Statistical modeling processes through the lens of instrumental genesis

Abstract

Digital technology is indispensable for doing and learning statistics. When technology is used in mathematics education, the learning of concepts and the development of techniques for using a digital tool are known to intertwine. So far, this intertwinement of techniques and conceptual understanding, known as instrumental genesis, has received little attention in research on technology-supported statistics education. This study focuses on instrumental genesis for statistical modeling, investigating students’ modeling processes in a digital environment called TinkerPlots. In particular, we analyzed how emerging techniques and conceptual understanding intertwined in the instrumentation schemes that 28 students (aged 14–15) develop. We identified six common instrumentation schemes and observed a two-directional intertwining of emerging techniques and conceptual understanding. Techniques for using TinkerPlots helped students to reveal context-independent patterns that fostered a conceptual shift from a model of to a model for. Vice versa, students’ conceptual understanding led to the exploration of more sophisticated digital techniques. We recommend researchers, educators, designers, and teachers involved in statistics education using digital technology to attentively consider this two-directional intertwined relationship.

Matemati̇k Öğretmenleri̇ni̇n Çevri̇mi̇çi̇ İstati̇sti̇k Öğrenme Platformu Kullanarak Geli̇şti̇rdi̇kleri̇ Etki̇nli̇kleri̇n Değerlendi̇ri̇lmesi̇

“…Ancak Amerikan Ulusal Matematik öğretmenleri Birliği'nin (NCTM, 2015) de belirttiği üzere matematik öğretimi sürecinde alana özgü olarak geliştirilmiş olan içerik odaklı teknolojilerin kullanılması daha önemlidir. Çünkü istatistik eğitiminde içerik odaklı teknolojiler; güncel yaşam verilerinin sınıf içerisinde kolaylıkla aktarılabilmesi, örneklem verileri üzerinden modeller oluşturması ve temsiler arasında esnek geçişler sağlaması gibi farklı birçok özelliğe sahiptir (Pratt, Davies & Connor, 2011;Van Dijke-Droogers, Drijvers & Bakker, 2021;Wilkerson vd., 2021). Benzer olarak GAISE (2016) raporunda da istatistik öğretiminde güncel teknolojilerin gerçek yaşam verileri ile işe koşularak kullanılması vurgulanmaktadır.…”

Introducing Statistical Inference: Design of a Theoretically and Empirically Based Learning Trajectory

“…Subsequent modeling activities involve applying gained knowledge into new contexts, where students deploy modeling activities to solve real-life problems. Applying similar digital techniques within varying contexts encourages students to identify context-independent patterns of technical actions (Van Dijke-Droogers et al, 2021). These context-independent technical patterns combined with a context-independent understanding of key statistical concepts facilitate the conceptual shift from a model of to a model for, known as emergent modeling (Gravemeijer, 1999;Streefland, 1991).…”

Characterizing Tasks for Teaching Mathematics in Dynamic Geometry System and Modelling Environments

“…In particular, to teach modeling, teachers must first have experimented with similar activities that provide them with knowledge on how to design and implement tasks effectively, as noted by Goldsmith, Doerr, and Lewis [8]. Teachers have to be encouraged to take part in exploring and developing techniques that let them use artifacts as digital tools and as tools for understanding specific concepts of the domain [9]. From this perspective, the design of tasks based on the experience resulting from modeling and simulating different situations represents an opportunity for in-service and pre-service teachers to build a set of knowledge associated with content, technology, and pedagogy for teaching mathematics [10].…”