1. Project Maths – information update NCCA Project Maths Team

2. 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

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

4. 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

5. 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

6. 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

7. 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

8. 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
problem-solving, with emphasis in applications
using ICT appropriately in maths learning
SET
business, finance
social sciences

9. 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 and the knowledge economy

10. Senior Cycle Key Skills Framework

11. 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)

12. 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

13. 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

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

15. 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

16. 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

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

18. 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 (JC)
In June 2017, full cohort with experience of revised syllabuses all through post- primary education

19. Syllabus structure

20. Syllabus Structure
Learning outcomes

21. Problem-solving skills

22. 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.

23. 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

24. 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

25. 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

26. 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

27. 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.

28. 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).

29. 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.

30. 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

33. 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

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

35. What’s happening in the classroom?

36. 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”

37. 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

38. Web links
[PMDT] [SEC]