Assessment & Feedback in Mathematics Colleen Young

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Assessment & Feedback
in Mathematics
Colleen Young

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Contents
3 16 32 39 46
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50 54 71 74 76
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Assessmentfor
Learning
Relationships LearningActivities Questions RetrievalPractice
Homework Marking Research Assessmentfor
Learning-Summary
FurtherReading

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Assessment for Learning
Assessment for learning, also known as formative assessment,
is about:
checking learning and giving
constructive feedback that informs
subsequent learning.

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The Assessment Reform Group (ARG) defines it as:
“…the process of seeking and
interpreting evidence for use by
learners and their teachers to decide
where the learners are in their learning,
where they need to go, and how best to
get there.” (ARG, 2002).

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Research (Hattie, 2002) shows that
giving learners feedback on their
learning errors and omissions, and
getting them to correct them or work
towards improving future work, is one
of the most significant methods of
improving their performance.

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Constructive feedback also has a
profound influence on learners’
motivation and self-esteem
(Black and Wiliam, 1999).

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Is the Feedback You’re Giving
Students Helping or Hindering?
(Dylan Wiliam, 2014).

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Is the Feedback You’re Giving Students
Helping or Hindering?
What the Studies Say
In their review of feedback studies conducted
between 1905 and 1995, Kluger and DeNisi
(1996) found that in 38% of well-designed
studies, feedback actually made performance
worse—one of the most counterintuitive
results in all of psychology.

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If there’s a single principle teachers need
to digest about classroom feedback, it’s
this: The only thing that matters is what
students do with it. No matter how well
the feedback is designed, if students do
not use the feedback to move their own
learning forward, it’s a waste of time.
(Wiliam, 2014).

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Add to that concept a second related
principle: Feedback should be more work
for the student than it is for the
teacher. Teachers who internalize and
practice feedback based on these
precepts will be well on their way to
teaching that improves learning.
(Wiliam, 2014).

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Assessment for Learning is not about
assessing quantity rather than quality
marking and grading, rather than
providing guidance for improvement
comparing individual learners
social and management purposes rather
than support for learning.

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Assessment and feedback is built in to
all successful teaching and learning
activities.

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“An assessment activity can help learning if it provides
information to be used as feedback by teachers, and by their
pupils in assessing themselves and each other, to modify the
teaching and learning activities in which they are engaged.”
Black and Wiliam 2002
Return to
contents

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What Makes Great Teaching?
1. (Pedagogical) content knowledge
As well as a strong understanding of the
material being taught, teachers must also
understand the ways students think about
the content, be able to evaluate the
thinking behind students’ own methods,
and identify students’ common
misconceptions.
What makes great teaching?
Review of the underpinning research.
Robert Coe, Cesare Aloisi, Steve Higgins and Lee Elliot Major October 2014

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2. Quality of instruction
Includes elements such as effective questioning
and use of assessment by teachers. Specific
practices, like reviewing previous learning,
providing model responses for students, giving
adequate time for practice to embed skills
securely and progressively introducing new
learning (scaffolding) are also elements of high
quality instruction.

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Student / Teacher
relationships
Relationships

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However, the thing that really matters in
feedback is the relationship between
the student and the teacher.
When teachers know their students
well, they know when to push and when
to back off.

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Moreover, if students don’t believe their
teachers know what they’re talking
about or don’t have the students’ best
interests at heart, they won’t invest the
time to process and put to work the
feedback teachers give them.

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Ultimately, when you know your
students and your students trust you,
you can ignore all the “rules” of
feedback.
Without that relationship, all the
research in the world won’t matter.
(Wiliam, 2014).

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Classroom climate (Moderate evidence
of impact on student outcomes)
“Covers quality of interactions between
teachers and students, and teacher
expectations.”
What makes great teaching?
Review of the underpinning research.
Robert Coe, Cesare Aloisi, Steve Higgins and Lee Elliot Major October 2014

Should be passionate and enthusiastic.
Patient.
Understanding.
Approachable.
Firm but kind.
Someone you can feel comfortable with.
Recognises achievements.
Genuinely caring about the students.
Someone who knows who you are.
Good Teachers...

Someone who you know won’t judge you.
Expect the best out of your students, but
don’t be angry if they don’t always achieve it.
Check with students individually if they are
stuck.
They should be able to cater to all abilities.
Good Teachers...

Lets you talk about the work in class.
Praises students.
Good Teachers...
More on good teachers…

A teacher who provides the student with
the opportunity to see what they need to
revise. Regular tests and quizzes do this.
Tests that don’t have further impact on
levels / grades. Just there for you to know
what you don’t know.
What helps students learn?

Low stakes tests are really good because
there is not much pressure and at the end
of them I can see how I’m doing and what
I need to improve on for later formal tests.
Going through and marking tests /
homework.

Practice exam papers.
Mark schemes (train them in marking!)
Remember that we have a lot of subjects.
Post tests (test after a formal test with
questions the students found the most
difficult)

Diagrams and other visual aids.
Online resources.
Worked examples. Good notes
Detailed explanations.
Regular checking of answers.

In the classroom–an example
Year 11
“5-a-day”
Following a
mock
examination I
used these
regularly

”Five-a-day” Year 11 Responses
Students completed a short questionnaire where they
rated the usefulness of the 5-a-day resources.

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Day to activities in
the classroomLearning
activities

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Bob’shomework
Markthis,correctingwronganswersandtellinghimwhyhe’srightorwrong
1) Simplify the following
ratios:
a) 4g:4kg
b) 13g:52g
c) 60cm:10m
d) 150ml:50ml
2) Share £42 between Henry and
Rhiannon in the ratio 3:4
3)If Jack shares some sweets with
Charlotte in the ratio 3:2 and Charlotte
gets 18, how many does Jack get?
4)Grandma’s cake recipe
3 eggs
165g flour
165g butter
165g sugar
I’ve got smaller cake tins, so I’m going
to use 2 eggs. How much of the other
ingredients do I need?
÷4 1:1
÷13 1:4
÷10 6:1
÷10 15:5
3+4 = 7
Henry gets 7x3 = 21
Rhiannon gets 7x4 = 28
18÷3=6
Jack gets 6x2=12
165g÷3 = 55g
2x55g = 110g
110g of each of the other
ingredients
Spot the Mistake

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Bob’shomework
Markthis,correctingwronganswersandtellinghimwhyhe’srightorwrong
1) Simplify the following
ratios:
a) 4g:4kg
b) 13g:52g
c) 60cm:10m
d) 150ml:50ml
2) Share £42 between Henry and
Rhiannon in the ratio 3:4
3)If Jack shares some sweets with
Charlotte in the ratio 3:2 and Charlotte
gets 18, how many does Jack get?
4)Grandma’s cake recipe
3 eggs
165g flour
165g butter
165g sugar
I’ve got smaller cake tins, so I’m going
to use 2 eggs. How much of the other
ingredients do I need?
÷4 1:1
÷13 1:4
÷10 6:1
÷10 15:5
3+4 = 7
Henry gets 7x3 = 21
Rhiannon gets 7x4 = 28
18÷3=6
Jack gets 6x2=12
165g÷3 = 55g
2x55g = 110g
110g of each of the other
ingredients
Units are
 different
1:1000

Units are
 different
3:50
 Not finished
3:1



There are 7 shares. Each share is worth £42÷7=£6
Henry gets 3x£6=£18
Rhiannon gets 4x£6=£24
Jack to
Charlotte is 3:2,
so Charlotte gets
2 shares
each worth
18÷2=9
So Jack gets 3x9
= 27


Start with
weights for 3
eggs so divide to
get weights for 1
egg then multiply
to get weights for
2 eggs
Return to
contents

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Revision Activities The resource above is from Tom Riley on TES, exam questions
and solutions but also with clues! Students match up the clues to a collection of
exam questions on 10 higher topics, then use the clues to answer the questions.

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Questions to get your
students thinking and
exercises to secure
skills
Questions

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Questions
We should plan for questions carefully in
our lessons, we need questions to really
make our students think and we need
questions to help them practise skills.
References
Questions worth asking – the Brighton
& Hove Assessment for Learning Project
Assessment without Levels, note Daisy
Christodoulou on using multiple choice
questions.
Diagnostic Questions

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Revision Activities Here’s the diagram – what’s the question?

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Algebra Snippetts What’s the question? Discuss question paper terminology

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The practice of
retrieving
information from
memory.
Retrieval
Practice

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Students need to recall information and
the evidence suggests that testing is a
better way of doing this than simply
rereading material, a method often
favoured by students. Mini-tests are low
stakes ‘Self-checks’ ,a learning tool, not
something to be stressed by.
Aristotle apparently wrote
“exercise in repeatedly recalling a thing
strengthens the memory.”

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How do we make it
meaningful?
How do we make sure
we build in time for
review and to act on
feedback?
Homework
Return to
contents

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Homework
some ideas…
Homework does not necessarily have to
be on the topic you are currently
studying and can offer the chance to
review previous topics or look ahead to
a topic you will be studying.
Some alternatives to the textbook:
Set some questions with solutions and
mark schemes
Students write questions on a given
topic and also provide solutions and a
mark scheme. In class their peers can
try the questions. This offers the chance
for some excellent class discussion on
why students think a question is a good
question, the difficulty of a question and
how it should be marked.

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Homework
some ideas…
Homework does not necessarily have to
be on the topic you are currently
studying and can offer the chance to
review previous topics or look ahead to
a topic you will be studying.
Ask them to write some diagnostic
questions with multiple choice answers.
Ask them to provide the question with
four possible answers. They should
indicate which answer is correct and
explain their reasoning behind the
options they have given.

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Homework
some ideas…
Revise and Recall
Help students recall material by setting
a homework to review a topic or topics
and then give a mini-test in class. I tend
to call them ‘Self-checks’ for the
students to emphasize the idea they are
just checking what they know and what
they may need further help with.
Do two!
Give two fairly / very similar homeworks
in a row, the second being a chance to
act on all the fabulous feedback you
gave for the first attempt!

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How do we make it
meaningful?Marking

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Main findings
The quality of existing evidence
focused specifically on written
marking is low.
April 2016

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Some findings do, however,
emerge from the evidence
Careless mistakes should be marked
differently to errors resulting from
misunderstanding. The latter may be
best addressed by providing hints or
questions which lead pupils to
underlying principles; the former by
simply marking the mistake as incorrect,
without giving the right answer.
No matter how well the feedback is
designed, if students do not use the
feedback to move their own learning
forward, it’s a waste of time.

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Awarding grades for every piece of work
may reduce the impact of marking,
particularly if pupils become
preoccupied with grades at the expense
of a consideration of teachers’ formative
comments.

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The use of targets to make marking as
specific and actionable as possible is
likely to increase pupil progress
Pupils are unlikely to benefit from
marking unless some time is set aside to
enable pupils to consider and respond
to marking
No matter how well the feedback is
designed, if students do not use the
feedback to move their own learning
forward, it’s a waste of time.

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Some forms of marking, including
acknowledgement marking, are unlikely
to enhance pupil progress.
A mantra might be that schools should
mark less in terms of the number of
pieces of work marked, but mark better.
Return to
contents

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The5MinuteMarking/FeedbackPlanThe big picture?
(The purpose of marking for this work?)
Key marking
points to share
with students?
Common Errors?!
Formative marking:
Re-teach?
Summative marking:
….print and scribble your way to focus on helping students to progress!
Grading system:
Directed Improvement
and Reflection Time?
What?
When?
How?
Student response to
feedback required?
Peer/Self assessment
opportunities?
to improve student learning
What is mastery for this work?
Follow up
Intervention?
Below?
On?
Above?
Plan for marking#5 minute plan series, Ross Morrison McGill, @TeacherToolkit

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What do ou tell
parents about
students’
engagement with
learning?
Reporting

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The best learners at Newstead
have these qualities
growth mindset, resilient,
curious, proactive,
imaginative, creative, innovative,
perseverance, determined

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Research in 100
words
Chris Moyse
Research

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Summary
Assessment
For
Learning

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Blogs – Learning & Teaching
As always – these are my favourites (see Emily Nussbaum writing for The New Yorker
on why she hates Top Ten Lists!); blogs I find thought provoking that I believe will
be of interest to any teacher / senior leader. It’s a short list, I read from many sources
but these are the blogs that I always check when I am alerted to a post.
The Learning Spy by David Didau. You can search for posts by category at the foot
of the blog. Every time I think I have something sorted out, David comes along and
challenges my thinking!
headguruteacher by Tom Sherrington. Note the top posts and pages, also the
categories.
@Leading Learner by Stephen Tierney. Note the Top Posts and (further down the
page) Categories
@TeacherToolkit by Ross Morrison McGill who is the author of the 5 minute
lesson plan you will find many references to on my own blog. Ross has a very clear
index here.
Class Teaching by Shaun Allison and the chosen blog of the week also
johntomsett by, unsurprisingly – John Tomsett!
Hunting English by Alex Quigly
Pragmatic Education by Joe Kirby
Thoughts on managing variability by Kev Lister
Further Reading

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Colleen Young
https://twitter.com/ColleenYoung
Mathematics, Learning & Technology
Mathematics for Students

Mathematics for Students Mathematics, Learning and Technology
Colleen Young

Assessment & Feedback in Mathematics Colleen Young

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