RADICAL TEFL

interaction in the context of maths learning, or EFL? How can we research the
learner's subjectivity? How can we understand how a student is trying to make sense
of a new difficulty?
2. Evidence
The processes, problems and wrong turnings in maths learning are visible, available
as evidence, as students write down stages in their thinking: Can a student's written
work supply evidence of the EFL learning (or failing to learn) process? Can we
empathetically enter into the student's subjective standpoint in this way using
evidence provided in student output? Could we do this for understanding the learning
of writing?
3. Learning from the study of history.
Documents and written records are used as evidence in the study of history. If all
mathematics learning (or failure to learn), as written down by the student, has taken
place in the (immediate) past, does this mean that a study of the learning of maths (or
EFL) is a kind of historical enquiry?
Alistair Maclean
SOME WORK ON UNDERSTANDING MATHEMATICS
LEARNING AND FAILURE TO LEARN
Gates, P, (ed)(2001), Issues in mathematics Teaching, RoutledgeFalmer
Glasersfeld, Ernst von (1991)(ed). Radical Constructivism in Mathematics Education. Kluwer
Academic Publishers.
Glasersfeld, Ernest von (1995), Radical Constructivism: A Way of Knowing and Learning, A
full statement of his thinking on constructivism. See esp. ch. 2 [philosophicalhistorical
context]; ch. 3 [on Piaget]; & ch. 10 [practical implications].
Gray, E., Processes and Concepts as false friends, in Tall D & Thomas (ed)(2002). On
understanding children's misconceptions in mathematics learning
Jaworski, Barbara (date ?), Investigating Mathematics Teaching: A constructivist enquiry,
Falmer Press. Ch. 2. Excellent introduction to constructivism in a school subject.
Johnston-Wilder, Sue et al (eds)(2004 2 nd . ed), Learning to teach mathematics in the
secondary school, Routledge, pp. 48-51 for a window on some thinking and issues in
mathematics education.
Mason, John (1994), Enquiry in Mathematics and in Mathematics Education, which is ch. 15
of Ernest (1994). Includes an overview of some issues in researching mathematics
education. Mason is leading researcher of mathematics education.
Mason, J. & Johnston-Wilder, Sue (eds)(2004), Fundamental Constructs in Mathematics
Education, RoutledgeFalmer / Open University
Orton, A, What cognitive demands are made in learning mathematics?, which is ch. 3 of
Orton, A (ed) (1987, 1992 2 nd . ed), Learning Mathematics: Issues, Theory and
Classroom Practice, Continuum
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