A Model for Analysing One-to- One teaching in the Maths Recovery Program

Abstract

This study was proposed as a first step to understanding teaching characteristics
particularly suited to one-to-one teaching in the Maths Recovery
Program. The teaching sessions of four teachers of Maths Recovery
were analysed to develop an experimental model of teaching
characteristics. Videotaped excerpts from teaching sessions of the Maths
Recovery Research Project were used in the analysis.
The experimental model of teaching characteristics draws on several
areas of research literature including Brophy and Good, 1986;
Cazden, 1986; Goodman and Goodman, 1990; Lyons, Pinnell and
DeFord, 1993; Mellin-Olsen, 1991; von Glasersfeld, 1990; Vygotsky,
1934/1962-1930/1978; Wood, 1990; Wright, 1995; and Yackel, 1990.
The characteristics identified were scaffolding, double bind, illusion
of competence, preformulating and reformulating questions, post
question wait-time, vague or ambiguous questioning, questioning and
prompting, and communication. Scaffolding refers to the gradual withdrawal
of adult control as a function of children’s increasing mastery of
a given task. A double bind is complementary to scaffolding. A double
bind produces dependence and results from repetition of a learning
task after a child experiences difficulty in understanding the task. An
illusion of competence refers to when the teacher and student produce
a solution together, with the student following teacher directives.
Preformulating and reformulating questions occurs when the teacher
prefaces the question with utterances which serve to orient the children
to the relevant area of experience and establish as shared knowledge
between the teacher and child notions essential to answer the question.
Reformulating refers to the simplification of a question when the
initial answer is wrong. The teacher knowingly or unknowingly reduces
the cognitive value of the question. Post question wait-time refers to
the length of time that a child has to respond to a question. Vague or
ambiguous questioning relates to when teachers ask questions, which
are vague or ambiguous to the child, and they are unable to respond to
the question. Questioning and prompting occurs when a teacher observes
closely what a child is doing and decides the appropriate question
or prompt which will help a child become a more independent
problem solver and less dependent on the teacher. Communication
refers to what is suitable and unsuitable communication in one-to-one
teaching.
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The methods used to develop and test the experimental model
draw on Vygotsky’s (1930/1978) methodological principles and Cobb
and Whitenack’s (1996) methodology for longitudinal analyses of data
on teaching in the form of videotaped recordings and transcripts. In
Phase One of the study characteristics of teaching were identified separately
from each other and used to build a preliminary model of characteristics
of one- to-one teaching. These observations were compared
and contrasted with the research literature until a fit was obtained. The
data was then compared with subsequent data until a newly formed
model of characteristics in one-to-one teaching evolved. Phase Two
was undertaken in order to test the usefulness of the experimental model.
The study found that the research literature which refers to the
classroom setting remains a suitable guide to analysing one-to-one teaching.
More study of one-to-one teaching with the focus on the teacher is
needed to evaluate directly as opposed to indirectly via student achievement,
the effectiveness of one-to-one teaching. In one-to-one teaching
programs, teachers need to be aware of appropriate and inappropriate
characteristics of one-to-one teaching and possible effects on students.
Scaffolding, post question wait-time, questioning and prompting support
the underlying principles of Maths Recovery Teaching. The theory
of a zone of proximal development as a method for understanding the
actual and potential development of a child can be usefully applied to
the Maths Recovery Program.