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MARCO TEÓRICO MATEMÁTICAS PISA 2012 POR DAVID TOUT. SEMINARIO DEL INEE. COMILLAS (CANTABRIA)

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MARCO TEÓRICO MATEMÁTICAS PISA 2012 POR DAVID TOUT. SEMINARIO DEL INEE. COMILLAS (CANTABRIA)

  1. 1. PISA 2012PISA 2012 Mathematical LiteracyMathematical Literacy Framework Symposiumy p Comillas, Spain, September 2013 Dave Tout D id T t@ dDavid.Tout@acer.edu.au
  2. 2. PISA Survey Cycley y 2000 2003 2006 2009 2012 20152000 2003 2006 2009 2012 2015 Reading Literacy Mathematical Literacy Scientific Literacy Questionnaire Major domain cycle in yellow/red In PISA, framework development takes place during the major domain cycle. For mathematical literacy this was in 2003 and 2009this was in 2003 and 2009
  3. 3. What is an assessment framework?  An assessment framework is an explicit An assessment framework is an explicit statement and discussion about what an assessment intends to measureassessment intends to measure.  Its purposes are: • To guide test development • To give a common language to stakeholders for discussion of the subject • To ensure continuity from one year or one grade l l hlevel to another • To communicate the purpose and features of the assessment program to the p blicassessment program to the public
  4. 4. What is in a framework?What is in a framework?  Rationale for and description of assessment programprogram  Definition of the subject  Description of variables  Bl i t f t t d l t Blueprint for test development  Examples of items Examples of items
  5. 5. Mathematical Literacy framework Challenge in real world context Problem in MathematicalF l tProblem in  context Mathematical  problem Formulate Employ Evaluate Results in  Mathematical Interpret context results Interpret
  6. 6. PISA Mathematical Literacy framework New 2012 Definition of Mathematical literacy Mathematical literacy is an individual’s capacity toMathematical literacy is an individual s capacity to formulate, employ, and interpret mathematics in a variety of contexts It includes reasoningvariety of contexts. It includes reasoning mathematically and using mathematical concepts, procedures facts and tools to describe explainprocedures, facts, and tools to describe, explain, and predict phenomena. It assists individuals to recognise the role that mathematics plays in therecognise the role that mathematics plays in the world and to make the well-founded judgments and decisions needed by constructive engaged anddecisions needed by constructive, engaged and reflective citizens.
  7. 7. PISA Mathematical Literacy framework New 2012 Definition of Mathematical literacy Mathematical literacy is an individual’s capacity toMathematical literacy is an individual s capacity to formulate, employ, and interpret mathematics in a variety of contexts It includes reasoningvariety of contexts. It includes reasoning mathematically and using mathematical concepts, procedures facts and tools to describe explainprocedures, facts, and tools to describe, explain, and predict phenomena. It assists individuals to recognise the role that mathematics plays in therecognise the role that mathematics plays in the world and to make the well-founded judgments and decisions needed by constructive engaged anddecisions needed by constructive, engaged and reflective citizens.
  8. 8. PISA Mathematical Literacy framework New 2012 Definition of Mathematical literacy Mathematical literacy is an individual’s capacity toMathematical literacy is an individual s capacity to formulate, employ, and interpret mathematics in a variety of contexts It includes reasoningvariety of contexts. It includes reasoning mathematically and using mathematical concepts, procedures facts and tools to describe explainprocedures, facts, and tools to describe, explain, and predict phenomena. It assists individuals to recognise the role that mathematics plays in therecognise the role that mathematics plays in the world and to make the well-founded judgments and decisions needed by constructive engaged anddecisions needed by constructive, engaged and reflective citizens.
  9. 9. PISA Mathematical Literacy framework New 2012 Definition of Mathematical literacy Mathematical literacy is an individual’s capacity toMathematical literacy is an individual s capacity to formulate, employ, and interpret mathematics in a variety of contexts It includes reasoningvariety of contexts. It includes reasoning mathematically and using mathematical concepts, procedures facts and tools to describe explainprocedures, facts, and tools to describe, explain, and predict phenomena. It assists individuals to recognise the role that mathematics plays in therecognise the role that mathematics plays in the world and to make the well-founded judgments and decisions needed by constructive engaged anddecisions needed by constructive, engaged and reflective citizens.
  10. 10. PISA Mathematical Literacy framework New 2012 Definition of Mathematical literacy Mathematical literacy is an individual’s capacity toMathematical literacy is an individual s capacity to formulate, employ, and interpret mathematics in a variety of contexts It includes reasoningvariety of contexts. It includes reasoning mathematically and using mathematical concepts, procedures facts and tools to describe explainprocedures, facts, and tools to describe, explain, and predict phenomena. It assists individuals to recognise the role that mathematics plays in therecognise the role that mathematics plays in the world and to make the well-founded judgments and decisions needed by constructive engaged anddecisions needed by constructive, engaged and reflective citizens.
  11. 11. PISA Mathematical Literacy framework New 2012 Definition of Mathematical literacy Mathematical literacy is an individual’s capacity toMathematical literacy is an individual s capacity to formulate, employ, and interpret mathematics in a variety of contexts It includes reasoningvariety of contexts. It includes reasoning mathematically and using mathematical concepts, procedures facts and tools to describe explainprocedures, facts, and tools to describe, explain, and predict phenomena. It assists individuals to recognise the role that mathematics plays in therecognise the role that mathematics plays in the world and to make the well-founded judgments and decisions needed by constructive engaged anddecisions needed by constructive, engaged and reflective citizens.
  12. 12. PISA Mathematical Literacy framework PISA 2012 uses three task characteristics in the construction of all mathematical literacy tasks:construction of all mathematical literacy tasks:  Contexts  Processes  Content See Handout titled “The PISA 2012See Handout titled The PISA 2012 Mathematical Literacy Framework item classifications” for more detailed descriptionsclassifications for more detailed descriptions.
  13. 13. PISA Mathematical Literacy framework Mathematical contexts  Personal  O ti l Occupational  Societal Societal  Scientific
  14. 14. PISA Mathematical Literacy framework Mathematical overarching ideas (content areas):(content areas):  Quantityy  Uncertainty and data  Space and shape  Change and relationships Change and relationships
  15. 15. PISA Mathematical Literacy framework Mathematical processes (new in 2012)  Formulate: recognise, identify, formulate, translate and provide mathematical structurep (from the Real World to the Maths World)  Employ: reason argue manipulate and Employ: reason, argue, manipulate and compute (work within the Maths World)  Interpret: interpret, evaluate, reflect, justify and explain (from the Maths World to thep ( Real World)
  16. 16. Blueprint in the PISA frameworkBlueprint in the PISA framework Mathematical contexts Personal Occupational Societal Scientific 25% 25% 25% 25% Mathematical Uncertainty Space & Change &Mathematical content areas Quantity Uncertainty & data Space & shape Change & relationships 25% 25% 25% 25%25% 25% 25% 25% Mathematical processes Formulate Employ Interpret processes 25% 50% 25%
  17. 17. Sample PISA SUBIDA AL MONTE FUJI item SUBIDA AL MONTE FUJI El Monte Fuji es un famoso volcán inactivo del Japón. PISA classification:PISA classification: •Context: Societal •Process: Formulate Q02 La ruta del Gotemba, que lleva a la cima del Monte Fuji, tiene unos 9 kilómetros (km) de longitud. Los senderistas tienen que estar de vuelta de la caminata de 18 F m •Content: Change & Relationship Los senderistas tienen que estar de vuelta de la caminata de 18 km a las 20:00 h. Toshi calcula que puede ascender la montaña caminado a 1,5 kilómetros por hora, como media, y descenderla al doble de l id d E t l id d ti t l dvelocidad. Estas velocidades tienen en cuenta las paradas para comer y descansar. Según las velocidades estimadas por Toshi, ¿a qué hora puede, como muy tarde, iniciar su caminata de modo que pueda estarcomo muy tarde, iniciar su caminata de modo que pueda estar de vuelta a las 20:00 h? ___________________________________________________
  18. 18. Sample PISASUBIDA AL MONTE FUJI El M t F ji f l á i ti d l J ó itemEl Monte Fuji es un famoso volcán inactivo del Japón. PISA classification:PISA classification: •Context: Societal •Process: Employ Q03 Toshi llevó un podómetro para contar los pasos durante su recorrido por la ruta del Gotemba. El dó t t ó di 22 500 l ió Emp y •Content: Quantity El podómetro mostró que dio 22.500 pasos en la ascensión. Calcula la longitud media del paso de Toshi en su ascensión de 9 km por la ruta del Gotemba. Expresa tu respuesta en centímetros (cm).( ) Respuesta: ______________ cm
  19. 19. Sample itemFRECUENCIA DE GOTEO Las infusiones intravenosas (goteo) se utilizan para administrar líquidos y(g ) p q y fármacos a los pacientes. PISA classification: •Context: Occupational P E l•Process: Employ •Content: Change & RelationshipRelationship Las enfermeras tienen que calcular la frecuencia de goteo G de las infusiones intravenosas en gotas por minuto. Utilizan la fórmula donde g es el factor de goteo expresado en gotas por mililitro (ml) v es el volumen de la infusión intravenosa en ml n es el número de horas que ha de durar la infusión intravenosa. Una enfermera quiere duplicar la duración de una infusión intravenosa. Explica exactamente cómo varía G si se duplica n pero sin variar g y v.
  20. 20. Sample item¿QUÉ COCHE? Cris acaba de sacarse el carné de conducir y quiere comprar su primer coche. La siguiente tabla muestra las características de cuatro coches q ue vio en un concesionario de la zona Modelo: Alpha Bolte Castel Dezal Año 2003 2000 2001 1999 Precio 4 800 4 450 4 250 3 990 ue vio en un concesionario de la zona. Precio anunciado (zeds) 4.800 4.450 4.250 3.990 Kilometraje (kilómetros) 105.000 115.000 128.000 109.000 Cilindrada 1 79 1 796 1 82 1 783 Cilindrada (litros) 1,79 1,796 1,82 1,783 Q01 PISA classification: •Context: Personal Cris quiere un coche que cumpla todas estas condiciones: • El kilometraje no debe superar los 120.000 kilómetros. • Debe haberse fabricado en el año 2000 o en un año posterior. • El precio anunciado no debe superar los 4 500 zeds ontext ersonal •Process: Interpret •Content: d • El precio anunciado no debe superar los 4.500 zeds. ¿Qué coche cumple las condiciones de Cris? A. El Alpha Uncertainty & dataB. El Bolte C. El Castel D. El Dezal
  21. 21. PISA: Fundamental mathematical capabilities Si F d t l M th ti l C bilitiSix Fundamental Mathematical Capabilities now described in the PISA framework  Representation Representation  Mathematising  Devising Strategies  Using Symbolic, Formal and Technical Language and Operations  C i ti Communication  Reasoning and argument Each one is described using a rating of 0 through to 3. Used to help predict item difficulty.
  22. 22. Thank youy For more information about PISA go tog www.pisa.oecd.org
  23. 23. QUESTIONS?

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