Abstracts for PLATINUM Webinar “Creating communities of inquiry: focus on students with special needs and on mathematical modelling”

Barbara Jaworski – PLATINUM: Working together in Communities of Inquiry for our Professional Development

Creating and working together in Communities of Inquiry (CoI) is central to activity in PLATINUM and to the six Intellectual Outputs we have developed. The PLATINUM “Partnership” is committed to working with colleagues, both within a Partner group and across Partner groups to promote inquiry-based learning and teaching of mathematics. We explore (inquire into) and share our practical activities and our ways of operationalising inquiry-based development. I will address the nature of a CoI in relation to the three-layer theoretical model which is the basis of PLATINUM. I will provide some examples of how the inquiry process contributes to our development.

Simon Goodchild – Communities of Inquiry – a context for Inquiry Based Tasks

This presentation about communities of inquiry begins with an outline of Community of Practice theory. Critical alignment (CA) and critical stance (CS) – for teaching development and learning mathematics – are explained. I will further assert that these (CA and CS) are important for the effectiveness of IBME and inquiry tasks.

Reinhard Hochmuth, Sarah Khellaf, Jana Peters – Spidercharts – a tool for describing and reflecting IBME activities

Scientific monitoring of developmental projects such as PLATINUM also raises questions that can be addressed with the help of standardised tools. These tools must, of course, take into account the specific conditions and goals of the intended developments. In the case of PLATINUM, an essential condition is the diversity of local situations in the development of communities of inquries. Against this background, the objectives include reflection and further development of IBME activities both at the local level and in the PLATINUM community as a whole. In our video we outline how the spider charts we have developed can contribute to these goals.

Lukáš Másilko, Stephanie Thomas – Students with Special Needs and Inquiry in Mathematics

Even though it is a student who conducts his/her inquiry, there are several pedagogical processes a teacher should pay attention to with regard to the student’s differences and needs. During our presentation we explain principles of Universal Design, a methodology to create an inclusive learning environment, and give examples of recommendations to facilitate inquiry in mathematics to as many learners as possible including those with special needs.

Morten Blomhøj – Mathematical modelling in epidemiology – an exemplary case for developing modelling competency

Based on experience with supervising students’ modelling projects and with teaching a mathematical modelling course for first year bachelor students, the talk will pinpoint ways in which modelling in epidemiology can by an exemplary case for how to support the students’ development of modelling competency. In particular, it will be discussed how modelling in epidemiology can support the development of the students’ critical reflections on the modelling process and on the application of model results in societal decision-making processes.

Gabriele Kaiser, Mustafa Cevikbas, Stanislaw Schukajlow – Systematic literature survey on modelling competencies – its conceptualisation, measurement and fostering

Research on modelling competencies has received high importance in the last decade. In the lecture, the results of a systematic literature survey on modelling competencies will be presented, with a specific focus on the conceptualisation and theoretical frameworks on modelling competencies, and methods to measure and ways to foster them.

Paul Hernandez Martinez – Is imagination important in Mathematical Modelling?

This talk will look at the concept of imagination and its role in the meaning-making process of students involved in mathematical modelling tasks. With a few examples, I will explore possibilities in which communities of inquiry can help students develop their imagination and become more creative in their approach to mathematical modelling tasks.

Iryna Mashkina – Teaching students how to create mathematical models in the process of solving applied tasks

We present approaches to the design and solution of modelling problems for mathematics and computer science students. The use of IBME in modelling offers better understanding of the relationship between mathematical concepts and real processes and phenomena in different areas of human activity. We discuss the following main steps in the solution of applied problems using the IBME approach to design models and ICT for the interpretation of the results:

  1. Construction of mathematical models – translation of applied problems into the language of mathematics. Selection of parameters, variables, and description of relationships between them.
  2. Analysis of mathematical models – solution of problems obtained after mathematization.
  3. Interpretation of obtained solutions using digital tools.

Serhii Martyniuk and Olga Barna – Teaching students to create digital scenarios for solving the transport problem of an applied nature

In this presentation we share our experience in the preparation and management of students’ mathematical modelling projects. We discuss student-centered approaches to learning used for the design and solution of a mathematical model for a transport problem with the particular focus on the selection of digital tools for finding solutions.

Nataliia Morze – Business incubator as an environment for implementing an inquiry approach

Today, mathematics forms the basis for new technological advancements and opens new business perspectives. The analysis of the modern market of start-ups shows that most start-ups that were successfully sold on the market have a mathematical background. That is why the student business incubator was created at the Borys Grinchenko Kyiv University to provide a practice-oriented learning that uses an inquiry approach for increasing students’ motivation to learn mathematics. We share our experience in preparing and conducting hackathons and discuss implications for student learning.

Farzad Radmehr – Teaching and learning of vertex coloring using an inquiry-based approach

In the past few decades, tertiary mathematics educators call for a change to more active, student-centred approaches to teaching and learning mathematics at university mathematical courses. This call has been supported by previous studies that reported active learning approaches improve university student mathematical performance.  In this presentation, I will report on a study that focuses on using an inquiry-based approach to explore the teaching and learning of vertex colouring, a common topic in graph theory and discrete undergraduate mathematical courses. A community of inquiry was established, including an associate professor of mathematics education, a senior lecturer of graph theory, a postgraduate student in mathematics education, and twenty-four undergraduate mathematics students who voluntarily participated in the study. Seven inquiry-based tasks related to vertex colouring were designed to teach this topic in an undergraduate graph theory course to students majoring in mathematics. I hope sharing these tasks and how they were perceived by students and the lecturer promote using inquiry-based tasks in discrete undergraduate mathematical courses. This study has been conducted as most resources (inquiry-based tasks) available at the tertiary level are related to calculus, linear algebra, and differential equation courses.

Helge Fredriksen – Combining inquiry-based learning with flipped classroom teaching of linear algebra in a digital environment

The flipped classroom approach of facilitating an out-of-class video preparation phase before entering the in-class sessions has become an accepted way to engage students in reflecting more conceptually about mathematics. We prepared two such flipped sessions in linear algebra with a set of first year engineering students in Norway, where in-class sessions were conducted as digital events, and tasks for these sessions were inquiry-based. After the intervention, we collected responses from the students through a questionnaire and analyzed them. What we learned from the experiment will be used in the second phase of the project for flipped sessions with first year engineering students in the Czech Republic.