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Improving the learning of numeracy through formative assessment. Dylan Wiliam National Numeracy Conference Edinburgh, March 2009 www.dylanwiliam.net. Raising achievement matters…. Which of the following categories of skill is disappearing from the work-place most rapidly? Routine manual - PowerPoint PPT Presentation
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Improving the learning of numeracy through formative assessment
Dylan Wiliam
National Numeracy Conference
Edinburgh, March 2009
www.dylanwiliam.net
Raising achievement matters…Which of the following categories of skill is disappearing from the work-
place most rapidly?
1. Routine manual
2. Non-routine manual
3. Routine cognitive
4. Complex communication
5. Expert thinking/problem-solving
…but what is learned matters too…
Autor, Levy & Murnane, 2003
The only 21st century skillSo the model that says learn while you’re at school, while you’re young, the skills that you will apply during your lifetime is no longer tenable. The skills that you can learn when you’re at school will not be applicable. They will be obsolete by the time you get into the workplace and need them, except for one skill. The one really competitive skill is the skill of being able to learn. It is the skill of being able not to give the right answer to questions about what you were taught in school, but to make the right response to situations that are outside the scope of what you were taught in school. We need to produce people who know how to act when they’re faced with situations for which they were not specifically prepared.
(Papert, 1998)
Assessment for learning is any assessment for which the first priority in its design and practice is to serve the purpose of promoting pupils’ learning. It thus differs from assessment designed primarily to serve the purposes of accountability, or of ranking, or of certifying competence. 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.
Such assessment becomes ‘formative assessment’ when the evidence is actually used to adapt the teaching work to meet learning needs. (Black et al., 2002)
Formative assessment
Types of formative assessmentLong-cycle
Span: across units, terms Length: four weeks to one year
Medium-cycle Span: within and between teaching units Length: one to four weeks
Short-cycle Span: within and between lessons Length:
day-by-day: 24 to 48 hours minute-by-minute: 5 seconds to 2 hours
Unpacking formative assessmentKey processesEstablishing where the learners are in their learningEstablishing where they are goingWorking out how to get there
ParticipantsTeachersPeersLearners
Where the learner is going
Where the learner is How to get there
TeacherClarify and share
learning intentions
Engineering effective
discussions, tasks and activities that elicit evidence of
learning
Providing feedback that moves
learners forward
PeerUnderstand and share learning
intentions
Activating students as learningresources for one another
LearnerUnderstand
learning intentions
Activating students as ownersof their own learning
Aspects of formative assessment
Five “key strategies”…Clarifying, understanding, and sharing learning intentions
curriculum philosophy (goals and horizons)
Engineering effective classroom discussions, tasks and activities that elicit evidence of learning classroom discourse, interactive whole-class teaching
Providing feedback that moves learners forward feedback
Activating students as learning resources for one another collaborative learning, reciprocal teaching, peer-assessment
Activating students as owners of their own learning metacognition, motivation, interest, attribution, self-assessment
(Wiliam & Thompson, 2007)
…and one big ideaUse evidence about learning to adapt teaching and learning to meet student needs
Keeping Learning on Track (KLT)A pilot guides a plane or boat toward its destination by taking constant readings and making careful adjustments in response to wind, currents, weather, etc.
A good teacher does the same:Plans a carefully chosen route ahead of time (in essence building the track)Takes readings along the way Changes course as conditions dictate
Eliciting evidence of student achievement
Kinds of questions: Israel
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.
[Vinner, PME conference, Lahti, Finland, 1997]
Draw an upside-down triangle…
Misconceptions
3a = 24
a + b = 16
Questioning in maths: discussionLook at the following sequence:
3, 7, 11, 15, 19, ….
Which is the best rule to describe the sequence?
A. n + 4
B. 3 + n
C. 4n - 1
D. 4n + 3
Eliciting evidenceKey idea: questioning should
cause thinking provide data that informs teaching
Improving teacher questioning generating questions with colleagues closed v open low-order v high-order appropriate wait-time
Getting away from I-R-E basketball rather than serial table-tennis ‘No hands up’ (except to ask a question) class polls to review current attitudes towards an issue ‘Hot Seat’ questioning
All-student response systems ABCD cards, Mini white-boards, Exit passes
Questioning in maths: diagnosisIn which of these right-angled triangles is a2 + b2 = c2 ?
A a
c
b
C b
c
a
E c
b
a
B a
b
c
D b
a
c
F c
a
b
Lines of symmetry
AB
C
D E F
Constructing hinge-point questions
Discriminate incorrect cognitive rulesVersion 1 (Hart, 1981)
If e+f = 8, then e+f+g =
A. 9
B. 12
C. 15
D. 8+g
Version 2
If f+g = 8, then f+g+h =
A. 9
B. 12
C. 15
D. 16
E. 8+h
What is the area of this trapezium?
Discriminate correct cognitive rules
b
a
h
b
b
a
a
h2A = (a + b) x h
A = (a + b) x h
b a
h A = h x (a + b)
Discriminate between incorrect and correct cognitive rules
Version 1
There are two flights per day from Newtown to Oldtown. The first flight leaves Newtown each day at 9:20 and arrives in Oldtown at 10:55. The second flight from Newtown leaves at 2:15. At what time does the second flight arrive in Oldtown? Show your work.
Version 2
There are two flights per day from Newtown to Oldtown. The first flight leaves Newtown each day at 9:05 and arrives in Oldtown at 10:55. The second flight from Newtown leaves at 2:15. At what time does the second flight arrive in Oldtown? Show your work.
Cognitive Rules Responses
A
B
C
D
Correct
Incorrect
Over- and under-generalization
B C DA
In which of the following diagrams, is one quarter of the area shaded?
Diagnostic item: mediansWhat is the median for the following data set?
38 74 22 44 96 22 19 53
A. 22B. 38 and 44C. 41D. 46E. 70F. 77G. This data set has no median
Diagnostic item: meansWhat can you say about the means of the following two data sets?
Set 1: 10 12 13 15
Set 2: 10 12 13 15 0
A. The two sets have the same mean.
B. The two sets have different means.
C. It depends on whether you choose to count the zero.
Diagnostic item: diagonalsWhich of the shapes below contains a dotted line that is also a diagonal?
Hinge-point questionsA hinge question is based on the important concept in a lesson that is critical for students to understand before you move on in the lesson.
Design requirementsEvery student must respond to the question within two minutes.You must be able to collect and interpret the responses from all students in
30 seconds
Priorities (in order) In no case should correct and incorrect cognitive rules map ontp the correct
optionEach incorrect option response (distractor) should interpret a single
cognitive ruleCorrect option responses (keys) should interpret a single cognitive rule
Practical techniques: feedbackKey idea: feedback should
cause thinking provide guidance on how to improve
Comment-only gradingFocused gradingExplicit reference to rubricsSuggestions on how to improve
Not giving complete solutionsRe-timing assessment
(eg three-quarters-of-the-way-through-a-unit test)
Practical techniques: sharing learning intentionsExplaining learning intentions at start of lesson/unit
Learning intentions Success criteria
Intentions/criteria in students’ language
Posters of key words to talk about learning eg describe, explain, evaluate
Planning/writing frames
Annotated examples of different standards to ‘flesh out’ assessment rubrics (e.g. reports of mathematical investigations)
Opportunities for students to design their own tests
Students owning their learning and as learning resourcesStudents assessing their own/peers’ work with rubricswith exemplars“two stars and a wish”
Training students to pose questions/identifying group weaknesses
Self-assessment of understandingTraffic lightsRed/green discs
End-of-lesson students’ review
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