concepts of Ergonomics for analysing, designing and sharing resources for mathematics teachers
Jean-Philippe Georget
DIDIREM, Université de Paris 7, France
Abstract: In this paper, we will first present the ergonomics concepts used in the field of computer supported learning environments (CSLE). Thus we will define the following concepts: utility, usability, adaptability, and acceptability, empirical and “by inspection” assessment and we will explain how they can also be used more largely beyond the CSLE field. Then we will present how we have used these to design resources for encouraging the practice of activities called “research problems” at the French primary level. We will illustrate particularly our approach with a case study.
Introduction
How to build and share resources for mathematics teachers? How to take into account the differences between the various existing practices within a community of teachers and the practices targeted by these resources? Our paper attempts to show the usefulness of the ergonomics approach used in the computer supported learning environments (CSLE) for analysing, designing and sharing resources for mathematics teachers. We will illustrate our contribution with some examples from an experiment that we have managed during three years. This experiment aimed at building and studying the ways to encourage the practice of mathematical research activities in some primary classes. This work relies also on the theory of communities of practice (Wenger, 1998) and we have already developed this aspect (Georget, 2007). This contribution is focused on the CLSE ergonomics concepts that we have used. First of all we will set out these concepts, then we will briefly present the context of our work. Finally we will use specific resource about the “Target Number” problem to illustrate our paper more precisely.
concepts of Ergonomics for analysing and designing resourceS
Utility, usability, adaptability and acceptability
For our study we have chosen to use several ergonomics concepts which are already used in the study of interactive systems (Scapin & Bastien, 1997) and especially in computer supported learning environment (CSLE) researches: utility, usability, adaptability, and acceptability . According to Tricot (2004, 2007), utility of a human interface is “the compatibility between the purpose of the interface and the user’s goals for a given domain, employment and environment; the user’s goal is to meet its need”. To share resources with some teachers, we need to study the appropriateness between the practices more or less embodied in the resources and what is effectively practised in the classrooms.
The usability of an interface can be seen as “the possibility of using this interface”. The usability of a resource can be assessed by studying the possibilities of using it and by studying its ability to present in a clear fashion the activities which need to be practised with pupils. One of the most important aspects of the usability is adaptability, that is to say the ability of an interface to adapt to the learner, his knowledge and his capacity to use this kind of interface. In particular, this assessment consists in evaluating how the resource can be adapted to the special needs of the teacher and her specific context of teaching and how it can take into account her own experience. The resources must thus be adapted to the teachers' use and we postulate that they must enlarge, and not reduce, their space of liberty.
It seems to be relevant to allow the teacher to customise the resources proposed to her in order to adapt them to her own practice. Therefore, using technology is more appropriate than the paper support even if we don't exclude the latter. For instance, it is possible to show a reduced resource to begin with and then to propose some developments and to build a composite document with other existing ones. So a specific design is required to build the original resources and also a specific artefact to mix the resources. Moreover, a teacher who uses the same resource several times might, for instance, like to mark the already completed activities, to add notes and to share information with other teachers. If these resources have been built to encourage changes in the teaching practice, we may be surprised that we don't see them evolving, whereas, the teacher's experience grows even during the first experiments. In other words, the resource must be able to take into account the user's experience.
Finally, acceptability is defined as the value given by a learner to the utility and the usability of an interface. This value allows the learner to decide to use or not to use the interface in order to achieve his goals. Several factors influence acceptability: culture, beliefs, motivation, practices, etc. By proposing resources to a community of teachers, the researcher often acts, more or less, as an author. Even if he wants to collaborate with teachers to build the resources, the ideas of each actor might be in contradiction. For example, the researcher would want to propose appropriate resources to take into consideration both the research in the field and the gap between practices that he wants to promote and the existing practices. So he would want to add details to enhance user's understanding. Teachers generally want short resources which are easily and quickly readable and exploitable to prepare their work. This is the paradox of the incompleteness of a resource: too complete, its acceptability is challenged; incomplete, its utility is challenged.
Tricot (2004, 2007) presents some of the relationships existing between the utility, usability and adaptability dimensions. These relationships might be of dependence and might be of independence. Let us look at an example adapted to our use of the utility and acceptability concepts. A given resource migth be accepted by some teachers because it seems useful to them. Thus the resource becomes effectively useful because it corresponds to the authors' goals. Nevertheless, it is also possible that the resource will be accepted but is not useful. For instance, this is the case if the information is not well understood by the teachers or if the information is not pertinent for the use planned by the authors. A resource can also be useful and not be accepted by the teachers. For instance, this is the case if the practice embodied is too far from the usual practices or if the information is difficult to understand for the teachers. Thus the resource will be rejected by the teachers.
Ergonomics studies can be of two main types: empirical or a priori (by inspection). In the first type, one investigates how the software is really understood and used by the learners, and if this is efficient. The second type consists of studying how software could be used by potential learners. Both kind of studies are different and yet complementary. They are also similar to the a priori and a posteriori analysis done in the field of mathematics education.
In the first part of our contribution, we have seen that the ergonomics concepts of the CSLE field allow us to address general questions about the analysis and the design of resources for teachers, especially for mathematics teachers. Let us see the use that we make of these concepts with a concrete example of resource at the primary level.
Ergonomics resource for Primary mathematics teachers
Before presenting our resource, we will begin by presenting the context of our experiment and especially the meaning of the expression “research problem” in the French context.
“Research Problems” in the French curriculum at the primary level
In the french syllabus and in the mathematics education textbooks for teachers, “research problems” are strongly and historically related to the problem solving approach (Artigue and Houdement, 2007). Essentially, “research problems” are given to the children to develop their capacity to make hypothesis, to organize their own solving process, to explain and to validate their solution between peers. Generally the goals of this kind of problems are less to introduce new concepts or techniques than to familiarize the children with the process of proof. Actually these problems and, more generally, the problem solving approach, are not frequent in the practices. The teachers' practice have to be accompanied to facilitate some changes and adaptations (Jaworski, 2003; Georget, 2007). We think that an ergonomics analysis of the resources proposed to the teachers is one of the work to be done if we want to enhance the problem solving approach. Thus in the described context, how to present an activity to a teacher if she did not practice “research problems”? How to favour its adoption? How to favour a “good” practice, that is to say, for instance, a practice which does not transform the activity in a simple application of a technique?
A first approach of this question would be to propose bringing additional information about the interest and about the practice of this kind of activities. We could also propose the integration of this activity in a larger set of similar activities. In both cases, we see that the quantity of the text to be read by the teacher will grow quickly which will be harmful to the acceptability of the resource.
A second approach could rely on a community of teachers. In this way, the main aspects of this kind of activity could be discussed in a flexible manner with the teacher that wants to initiate these activities with her pupils. The necessity of reading a huge quantity of information would be reduced and that could increase the resource acceptability. The sharing of information between teachers could also increase the usability of the resource because different uses of resource could be discussed. One could also criticize the uncertainty of the phenomenon because it would be based on discussions that can not be easily controlled. One could even imagine that the resource utility would decrease because of the development of undesired practices. In our point of view, the interactions between the teachers and the undesired practices are not faults of this second approach but are the means of an empirical ergonomics study.
The third approach that we have used in our experiment is situated between the first and second ones. It consists both of sharing a set of more or less satisfactory resources from the point of view of an a priori ergonomics study and relying on a community to facilitate their adoption. To illustrate our choices with more precision, we present a resource dedicated to the “Target Number” problem in the following section.
The “Target Number” problem
In the “Target Number” problem, we must add multiples of two given numbers (e.g. 3 and 8) in order to obtain a given target number (e.g. 41). The problem consists in finding all the ways of obtaining the target number (there is two solutions with the given example: 4x8+3x3 and 8x8+11x3). At the primary level, this activity mainly allows to make the children enhance their capacity to solve a mathematics problem. It asks to the children to find a way to ensure that they really have all the solutions and to convince their peers to validate their method.
Now let us look at the resource that we have built to present the “Target Number” problem without speaking generalities about “research problems”. In our experiment, this resource is web-based. Our contribution shows that the ergonomics concepts are also useful for a paper-based resource.
The resource is shared in four parts titled Presentation, Examples, Answers and Proofs, Elements of Potential Researches and Debates. We reproduce them below and we explain our choices.
Presentation
The problem
The problem consists of reaching a number from multiples of two other numbers.
One example
Reach 23 with the help of multiples of 2 and 5.
For instance, we found 2 × 4 + 3 × 5 = 23.
This example is proposed in the ERMEL CE2 textbook.
The text of the presentation is built to be easy and fast to read and the example is used to facilitate the understanding of the general problem. The text is not really well adapted for the pupils. It is mainly built for the teacher supposing that she is the person the most well informed to propose one or more versions adapted to her pupils. By this way, we take into account the resource's adaptability. The reference to a well known even if not so used ERMEL CE2 textbook – which is mainly constructivism oriented – allows the teacher to access, indirectly, to other information. That increases the ergonomics of the resource, in particular from the point of view of the user's experience.
The goal of the next part of the resource is to give several instantiations of the problem for managing this activity. These instantiations are options for the teacher to use the problem in her class.
Examples
Example 1
There are several solutions (exactly 2) :
Reach 41 with 8 and 3
– 4 x 8 + 3 x 3
– 8 x 8 + 11 x 3
Example 2
Reach 97 with 8 and 3
Here, the number of solutions is greater than the previous example:
– 11 x 8 + 3 x 3
– 8 x 8 + 11 x 3
– 5 x 8 + 19 x 3
– 2 x 8 + 27 x 3
One might ask the pupils to find the biggest number of solutions.
Example 3
Reach 92 with 5 and 3
The solutions are:
– 16 x 5 + 4 x 3
– 13 x 5 + 9 x 3
– 10 x 5 + 14 x 3
– 7 x 5 + 19 x 3
– 4 x 5 + 24 x 3
– 1 x 5 + 29 x 3
One might ask the pupils to prove that they obtain all the solutions.
Example 4
Reach 23 with the help of multiples of 2 and 5.