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Assessment of students´ performance in Secondary education in Mathematics .

This paper explores the impact of PISA results on the national debate in Italy, discusses in-service teachers' training about national and international assessments, and examines the Italian Assessment System (SNV-INVALSI) and its frameworks compared to PISA. The paper also showcases two examples of mathematical modeling and argumentation and proof, and addresses open problems in looking for mathematical literacy.

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Assessment of students´ performance in Secondary education in Mathematics .

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  1. Assessment of students´ performance in Secondary education in Mathematics. The Italian perspective StefaniaPozio & RossellaGaruti INVALSI - ITALY Baeza, 22-24 of May 2015

  2. Layout 1. The impact of PISA results in Mathson nationaldebate 2. In-service teachers’ training aboutnational and internationalassessments 3. ItalianAssessment System (SNV-INVALSI) 4. Frameworks for ItalianAssessment System and PISA: similarities and differences 5. Twoexamples: mathematicalmodellingand argumentation and proof 6. Open problems: looking for mathematicalliteracy

  3. 1. The impact of PISA studies on nationaldebate 1.1. Discussionabout PISA programin Italystarted from the 2003 resultswhenItalyscored BELOW the OECD mean. In Italytherewasn’t a PISA-shocklike in Germany…..only a «little» suprprise! VS Newspaper on-line Corriere.it One of the mostimportantnewspaper in Germany

  4. 1. Italian PISA results • 1.2. Italian PISA results from 2003 to 2012 • The Italianmeanscores (466 in 2003 and 485 in 2012) continue to be below the OECD mean • Thereis a greatvariabilitybetween the Italianregions: while in northernregionsthere are resultsabove the OECD mean, the opposite happens in the southernregions. • HOWEVER • From 2003 to 2012 in Mathstherewas a positive trend • The better performance is due to the betterresults in the southernregions

  5. 1. Italian PISA results • Figure I.2.16 • Curvilinear trajectories of average mathematics performance across PISA assessments Rate of acceleration or deceleration in performance (quadratic term) OECD 2013 (VOL. I pag. 54) p. 485 (OCSE, p. 494)

  6. TREND MATEMATICA PISA 2003-2006-2009-2012 The better performance is due to the betterresults in the southernregions v v

  7. RESULTS PISA 2012- Italianregions P=509 OCSE= 494 P=514 P=485 P=464 P=446 P=485

  8. 1. The impact of PISA studies on nationaldebate • Summarizing: • Meanmathematics performance among 15-year-olds in Italyisbelow the OECD average, butItalyisone the countries with the largestimprovementin mathematics performance. • Between 2003 and 2012 the share of low performers decreasedby 7 percentagepoints and the share of top performers increaseby 2.9 percentagepoints. • PISA revealslarge regionaldifferences in mathematics performance.

  9. 1. Onemightwellask… Italian trends from 2003 to 2012 Whathappenedhere?

  10. 2. In-service teachers’ training aboutnational and internationalassessments MIUR Southern regions UMI-CIIM INDIRE Istituto Nazionale di documentazione , innovazione e ricerca educativa

  11. 2. In-service teachers’ training aboutnational and internationalassessments 2008-2010 MIUR Four Southern regions “Piano di informazione e sensibilizzazione sull’indagine OCSE-PISA” • GOALS • To bridge the gap betweennorthern and southernregions • Informingteachersabout OECD-PISA studies • Analysing the PISA Mathematical framework • Comparingit with the most common didacticalpractices in classroom • The programinvolved the teachers of grades 8, 9 and 10 • Altogether 20.000 teachers (Maths, Science, Italian)

  12. 2. In-service teachers’ training aboutnational and internationalassessments INDIRE Istituto Nazionale di documentazione , innovazione e ricerca educativa • STEPS • Measurement of learning input (diagnosis) • Teachingunits (online) • Measurementof learningoutput • Teachers of lowersecondaryschool (grades from 6 to 8) http://www.indire.it/pqm2012/

  13. 2. In-service teachers’ training aboutnational and internationalassessments UMI-CIIM & MIUR http://www.umi-ciim.it Starting with : “Mathematicsfor the citizen” ( UMI- 2001-2003) New mathematicalstandards for K 5 to 13° grade school • Teachingunitsaccording with the goals of “mathematics for the citizen”, available on line • blendedteachers’ training “blended”(both on- line and in presence) • Teachers of lower and uppersecondaryschool (from 8 to 13 grade)

  14. In 2008 starts the new National Assessment System: SNV-INVALSI • In the finalexamination of the first cycle (8 grade) wasintroduced a national test (READING and MATHS) withouteffect on grade of examination. • From 2010 the result of the test affect for 1/7on grade of examination • For the first time the test was the same for allstudents on the contrary the theotherparts of examination (Italiano, Maths, English,…) depending on teachers

  15. 3. ItalianAssessment System SNV- INVALSI • NOW: • Tests are administeredeveryyear to allstudents of grades 2-5-8-10 atthe end of eachschoolyear. • The Grade 8 test isincluded in the finalexaminationat the end of the first cycle of instruction. • The results of a national sample are annualyreported(9 of July 2015) • The results of the national sample are pubblicaswellas the test items • The results of eachschoolare deliveredconfidentially to the principalat the beginning of the followingschoolyear(i.e. September 2015 for the 2015 survey) http://www.invalsi.it/invalsi/index.php

  16. 3. ItalianAssessment System SNV- INVALSI National Surveys

  17. 3. ItalianAssessment System SNV- INVALSI National Survey 2014 booklets

  18. 3. The ItalianAssessment System SNV Framework Framework SNV- INVALSI National guidelines 2010- upper sec. school 2012- first cycle (primary and lowersec.school) Frameworks of International researches (PISA, TIMSS) Classroompractices Results of previous surveys 18

  19. Comparingframeworks PISA & SNV Mathematical literacy in PISA 2012 Framework

  20. Framework SNV-INVALSI Matematics for the citizen (2001-2003) National Guidelinesfor the curriculum (2010-2012) The ItalianAssessment System Framework (2009-2015)

  21. Comparingframeworks PISA & SNV Differentaims To compare in differentcountries, with different curricula and tradition «what the students are able to do usingwhattheyhavelearned» To compare in the same grade with the samenationalGuidelines «what the studentshavelearned»

  22. 4. FrameworksPISA & SNV • The National Guidelinesexplicitystatesboththeinstrumentaland culturalfunction of mathematics • According to National Guidelines: • Instrumentalaspect(likedoingcomputations, reading data, measuring, determiningprobability), always include a cultural component thatlinksthosecompetencies to our cultural traditionand evolution • Cultural aspect of mathematics, whichrefers to theoretical, historical and epistemologicalknowledge, wouldnotmakesensewithoutcomputations, trial and errormethods,….. Bothaspetcs are essential for a wellbalancededucation

  23. Examples from SNV 1. The elongation of a spring: item PISA-like GRADE 8 GRADE 10 SNV 2010

  24. Examples from SNV 1.The elongation of a spring: item PISA-like Percentage of studentschoosingeach option in the nationalsample (in REDcorrectanswer)

  25. ITEM PISA 2003

  26. 5. Twoexamples from SNV Bothitems, Elongation of a springand Walking, represent a physicalphenomenonthroughmathematicalformulas

  27. Examples from SNV 2. Natural numbers: justifying and proving SNV 2012 Grade 8 Correctanswer

  28. Examples from SNV 2. Natural numbers: justifying and proving SNV 2013 Grade 8

  29. Examples from SNV SNV 2013 Grade 8 TWO EXAMPLES NON LIKE-PISA

  30. 4. FrameworksPISA & SNV PISA frameworktakesinto account ONLY the first aspect(instrumentalcompetencies), butwethinkthatwithoutthe othertwoaspects, Mathematicswould be a series of recipeswithoutmethod and justificationwith an insufficient cultural and educational impact today, . • In particular: • The approach to theoreticalthinking, arguing, proving are fundamentalaspects of mathematicseducation (literacy, alfabetisaciònbasica) . They are neededin a time wherestudentsonlyhaveaccess to communicatethrough brief declarations(sms, whatsup,…); • The semioticaspects of mathematicsisanotherimportantfeature of mathematicseducation: masteryngsystems of symbols and reflect on them and moving from a registerr of representation to another, are needed to face the variety and complexity of the present man-computer-relationships.

  31. Nomina omen ComparingContents

  32. 6. Open problems: Mathematical literacy for what? For who? Given the different cultural perspective on priorities in MathematicsEducation and on Mathematical literacyderiving from the comparison of PISA definition of Mathematical Literacy and the ItalianGuidelines for the curriculum some relatedquestionsare:

  33. 6. Open problems: Mathematical literacy for what? For who? • Whatis Mathematical literacy? • Whatrelationship with cultural nationaltradition? • Whatis the impact of PISA- mathematicalliteracy on the world? (OCSE_PISA ispowerful) • Whatis the impact of PISA Mathematical Literacy on the countries with a weak cultural tradition in education? • Whatis the impact of PISA-mathematicalLiteracy on nationalcurricola? Overlapping or blending?

  34. GRAZIE!

  35. A suggestion ASSESSING MATHEMATICAL LITERACY The PISA Experience, 2015 Springer Kaye Stacey & Ross Turner (Eds)

  36. http://www.invalsi.it/invalsi/index.php http://www.gestinv.it/login.aspx

  37. Whathappens NOW in Italy? A NEW REFORM: The goodschool GENERAL STRIKE 5 of May 2015

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