# Seven questions with... Dr Javier Díez-Palomar

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- Seven questions with... Dr Javier Díez-Palomar

## Seven questions with... Dr Javier Díez-Palomar

Javier Díez-Palomar began teaching maths to adults as a volunteer in an adult school in Barcelona. He completed a PhD in mathematics education and worked at the University of Arizona researching maths education with Latinos/as. He then became an associate professor of Mathematics Education at the University of Barcelona. He is now the President of the Association of Multidisciplinary Educational Research, a Spanish member of the International Commission for the Study and Improvement of Mathematics Teaching, and a Trustee of the Adults Learning Mathematics association. He has served as link convenor for Network 24 (Research in Mathematics Education) at the European Conference of Educational Research. He has also been the principal investigator for several European Commission and Spanish Government Research grants on mathematics education. He is a member of the Numeracy Expert Group (OECD) working at the PIAAC survey, the chief editor for *REDIMAT: Journal of Research in Mathematics Education*, and former chief editor and current member of the Editorial Board for *Adults Learning Mathematics: An International Journal*.

**1. What’s your earliest memory of doing mathematics? **

I remember that I had always liked math until I got to high school. I loved going with my brother to the city library, to read science and math books and magazines. We used to spend a good part of our holidays there. But in high school, I had a bad experience since two teachers started to speak to me in a language that I did not understand. Only the last year before going to university, my luck changed: I had a teacher who was passionate about mathematics. He restored my self-confidence. Years later, when I was looking for programs to do my PhD, a professor and friend of mine advised me to go back to mathematics. I started volunteering at an adult school, teaching math, and I can say that that experience was my rebirth from the point of view of doing math. The adult learners, who had never been to school before and had just become literate, taught me two things: one, that mathematics is part of our lives, in every way; and two, they taught me how to teach mathematics. They made me a math teacher with a passion for math. And despite having had many memories of doing mathematics before, I can say that this is undoubtedly the one that changed my life and focused me on mathematics forever. Since then, I have had the dream that no one else loses the passion for mathematics. For this reason, I dedicate myself to mathematics education.

**2. How has mathematics education changed in the time you have been involved in it?**

The way of teaching mathematics has been changing in the last three decades. Many people, good researchers, have transformed the traditional lessons in which the teacher presents a series of concepts and procedures, waiting for the students to repeat them mechanically. Now the aim is for students to understand mathematics. The fundamental idea is that they are competent to solve mathematical problems and apply mathematics to different contexts. Problem-solving continues to be one of the fundamental pillars of teaching mathematics. Also, to encourage the taste and passion for them. There is a lot of literature on the different types of math activities, how to sequence the concepts, learning trajectories, procedural and conceptual understanding, socio-mathematical norms and mathematics, etc. In recent years, there has been an increasing interest in interactions around learning mathematics. We know that it is very different to learn individually than in a small group, in pairs, or in a group class. The effort to argue an answer to others’ questions in a group is a crucial aspect of learning. We know that when the *egalitarian dialogue* appears in the group, which is focused on the exchange of arguments oriented towards understanding, the learning opportunities are greater than when the type of dialogues that appear in the group are unidirectional, based on the power position of the person who is speaking, not on whether or not the idea you want to convey is understood. We still need more research on these types of dialogues. But what is already undeniable is that learning mathematics is a social process in which many people participate (teachers, families, classmates, TV, Internet, etc.). Therefore, future learning spaces will have to consider the interactions in the different spaces, identify learning difficulties, and maximise learning opportunities.

**3. Tell me about a time in your career when something totally flabbergasted you.**

A friend who was an elementary teacher told me about two boys doing mathematics in interactive groups. One of the boys was a newcomer from Senegal. He never went to school in his country of origin. He was in grade 4, learning the basics (to write, read, etc.). But in the interactive group, he was dividing with the lattice algorithm! His classmate was teaching him a way to understand how the lattice algorithm works: he drew three people on his sheet of paper; then, he distributed fifteen circles among the three people, ending with five each. Then, he pointed with his finger to the lattice algorithm in the paper and said: look, this is the divisor, this the dividend, and this the quotient. It was fascinating to learn how that boy was able to go beyond my friend's explanation of the lattice algorithm and connect it to a different model of dividing to help his classmate.

**4. Do you practise mathematics differently in company?**

Yes, of course. I learn other ways of doing math by listening to others, especially when I am in groups with diverse people. When I participate in *Mathematics Dialogic Gatherings*, some of the participants always surprise me with unexpected ways of solving a problem or explaining a concept. Reading math books in their company allows me to enrich myself with a broader vision of mathematics and leads me to explore new paths and points of view. I love it because, thanks to that, I discovered the tremendous complexity that mathematics has and how fascinating it is to explore it and find those little "treasures." Of course, alone, I would be unable to do so.

**5. Do you think a brilliant maths teacher is born or made?**

Without a doubt: made. Everyone can learn to teach math. We have a lot of research on the competencies that a good math teacher must develop. We know that mathematics teacher training (as in other domains of teachers’ professional knowledge) must be based on scientific evidence. We cannot hope that training our future teachers drawing on occurrences will convert them into good teachers. Just as a doctor must learn the parts of the body, how they work, and how they respond to treatments when they get sick, teachers also must know the contents of mathematics, how they work, and how to teach them when students have difficulty understanding them. All that is learned, of course.

**6. What’s the most fun a mathematician can have?**

Probably finding an unexpected relationship and why it happens that way. But if the question is what's the most fun a mathematics teacher can have, it would be to enjoy solving problems with the students. So often in class, I feel that my students become "fellow travellers" in solving a difficult problem. In the end, we look like "Sherlock Holmes," trying to find the clues that lead us to unveil the answer. It is difficult to describe the feeling: it is just the joy of doing mathematics together.

**7. Do you have a favourite maths joke?**

I always liked that video where you can see a man trying to explain that 25% divided among five persons gives 5% for each one; but the old man (Pa) and the old woman (Ma) reply that this is not true, because *25% divided among the 5 of you, that’s 14% for each one*. I always ask myself: who is the smartest one in this piece? ;-)

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