1 Assessment for Learning Assessment for Learning Maths
Jan 13, 2016
1 Assessment for Learning
Assessment for Learning
Maths
2 Assessment for Learning
I taught my dog to whistle
I can’t hear him whistle
I said that I’d taught him – I didn’t say that he’d learned
how to
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Estyn Inspection Comments… assessment is used
consistently … However, not all assessments are
rigorously evaluated, monitored or used to direct
pupils’ work.
… the quality of feedback is unsatisfactory. Much of the
feedback focuses on curriculum coverage, rather than what pupils achieve.
Although teachers assess pupils’ standards, such
assessments are not used effectively to set targets for individuals and groups; they do not help pupils to achieve
higher standards..
All work is regularly marked. Positive comments are
added on occasions. Few suggestions, however, are
made to show pupils how to improve their work & to
raise their own standard of achievement..
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Inspection findings
“Maths teachers are not always using effective strategies to ensure that assessment improves the quality of learning. Much assessment is summative in nature.”
“Many maths departments have developed good test materials that are focused,accurately marked and levelled,and used to record progress over the key stage.”
“Some maths departments have developed strategies that extend the use of assessment. These approaches to assessment have been identified as a key factor in raising standards of teaching and learning (and attainment) in these schools.”
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“ Overall the purpose of assessment is to improve standards, not merely measure them”
Ofsted “Good assessment in secondary schools” March 2003
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Moving On …
explore number; calculate accurately and efficiently, selecting mental strategies where appropriate; deal with measurement accurately; handle and interpret data; reason mathematically, making predictions and
asking questions; adopt a range of strategies for solving problems; communicate mathematically and present their
work for different audiences and purposes.
Aiming for pupils to …
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How is assessment used ?
Assessment of learning (summative assessment)
e.g. teachers use evidence collected from an end-of-unit test to make a judgement about pupils’ performance against national standards.
Assessment for learning (formative assessment)
e.g. teachers use evidence from testing to decide what pupils achieved against their targets and plan for the next step.
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Although many teachers mark pupils’ work regularly and record these marks, this information is not used to influence teaching and learning.
Pupils often do not understand the meaning of marks or grades. In these circumstances marking can actually be de-motivating.
Assessment issues in schools
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Assessment for LearningInvolves: Gathering and interpreting evidence about pupils’ learning
Pupils & their teachers using that evidence to decide where pupils are, where they are going and how to take the next steps
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1998 : Inside the Black BoxEvidence suggested: Improving formative assessment raised standards,
particularly among low attainers
Existing assessment methods were not effective in promoting good learning
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Assessment was effective when:
It was embedded in the planning
Teachers used a range of assessment techniques
Teachers made use of manageable systems for recording pupil progress
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1999 : Beyond the Black Box
Improving learning depended on: The provision of effective feedback Pupils actively involved in learning Adjusting teaching according to assessment
results A recognition of the profound influence of
assessment on motivation and self esteem The need for pupils to assess themselves and
understand how to improve
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Inhibiting factors A tendency to assess quantity &
presentation rather than quality of learning
Attention to marks & grades Comparing pupils with each other Feedback which is often social/managerial Teachers not knowing their pupils’ needs
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A for L in practice: Is an essential part of teaching & learning Involves sharing learning goals with pupils Aims to help pupils know what they are
aiming for Involves pupils in self assessment Provides feedback Every pupil can improve Involves reviewing and reflecting
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2002 :
Working inside the black box
Questioning Marking Self & peer assessment The formative use of summative tests
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Strategies
Teachers: Planned their questions Allowed an appropriate wait time Gave feedback intended to cause thinking Ensured lesson time for self and peer
evaluation
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Elements of AfL Formative use of summative assessment
Shared learning objectives and expected outcomes
Effective questioning
Effective feedback (oral and written)
Self and peer assessment
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5 Key Principles of Learning
1. Start from where the learner is2. Students must be active in the
process3. Students need to talk about their
ideas4. Students must understand the
learning intention5. Feedback should tell pupils how to
improve
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Formative use ofSummative testing
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Formative use of summative tests
Having end-of-unit tests analysed by HoD/KS3 Co-ordinator/colleagues to give feedback on any significant weaknesses in pupils’ response to questions.
Returning marked end-of-unit tests to pupils, along with mark schemes, to help them see what they understand, where they have made errors and, most importantly, what they need to do next to improve.
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Formative use of summative tests
Using end-of-unit tests earlier in the unit, perhaps two thirds of the way through, which allows time for significant weaknesses in learning to be dealt with.
Use ACCAC’s “Implication for Teaching and Learning” reports & GCSE Examiners’ Reports to identify national strengths and weaknesses shown by the tests at the end of KS3 and 4
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Sharing Objectives and Success Criteria
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Draw a house
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“If you don’t know where you are going” said Alice
“then how will you know when you get there”
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“How will pupils know what a ‘good’ piece of work looks like?”
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“Learning Objective” …
The LEARNING OBJECTIVE (or ‘intention’) is what
teachers hope children will know, understand, or be able to do by the end of the lesson or
set of lessons.
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Two groups of ‘objectives’ those objectives which focus on what pupils
will learn. e.g. “we will learn how to calculate a side of a
right-angled triangle, given the lengths of the other two sides.”
those objectives which focus on how the learning will take place.
e.g. “we will use a spreadsheet to investigate the purchases required for maximum profit.”
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… these are most effective if they are in “pupil speak”
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Objectives are statements of what pupils are to learn rather than what activities they will do.
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Pupils’ Confusion with Objectives
Pupils may not know what is meant by the language in which they are written
e.g. to understand quadratic factorisation e.g. to understand units Objectives or titles written on the board may
‘give the game away’ e.g. Today we are going to find out…. e.g. We are going to do an investigation to
…. Pupils may forget the objectives during the
course of the lesson
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Success Criteria
Success criteria for pupils should make clear :
What pupils need to say, do or produce to demonstrate achievement of lesson objectives
What evidence the teacher is looking for when assessing a pupils’ progress during the lesson and when marking work
What is expected of them so that they can assess their own and each other’s progress (self and peer assessment)
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Another way of thinking …
‘How will I know that you have learnt how to ………….…………………
(refer to learning intention)
… What will I see ?’
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Strategies for writing objectives and sharing success criteria
WALT WILF and TIBS
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Strategies for Sharing Objectives
WALT “We Are Learning To …”
Shirley Clarke 2001 ‘ Unlocking Formative
Assessment’
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Strategies for Sharing Objectives
WALT “We Are Learning To …”
WILF “What I’m Looking For …”
Shirley Clarke 2001 ‘ Unlocking Formative
Assessment’
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Strategies for Sharing Objectives
WALT “We Are Learning To …”
WILF “What I’m Looking For …”
TIBS “This Is Because …”or ‘ASIDE’ (helps pupils understand the purpose of the activity, and put
the learning into context)
Shirley Clarke 2001 ‘ Unlocking Formative
Assessment’
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Teaching objectives are from the NC Programmes of Study
WALT
Learning objectives are what you intend the pupils to achieve in lessons. They are best written and explained in pupil friendly language.
TIBS / ASIDE
The big picture helps pupils identify the purpose behind their learning and to generalise and develop transferable skills
WILF
Success criteria help both teachers and pupils be clear about what would need to be demonstrated in order to achieve the learning objective.
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Alternative forms “We are learning how to …” “We’ll know we’ve achieved this because …” OR “Remember to …”
… instead of WALT & WILF
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Examples “We are learning HOW to measure accurately to
the nearest cm, & record our answers” “Remember to :
Start from zeroUse the rounding rulesRecord the unit of measurement”
Context : Measuring classroom objects Jigsaw piece : Comparing lengths of objects
Drawing lines accurately
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Alternative form Learning intention :
“To be able to make predictions & use a spreadsheet to check them”
Success criteria :“That you make a prediction, use a spreadsheet, using formulae to calculate totals in cells, and use the graphs tool to create a graph to help you answer the problem”
Context : “Finding a maximum area of a rectangle, given its perimeter.”
Aside : GCSE Coursework will require you to test a hypothesis
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Sharing Assessment Criteria
e.g. GCSE coursework criteria
criteria need to be simplified into ‘pupil-speak’
pupils need to see good practice by being given examples of high quality work by other pupils
pupils need to see the criteria applied to exemplar coursework
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Assessing Objectives & Success Criteria
Will pupils understand the
language in which the
objective is written ?
Will pupils understand what
they are expected to
write, talk about or demonstrate to achieve the
objective?
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Class Concept Web
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During the week/unit
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During the week/unit
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During the week/unit
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During the week/unit
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During the week/unit
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During the week/unit
abc
abc
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Ideas
keep to one or two objectives in any one lesson record objectives where pupils can easily see them objectives include what is going to be taught
and/or how it will be taught to aid learning at the end of the lesson ask ‘What have you
learned today?’ and other questions which refer pupils back to the objectives & success criteria.
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Questioning
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What is 3 add 7? How many days are there in a week? How many centimetres are there in a metre? Is 31 a prime number?
Recalling facts
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Tell me two numbers that have a difference of 12. What unit would you choose to measure the width of the table? What are the factors of 42? 8 x 6 = 48, so what is 8 x 60? … 16 x 6?
Applying facts
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Estimate the number of words on this page. If we did our survey again on Friday, how likely is it that our graph would be the same? Roughly, what is 51 times 38? How many crosses in the next diagram?
+ ++ +++ … and the next? … in the tenth? … hundredth?
Hypothesising or predicting
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How might we count this pile of sticks? How could you subtract 37 from 82? How could we test a number to see if it is divisible by 6? How could we find the 20th triangular number? Are there other ways of doing it?
Designing and comparing procedures
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So what does that tell us about numbers that end in 5 or 0? What does the graph tell us about the most common shoe size? So what can we say about the sum of the angles in a triangle?
Interpreting results
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The seven coins in my purse total 23p. What could they be? In how many different ways can four children sit at a round table? Why is the sum of two odd numbers always even?
Applying reasoning
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Odd One Out
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Sometimes, always, never?
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Questions to ponder
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Sum and Product
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Questioning should … not just supply knowledge provide a model of an experienced thinker set up the thinking agenda by asking
open questions that demand children to think
get progressively more thoughtful and probing
encourage pupils to make connections and distinctions
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It is important to consider before a lesson:
what questions will be asked when questions will be asked how the questions will be asked
Thinking about Questions
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Thinking about Questions
1. Are you clear about the purpose of asking the questions ?
2. Do you limit how long you spend asking questions at the start of the lesson ?
3. What strategies do you use to ensure that everybody is engaged during the question-and-answer time ?
4. When summarising what has been learned have you involved some pupils to provide feedback to the class?
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5. Have you considered how you ask the question? Is your body language, including hand gestures, supportive and encouraging?
6. Do you provide time for pupils to think?
7. During practical/group work, do you use questions to challenge pupils at a different level of understanding ?
8. Do you use questions to check pupils’ understanding and use the information to adjust your planning for the next lesson ?
Thinking about Questions
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Bloom’s Taxonomy of Questioning
Higher Order
Middle Order
Lower Order
EVALUATION
SYNTHESIS
ANALYSIS
APPLICATION
KNOWLEDGE COMPREHENSION
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Useful words to use for “deepening the curriculum” :
Draw State Record Recognise Identify
Sort Describe Select PresentLocate
information from text
Decide Discuss Define Classify Explain how
Devise Calculate Interpret Construct Clarify
Plan Predict Conclude SolveDetermine
the key points from ….
FormulateExplain
why
Use the pattern to
….Recognise
Explain the difference between …
Link/make connections
with
Use the idea of ….
to ….
Use the model of …
to ….
Provide evidence
for ….
Evaluate for evidence of
….
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Quality Questions
Quality questioning often includes the following characteristics:
it probes more deeply into pupils’ understanding, using a follow-up question with the same pupil
it requires pupils to think before answering it is frequently more open in nature, permitting a
range of correct responses it uses questions beginning with stems such as…. Why….? How come…….?
How do ……….? What would happen if ………?
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Effective questions Why is … an example of …? How can we be sure that …? What is the same & what is different about …? Is it ever/always true/false that …? Why do …, …, … all give the same answer? How do you …? How would you explain …? What does that tell us about …? What is wrong with …? Why is … true?
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The Effect of Changing a Question
Instead of asking :
“Is 7 a prime number?”
what would be the effect of asking:
“Why is 7 an example of a prime number?”
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Which fraction is the smallest?
a) 16
, b) 23
, c) 13
, d) 12
.
Success rate 88%
Which fraction is the largest?
Success rate 46%; 39% chose (b)
a) 45
, b) 34
, c) 58
, d) 7
10.
Choosing questions & analysing responses
How do we decide which fraction is the smallest?
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Less effective questions What is 127 + 99, 25 + 201 and 198 + 28? Where are the lines of symmetry on this shape? What do the angles of a triangle add up to? Sort these shapes into two groups Are these triangles congruent? What is 2/3 of 24? What is 17 x 0.3? Is 46 a multiple of 3? What is the probability of drawing a red card from
a pack? What is an odd number plus an odd number?
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More effective questions How do we know that 127 + 99, 25 + 201 and
198 + 28 will all give the same answer? Why is this picture an example of a shape that
has symmetry? Explain the way you have sorted these shapes. How do we know these triangles are congruent? How do you find 2/3 of a number? Is it always true that multiplying makes
numbers bigger? Why is selecting a red card from a normal pack
an example of an event that has an even chance?
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Question starters …
What maths do you think you’ll use to
solve this
problem? What is similar … ? What is different … ? Which of these questions do you think will
be
easy? … hard? What makes those questions hard? What advise would you give to someone …
?
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Strategies to support better thinking and improved responses by pupils:
Use responses as a focus for teaching Use questions to identify and tackle
misconceptions Extend thinking time after you have asked a
question Adopt a rule ‘no hands up’ Avoid the temptation to prompt, provide the
answer or move on to someone else Ask pupils to work in pairs on questions.
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Effects of increased ‘wait time’ Longer answers Decreased failure of response Increased confidence when responding Pupils challenged or improved other pupils’
answers More alternative responses were offered
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Analysing your questioning
Use a tape or video recorder to record a whole-class question-and-answer session. Replay the tape to help you to evaluate the different aspects of your own questioning. You may find it useful to focus upon whether:
you asked too many questions you had a balance of open and closed, high- and
low-order questions you encouraged opinion, informed speculation
and tentative answers you handled incorrect answers effectively you provided thinking time
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Effective Feedback & Marking
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“ ‘not very good work’ doesn’t help me to know how to do it better”
University of Bristol School of Education - learn project
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“where anyone is trying to learn, feedback about their efforts has three elements – the desired goal, the evidence about their present position and some understanding of a way to close the gap between the two.”
[Sadler,1989]
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Characteristics of Positive Feedback
Feedback does not always have to be made through marking books
Feedback is more effective if it focuses on the lesson objectives & success criteria and is given regularly while still relevant
Feedback is most effective when it confirms that pupils are on the right track and when it stimulates correction of errors or improvement of a piece of work
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“Feedback to any pupil should be about the particular qualities of his or her work, with advice on what she or he can do to improve, and should avoid comparisons with other pupils.”
Black,P (1998)
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Comments v. Marks
Research on marking indicates that pupils’ learning can be enhanced by quality written feedback but that giving marks or grades acts as a disincentive
Pupils’ perceptions of what marks or grades mean are often different from what the teacher intended
A numerical grade or mark does not tell you how to improve
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Effect of Marking on Motivation
Feedback Progress Top Bottom
Marks none +ve -ve
Comments 30% +ve +ve
Marks andComments
none +ve -ve
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• Focus attention on those skills which coincide
with the meaning & purpose of the work
• Early intervention
• Give specific prompts which explain exactly
what pupils are doing well & where and what
pupils need to improve
• Clear & manageable targets
• Expect pupils to respond to the prompts
Effective marking
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FEEDBACK THROUGH MARKING
Reference “Unlocking Formative assessment” Shirley Clarke
• Mark to learning objective• Highlight (Green) places where success has been achieved against those learning objectives•* (Red) one place where improvement can be made. Take an arrow to the next white space and write a closing the gap statement.• Allow time during the next lesson for students to respond to this comment.
___________________________________________________________________________________________________________________________________________________________________________________________________________________________ *_______________________________________________________________________________________________________________________________________________________________
Closing the gap comments
Students responses
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FEEDBACK THROUGH MARKING
Reference “Unlocking Formative assessment” Shirley Clarke
• Mark to learning objective• Highlight (Green) places where success has been achieved against those learning objectives•* (Red) one place where improvement can be made. Take an arrow to the next white space and write a closing the gap statement.• Allow time during the next lesson for students to respond to this comment.
___________________________________________________________________________________________________________________________________________________________________________________________________________________________ *_______________________________________________________________________________________________________________________________________________________________
Closing the gap comments
Students responses
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FEEDBACK THROUGH MARKING
Reference “Unlocking Formative assessment” Shirley Clarke
• Mark to learning objective• Highlight (Green) places where success has been achieved against those learning objectives•* (Red) one place where improvement can be made. Take an arrow to the next white space and write a closing the gap statement.• Allow time during the next lesson for students to respond to this comment.
___________________________________________________________________________________________________________________________________________________________________________________________________________________________ *_______________________________________________________________________________________________________________________________________________________________
Closing the gap comments
Students responses
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FEEDBACK THROUGH MARKING
Reference “Unlocking Formative assessment” Shirley Clarke
• Mark to learning objective• Highlight (Green) places where success has been achieved against those learning objectives•* (Red) one place where improvement can be made. Take an arrow to the next white space and write a closing the gap statement.• Allow time during the next lesson for students to respond to this comment.
___________________________________________________________________________________________________________________________________________________________________________________________________________________________ *_______________________________________________________________________________________________________________________________________________________________
Closing the gap comments
Students responses
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FEEDBACK THROUGH MARKING
Reference “Unlocking Formative assessment” Shirley Clarke
Closing the gap comments: A reminder prompt. Most suitable for more able students. It simply reminds students of whatcould be improved. A Scaffolded prompt. Suitable for students who need more structure than a simple reminder, this prompt provides some support. An example prompt. This can be appropriate in all cases but is of particular value when supporting less able students.
___________________________________________________________________________________________________________________________________________________________________________________________________________________________ *_______________________________________________________________________________________________________________________________________________________________
Closing the gap comments
Students responses
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Peer and Self Assessment
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Pupil Involvement in Self Assessment
Give pupils opportunities to talk about what they have learned and what they have found difficult, using the objectives as a focus
Encourage pupils to work and discuss together, focusing on how to improve
Ask pupils to explain the steps in their thinking Give time for pupils to reflect upon their learning Identify with pupils the next step in their learning
that will enable them to meet their target(s)
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Theory into Practice:Supporting Self Assessment
To support self assessment, teachers need to: explain systematically the objectives for the
lesson explain to pupils what is expected of them frequently encourage pupils to talk about
improving the quality of their work frequently and consistently encourage pupils to
reflect on their learning through planned strategies
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To support self assessment, teachers need to: give time for self assessment
give time for pupils to reflect on how they
thought through a problem and how they might
do it differently – and advise other pupils how to
approach it
Theory into Practice:Supporting Self Assessment
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Pupil Log“I can explain what an equation is”
“I can draw a straight line graph from a given equation”
etc.
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Pupil Log
AT2 Number Start of module End of module
I can :
“… explain what an equation is”
“… draw a straight line graph from a given
equation”
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Self-Assessment & Target settingDate Topic Pre-
Post-
Comment Target?
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Concept Web
abc
abc
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At the end of the week Pupils summarise what they have learnt / what
skills they now have / key points
Pupils recall the week’s ‘tripwires’
Pupils recall as many of the week’s keywords as they can.
Pupils draw their own version of the class concept web.
abc
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Self-assessment ‘tools’: graphic organisers
Traffic lights
Thumbs up / thumbs down
Talk partners
Smiley faces
Ladders
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Self/Peer Assessment Techniques
Pupils: write a list of key questions and find answers make up differentiated questions to test each other produce a written account for an audience (and make a presentation) construct a concept web (pupils may comment on each other’s web)
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Have you achieved the learning intention of the lesson? What did you find easy? What did you find difficult and what helped you to learn something new? What do you need more help with next? What are you most pleased with? What have you learned that you didn’t already know? How would you change this activity for another
class?
Plenary reflection
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Developing Quality in Self-Evaluation Sessions:
Constantly relate back to the learning objectives Think about the language used
Keep pupils focused on the objectives and success criteria by ‘pulling them back’
Give feedback focused on self-evaluation strategies and strategies used to meet the success criteria
Generally bring in more talk about thinking processes
Gillingham Partnership Formative Assessment Project 2000 - 2001
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The 10 Principles of Assessment for Learning
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The 10 principles of assessment for learning
Assessment for learning should: be part of effective planning of teaching and learning focus on how pupils learn be recognised as being central to classroom practice be regarded as a key professional skill for teachers should be sensitive and constructive because any
assessment has an emotional impact
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The 10 principles of assessment for learning
Assessment for learning should: take account of the importance of learner motivation promote commitment to learning goals and a shared
understanding of the criteria by which they are assessed
provide learners with constructive guidance about how to improve
develop the learners’ capacity for self-assessment so that they can become reflective and self-managing
recognise the full range of achievement of all learners
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What now?
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Moving Forward select one strategy and introduce it with one class
of pupils who you think will respond well. for a topic you are about to teach, develop a bank
of challenging questions. for a topic you are about to teach, identify one or
two lessons that would be appropriate to indicate whether pupils are moving towards a ‘learning objective’. Mark their work, based on the success criteria, and identify, where applicable, the next stage in the pupils’ learning.
Encourage pupils’ to respond to your comment.
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Review departmental Schemes of Work to evaluate whether they support ‘AfL’ strategies in term of:
having appropriate success criteria linked to objectives
providing opportunities for monitoring progress, other than through the use of tests
Moving Forward
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For each strategy your department tries, reflect on how it :
informs you about what pupils know and understand
is used by pupils to improve
Moving Forward