The teacher and the tool: instrumental orchestrations in the technology-rich mathematics classroom

Abstract

The availability of technology in the mathematics classroom challenges the way teachers orchestrate student learning. Using the theory of instrumental orchestration as the main interpretative framework, this study investigates which types of orchestrations teachers develop when using technology and to what extent these are related to teachers' views on mathematics education and the role of technology therein. Data consisted of videotapes of 38 lessons taught by three teachers, who also provided information on their views through questionnaires and interviews. Qualitative analysis of these data led to the identification of orchestration types and teacher profiles. The orchestration preferences of the three teachers proved to be related to their views. A detailed analysis of one exemplary episode suggests how other theoretical perspectives might complement the theory of instrumental orchestration.

Kindergarten teachers’ orchestration of mathematical activities afforded by technology: agency and mediation

“…Our research findings share similarities with some orchestration types found by both Drijvers et al (2010Drijvers et al ( , 2013 and Gueudet et al (2014) but there are also substantial differences.…”

“…Drijvers et al (2013) isolated nine orchestration types (see Table 1) but notes that this should not be regarded as Drijvers et al (2013) also note whether each orchestration type is used with the whole class or with individual students. We regard this extension of instrumental orchestration as well considered/argued but we have one reservation, which is especially evident in Drijvers et al (2010), that orchestration types used are, in general, viewed as teachers' choices. This general statement does have exceptions, for example, BTechnological and time constraints as well as control issues may influence the choice and exploitation of the orchestrations^(p. 229).…”

“…A virtual abacus, focusing on base-ten numeration, was used with one class and 'passenger train' (freeware designed to facilitate student use of numbers to record the position of passengers, rabbits, on a train) with the other class. Gueudet et al (2014) note similarities and differences with Drijvers et al (2010). Regarding similarities, BFor the introduction of a new software, the Technical-demo, Explain-the-screen, and Discuss-the-screen orchestration types introduced by Drijvers (2012) are still present ( Gueudet et al, 2014, p. 230).…”

“…They (like us) found Technical-demo and Explain-the-screen but (unlike us) found Discuss-the-screen orchestration types were present in their observations. However, Gueudet et al (2014) augment the orchestration types with two new ones, autonomous-use and supported-use which concern supporting individual children in need (orchestration types to support individuals was not considered in Drijvers et al, 2010 but was considered in Drijvers et al, 2013). In our work with kindergartens we did not find it productive to differentiate between individual and whole-class orchestrations as the social division between children who have/do not have difficulties (which prompted Gueudet et al's (2014) two new orchestration types) was not apparent in our KTs' actions.…”

“…Our KTs are making choices in these excerpts but these are situated choices which are interrelated with the affordances of the environment. We think that Drijvers et al (2010) use the phrase teachers' choices in an everyday manner. In day-to-day life we speak of choices when we know they are really bounded and this is implicitly recognised by Drijvers et al (2010).…”