2 ESTRUCTURA Y ORGANIZACIÓN DE LA TAREA DE APRENDIZAJE.

The objective was not highly proficient use of the Fathom software tool, but that the software tool became a part of students’ mathematical repertoire progressively and allowed the students to focus on the underlying mathematical concepts under investigation rather than dedicating intellectual effort into using the software or being distracted by the software. Students were not expected to design simulations or develop a level of proficiency that allowed students to work independently because the software was not available outside of the classroom. Students were provided with the opportunity to acquire skills sufficient for the task only. The software supported learning indirectly through promoting acceptance of the simulation and cultivating students’ sense of

94 accomplishment and self-efficacy. Students’ development of use of the software was intended to be both efficient and productive.

The study adopted the principle from statistics education research of using the technology tool in an entirely new way to exploit the potential of the tool, rather than simply incorporating the software into existing professional practices or extending existing practices. An example of incorporating the software into existing practices is to substitute physical simulation with virtual simulation without attending to students’ acceptance of the software tool or using statistics education best practice pedagogical principles. An example of extending existing practices is to include a limited number of features such as exploring the large sample sizes readily available in virtual simulation. The study used virtual simulation in a novel way for traditional education practice by introducing re-sampling to a high school classroom.

Instrumental genesis provided the philosophical framework to introduce and use Fathom in the classroom and subsequently to analyse students’ responses. Instrumental genesis recognises that students’ familiarisation and internalisation of any tool can be complex, time-consuming, reciprocal, and personal (Section 2.5.6.1).

The importance of the development and refinement of statistical language as part of the process of statistical enculturation is well recognised in the statistics education literature. In this study an element of this vocabulary was the terminology used in the Fathom software, and this terminology was not necessarily familiar to students, or identical to that used elsewhere in the mathematics curriculum. In Fathom the term case is a datum point, an attribute is a data variable (e.g., height), a collection is a data set, and a measure is a statistic (Fathom, 2005).

Fathom’s modular nature lends itself readily to the use of a constructivist approach. Students assembled the modules into a functioning simulation and progressively checked that the simulation behaved as anticipated. This step-wise assembly and checking approach had several objectives that included building confidence in the software and creating ownership of the simulation, providing opportunities for practice in assembling simulations and key simulation sub-skills, and slowing students to encourage reflective thinking about the simulations. Each subsequent simulation extended students’ knowledge of Fathom by introducing an additional software feature. Students progressively developed a basic repertoire of skills, used key terminology, and

95 acquired a set of procedures in the software. This established a classroom routine that could find application elsewhere with Fathom:

1. assemble the simulation and the data representation from the individual modules,

2. methodically check that the simulation behaved as anticipated, and

3. critically evaluate the data generated as a deliberate sense-making process. The education literature categorises software as either black-box route-type software where the functionality of the software is largely set and obscure, or as a white-box landscape tool where the user constructs the simulation or where the functionality is visible (Section 2.5.5). The term grey-box was introduced in this study to describe the software’s use along a spectrum between white and black-box use. Constructing the simulation was somewhat of a misnomer because student did not construct the simulation at the fundamental computer coding level, but instead assembled the simulation from its component modules, so the term assemble was used.

Students assembled the Fathom simulations guided by hardcopy worksheets (e.g., Figure 3.1). To cultivate a routine the worksheets adopted a consistent approach that had three key features of (a) screen-grabs of Fathom, (b) dialogue boxes giving specific instructions, and (c) arrows indicating the screen location of the operation, feature, function, or drop-down box. The screen-grabs allowed students to compare the appearance of their own simulation with the model provided in the worksheet, and this reassured students that the simulation was being assembled correctly.

96 The worksheet also provided a short series of questions designed as a natural entry into more formal analysis of the simulation and as a boundary object to promote classroom discussion. The approach adopted here was to offer a range of task complexity within any one activity to cater for the inevitable diversity of student abilities within any class group. For even the least able students the relatively straight-forward task provided an opportunity and the satisfaction of successfully assembling a simulation. The Fathom worksheets are attached in Appendices A.6, A.8, A.9, A.12, A.14, and A.16.