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Problem Solving Problem-­‐solving Session 1 Whole-School Approach 1 Key Messages in Problem-­‐solving Problem solving is mul1-­‐dimensional and can be viewed as Problem-­‐solving Skill Content Methodology 2 Overview of Problem-­‐solving Sessions Session One • Theory & Prac>ce of Problem-­‐ solving Session Two • Problem-­‐solving Support Materials, ICT, Assessment & Diﬀeren>a>on Session Three • Reﬂec>ve Prac>ce -­‐ Suppor>ng Teaching and Learning 3 Objec>ves Session One • To contextualise problem-­‐solving • To introduce an instruc>onal framework for problem-­‐solving • To explore mathema>cal language, oral and mental math in problem-­‐solving 4 What is Problem-­‐solving? • How would you deﬁne Problem-­‐solving? Flipchart Ac>vity* 5 Problem-­‐solving is ... ‘..the ability to analyse mathema0cal situa0ons; to plan, monitor and evaluate solu0ons; to apply strategies; and to demonstrate crea0vity and self-­‐reliance in using mathema0cs’ (PSMC: p.8) 6 What is Numeracy? “Numeracy encompasses the ability to use mathematical understanding and skills to solve problems and meet the demands of day-to-day living in complex social settings.” (Literacy & Numeracy Strategy: p.8) 7 Na0onal & Interna0onal Perspec0ve “Ensure that the curriculum contains addi>onal guidance for teachers on approaches to teaching and learning advocated in areas such as es>ma>on, shape and space, measures, the use of co-­‐opera>ve group learning and problem-­‐solving approaches” Literacy & Numeracy Strategy (2011: 56) “Irish pupils displayed rela>ve strengths on number and knowing and rela>ve weaknesses on geometric shapes and measures, data display and reasoning” (PIRLS & TIMSS: 2011) 8 Problem-­‐solving as a Skill of the Curriculum Applying & Problem-­‐Solving Understanding & Recalling Communica>ng & Expressing Implemen>ng Integra>ng & Connec>ng Reasoning Class Groups Ac>vity* (PSMC:1999: 68) 9 Problem-­‐solving – as Content Within the Mathema0cs Curriculum Junior & Senior Infants Shape & Space (2D Shape) Solve problems involving shape and space First & Second Class Shape & Space (2D/3D Shape) solve and complete prac>cal tasks and problems involving 2-­‐D and 3-­‐D shapes The child should be enabled to Third & Fourth Class Measures (Length) Solve and complete FiJh & Sixth Class prac>cal tasks and problems involving Data (RepresenMng & InterpreMng Data) the addi>on, subtrac>on,mul>plica>on Use data sets to solve problems -­‐ Solve and simple division of units of length problems based on data sets and (m, cm, km). representa>ons used in class -­‐what were the most popular buns at a cake sale? 10 Problem-­‐solving as Content Within the Wider Curriculum SPHE Make decisions, solve problems and take appropriate ac>ons in various personal, social and health contexts SESE Develop a scien>ﬁc approach to problem-­‐solving which emphasises understanding and construc>ve thinking Children will be enabled to: Visual Arts Solve problems crea>vely through imagina>ve thinking and so encourage individuality and enterprise Physical Educa1on Be inven>ve, make decisions, solve problems and develop autonomy through movement ac>vi>es 11 Key Methodologies of PSMC Problem Solving – An Overarching Methodology • Talk & Discussion • Ac>ve Learning / Guided Discussion • Collabora>ve / Co-­‐opera>ve Learning • Use of the Environment • Skills Through Content ‘Strong emphasis should be based on developing the ability to ques>on, to analyse, to inves>gate, to think cri>cally and to interact eﬀec>vely with others to solve problems’ (PSMC: 1999: 19) 12 Problem-­‐solving and Co-­‐opera0ve Learning • It is more likely that children will develop a sense of ownership over what they have learned and be able to transfer it to diﬀerent situa>ons when they have been acMvely involved in the learning process. • While independent learning is fostered, it is equally essen>al that children are given opportuni>es to interact with others and with their environment and to learn to co-­‐operate with their peers. • The role of the teacher will be central to the use of eﬀec>ve ac>ve learning and teaching techniques in the classroom. He/she will need to structure acMviMes and guide and direct the work in such a way that a child can parMcipate in a real and meaningful way and can develop a sense of responsibility for his/her own learning. (SPHE Curriculum 1999, p.6). 13 Problem-­‐solving The Key Ques1on What are the most common diﬃcul>es your pupils encounter whilst engaged in problem-­‐ solving exercises? 14 Problem-­‐solving DiﬃculMes Classroom Experiences • Reading the problem with understanding • Selecting the relevant information • Using the necessary mathematical expression • Seeing relationships and using patterns • Using existing mathematical knowledge / language • Developing a systematic / strategic approach • Making the required calculation correctly 15 Reﬂec0on -­‐ Our Classroom Culture ‘When a teacher succeeds in seKng up a classroom in which students feel obligated to listen to one another, to make their own contribu1ons clear and comprehensible, and to provide evidence of their claims, that teacher has set in place a powerful context for student learning’ (Chaplain, O’Connor & Anderson, 2009) Diamond Nine Ac>vity* 16 Instruc>onal Framework Ac>vity Extending Elici>ng Suppor>ng Home Expert Group* 17 Asking ques>ons such as... ? t a th t e ug o Estimate y d i d How Could it be done another way? Compare Put into your own words Des c r ib How does that connect with…? e 18 19 Sample Problem : Weights 20 Development of Mathema1cal Language “Many children fail at mathema0cs because their mathema1cal vocabulary is insuﬃcient to cope with the terminology of problems. Development of the necessary vocabulary in a consistent manner throughout the classes must be stressed” (PSMC :Teacher Guidelines: p.36) 21 Developing Mathema>cal Language A Classroom Approach Input InteracMon Output ‘A\er all the gene for language development and mathema1cal development are the same’ (Devlin: 2001) 22 The Language of Number OperaMons AcMvity StaMons AddiMon Sum Plus Total MulMplicaMon Times Product Groups Of SubtracMon Minus Take Less Division Split Share Distribute AcMvity 1 : Flashcards AcMvity 2: Math Language Test / Task AcMvity 3: Math Vocabulary Crosswords AcMvity 4: Highlight Maths Language AcMvity 5: Interac>ve Maths Dic>onary *Discuss possibility for extension of these ac>vi>es to other Strands / Strand Units 23 Developing Problem-­‐solving Skills Es>ma>on Strategies See Handout Ac>vi>es Mental / Oral Maths Infant Data Maths Video 24 Suggested Reading ‘The Elephant in the Classroom’ (Jo Boaler: 2009) ‘Transforming Primary Mathema>cs’ (Mike Askew: 2011) PDST Website ‘Elementary Middle School Mathema>cs’ (J. Van De Walle: 2009) ‘Teaching Problems and the Problems of Teaching’ (Magdalene Lampert: 2001) 25 Possible Between Session Tasks A. ReﬂecMon Maths Lesson – Skills & Methodologies B. Maths Language AcMviMes – Classroom-­‐based C. EsMmaMon, Oral & Mental Maths AcMviMes Classroom-­‐based 26