Monday Morning Discussion of Sunday's Work

1. Wes: Wikipedia is "best" textbook available - not because of what's written, but because of what is not written - missing points, question marks, edited comment that "this does not suffice" etc., so the reader is left to fill in these places on their own.

Peter: book from the 70s where at least a third of the page is left blank for students to comment and fill in their remarks; the book with the student comments became the final book.

On-line textbooks make this collection of meta-comments part of what will be the textbook.
We discussed also the ways that internet sets of reviews and links (through algorithm) to other books/films/etc.... for us we might think of reviews by other teachers, students, ...

Juxtapose: Literature (ex: the one version of Shakespeare's Romeo & Juliette). Textbooks direct the attention of the person toward what y ou want them to do.

2. Peter : Reprise of idea that textbook is collaboration of artist and the reader. A textbook might be like the painting of Olympia, looked at an hour a week, studying historical context, extending, technique, where does it take us...
Online might allow for this in a different way. For the teacher to control the wealth of thing, harness it all, turns teaching into curating materials??
Online, student can overwhelmingly find new things and input them. This might change the relationship among teacher, text and student: teacher does not have to see everything, even though a teacher's acknolwedgement and interaction is powerful and important.
Control has to be let go, loosened, allowing others to collaborate on the curatorship.

3. Lucie: Smartboard... imagine teacher presents algorithm/explanation. Record content of smartboard; then students listen later and in the class have textbook as resource on problem solving. Students go on blog of teacher. Always start from problem solving.
Compared with BC consumable workbooks as textbook, changes year by year. No explanations, no worked examples. Big/small questions. Teacher does what Lucie described.

4.Miroslav: start with objectives. Course starts with list of questions we want student to be able to answer at the end. Course itself creates a textbook that does it.
Kathy, Peter & Osnat: create course around only problems. Ideally students create the problems but we're not sure if the problems would be good enough or lead to the right outcomes. Final exam: they create the questions, not answering them.
The tension between teacher and student knowing what questions to ask might be a false issue if we see it in a more interactive and dynamic way. e.g., after students ask some, a teacher might react with a question based in his or her own agenda for objectives; or, learning about asking questions includes looking at other mathematicians' questions and thinking about them, too.

Lucie: this indicates the importance of the domain / big ideas in mathematics, makes it easier to invite students to make their questions.

Joan: teachers create text(books); this can serve as data in research about teachers' understanding, relationship with/to students, texts, expectations for textbooks, etc. etc.

Blackboards from Day 2 of our working group

Peter Taylor's publications and textbooks available online

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Peter Taylor, Queen's University, publications

Peter's burning questions

1) Identifying textbooks as opposed to something else
What is a textbook, and how is that different from using something as a text with students?

2) The intransigent nature of the text as codification of the discipline
Despite the documented successes of non-standard uses of textbooks (e.g., students critiquing rather than using, re-writing ...) and disruption of the authors and audiences for the texts (students making their own textbooks for themselves and others, different groups of students comparing different texts as resources for their own learning, ...), the place of the textbook and its positioning of teachers and students persists. Why, how, and in whose interests?

3) Textbooks are sites of work-life struggle

Text materials are commonly used to de-skill teachers (they become cogs or conduits rather than designers of experience). When teachers approach their work creatively, responding to the lives of their students, this is often considered inappropriate. What are the implications?

4) People need to see the textbook to know what the curriculum "is" - or else?
Isn't anything and everything in one's lifeworld a mathematics textbook? Why does this not so easily translate into understanding everyone as a mathematician whose "inner mathematician" has been thwarted from expression by school mathematics?

Rhizome - a la Deleuze & Guattari

Curriculum Discourses (a canon?): Notes on Mathematics as …

·  Aesthetic Text

o   Sinclair, Nathalie, Notes on the Aesthetic Dimension of Mathematics

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]

o   Ancient Egyptian autobiographical tomb texts

 

  


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   Rotman, Brian, Signifying Nothing: The Semiotics of Zero

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

·         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

o   The Algebra Project

(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

·         Poststructuralist, Deconstructed, Postmodern Text

o   Appelbaum, Peter Embracing Mathematics

o   Walshaw, Margaret, Mathematics Education within the Postmodern [a sample review]

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?