Post on 05-Jul-2015
PISA 2012PISA 2012Mathematical LiteracyMathematical Literacy
FrameworkSymposium y p
Comillas, Spain, September 2013
Dave ToutD id T t@ dDavid.Tout@acer.edu.au
PISA Survey Cycley y
2000 2003 2006 2009 2012 20152000 2003 2006 2009 2012 2015Reading LiteracyMathematical LiteracyScientific LiteracyQuestionnaire
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
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
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
Mathematical Literacy frameworkChallenge in real world context
Problem in MathematicalF l tProblem in context
Mathematical problem
Formulate
EmployEvaluate
Results in Mathematical Interpretcontext results
Interpret
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.
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.
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.
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.
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.
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.
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.
PISA Mathematical Literacy framework
Mathematical contexts
Personal
O ti lOccupational
Societal Societal
Scientific
PISA Mathematical Literacy framework
Mathematical overarching ideas (content areas):(content areas):
Quantityy
Uncertainty and data
Space and shape
Change and relationships Change and relationships
PISA Mathematical Literacy framework
Mathematical processes (new in 2012)
Formulate: recognise, identify, formulate, translate and provide mathematical structure p(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 the p (Real World)
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
& dataSpace & shape
Change & relationships
25% 25% 25% 25%25% 25% 25% 25%
Mathematical processes Formulate Employ Interpretprocesses
25% 50% 25%
Sample PISA SUBIDA AL MONTE FUJI itemSUBIDA AL MONTE FUJIEl Monte Fuji es un famoso volcán inactivo del Japón.
PISA classification:PISA classification:•Context: Societal•Process: Formulate
Q02La 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? ___________________________________________________
Sample PISA SUBIDA AL MONTE FUJIEl 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
Q03Toshi 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
Sample itemFRECUENCIA DE GOTEOLas infusiones intravenosas (goteo) se utilizan para administrar líquidos y (g ) p q yfármacos a los pacientes.
PISA classification:•Context: OccupationalP 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 mln 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.
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 que vio en un concesionario de la zona
Modelo: Alpha Bolte Castel DezalAño 2003 2000 2001 1999Precio 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 783Cilindrada (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 AlphaUncertainty & dataB. El Bolte
C. El CastelD. El Dezal
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.
Thank youyFor more information about PISA go tog
www.pisa.oecd.org
QUESTIONS?