13th International Congress on Mathematical Education Hamburg, 24-31 July 2016 1 - 1 USING THE GRAPHING CALCULATOR IN A DIGITAL WORLD Jaime Carvalho e Silva Department of Mathematics, University of Coimbra, Portugal Dedicated to the memory of José Carlos Balsa In this paper we present briefly some ideas behind the use of technology in schools, as well as some difficulties. We present some reasons why graphing calculators are still important for mathematics teaching, even with the entrance in the school scene of much more sophisticated technologies. Some difficulties around national examinations are summarized and the case is made for a wider use of graphing calculators in national examinations. WHY TECHNOLOGY The use of technology in mathematics teaching is recommended in a number of studies and international documents, but technology use in education remains somewhat controversial, at the national or international levels. The best stated goal for the use of technology is, in my opinion, the one found in the new American Standards for School Mathematics (Common Core State Standards Initiative, 2011): Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. It is not just a question of adding new competencies involving new technologies; students should be able to choose, at each instance, which tools, from the old ones and new ones, are more appropriate. Controversy came up again in 2015 when a new study (OECD, 2015) was presented with conclusions that are based in data from the PISA studies. All international press reported on it with unfriendly titles like “Computers 'do not improve' pupil results, says OECD” (BBC, September 15, 2015). This study does not imply that computers are useless but that the sole investment in hardware does not produce automatically good results. Not a big surprise. Of course our task is not easy. ICMI produced already two studies around the ideas of using technology to teach and learn mathematics with numerous interesting discussions but its impact is not what we might expect. I extract from the second study what I consider to be a very fruitful idea: Making technology legitimate and mathematically useful requires modes of integration (...) requires tasks and situations that are not simple adaptation of paper and pencil tasks, often tasks without equivalent in the paper and pencil environment, thus tasks not so easy to design when