The CK-PCK test on optics
Two questions (Q1, Q11) are designed as PCK items, with a part concerning the conceptual
aspect (the CK part) and a related parte where teachers are request to analyze typical
students’ answers individuating the reasoning at the origin of each answer
Q1.
A) What represent the lines ST1 and ST2?
B) Considering the points a, b, c, d and the
point t on the surface of the screen, from
which of them is visible the light source ?
C) In what areas there is light?
source
D) In what areas there is shadow?
cardboard
1.1 What answers to each question?
Screen
1.2 The questions was posed by a teacher and three children trigger a discussion:
• Michele: lines are the rays of light coming out from the flashlight and you will see the
screen lit up around the shadow
• Teresa: if they were all the rays coming out from the torch, the cardboard would not be
illuminated
• Aldo: in t you cannot see the light of the torch, but perhaps in d a bit
Discuss the position of each student, indicating the conceptual learning knot underliyng it.
Elab From Kaminski 1989
Analysis of test (implemented during the FIM) –N=54
A) What
represent the
lines ST1 and
ST2?
Rays passing
beyond the card
B) Considering
the points a, b,
c, d and the
point t on the
surface of the
screen, from
which of them is
visible the light
source ?
C) In what areas
there is light?
D) In what areas
there is shadow?
abc
Light
6 beam/rays
46
cb
abc
26
On the
screen
dt
20
d
22
Limits of the
Light/shad
light cone from 10 ows limit 12
the torch
rays
3
2
5
b
b
t
bdt-abcd
2
NA
2
In all positions
(different
intensity)
5
NA
14
4
3
NA
19
1
2
NA
4
bt-ac
Analysis of test (implemented during the FIM)
How teachers analyze the student sentence (Michele: «lines ST1 and St2 are the rays emerging
from the light source»)  individuate the learning problem, the reasoning at the base of the
student sentence:
Learning knot
light propagate in rectilinear way (and “S-t1 S-T2 are border rays”)
n (N=51)
10 (2)
He perceives light only as its limits
7
Describe the situation
2
He tells the truth/is correct, identifying light/shadows regions
9
The cardboard prevents light pass
5
NA
17
Analysis of test (implemented during the FIM)
How teachers analyze the student sentence (Teresa: if they were all the rays coming out from
the torch, the cardboard would not be illuminated)
Learning knot1
n (N=51)
There are only two rays
2
This is what happens pointing a light on a card
2
There are other rays (not only the two limit rays)
18
Property of the light produced by a source
3
She’s wrong
4
She looks beyond the card
2
It has doubts
1
NA
19
Analysis of test (implemented during the FIM)
How teachers analyze the student sentence (Aldo: in t you cannot see the light of the torch, but
perhaps in d a bit)
Learning knot1
n (N=51)
The concept of shadow and penumbra
There are shaded areas and penumbra (light spreads near the beam)
Diffusion that there is’nt in the case of point source
8
9
4
d is in the same region of t (flat conception of shadow)
2
The rectilinear propagation of light (a body block the propagation)
2
He senses the existence of shadows and twilight
It depends on the condition (of source, position, thikcness of the card)
[Aldo is correct]
4
3
NA
19
21
7
Analysis of test (implemented during the FIM)
Q3.
A represent a light source
B is a black screen
S is a mirror placed on the wall P
Can a person who is in the room to see the reflected
image of the source?
If yes where should position?
Draw the locations and explains the drawing.
Elab. from Eylon, Rounen 1993
Analysis of test
(implemented during the FIM)
30/54
Reasoning based on
reflection law
Also and limit rays (17/30)
only reflection law
(13/30 Partial explanation)
Analysis of test
(implemented during the FIM)
9/54
over the AP line
9/54 back to the mirror
[wrong but coherent idea]
2/54 back to A on the line AP
4/54 NA
Q5. The figures represent some plexiglass boxes that contain planar mirrors
variously oriented. In the figures, the reflective side of the mirrors is black.
As it will be reflected on the mirrors, and as comes out from the boxes, a
Q5. Le figure rappresentano alcune scatole di plexiglas che contengono degli specchi piani
parallel
beam of light that enters as is indicated in Figure 1? The edges of the
variamente orientati. Nelle figure, il lato riflettente degli specchi è quello nero. Come si rifletterà
beam
of light
areuscirà
distinguished
one
double
the
other
sugli specchi,
e come
dalle scatole, un
fasciofrom
di luceaparallela
che arrow,
entra com’è
indicato
nellaby a
figura 1? I bordi del fascio di luce sono contraddistinti uno da una doppia freccia, l’altro da una
single
arrow. The figure 1 represents the output configuration relative to one
freccia semplice. La figura 1 rappresenta la configurazione d’uscita relativa a una delle tre scatole
of the three boxes
A - 27/54
A & B 8/54
B 4/54
2/54
13/54 NA
Point sources, extense sources and shadows formation
Q11.1 What do you expect to see on the screen putted at the same distance of the
source? Represent what you would expect to see on the screen with each of the
three sources considered and explain the answer.
- N of illuminated zones
- Shape of that zones related to the hole shape
- Shape of that zones and the source
Da McDermott et al.
Point sources, extense sources and shadows formation
29/54 NA
8/54
Reasoning:
proiection of
the hole using
rectilinear
propagation
But also with
doubts
Halo model and extense
immagine
Point sources, extense sources and shadows formation
Triangle
Two triagles
1 triangles
model (5/54)
Obscure chamber
mechanism
1/5
Point sources, extense sources and shadows formation
Halo model (12/54)
Point, two points, halo model
1/12
Point sources, extense sources and shadows formation
Point, two points, triangle model
You see the point resulting from the straight beam that passes the triangle
You see the point resulting from the straight beam that passes the triangle
Being the source point-like, the rays are propagated in all directions.
It is observed on the screen the triangle
Q13. They are given these two
systems of mirrors.
Q13.1 Draw the reflected rays
in the two cases.
Q13. Sono dati questi due sistemi di specchi.
Q13.1 Disegnare i raggi riflessi nei due casi.
Q13.2 Nelle figure sono riportate alcune tipiche risposte degli studenti.
Q13.2 Figures are some
typical student responses.
Which is correct?
Da Heron
Explain in response to
learning difficulties that it
implies.
Quali sono corrette? Spiegare nella risposta la difficoltà di apprendimento che essa sottende.
______________________________________________________________________________
______________________________________________________________________________
23/54
11/54
3/54
17 NA
In merito al commento sui disegni fatti degli studenti:
33/54 individuano come corrette le prime due figure,
Indicando come difficoltà:
a) l’individuazione della perpendicolare (7/33)
b) l’uguaglianza degli angoli (9/33)
c) L’individuazione della normale e l’uguaglianza degli angoli (10)
Non motivando affatto (7/33)
Solo in pochi casi vengo indicate come corrette le seconde due figure (3/54)
Più spesso il quesito viene disatteso (18/54)
Q17. Which of the following figures represents better where it forms
Q17. Quale delle seguenti figure rappresenta meglio dove si forma l’immagine di un oggetto riflesso in uno
an image
of an object reflected in a plane mirror? explain
specchio piano? Spiegare,
immagine
Da Viennot
NR
13
A
28
B
8
C
5