**Modelling in education! Modelling and statistics in research**

By Marcelo de Carvalho Borba (mborba@rc.unesp.br; Facebook Marcelo Borba)

and João** ** Frederico C. A. Meyer (joni@ime.unicamp.br)

*Keynote presentation at the 11th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics, ‘Brazil Delta 2017’ for short, 27 November 2017*

How to teach modelling to teenagers? There has just been the 10^{th} conference on Modelling in Education in Brazil – we can say this topic has become a trend.

Modelling may help to answer the question, “Why am I studying this?”

Bringing modelling to teacher education may help teachers to use modelling in school teaching and keep students interested in STEM career paths.

Annual Perspectives of Mathematics Education, the yearbook of the National Congress of Mathematics Teachers in America had Modelling as a theme for the yearbook – a sign that this is a topic becoming of greater interest.

Example: Students had data on the size of glaciers and wondered if they could predict if or when the glacier would disappear. They needed to use more knowledge than was in their curriculum, so they followed the leads that emerged. [How would assessment work when the topics are not predetermined?]

Mathematics syllabuses are the same although there are many other changes in technology. Have you considered that pencils are 5^{th} century technology? Paper is BC technology.

Some new technologies do nothing but repeating same old procedures.

- They have nothing to do with ‘seeing’ and trying to understanding the world
- Very little dialogue – crucial for learning
- Very little criticism of learnt or constructed concepts
- Very little contact with social, natural needs

Modelling in real life situations

- No more absolute truths, e.g. parallel lines
- No more correct, exact answers
- Needs trial and error besides subjective choices
- Learning to trust our mathematical solutions

Should we still be considering/trying to master:

- Mathematical expressions
- Special angles, how common are they in real life
- The quadratic formula (Bhaskara’s formula)
- Indefinite integrals (Joni says solving a long integral by hand was boring, long and very unlikely to be used in life)

Is it really possible not to consider:

- Data, e.g. what does it mean to say 30% of Brazilians earn 40% of the gross domestic product (GDP), 0.8% growth in the Brazilian population?
- Discrete mathematics
- Higher order polynomials (Taylor’s series and the like)
- Learning new technologies e.g. Geogebra, Mathematica, etc. What ones will be here still in 10 years’ time? Joan says none of them. Students need to know how to learn new technologies.

Situations modelling can be used in:

- Voting systems
- Water and air pollution
- Fighting diseases e.g. in Yemen civil war destroyed sanitation. Maths is needed to use data to solve health problems
- Interpreting media information

Differential equations to consider environmental rules

- Solving by separating the differential equation dP/dt = kP(1-P/K) is not needed if you can see from the equation that growth is low with P is close to 0 or close to K.

Until last month, students were by Brazilian law not allowed to use a cell phone in a class (unless for directed learning).

A teacher used real data from the internet to teach statistics, e.g. number of people infected and cured from a disease. New scenarios every day.

Mathematics requires transdisciplinarity to be relevant. Real life problems are problems – they are messy and make us learn new things beyond our speciality discipline.

Why can’t we continue with the maths syllabus in the way we have been?

- Because we’re ambitious. We don’t want to be famous and be interviewed by Time magazine but we want to make a difference in the world.

Muito obrigado, tchê!

Q&A

Get students to make videos. We have to adapt to technology. When you write a mathematics journal article, you must write very formally. When you are explaining at the board, you can use gestures and other expressions to convey meaning. When getting students to make video explanations, are we decreasing their ability to write precisely? Or strengthening their ability to express?

Challenge to the idea that integrals are not worthwhile: Joni brings in real life problems that lead to the need for a technique for integrating. Flip: problem first then learning the techniques.

Most integration techniques came from the need to solve a real life problem, not just from the maths alone.

How should phones change our assessment? If you teach with a phone, can students use them in the test? Maybe group assessments, google documents, students challenging what the lecturer says based on what they see on Wikipedia.

How best can I use the 12 weeks I have with students to impact the way they think about maths? How can we help school teachers to best help students?

**Classrooms like we have now will not exist in the next century.**

A phone can give you a way to check answers and see other approaches. Am I being conservative because I want my students to learn the way and things that I use?

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