Volume 38 (October 2006) Number 5ZDMZentralblatt für Didaktik der Mathematik
Practice makes perfect on the blackboard: A cultural analysis of mathematics instructional patterns in Taiwan Bih-jen Fwu, National Taiwan University (Taiwan) Hsiou-huai Wang, National Taiwan University (Taiwan)
Abstract:
Studies show a sharp difference in math achievement between students in the U.S.
and students in several East Asian countries, amongst
them Taiwan. It is suggested that the patterns of math instruction
applied by teachers may have contributed to these differences.
This study intends to investigate the patterns
of math instruction applied by the Taiwanese teachers and to delve into the
cultural roots of these patterns. Data source includes videotaping of
instruction by three middle school math teachers and a questionnaire survey of
297 eighth-graders. It was found that the
Taiwanese math instruction pattern may be summarized as a cultural activity of
“practice makes perfect, on the blackboard.” The underlying cultural beliefs are
further explored, including the incremental view of human intelligence,
self-improvement through diligent effort, and the teacher’s role as an authority
figure.
Using International Research
to Contest Prevalent Oppositional Dichotomies Abstract:
International comparative research has the capacity to problematise our most
basic assumptions.
Dichotomies such as teacher-centred versus student-centred classrooms, telling
versus not-telling, speaking versus listening, and even teaching versus learning
can restrict educators and educational theorists to a fragmented view of the
classroom. Constructing such dichotomies as oppositional creates a set of false
choices, sanctifying one alternative, while demonising the other. International
research offers insight into possible explanatory frameworks within which such
dichotomies are no longer oppositional, but instead can be seen as complementary
and fundamentally interrelated. The acceptance of such complementarities is a
first step towards an inclusive theory of classroom practice and learning
How much time do students have to think about
teacher questions? An investigation of the quick succession of teacher questions
and student responses in the German mathematics classroom
Abstract: Several studies have shown that the style of the German
mathematics classroom at secondary level is mostly based on the so called
“fragend-entwickelnde” teaching style which means developing the lesson content
by a teacher directed sequence of teacher questions and student responses. In
this article we describe a study on the time the students have for thinking
about a teacher question in the public classroom interaction. Our investigation
is based on a re-analysis of 22 geometry lessons from grade 8 classes which
mainly deal with a challenging proving content. The results show that the
average time between a teacher question and a student response is 2.5 seconds.
There are no remarkable differences between different phases of the lessons like
comparing homework, repetition of content or working on new content. Moreover,
for 75% of the teacher questions the first student was called to answer within a
three second time interval.
Cognitive
level in problem segments and theory segments
Abstract:
Problems play an important
role in mathematics instruction and are therefore frequently seen as central
points of application for measures of instructional development.The
research project “Quality of instruction and mathematical understanding in
different cultures” examines the cognitive level of practice problems and theory
problems in a three-lesson unit on the Introduction to Pythagorean theorem:
Analogously to the TIMSS 1999 video study, a differentiation was made between
the cognitive level of problem statement and the cognitive level of problem
implementation. Additionally, the lesson time was also divided into practice and
theory segments. The results show that teachers with a high proportion of
connection activities in practice segments do not necessarily also spend a
greater proportion of time on an analogous level for theory.
Video technology in the assessment of an in-service teacher learning program
–Differences in mathematics teachers’ judgements on instructional quality Abstract:
Video technology offers the possibility to make instructional situations
available for discussion in teacher learning projects. For the confrontation
with videotaped instructional situations, the teachers’ rating of
characteristics for instructional quality plays an imminent role. As criteria
for instructional quality are often linked to the goals of the teacher learning
project, the teachers’ views offer possibilities to evaluate these projects. For
the example of instructional situations in German classrooms concerning
geometrical proof, differences in judgements on instructional quality are
analysed. The study focuses on data of a cluster analysis showing initial
divergencies in the rating of videotaped instructional situations and it
describes how the teachers’ views evolve.
Learning with Classroom
Videos: Conception and first results of an online teacher-training program
Abstract:
Within the framework of a yearlong teacher education program we examined the
conditions and effectiveness of learning with classroom videos. In online phases
and face-to-face sessions (blended learning), 20 teachers from two different
countries (Germany and Switzerland) analyzed videos of their own math-lessons
and math-lessons of other teachers. Using different instruments, the training
program was evaluated from a scientific perspective. The evaluation aimed to
obtain information about processes within the training, about the acceptance of
the training by the teachers and about changes of the professional knowledge and
the patterns of perception of teaching processes of the teachers. |