Stephen Hegedus

Integration of Technology, Curriculum, and Professional Development for Advancing Middle School Mathematics Three Large-Scale Studies

The authors present three studies (two randomized controlled experiments and one embedded quasi-experiment) designed to evaluate the impact of replacement units targeting student learning of advanced middle school mathematics. The studies evaluated the SimCalc approach, which integrates an interactive representational technology, paper curriculum, and teacher professional development. Each study addressed both replicability of findings and robustness across Texas settings, with varied teacher characteristics (backgrounds, knowledge, attitudes) and student characteristics (demographics, levels of prior mathematics knowledge). Analyses revealed statistically significant main effects, with student-level effect sizes of .63, .50, and .56. These consistent gains support the conclusion that SimCalc is effective in enabling a wide variety of teachers in a diversity of settings to extend student learning to more advanced mathematics.

From New Technological Infrastructures to Curricular Activity Systems: Advanced Designs for Teaching and Learning

We suggest an “advanced design” for teaching and learning should offer a plan for bridging the gap between new technological affordances and what most teachers need and can use. We draw attention to three different foci of design: (a) design of representational and communicative infrastructure (b) design of curricular activity systems, and (c) design of new classroom practices and routines. Two different SimCalc projects are presented to illustrate these design foci; both concern the use of technology to democratize access to conceptually demanding mathematics among adolescents. We particularly emphasize curricular activity systems because we are finding that attention to this focus of design has been critically important in our ability to measure learning outcomes at the scale of hundreds of teachers.

Investigating the Mathematical Discourse of Young Learners Involved in Multi-Modal Mathematical Investigations: The Case of Haptic Technologies

In this chapter, we examined the experiences of 10-year old (fourth grade) students in the United States involved in a dynamic multi-modal environment as they explored the characteristics of 3D geometrical shapes. The environment we developed provided visual and physical feedback to students through the PHANTOM Omni® haptic device. This dynamic multi-modal environment enabled semiotic mediation where meanings are generated and substantiated through social interaction as students worked in groups. Adhering to a socio-cultural theoretical perspective, we mainly focused on students’ discourse when exploring the affordances of multi-modal technologies in their mathematical experiences. Our preliminary findings indicated that such technologies have the potential to present students with the opportunities to explore 3D objects through multiple perceptions, supporting meaningful discourse as students engage in mathematical activities such as exploring, conjecturing, negotiating meaning, and sense-making.

SimCalc and the Networked Classroom

This chapter describes five major categories of learning activity designs which span a range of possibilities for leveraging the combined representation and communications infrastructure (Hegedus and Moreno-Armella, 2009) of classroom network technologies. These five activity structures, including mathematical performances, participatory aggregation, generative activities, small groups, and participatory simulations, have emerged over the past fifteen years from work both within the SimCalc project and in several independent lines of inquiry among researchers in the Kaput Center network. We present examples of each activity structure, and draw on Roschelle and Teasley’s (1995) framework for examining computer-mediated collaborative problem solving in order to assess developments in the study of group-centered learning that have been enabled by this research.

Reflections on Significant Developments in Designing SimCalc Software

We designed and developed the SimCalc software using technological affordances as a way to introduce new mathematical affordances into the classroom. This view was especially advantageous as available technology changed significantly during SimCalc’s development cycle. Driven by observations and opportunities, we frequently modified our software according to our changing understanding. In this chapter, we describe the rationale for changes to the software by looking at decisions that resulted in significant modifications; we examine how our work on this software altered our view of the learning affordances SimCalc provides. Our examples are within three main areas of research: Representational Infrastructures to support mathematically meaningful representations, Activity Structures (some that guided design and some that emerged from new affordances), and Classroom Connectivity which offered new forms of student participation. These and other decisions extend SimCalc beyond the development cycle, allowing it to continue to be useful to its existing base of users and extending its reach to a wider variety of students around the world.

Learning and Participation in High School Classrooms

In this chapter, we report quantitative and qualitative findings of a curricular approach to investigating quadratic and exponential functions in conjunction with the representationally rich software. The quantitative findings we report demonstrate the positive effects SimCalc has on student learning in comparison to similar algebra classrooms, as measured by pre and posttests. The qualitative findings show us the positive effects SimCalc has on students’ participation in the SimCalc environment through participatory discourse where students partake in mathematical communication to add ideas, justify their ideas, and challenge one another’s ideas about varying rate using the various representations available in the SimCalc technology. We present our qualitative findings through two classroom case studies in which we analyze the classroom discourse.

HLM in cluster-randomised trials – measuring efficacy across diverse populations of learners

We describe the application of Hierarchical Linear Modelling (HLM) in a cluster-randomised study to examine learning algebraic concepts and procedures in an innovative, technology-rich environment in the US. HLM is applied to measure the impact of such treatment on learning and on contextual variables. We provide a detailed description of such methods, methodically analysing nested classroom data with respect to various outcome measures through HLM.

Impact of Classroom Connectivity on Learning and Participation

Our study reports the development of the SimCalc environment that integrates interactive and connected mathematical representations with the latest affordances in wireless connectivity. We describe the development of several instruments to measure the interaction between learning and participation in terms of changes in attitude over time. In addition to empirical data from a quasi-experimental study, we qualify our findings through analysis of discourse patterns in specific forms of participation and explain how the communication infrastructure of an algebra classroom can be radically enhanced.

Introduction: Major Themes, Technologies, and Timeline

The long-term imperative of the SimCalc project has been to democratize access to the Mathematics of Change and Variation (MCV) (Kaput, 1994)—especially algebraic ideas underlying calculus (Kaput and Roschelle, 1998)—using a combination of new dynamic technologies for representing and communicating mathematics with new curriculum materials for grades 6–13 and aligned teacher professional development.

Preface to Part VII

In this 21st Century, it is important to contextualize the great mass of technological evolution within the present advances and constraints of the mathematics classroom. And this becomes even more relevant when we question the role of educational technology in such environments. Luis and Bharath provide an important contribution to defining new perspectives on mathematics education theory by situating their paper in this context; appreciating the changing role of educational technology but also drawing deeply on evolutionary and semiotic theory to help us analyze present and future change.