Ioannis Karagiannakis “Mathematics and Its Relevance in a Global World Preparing Children for the Future” from the face-to-face sessions by Katherine K. Merseth. I selected this subject because I am currently working on my PhD research with regard to the difficulties that Greek students face in mathematics. All began when you asked us “What is 1/2 divided by 2/3 ?”. To my surprise, I realized that although I could find the answer following the rule of division of fractions, I couldn't give a concrete example to make my students clearly see what this division really represents. After consideration, I planned a new multisensory activity to teach the division of fractions using concrete material, educational software and internet applications. I have been piloting this practice since December in:  a team of three 5 th grade dyslexic students  a 5 th grader boy who faces difficulties in mathematics, according to the evaluation of his schoolteacher. 1 Get a little taste of practical…

2 CONNECTIONS WITH COLLEAGUES I presented such practices in teaching math concepts in a math conference in Athens and in a teachers’ training seminar in Mytilini.  Most of the participants were thrilled with these techniques. They told me that they also had not understood these simple mathematical concepts because no one had ever explained them neither at school nor at the university. For this reason, they felt that so far, they transmitted mechanistic knowledge to their students.  There were some teachers who argued that there is no need to analyze mathematical concepts so much for various reasons like lack of time or because the essence of mathematics lies at higher levels. 6 : 2 = ? The usual question: The proposed question : Reaching … to the answer: What is 6 divided by 2?How many 2 fit in 6? 6 : 2 = 3 What is 6 divided by 1/2? How many 1/2 fit in 6? 6 : 1/2 = ? : 1/2 = 12 What is 1/2 divided by 2/3 ?How many 2/3 fit in 1/2? 1/4 1/2 : 2/3 = 3/4 1/2 : 2/3 = ?

3 SUCCESSES The biggest success was that my students were much more interested in math during lessons. My students felt comfortable with this kind of teaching because it was based on the prior knowledge they had. Each student in his own way could represent mathematical concepts in a way that made sense for him. Some worked on more tangible material, other with educational software and/or gambling games on the internet. Moreover, it was important for the students to have choices. A change for me using this method of teaching was that for the first time I felt the dynamics between my teaching and my student’s reactions, while before I simply concentrated on ‘teaching’…

4 CHALLENGES The students were initially reluctant to the new teaching method. They wondered why they had to do all this to learn for example how to divide fractions. They told me that they wanted to learn the procedure, the rule of division of fractions. When I asked them: “Don’t you want to understand what is really happening’? they replied “No one will ask us about it”. When I informed their parents about the new teaching method, they said that this method would be interested only if it helped their children to score higher in tests; otherwise it would be a waste of time….A typical response from parents was: “ We had understood all that, but we did fine”. A personal challenge I had was: I thought I had completely simplify the mathematical concepts that I had to teach to students. But during teaching I realized from the students' questions that there were points which had not been fully clarified.

5 NEXT STEPS The next steps are to extend this kind of techniques to cover all those mathematical concepts which are not understood. Students who will show us these concepts enough to have our eyes and ears open. Priority is I can understand the seemingly simple mathematical concepts. I fully agree with the statement of David Cohen: “How can teachers be expected to teach a mathematics they never learned in ways they never experienced?” Thank you for the multiple stimuli that you gave us to become better teachers.