Project Maths information update NCCA Project Maths Team

Project Maths – information update NCCA Project Maths Team

Background to Project Maths • Concerns re uptake and performance • Transitions • International trends • Impact at third level • Research in Irish classrooms • JC Maths syllabus changes in 2000, first examined in 2003 • Results of PISA in 2000, 2003 2

Reviewing post-primary maths education • Discussion Paper in 2005 for consultation • Research Paper by Conway and Sloane • Report on the Consultation • Syllabus and Assessment • Teaching/Learning • Understanding and application • Attitudes 3

Discussion and consultation Review to consider • nature and purpose of mathematics education at second level • the need for syllabus change; assessment issues • requirements of third level • role of ICT in mathematics education • ‘culture’ of mathematics • teacher professional development needs 4

Main feedback comments (1) Curriculum • • syllabus levels; syllabus content; ‘gaps’ underpinning philosophy different for P and PP Teaching and learning • • • qualifications of teachers; focus on rote learning and routines/procedural emphasis discontinuity between primary and post-primary approaches to teaching and learning lack of contexts and applications of mathematics 5

Main feedback comments (2) Assessment • • backwash effect of examinations on T + L emphasis on practised routines predictability of examination questions lack of other forms of assessment Culture related to mathematics • • • negative perceptions and attitudes poor mathematical self-perception influence of teachers, parents, wider community 6

Points to ponder • How students encounter mathematics • The kind of mathematics they might experience • New approaches to teaching and learning • How mathematics might be assessed • Applied Mathematics – potential developments • Supporting the change – a new model of curriculum development 7

Project Maths – focus points Improving student learning • teaching for understanding • increasing student competence and confidence at all levels • making connections within maths and across subjects Developing student skills • critical thinking and logical reasoning SET • problem-solving, with emphasis in applications business, finance • using ICT appropriately in maths learning social sciences 8

Wider context of change School completion targets Access to and participation in third level Junior cycle and senior cycle changes • • • focus on the learner, on understanding and skills Key Skills role of assessment; recent developments Needs of society • Ireland the knowledge economy 9

Senior Cycle Key Skills Framework 10

Developing the proposals • Report on the consultation (April 2006) • Committees, Board of Studies (from Sept. 2006) • Outline proposals to Council (Dec. 2006) • Strands and sequence proposal (March 2007) • Final proposals (June 2007) • Indicative costs (July 2007) • Refinement and revised timescales (Dec. 2007) • DES approval in principle (March 2008) 11

Project Maths • Syllabus change at both junior cycle and senior cycle • Closer curriculum alignment across levels • HL uptake targets: 60% (JC) and 30 %(LC) • Phased introduction of change; 24 schools initially • Teacher professional development in parallel with changes; commitment to sustaining ongoing support • Incremental changes to examination questions 12

Increased emphasis on understanding and skills • Building on existing knowledge and skills • Progressing from concrete to abstract, from informal to the formal; developing conceptual understanding • Improving learner confidence and competence • Developing and using problem-solving skills • Applying knowledge and skills to familiar and unfamiliar contexts/problems 13

Phasing of developments Bridging framework to link primary and postprimary mathematics Phased syllabus changes at junior cycle and senior cycle – 5 strands over 3 years 1. Statistics and probability 2. Geometry and trigonometry 3. Number 4. Algebra 5. Functions } Phase 1 } Phase 2 Phase 3 14

Supporting change • • • Schools as sites of change; teachers as agents of change Project Maths Development Team (PMDT): full-time seconded teachers to develop and conduct workshops National Centre for Excellence in Mathematics and Science Teaching and Learning (NCE-MSTL) Collaboration with other agencies and groups Building capacity to sustain change 15

Areas of support for Project Maths • Resources to support teachers; Teaching and Learning Plans; school network/forum • Resources for students in newer topics • Web-based exemplification and support materials • Assessment support and exemplification • Project Maths Implementation Support Group • Linking Project Maths to other initiatives 16

Project Maths – ongoing work Syllabus revision Resources development Experience in schools • Teacher support to address needs mathematics methodology time allocation for maths • School practice student choice of syllabus level timing of student choice Assessment developments 17

Current state of play for syllabuses • From September 2012, all schools are working from syllabuses containing all 5 strands (first years and fifth years) • Full examination changes, based on these syllabuses, in June 2014 (LC) and June 2015 (JC) • In June 2017, full cohort with experience of revised syllabuses all through post-primary education 18

Syllabus structure 19

Syllabus Structure • Learning outcomes 20

Problem-solving skills 21

The five strands Strand 1: Statistics and Probability • • • Probability underpins learning in statistics Experiments and simulations Posing questions Designing investigations, collecting data Exploring patterns and relationships in data Making interpretations and communicating findings. 22

Strand 2: Geometry and Trigonometry • Synthetic geometry, co-ordinate geometry, trigonometry and transformation geometry. • Students encounter geometrical results through investigation and exploring pattern. • Idea of mathematical proof is developed • Students become familiar with formal proofs 23

Strand 3: Number • Students continue to make meaning of the operations of addition, subtraction, multiplication and division of whole and rational numbers. • These understandings are extended to complex numbers • Work on proof is extended; use of algebra and induction to show something is always true. • Proportionality, logarithms, indices 24

Strand 4: Algebra • Real-life problems as motivators for developing algebraic thinking • Patterns-based approach • Students move fluidly between different representations: equations, graphs and tables 25

Strand 5: Functions • Students develop an understanding of the relationship between algebra and functions • Connecting graphical and symbolic representations of functions • Calculus as the study of how things change • Using derivatives to solve problems • Integration as reverse of differentiation 26

Examinations Concerns with the ‘old’ exam: • Impact of exam on the learning experience • Choice of option sometimes resulted in omission of core units of study • Predictability • Chief Examiner reports – students unable to apply their knowledge in unfamiliar situations. 27

Chief Examiner reports: Candidates’ conceptual understanding of the mathematics they have studied is inferior to that which one would hope for and expect at this level [LC-HL]. Procedural competence continues to be adequate, any question that requires the candidates to display a good understanding of the concepts underlying these procedures causes unwarranted levels of difficulty (Chief Examiner’s Report 2005, page 72). 28

Chief Examiner reports: Syllabus Section: Functions & Calculus Candidates showed little perseverance, and, in general, were quick to abandon their work when they encountered difficulties Candidates recognised the relevance of the derivative and found it correctly. Nonetheless, candidates tend to be poor at expressing clear and correct conclusions from their work. A good number simply stopped after finding the derivative. 29

Structure and format of exam • Two papers • Two sections: • Concepts and skills • Applications (real-life and/or mathematical) • Students answer all questions • Changes to marking scheme 30

31

32

What’s happening in the classroom? • • • Constructivist approach to learning Inquiry based – students are discussing maths Comparing strategies, evaluating the effectiveness of strategies Discovering maths for themselves Building up mathematical concepts from the concrete to the abstract. Formative assessment to improve students understanding 33

What’s happening in the classroom? § Increased use of IT § Communities of practice 34

What’s happening in the classroom? https: //vimeo. com/49396809 35

What the teachers say “My methods have totally changed since Project Maths came in. ” “(In the past) It was book led – all about ticking of chapters with the result tested in the exam” “I have so much learning to do. I’m still not in the comfort zone with Strands 3, 4, 5” “In the long run it’s positive, the kids can see the relevance of maths to their lives. It was hard at the start but once everything settles down I wouldn’t go back” 36

A new type of maths student entering third level? • Increased understanding of maths • An ability to apply their mathematical knowledge to new and unfamiliar situations • A proficient problem-solver • An independent learner 37

Web links http: //www. ncca. ie/projectmaths Email: projectmaths@ncca. ie http: //www. projectmaths. ie [PMDT] http: //www. nce-mstl. ie http: //www. examinations. ie [SEC] 38