a substitute for religion; infinity for god; historically,
conceptions of infinity have brought people closer to god
(b) Intellectual
“cleansing” via mathematics and logic is sometimes related to a spiritual
cleansing via baptism, purging, etc.
Comments: Ralph Tyler's Basic principles of Curriculum and Instruction (1949) set up expectations for curriculum development that have been either worshipped or challenged ever since:
Start with objectives (determined by the content/subject, by the needs of students, and by social needs)
Collect experiences that will help learners meet these objectives, an
Then build in ongoing assessment to help you make sure you are meeting the objectives along the way.
To be a textbook, must a "book" be designed in this way? Did the geneaology of textbooks inform his approach to curriculum? A century later, are we still acting out his fantasies and fears in our creation and use of textbooks?
Comments: Ralph Tyler's Basic principles of Curriculum and Instruction (1949) set up expectations for curriculum development that have been either worshipped or challenged ever since:
Start with objectives (determined by the content/subject, by the needs of students, and by social needs)
Collect experiences that will help learners meet these objectives, an
Then build in ongoing assessment to help you make sure you are meeting the objectives along the way.
To be a textbook, must a "book" be designed in this way? Did the geneaology of textbooks inform his approach to curriculum? A century later, are we still acting out his fantasies and fears in our creation and use of textbooks?
Friday, May 18, 2012
 |
| Reissued by NCTM in 1995 |
(Students here are creating their own textbook - as the ostensible main project of the classroom curriculum.)
The original book: http://www.eric.ed.gov/PDFS/ED096174.pdf
A comment: http://www.cut-the-knot.org/ctk/NatureOfProof.shtml
A review of it: http://www.jstor.org/discover/10.2307/3028523?uid=3739864&uid=2129&uid=2&uid=70&uid=4&uid=3739256&sid=21100811633841
In today's classroom - one view: http://www.math.umt.edu/tmme/vol1no2/TMMEv1n2brev2.pdf
Joe Bellacero & Tome Murray, "Students write tabloid tabulations in math gossip magazine" (national writing project)
Alternatives to a "traditional" textbook genre? Story-telling didactic "texts"
Number Stories and Storytelling
David Eugene Smith's Number Stories of Long Ago (1919)Hans Magnus Enzensburger's Number Devil
Freudenthal Institute and story paths: http://www.nap.edu/openbook.php?record_id=12519&page=175
Ron Eglash's page on African Fractals
Puzzles and "recreational mathematics"
Sam Loyd's Cycopedia of PuzzlesDavid Suzuki's video tribute to Martin Gardiner
"Coloring Books" that foster investigations:
Excerpt from Herb Kohl & Winky Adam, Insides, Outsides, Loops and Linesclick for excerpt
Literature as Classroom text(book)?
Pat Hutchins, Clocks and More Clocks
Anno's Magic Seeds
Rod Clement's Counting on Frank
Denis Guedj's The Parrot's Theorem
Sarah Flannery's autobiography, In Code: A Mathematical Journey
Passover Haggadah as Ur-Text
Alan Block, "Even if we were all scholars: The teacher's authority"Landscapes, Soundscapes, ...
Marta Civil, unearthing the mathematics of a classroom garden (working paper on-line, later published in another form as Kahn, L. & Civil, M. (2001). Unearthing the mathematics of a classroom garden. In E. McIntyre, A. Rosebery, & N. González (Eds.) Classroom Diversity: Connecting School to Students' Lives (pp. 37-50). Portsmouth, NH: Heinemann.)
Breaking away from the math book (Pat Bagget & Andrzej Ehrenfeuch)
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