Appendix C: Information Given to Participants re

the Construction of a Repertory Grid

The information on the following pages, concerning repertory grids and how they are constructed, was given to each participant at least two weeks prior to developing their grid. Further information concerning the construction and interpretation of repertory grids was provided in person prior to beginning the development of the grid. Participants were requested to consider, prior to our meeting, the school subjects that they would like to use as elements for their grid.

An interview was scheduled after the completion of the grid to permit collaborative analysis of the results. At these interviews the principal components (PrinCom) display of the grid was employed as the focus of discussion.

Exemplary Mathematics Teachers:

Subject Conceptions and Instructional Practices

Repertory Grid

Repertory grid technique originated in the theory of personal constructs developed during the 1950's by the psychologist, George Kelly. A "personal construct" is an individual's unique image of some aspect of the world around them. Our personal constructs are the way we understand and interpret the world. Repertory grid technique is a way of helping one identify constructs that may be well hidden in the mind.

To begin the process of building a grid we identify a set of items or Elements to think about. For this project, school subjects or academic disciplines will be the Elements. A random triple out of the set of Elements is selected and these are examined for similarities and differences by identifying some way in which two are alike and dissimilar from the third. This process generates a Construct or a scale upon which the Elements may be arranged. For instance a set of TV shows could be arranged along a line with ends labelled "like" and "dislike". The process of selecting triples and identifying Constructs is repeated a number of times. Once this activity is completed the computer program, RepGrid, will be used to analyse the data. This software looks for clustering in the arrangements of Elements along the various Constructs and arranges these in a matrix (FOCUS) with similarly viewed items placed in close proximity. A more graphical display (PrinCom) with Elements arranged as points and Constructs treated as line segments is also provided. Attached are samples of the FOCUS and PrinCom displays of a grid produced by one of my students when thinking about elementary school pupils she had met. Note all names are pseudonyms.

All of the above will be further explained and illustrated when we begin developing the grid. The output from the computer analysis will be used as the focus of a subsequent interview.

To prepare for building the repertory grid I would like you to begin identifying possible Elements. Obviously Mathematics will be an Element and I would also like to include English and Physical Education. The other Elements I would like to select from various groupings. Please pick one or two examples from each group - subjects with which you may have had some experience as a student or teacher or ones about which you have some opinions. I think that a set of about eight to ten subjects should be sufficient.

 Biology Chemistry Physics French German Spanish any Language Dance Drama Music Visual Art Economics Geography History any Technology any Commercial Computer Studies