1 We present a model for assessment against the backdrop of the - PDF document

Good afternoon colleagues. In this presentation, we present a model of assessment which is in some respects an extension of my PhD thesis, but has also been the product of discussions with my co-author. 1

We present a model for assessment against the backdrop of the educational crises which are evident in this country. We present assessment in the larger context and describe some dangers and challenges. Then some measurement principles and technological resources, features of Rasch measurement theory. Finally we present an example of assessment and extrapolate from this example to an extended model. 2

“Educational crises” has been presented by Jonathan Jansen. The crisis of the youth identity is part of this bigger crisis. Crisis in our view is not altogether negative: it rather presents a ferment from which change can emerge. The response to these crises by the education department and the government has in my view not addressed the problem. By trying to exert stricter controls and cracking down on freedom of expression they are working against democratic principles. 3

While some may assert that education supports democracy (and blame the lack of democracy on lack of education), it is more apt to say that at best we have two contrasting aims. Robert Young in a book “Habermas and our children’s future” notes that the authority and conformity bred in our schools leads to blind followers rather than critical thinkers. Recently, PDU told this story. In his visit to schools around the country, he asks What is democracy? The answer came, Mandela!. He said yes and what else. They said No apartheid. And what else. He said we will have achieved democracy when each one of you is the most important person in this country. Perhaps this is what we should strive for. A society where each person, including both teachers and learners are accorded their rightful place in society. 4

The fact is that our assessment practices have not always accorded teachers and learners the respect they deserve. From history we know that the purposes of the earliest forms of assessment were that of discrimination and selection. We have evolved to a view of assessment where the development of each individual is important. The dangers however still lurk. We still have blunt instruments that spew out a single number, and some of our systemic assessment practices leave teachers bewildered and with little useful information. The challenge for researchers is to adhere to sound scientific practice (more of which will be explained) and for teachers to demand relevant contextual information 5

We do need accountability it seems but we also need a formative component where teachers can explore safely within the confines of their classroom, and in relation to the learners, strategies which she thinks may work. Alongside both these components we need professional development (also looking at the work of Bennett & Gitomer from the ETS) . 6

But if one starts with the idea of a concept, for example ratio. And then adds to this primary concept, a number of related concepts: fraction, proportion, rate, percent, probability … and the set of problem situations which require these concepts for their solution we have a 9

But if one starts with the idea of a concept, for example ratio. And then adds to these concepts, a number of related concepts, fraction, proportion, rate, percent, probability … and the set of problem situations which require these concepts for their solution we have a 10

Here we have the person-item map where persons and items are located on the same scale. The five items discussed in the paper are located at graded difficulty levels. Levels aligned with logits are demarcated in bands. 13

This table again depicts the 5 items of graded difficulty level in the vertical dimension. After the level and the description, five analytic categories are shown. Hierarchical development can be identified. Here we focus on one category, mathematical structure. Vergnaud investigates the underlying mathematical structure of the elements of the mcf . The underlying structure of many of these concepts may be depicted as “measure spaces”. While the underlying structure may be the same, the position of the unknown in the item problem may determine the item difficulty. The problem in item 1: For each bottle collected by Zanele, Mishack collects three. If Zanele collects 9, how many will Mishack have collected. This problem is solved through multiplication and may be solved in two ways. Item 20? The items 5 and 10 are more complex. Item 30? 14

This table again depicts the 5 items of graded difficulty level in the vertical dimension. After the level and the description, five analytic categories are shown. Hierarchical development can be identified. Here we focus on one category, mathematical structure. Vergnaud investigates the underlying mathematical structure of the elements of the mcf. The underlying structure of many of these concepts may be depicted as “measure spaces”. While the underlying structure may be the same, the position of the unknown in the problem may determine the difficulty. The problem in item 1. For each bottle collected by Zanele, Mishack collects three. If Zanele collects 9, how many will Mishack have collected. This problem is solved through multiplication and may be solved in two ways. The items 5 and 10 are more complex. The category response process is explored in more depth in the thesis. 15

The empiricaldifferences in difficulty level are shown here. Item 1 and Item 30. 19

This table provides a composite summary of item analyses and interview analyses. A diagonal line across this table shows a plausible zone of proximal development for a class comprising the current proficiencies of learners in this cohort. 21

This table provides a composite summary of item analyses and interview analyses. A diagonal line across this table shows a plausible zone of proximal development for a class comprising the current proficiencies of learners in this cohort. 22