# Teaching and learning about indices and their application in society

## Project owner

Western Norway University of Applied Sciences,

## Project period

September 2015 - August 2018

## Project summary

The aim of the project is to study and evaluate teaching related to our own practice in teacher education. We wish to develop teaching on indices and their applications in society and how this can be linked to the students’ curriculum literature.

Indices are a form of mathematical model which is commonly used in society: Body Mass Index (BMI), Gross National Product (GNP), Human Development Index (HDI), Happiness Index, Nature Index etc. Indices have in common that, based on a mathematical model, a single number, the index, is calculated in such a way that it represents several variables. They thereby reduce more complex systems or multifaceted situations to a simplified representation. Indices are broadly applied in society and common in decision making of all sorts.

Mathematical modelling is considered relevant in mathematics education for several reasons. Barbosa (2006) builds on Julie’s (2002) categories of purposes for working with modelling in school: 1) to learn mathematics (modelling as content), 2) to learn modelling (modelling as vehicle) and 3) to support critical reflection (modelling as critique). All three purposes could be served through working with indices in mathematics education. Such work could be about decomposing and critiquing existing indices, with the aim of understanding their construction and discussing their relevance and impact on society. Julie (2002) reports on modelling sessions with mathematics teachers where they constructed a Human Development Index. Although the teachers applied only simple arithmetic, Julie argues that working with models like the HDI is relevant in mathematics class to reflect on the desirable and undesirable effects of applied mathematics in society. From an affective point of view, Kacerja (2013) used the HDI for discussing about community matters with 14-16 years old students and reports that students were interested in using mathematics to learn about the level of development of their community.  Jablonka (2000) argues that mathematical literacy should include understanding the limitations of indices used for economic policy. All these examples fulfil at least Barbosa’s (2006) third category (see above) and are relevant for what Skovsmose (1992) calls the formatting power of mathematics: how mathematics influences the understanding of reality. He argues that the ability to recognize this formatting power, and reflect on it, is an essential democratic competence.

In this project, we will develop teaching and learning situations in two teacher education courses: in a master course in mathematics education and in a mathematics electives course. The aims of the lessons are to learn concepts and ideas within statistics and/or mathematical modelling and to reflect on mathematics in society. We will initiate classroom discussions and give the students assignments as explorative approaches to learn about indices and reflect both on their application in society and how the topic can be used for educational purposes on their later practice. The discussions and the assignments will link the topic of indices with the students’ curriculum literature. The latter will be related to education literature on mathematical modelling, dialogue and learning and critical mathematics education.

Research questions addressed in the project on indices will include:

• What modelling competences do the students express?
• How are critical democratic competences expressed?
• How does dialogue in these classes support learning?
• How do the students link their index related activities to their future practice?
• What did we, the lecturers, learn from developing the lessons on indices?

The project will thus contribute to further development of teaching and learning on index related topics.

## Method

Together the team will develop teaching and learning situations in two teacher education courses: in a master course in mathematics education and in a mathematics electives course. The team meetings, the classroom discussions and student presentations will be audio recorded. Student assignments will be collected. Standard research ethics procedures will be followed. The research design is therefore based on action research.

We will apply the model on developing teaching by Skovsmose and Borba (2000) as the project can be denoted as a teaching experiment. The model consists of three teaching situations: the present, the ideal and the arranged situation. The arranged situation is what we will study, while the ideal situation is what we imagine. These situations will be discussed when we plan the teaching and learning situations.

Further, we will apply Alrø and Skovsmose’s (2002) inquiry co-operation model (the IC-Model). The model denotes a way of communication and its elements: “the IC-Model consists of communicative acts among teacher and students that support learning in a particular way” (Alrø & Skovsmose, 2002 p. 62). The elements are i) getting into contact, ii) locating, iii) identifying, iv) advocating, v) thinking aloud, vi) reformulating, vii) challenging and viii) evaluating.  Getting into contact includes taking responsibility as a listener and to have mutual attention in the classroom dialogues. Locating is about examining student perspectives and different approaches. Identifying is about mathematising an approach. Advocating ideas or points of view and thinking aloud are also part of an inquiry and makes it possible for others to investigate perspectives. Formulations of ideas and views can be reformulated for clarification purposes. Challenging and evaluating perspectives are also central parts of an inquiry.  The model is relevant for both research arenas: the planning meetings and the classroom studies.

Because the project has multiple research questions, several analytical tools will be applied.