QUT ePrints

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

Ewing, Bronwyn F. (2004) A Model for Analysing One-to- One teaching in the Maths Recovery Program. Post Pressed, Flaxton, Qld.


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. 8 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.

Impact and interest:

Citation countsare sourced monthly from Scopus and Web of Science® citation databases.

These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.

Citations counts from the Google Scholar™ indexing service can be viewed at the linked Google Scholar™ search.

ID Code: 14362
Item Type: Book
Additional Information: For more information about this book please refer to the publisher's website (see link) or contact the author.
Additional URLs:
Keywords: Maths recovery, one, to, one teaching of mathematics, early childhood mathematics teaching and learning
ISBN: 1876682779
Subjects: Australian and New Zealand Standard Research Classification > EDUCATION (130000) > EDUCATION SYSTEMS (130100) > Early Childhood Education (excl. Maori) (130102)
Australian and New Zealand Standard Research Classification > EDUCATION (130000) > CURRICULUM AND PEDAGOGY (130200) > Mathematics and Numeracy Curriculum and Pedagogy (130208)
Australian and New Zealand Standard Research Classification > EDUCATION (130000) > SPECIALIST STUDIES IN EDUCATION (130300) > Learning Sciences (130309)
Divisions: Current > Research Centres > Office of Education Research
Current > QUT Faculties and Divisions > Faculty of Education
Copyright Owner: Copyright 2004 Bronwyn F. Ewing
Deposited On: 11 Aug 2008
Last Modified: 15 Jan 2009 18:26

Export: EndNote | Dublin Core | BibTeX

Repository Staff Only: item control page