· 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?
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