Fractions is an aspect of the primary mathematics curriculum with which some struggle. … .explore why Maybe …application is an issue ? – some may not see the need for them … manipulation of and calculation with fractions is abstract and difficult to grasp We need to support learning from Foundation Stage and throughout primary curriculum for mathematics (see Draft NC – cuurently there are learning objectives for each year group)
We are keeping registers and need to know reasons for absence. Punctuality is important too.
This, in my mind, is still appropriate...........
Early Years Maths Session 1
Primary PGCELearning and Teaching the CurriculumMathematics - Introduction
Irene Wooldridge email@example.comMaria McArdle Maria.firstname.lastname@example.orgSarah Cousins Sarah.email@example.comIf you are unable to attend a session,please inform your tutor.
Aims of session Part 1•To acknowledge that some peoplefind maths scary• To communicate the structure ofthe course•To communicate some key principlesembedded in the course
Success Criteria• I am feeling a bit more confident aboutthe mathematics element of the course• I am aware of the aspects of subjectknowledge I need to develop•I know of sources that can support thedevelopment of my subject knowledge forteaching mathematics
Our Maths Stories10/03/12 I Wooldridge & S Cousins
About the course -The challenge …• How children learn maths• What to teach Hmmmm… quarts• When to teach it and pint pots ?• How to teach it• How to assess it… in approx 20 hours.....+ Pause points
.........we can’t cover everything!Our aim is to develop a broader understanding, generalprinciples and approaches that you can apply in a widevariety of contexts as you develop your mathematicsteaching career.......The course• Seminars - looking at approaches to developingmathematical skills and understanding• School placement experience• Tasks M1 M2, & M3• And personal study ....You might want to do yourresearch project with a mathematical perspective
Shulman, 1986 ‘Those who understand: knowledgegrowth in teaching’, Educational Researcher, 15(2):4-14 Knowledge bases needed by teachers.Generic in nature:• general pedagogical knowledge;• knowledge of learners;• knowledge of the context;• knowledge of the purposes of teaching and learning
Content specific knowledge:• subject-matter knowledge• (facts, skills, concepts & processes and the links between them, awareness of purpose, knowledge of errors and misconceptions, theoretical underpinning and beliefs about mathematics)• pedagogical content knowledge• (the mathematical pedagogy which the teacher brings to the teaching situation and how teachers transform their knowledge into a form that makes it accessible to learners)• curriculum knowledge• (knowing what it is that children are expected to learn and knowledge of related resources)
Cockcroft Report (1982) Mathematics teaching at all levels should include opportunities for• exposition by the teacher;• discussion between teacher and pupils and between pupils themselves;• appropriate practical work;• consolidation and practice of fundamental skills and routines;• problem solving, including the application of mathematics to everyday situations;• investigational work.
Jerome Bruner’s 3 Modes of RepresentationThe Enactive Mode:- This involves representing ideas through undertaking some form of action. For example, manipulating physical objects.The Iconic Mode:- This involves representing ideas using pictures or images.The Symbolic Mode:- This involves representing ideas through language or symbols. ELPS helps
The Williams Review• The importance of scribbles and mark- making• Thinking made visible• The importance of having a skilled workforce to support children’s mathematical development10/03/12 I Wooldridge & S Cousins
Some of our key messages:• Maths isn’t just about doing sums, it’s about learning to think mathematically• Develop your own subject knowledge• Representation is key – find ways to communicate concepts through images• Make the connections between different bits of maths and previous learning• Talking is an important part of learning• Observe and listen to children explaining their maths• Solve problems with the children
Mathematics is everywhere10/03/12 I Wooldridge & S Cousins
Real resources10/03/12 I Wooldridge & S Cousins
Maths and routines10/03/12 I Wooldridge & S Cousins
Corporeal knowledge • Children need to experience learn with their whole bodies • Adults need to support children in the process • How can adults do support chidlren to develop their thinking?10/03/12 I Wooldridge & S Cousins
NCETM: www.ncetm.org.ukRegister with this site (email address andpassword required) and then start to explore it.Look at the self-evaluation tools. These will helpdevelop understanding of ways to teach differenttopics.
ATM - The Association of Teachers ofMathematicswww.atm.org.ukClick on Resources, then Gaps and Misconceptions.Information, ideas and resources relating tosubtraction, division, and fractions decimals andpercentages (FDP) – areas that teachers findharder to teach and children find harder to learn.
Core subject knowledge reference book:Understanding Mathematics for YoungChildren: A guide for the Foundation Stageand Lower Primary Teachers. (2008),Haylock, D. & Cockburn, A.Read relevant sections BEFORE each week’sseminarLook at relevant sections when you areplanning your teaching in school
Follow-up maths subject knowledge audit: (‘Clouds; Links sheet’ introduced at start ofcourse )http://www.cimt.plymouth.ac.uk• Click on Resources, Tests and Audits,Mathematics Attainment Test, Pick A Test AtRandom• Make sure you are working in full screen• Enjoy!
QTS Skills testDo this earlier in the year in order to get it outof the way. For practice material go tohttp://www.tda.gov.uk/skillstests/numeracy/practicematerials.aspxPeople who find this test hard usually find thetimed mental arithmetic section hard – it’s oftenabout finding easy ways to do sums that lookhard.For example you could do 25 x 88 by first doing100 x 88 (easy!) and then dividing by 4 (also easywith these numbers)
Thank you for participating in the session Sarah.Cousins@beds.ac.uk