1 ANTERIOR & POSTERIOR COMPARTMENTS OF ARM BY PROF. ANSARI 23/10/07, LECTURE- 2.30/3.30 PM.
2:00 pm to 3.30 pm Assessment. Opportunity to… ·learn ·show ·know what to show.
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Transcript of 2:00 pm to 3.30 pm Assessment. Opportunity to… ·learn ·show ·know what to show.
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2:00 pm to 3.30 pm
AssessmentAssessment
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Opportunity to…
· learn· show· know what to show
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Marking(in Sweden, secondary and upper secondary school only
In communication during day-to-day classroom work In communication
during entire class sessions at the end of teaching units
In connection with diagnostic and other test
In connection withteacher/student/parent meetings
Summary in assessment forms/matrices
AssessmentImplicit and explicit
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Lisa Björklund BoistrupDiscourses in mathematics classrooms: a multimodal social semiotic study
su.diva-portal.org/smash/record.jsf?pid=diva2:355024
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(Pettersson, 2005)
The consequences of assessment
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Classroom assessment
• Summative assessmentTest on a local or national level
• Formative assessment“all those activities undertaken by teachers, and/or by their students, which provide information to be used as feedback to modify the teaching and learning activities in which they are engaged” (Black and Wiliam, 1998)
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Feedback
Information provided by an agent
(e.g. teacher, peer, book, parent, or one’s own experience) about aspects of one’s performance or understanding” (Hattie, 2009)
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Feedback• Feed back
what has happened ←
The teacher evaluates the student´s demonstrated performances in terms of ”good” or ”bad”.
Rewarding. Punishing, approval, disapproval
• Feed forwardthe future →
The teacher use the student´s demonstrated (lack of knowing) as a basis for continued learning
• Feed upStudents´demonstrated knowing
↕
explicit goals/criteria that should/could have been
reached and/or to be reached in the future
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In Sweden
Presence of Assessment acts in Classroom visited
• Feed back 58• Feed forward 72• Feed up 2
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Analysis of knowledgeHigher quality can e.g. be that the pupil shows his/her understanding of a concept in different ways and in different situations.
Therefore the analysis ought to focus in what extent the pupil has access to his/her knowledge in different situations.
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1/4
1/4 of a string
1/4 of water in a glass
1/4 of a lump of play dough
1/4 of 8 stones
1/4 of a paper
Length
Volume
Weight
Quantity
Area
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Deep understanding of a mathematical item or topic is displayed by the ability to transfer the idea between different representations: pictorial, verbal, symbolic and the real world.
Weakness in understanding are often pinpointed by weakness in representations.
(Alistair McIntosh)
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Four kinds of representations
Event
Picture Number
Word Symbols
The fishing huts
# 1 1 + 1 · 4 = 5
# 2 1 + 2 · 4 = 9
# 3 1 + 3 · 4 = 13
# 4 1 + 4 · 4 = 17
etc
First I built a hut with 5 sticks, then I built a second hut with 4 sticks. After that I continued …
1 stick + 4 sticks for each new hut
1 st + 4 st · number of huts
1 st + 4 st · n
1 + 4 · n
1 + 4n
4n + 1
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Documentation which highlights the mathematicsDocumentation which highlights the mathematics
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Documentation which highlights the mathematicsDocumentation which highlights the mathematics
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Assessment concerning …
· Problem solving capability · Comprehension and method · Accomplishment
· Communication capability · Mathematical language and/or representation · Clarity of presentation
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Three levels
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Qualitative levels
Mathematical language and/or representation
Poor and occasionally wrong
Acceptable but with some shortages
Correct and appropriate
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The area of a triangle The area of a triangle on small pieces of paperson small pieces of papers
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Documentation which shows development of knowledge
What I know about …
What I have learnt about …
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Documentation which shows development of knowledge
What have you learnt since …?
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Documentation which highlights the mathematics
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Documentation which shows development of knowledge
The ellipse model
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Similarities
Differences
Name:______________________ Class:____
Triangle – Rectangle
· both consist of straight lines· both have angles· you calculate the perimeter in the same way: you add the sides· both have a base and height· both have an area
· three sides· three angles· have not parallel sides· the three angles are not always the same· maximum one angle is a right angle
· four sides· four angles· have parallel sides· the four angles are always the same· all angles are right angles
Similarities Similarities andandDifferencesDifferences
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Addition• I think it is when you are doing different sports• I think it is computor• I don´t know, but I take a chance: it´s different jobs• When you are outdoors walking• Something with a pocket calculator• I think it is what ever … or theatre• It means plus, because it sounds like that • Something on the car• It is plus• It is like 3+3=6• Addition is when you get warm when you are running• Additon is a counting sign. The signs name is addition and is
plus. You use plus when you are plussing something like 4+4=8• Additon is when someone is alone and another one is coming.
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Oral analyses
• The pupils discuss in pairs or in small groups. A respondent is speaking on behalfs of others.
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Oral analyses
• The pupils discuss in pairs or in small groups. A respondent is speaking on behalfs of others.
• Ask all to write down an answer and then reading out a selected one
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What happens …?· Make an equilateral
triangle. · What happens with the
shape if you add another side to the triangle?
· Describe the shape!· Check!
Triangle (3 sides)
Quadrilateral (4)
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What happens …?
· What happens if you add another side …
· What´s the name of the new shape?
Pentagon (5)
Hexagon (6)
Heptagon (7)
Octagon (8)
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Oral analyses
• The pupils discuss in pairs or in small groups. A respondent is speaking on behalfs of others.
• Ask all to write down an answer and then reading out a selected one
• Give pupils a choice between different possible answers and ask them to vote on the options.
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Ecolier 2007
Small cubes in a big cube
Daniela has got cubes of equal size. She has put some of them into a box shaped like a cube in the way you see on the picture. What maximum number of cubes can she put into the box?
a/ 9b/ 13c/ 17d/ 21e/ 27
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Benjamin 2007
Area and perimeter
A parallellogram is divided in two parts P and Q as shown in the figure
What statement is surely true?a/ P has a bigger perimeter than Qb/ P has a smaller perimeter than Qc/ P has a smaller area than Qd/ Q and P have the same areae/ Q and P have the same perimeter
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Eccolier 2006
Four routes
Between two points four routes are drawn.Which route is the longest?
A B C D E: All are equal
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Ecolier 2008
We are going to build a cube like this
Which of the following foldings are impossible?
a/ 1 and 3 b/1 and 5 c/ 3 and 4 d/3 and 5 e/ 2 and 4
Folding cubes
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National tests in mathematics
The side in an equilateral triangle is 5 dm.How large area has the triangle?One choice is right. Circle your answer.
6,3 dm2 10,8 dm2 12,5 dm2 15 dm2 25 dm2
Solution frequencyGirls: 0,10 Boys: 0,13
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Area with sticks
area < 0,5 a.u.
area ≈ 0,43 a.u.
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Pedagogical materialGeoboardsGeoboards
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National tests in mathematics
– The area of the rectangle is 18 cm2
and the perimeter is 22 cm.
– Draw another rectangle with the same area (18 cm2) but with a shorter perimeter. Each of the four vertices of the rectangle must be located at a dot.
– Find the perimeter of your rectangle. Show your calculations
here:
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