Research reports 1 - Room 8

Leslie Dietiker: Narrative Characteristics of HS Math Lessons Students Find Interesting

This study compares the way the mathematical ideas emerge and develop across enacted lessons in lessons students rate as most interesting with those the same students rate as least interesting. Using the mathematical story framework, which interprets unfolding mathematical ideas as a form of narrative, it begins to answer the question: When enacted high school mathematics lessons are interpreted as mathematical stories, what narrative characteristics, if any, distinguish the lessons that hold broad aesthetic appeal from those that do not? This study offers clear evidence that the lessons that held broad appeal for students have distinctive characteristics of their mathematical plots, namely, their mathematical questions stayed open for more parts of the story, collectively spanned more of the story, and offered incremental progress periodically throughout the lesson. Furthermore, as a group, captivating lessons offered a far greater number of instances of misdirection. In contrast to lessons with low aesthetic value, the captivating lessons offered a dramatic rise in how many questions were open simultaneously, reflecting a thickening of the plot. The analysis demonstrates how analyzing lessons with this framework can enable a new way of understanding mathematical learning experiences and their impacts on students.

Beverly Irby and Rafael Lara-Alecio: Designing Research-based Virtual Professional Development and Virtual Mentoring and Coaching

Addressing professional development needs of leaders and teachers can be addressed through the use of effective Virtual Professional Development (VPD). This presentation will share the design and development of the VPD, along with Virtual Mentoring and Coaching (VMC), and we will share research that exemplify the impact of large scale efforts to provide school districts across the United States with access to a variety of online learning options to meet the growing professional needs. While VPD occurred before the COVID-19 pandemic, educators have found value in the expansion of the online offerings throughout the pandemic due to the value of timely and flexible professional development offered as a VPD, along with VMC.

Research reports 2 - Room 8

Janette Bobis: Designing sequences of challenging tasks to promote student agency and inclusion

We report on the Exploring Mathematical Sequences of Connected, Cumulative and Challenging tasks [EMC3] research project that is examining how Variation Theory can inform the construction and implementation of sequences of learning experiences to promote student agency in mathematics learning for a diverse range of students. In this presentation we outline the rationale and some key components of the approach to teaching mathematics we adopted while working with early years students (5-8 years of age) and their teachers from two large Australian school systems over three years. Teacher questionnaire responses (n = 100) and interview data (n = 10) will be drawn upon to report their perspectives of the effectiveness of certain task design features and various teaching practices aimed at developing student conceptual understanding, agency and inclusion in mathematics.

Minoru Ohtani: Development of STEAM education in KUSH

This paper presents a development of STEM approach in mathematics at Kanazawa University Senior High School, which aims at inquiry-based, collaborative, and cross-curricular learning in high school mathematics. The mathematics department at Kanazawa University is focusing on the potential richness of the RME theory developed by the RME approach and is engaged in three main activities. These are (1) the use of Math A-lympiad tasks in integrated learning time, (2) the improvement of the content and teaching of existing subjects by utilizing the cross-curricular modules developed in the Mascil project, and (3) the organization of inquiry activities by extracurricular clubs using the National Common Exam questions developed by Cito. These activities are generally aimed at developing the ability to understand the phenomena of daily life and society mathematically, and to process and solve problems mathematically. In this paper, we discuss the qualities and abilities we aim to cultivate by presenting concrete examples of the three activities and point out the importance of the "reality principle," "interaction principle," and "association principle" in RME theory, respectively, for designing inquiry-based, collaborative, and cross-curricular learning.

Marita Barabash and Elena Naftaliev: Educated use of technology-based interactive resources: flexibility and versatility of the teachers’ mathematical knowledge is one of the crucial factors for success

The study focuses on ways of enhancing mathematics teachers’ educated use of Technology-Based Interactive Resources (TBIRs) in merging the Experimental-Mathematics (EM) with Formal Mathematics (FM). The study implies amalgamation of three aspects of teachers’ professional knowledge: mathematical knowledge needed for EM – FM merging (e.g., Borwein, 2016); pedagogical functions of TBIRs (e.g., Naftaliev, 2018); instrumentational orchestration (e.g., Gueudet & Trouche, 2012). Our search for causes enhancing and those impeding the teachers’ ability and vigilance in implementing this approach is ongoing. Nevertheless, one of our conclusions already at this point is that the teachers face the necessity of adjusting the familiar concepts, their definitions, appearances, and concept images to those relevant and applicable in computer platforms. Teachers’ versatility and flexibility in dealing with mathematical concepts appears to be sine qua non for successful and lasting implementation of the approach.

Research Reports 3 - Room 8

Elena Naftaliev and Marita Barabash: Experimental mathematics at school: teachers’ engagement with interactive resources

The study focuses on ways of enhancing mathematics teachers educated use of Technology-Based Interactive Resources (TBIRs) in merging the Experimental-Mathematics (EM) with Formal Mathematics (FM). In the research we refer to factors that, merged, have the potential not only of adjusting present teaching practices to newly available platforms and resources but also of supporting mathematics teachers in developing professional orientations that will lead them down the ever-evolving paths of educational technology, helping them to make educated choices about this aspect of their professional lives. We have designed and analysed professional development program offering the teachers relevant experience in learning, teaching, and designing resources on their own.

The study implies amalgamation of three aspects of teachers’ professional knowledge: mathematical knowledge needed for EM – FM merging (e.g., Borwein, 2016); pedagogical functions of TBIRs (e.g., Naftaliev, 2018); instrumentational orchestration (e.g., Gueudet & Trouche, 2012).

Tony Hall, Michelle Millar, Connie O'Regan, Natalie Walsh & Grace Mannion: Designing Futures: The role of educational design in embedding a large-scale transformative university initiative

Funded by the Irish Government (2020-2025), Designing Futures is a flagship educational programme at the University of Galway, Ireland, the purpose of which is to enhance students’ holistic learning experience in higher education, supporting their entrepreneurial confidence and capacity and their personal and professional career development. Designing Futures achieves national policy objectives in higher education, specifically in terms of preparing students for the complex and uncertain world we live in today. This research presentation focuses on how we can best deploy educational design to create sustainable and scalable, innovative initiatives in higher education, to enhance the experience of all students, across all disciplines, promoting student engagement, diversity and inclusion. The research presentation will outline the design and development of the Designing Futures project so far, including the range of innovations being implemented across campus in Galway. These include research-based collaborative projects undertaken by students alongside faculty (vertically integrated projects (VIPs); Stanford University’s Design Your Life/Life Design, to enhance student’s personal and career development; and the IdeasLab on campus, a bespoke space promoting students’ capacity for innovation and entrepreneurship, through design thinking, for example.

Shelley Rap and Alex Friedlander: Possibilities and limits in the design of an interdisciplinary program

Workshop 4a - Room 8

Marc Neesam: Designing professional development solutions for ministries of education: ideal vs practical vs reality

Ministries of education around the world issue tenders/requests for proposals and work directly with international and local organisations to generate and implement solutions to meet their needs e.g. a country shifting to competency-based learning may seek to support their teachers in that shift or a country implementing a new curriculum will want to upskill their workforce in the new expectations. At Cambridge, I lead the design of solutions focused on school leader and teacher professional development, both in response to ToRs/RfPs and through pro-active discussion with ministries. While we often start the design from an a position of providing an 'ideal' research informed solution the solution often needs to change to account for practical considerations and the reality the ministries are in such as; working at national scale, providing solutions within a fixed timeframe, having a limited budget or evolving needs. This workshop will explore the challenge of adaptive solution design for ministries of education through raising some case studies, discussion and a role-play game where participants can act as Cambridge solution designers who have to adapt to emerging information.

Workshop 5a - Room 8

Jo Sibley: What's so hard about the C in CPD?

Why are teachers not just students, but taller? At MEI we're trying to address the subtle and less-subtle ways in which designing PD for teachers is different from lesson design for students and how these differences must be attended to if teachers are to be able to access AND engage with high quality ongoing development throughout their careers. We'll take a look at some examples of activities designed with this in mind.