Resource 1

Numeracy Energiser Trainer Notes
Session 2: Problem solving, learning and assessment
Session 2
learning and
Consider what it means to be
mathematically accomplished
Explore aspects of own
mathematical thinking
Develop problem solving
Consider the implications of the
above for assessing learners’
aptitudes and knowledge
(particularly at initial
Consider ways of conducting
initial assessment appropriate
for a learner centred, lifelong
learning approach
Introduction to the session
Golden zeros exercise
Billiard table exercise
Problem solving strategies
Purposes of assessment
Approaches to assessment
Summary and questions
S2H1 Billiard Table
S2H2 Making
S2H3 Are you stuck?
S2H4 Top Tip
Energiser Session 2
Trainer Notes
Flipchart and pens
Flipchart paper
Squared and graph
Pencil, rubber, ruler for
each participant
Trainer Notes
Session 2
120 minutes
Problem solving, learning and assessment
By the end of this activity, participants will have:
 explored their own mathematical thinking and their problem solving strategies
 considered the purposes of assessment and a variety of methods for assessing learners’
knowledge, skills and understanding.
Whole group
Yourself as a Problem Solver
85 minutes
Introduction (5 min)
S2PP 1 - 2
The exercises will encourage you to reflect on yourself as a problem solver and investigator.
You don’t need to be a mathematician.
Concentrate on how you tackle the exercises rather than on getting the answer.
Being stuck is part of the process in problem solving.
Golden Zeros energiser
Work individually (5min)
Share methods and progress in pairs (5min)
PP 3
Whole group (10 min)
Volunteers to demonstrate their methods on flipchart
One method on PowerPoint if not already covered
Further questions?
PP 4
PP 5
Pairs (5 min)
Discuss your feelings and your perception of other people’s feelings
PP 2
Whole group (20 min)
Learning points from the activity?
different methods get to the same answer
persistence required
false trails are part of the process
collaboration may or may not be helpful for individuals
emotional response can be strong – positive and negative
Mathematical Behaviours
Session 2 Trainer notes
PP 6
Billiard Investigation
PP 7
Introduction (5 min)
This is an investigation with no clear answers
What kind of things might you investigate?
Small group and individual (25 min)
You have 25 minutes - take a break when you need to.
Work individually or with others to start with
Share your findings and compare work
Whole group (15 min)
 What questions did you ask in exploring this task?
 What mathematical behaviours did you exhibit?
 What emotional responses did you have?
 What would learners gain from this kind of task?
Summary PowerPoint and points from discussion
Whole group
Making Assessment Meaningful
PP 2 & 6
35 minutes
Introduction (5min)
PP 8 - 13
Assessment is a crucial part of learning and happens at all stages of learning:
 as part of negotiating a learning plan
 as part of learning and teaching to provide feedback for both tutor and learner
 at the end of a programme of learning to recognise what learning has taken place.
Fours (15 min)
Flipchart a variety of ways of learning about your learners.
Refer to S2H3 as a prompt to the kind of things you may wish to assess
or make your own list to correspond with the learners you are working with.
For each item on your list suggest an assessment method or activity.
Whole group (15 min)
Points may include:
 find out about mathematical behaviour as well as calculation skills
 use investigations and problem solving as well as checklists and multiple choice
 self assessment by learner
 discussion and worksheets
 group as well as individual activities
‘Assessment should be challenging for learners, involve creativity, strategic thinking and problem –
solving,’ Adult Literacy and Numeracy Curriculum Framework for Scotland, p 23. Refer to Pages 21 24 on assessment in the Currriculum Framework for own reading.
Questions and Close
Session 2 Trainer notes
Session 2
Energiser Session 2 PowerPoint
Computer and data projector
Flipchart, pens, blutak
Selection of unibricks on each table
Graph and squared paper
Pencil, rubber, ruler and calculator for each participant
Adult Literacy and Numeracy Curriculum Framework for Scotland
Session 2 Handouts
Are you stuck?
The Billiard Table Investigation
Making Assessment Meaningful
Top Tip Crossword
Session 2 Trainer notes