Fís

Fogh

laim

Forb

airt

www.pdst.ie© PDST 2016

This work is made available under the terms of the Creative Commons Attribution Share Alike 3.0 Licence http://creativecommons.org/licenses/by-sa/3.0/ie/. You may use and re-use this material (not including images and logos) free of charge in any format or medium, under the terms of the Creative Commons Attribution Share Alike Licence.

ww

w.p

dst

.ie

Problem-solvingWorkshop 2

www.pdst.ie

ww

w.p

dst.

ieKey Messages for Problem-solving

Classroom climate and choice of task can enable all pupils to achieve success

Effective questioning and classroom discussion develops pupils’ higher order thinking skills

Using a variety of strategies is essential for problem-solving

ww

w.p

dst

.ieObjectives

Teachers will experience

how maths language is developed in context and facilitated through productive classroom discussion

how pupils can grow in confidence and be enabled to utilise maths language to create their own questions

how a variety of approaches and strategies is drawn upon to get started and progress through problem-solving

ww

w.p

dst

.ie

Same / Different

25 351

ww

w.p

dst.

ie

Feedback

• How did classroom climate and LTHC task enable all pupils to participate?

• How did facilitating discussion work?

• What strategies did pupils use?

ww

w.p

dst.

ieClassroom

ClimateHOTS

Success

Knowledge is shared

Mistakes are valued

Struggle is productive

Strategies

ww

w.p

dst

.ie

ww

w.p

dst

.ie

Language plays as important a role in mathematical learning as in other subjects

(Schleppegrell, 2010)

Opportunities to improve knowledge and skills of specific math language include use of

clear language by the teacher, meaningful practice in “every-day situations,” and

continuous verification through informal observations.

(Toll and Van Luit, 2014)

ww

w.p

dst

.ie

Headline Stories

• I have 9 centStatement

• Conor bought 12 rolls of yellow wrapping paper and 9 rolls of brown wrapping paper. How many metres of wrapping paper did Conor buy in all?

Missing information

• Sam picked 8 plums and Mary picked 3 plums from a tree. Melanie picked 6 apples from a tree. How many plums were picked altogether?

Extra information

• Omar had €6. Then he saved €5 from his allowance and spent €3 on a comic book and €3 on a puzzle. How much money does Omar have left?

New questions

ww

w.p

dst

.ie

ww

w.p

dst

.ie

Solver - recorder

Tell me more

Are you

sure?

How do you know?

ww

w.p

dst

.ie

• Draw a diagram

• Use equipment

• Break it down

• Solve simpler

version

• Evaluate• Generalise• Verify• Prove

• Look for a pattern• Make a conjecture• Make a chart / table• Trial and error• Work backwards

ww

w.p

dst

.ie

Rainbow Activity

Sports Fans

Autumn Antics

Chasing Cars

Andy’s Marbles

ww

w.p

dst.

ie

Sports Fans

A survey of 4th class showed that ⅚ of the pupils play Gaelic football. ½ of the pupils

who play football also play hurling.

What fraction of the pupils play both sports?What strategies did you use?

ww

w.p

dst.

ie

Autumn AnticsIt was ten to eleven in the morning when Sally began raking the yard. She raked all the leaves

into piles and stuffed them into bags. She finished at twenty to three in the afternoon.

How long did it take Sally to rake the yard?What strategies did you use?

ww

w.p

dst.

ie

Chasing CarsHow many hours will a car travelling at 65 kilometres per hour take to catch up with a car traveling at 55 kilometres per

hour if the slower car starts one hour before the faster car?

What strategies did you use?

ww

w.p

dst

.ie

Andy’s Marbles

Andy was walking with Sam when his bag of marbles burst.

• ⅓ of the marbles rolled down the road.

• ⅙ of all the marbles fell into the gutter.

• Andy and Sam picked up all they could but ½ of the remaining marbles were picked up by Tom who ran away.

• Andy counted all the marbles he and Sam had rescued.

• He gave ⅓ of these to Sam for helping him and put the remaining 14 into his pocket.

How many marbles were there in Andy's bag before it burst?

What fraction of the total bag had he lost or given away?

https://nrich.maths.org/2421

ww

w.p

dst.

ieProblem-solving

Key LearningHOTS

Success

Knowledge is shared

Mistakes are valued

Struggle is productive

Strategies• Draw a diagram• Use equipment• Break it down• Solve simpler

version

• Look for a pattern• Make a conjecture• Make a chart / table• Trial and error• Work backwards

• Evaluate• Generalise• Verify• Prove

ww

w.p

dst

.ie

Resources

Assessment

Differentiation

Key Questions

Opportunities for sharing learning

Focus of the lesson

ww

w.p

ds

t.ie

Elevator Pitch

What will you take from today to inform problem-solving in your school?

School-Self EvaluationTeaching & Learning Framework; 6 Step SSE Process; gathering, collating & analysing relevant data; implementing the SIP for

literacy, numeracy and any other area of teaching & learning.

Health and Wellbeing➢ SPHE including Child Protection and Stay Safe➢ Relationships and Sexuality Education (RSE)➢Active Learning Methodologies ➢Anti Bullying-Procedures and Policy, Awareness

Raising, Prevention and Intervention Strategies➢ PE➢ Wellbeing for teachers

PDST Websites

➢www.pdst.ie➢pdsttechnologyineducation.ie➢scoilnet.ie (portal for resources)➢teachercpd.ie (on-line courses)➢ollscoil.net (ITE students awards)

Overview of PDST Primary Supports for Leading Learning in the 21st Century

www.pdst.ie/schoolsupport

Models of support:in-school support (in-class modeling, meeting principal/groups of teachers, Croke Park hrs), seminars, workshops, clusters

Literacy SSE & strategies for improving

oral language, writing, reading and the use of broadcast /digital media.

NumeracySSE & strategies for improving

numeracy. Supporting the development of Mathematical

thinking.

GaeilgeTacaíocht chun Curaclam na Gaeilge a chur i

bhfeidhm i Scoileanna T1&T2, Féinmheastóireacht Scoile, chomh maith le

tacaíocht lán Ghaeilge a sholáthar do Ghaelscoileanna agus scoileanna sa

Ghaeltacht.

Integrating ICT - Primary➢Active Learning Methodologies- Key methodologies of the primary curriculum through the effective use of ICT.➢Literacy & Numeracy – Creating, developing and using ICT to create teaching resources in all areas of primary literacy and numeracy.➢SSE – Online tools for gathering, collating & analysing relevant data.➢eAssessment & ePortfolios – Assessment of / for learning with ICT.➢ePlanning & Collaboration – Google Apps for Education.➢Tablet Technology Integration – Pedagogy, Curriculum & SEN ➢Virtual Learning Environments (VLEs) – Google Classroom, Edmodo

PDST Leadership ProgrammesMisneach.....New PrincipalsTánaiste.......New Deputy PrincipalsTóraíocht.....Aspiring Leaders accredited by

Maynooth UniversityForbairt .......Experienced Principals & ALNsSpreagadh...NAPD & PDST collaboration