Norma 08 - Day 3

A bit late, but here are my notes from the plenary lecture from the third day at Norma08:

Plenary lecture - Eva Jablonka

PART 1 - "Mathematics for all. Why? What? When?"

Math as a core subject in compulsory education (empirical fact). Industrialised countries provide basic maths for all (in school). BUT - many children don't go to school in several countries around the world. It varies between countries when children can stop taking mathematics courses.

Mathematics for all, beyond primary level - why?
Goals as an apologetic discourse.
Common list of justifications:

  • Skills for everyday life and activities for workplaces (useful)
  • Sharing cultural heritage
  • Learning to think critically (formative goal)
Examples of critical thinking in classrooms (Harols Fawcett, 1938)
  • Selecting significant words and phrases, careful definition
  • Require evidence to support conclusions
  • Analyzing evidence
  • Recognize hidden assumptions
  • Evaluate the argument itself
  • etc.
"Everybody counts" (National Academy of Sciences, 1989)
Help develop critical habits of mind, understand chance, value proof etc. (p. 8).

The notion of "thinking critically" - what is it?
Fawcett - precision of language
Swedish example - relation to environment, etc. (global view, more vague)

Is there an epistemic quality of mathematics that is linked to thinking critically? (interesting question!)

Recent descriptions - renaissance of formative and methodological goals
- Communicating mathematically (discuss, advantages, disadvantages, etc.)

    Communicating freely and critical thinking takes place in some sort of an ideal democratic environment.

    Are mathematics classrooms ideal speech communities?

- Learning to model and solve problems mathematically
    Danger of overemphasizing utility (connections with engineering, social science departments, etc.)

- Recruitment into the mathematics, science and engineering pipeline as justification (economic development in a country, etc.)
    There has to be a "critical mass" from which to select future mathematicians. (similar argument to sports, being successful in sports)

How successful are the students in compulsory mathematics courses for all?
International tests (PISA, TIMSS, etc.) - only a small percentage will reach the highest level. Discussions of "average achievements", comparisons between countries.

Compulsory mathematics, not for all. Global failure of math education?
Which groups of students are successful/less successful? (interesting question)

PART 2 - "Mathematics for all!" (mission statement)
  • Demographic development (declining number of students, in many industrialised countries)
  • "Learning to leave?" - Successful students often end up moving away (from their country, local area, etc.) - How can a mathematics curriculum serve the local needs of local communities?
  • Organization of participation - students' choices. Why do so many students choose not to pursue further studies in mathematics after the compulsory course? To what extent should we "force" them to choose mathematics?
  • Changes in social contexts
  • Increased stress on instrumental knowledge and of the marketability of skills. Danger of oppositions between rationales for mathematics and liberal arts for instance.
  • Professional groups fighting against the "contamination of mathematical knowledge". Consequence of shift towards process skills in the curricula. (Back to basics movement, math wars, etc.)
  • A widening gap of mathematical knowledge between constructors and consumers of mathematics (Skovsmose, 2006) - threat to democracy (you have to rely on the experts).
  • The "de-mathematizing" and restricting effects of mathematical technology. Use of technology liberates us from the details of mathematics.
  • Confrontations of local knowledge and mathematical knowledge acquired at school. (Students don't appear to use the mathematics they learned in school outside the classroom)
Research is addressing some of these challenges:
  • Classroom research looking into these speech communities
  • Concern about "mathematical literacy"
  • Empirical studies of local mathematical practices at work-places (and local communities)
  • Students' goals and motives
  • Consequences of changes in students' backgrounds
  • Problem of transition between different tracks of mathematics education
Jablonka doesn't think there will be a universal curriculum for all.