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?