ical/vocational or only
work-related (non-theoretical) knowledge.
3Statement in which a scientific-mathematical/vocational fact and a work-related
fact are combined.
4Reasoning with both scientific-mathematical/vocational and work-related
knowledge
Results
At every school we observed four lessons, all practice lessons. At school 1 we also
observed a prototype lesson. At school 2 there were no separate prototype lessons;
the subject-matter teachers at that school were present during the regular practice
periods and the content of the prototype lessons was taught in the context of those
practice lessons. All together we gathered almost 12 hours of video data (see table
2).
Martijn van Schaik | 04/27/13
Table 2
Video data and number of representations
When we look at the number of presentations (drawings and models) during the
observations we can see that school 1 had six more in total. However at school 2
representations were still present at the end of the process, whereas at school 1 as
the process evolved the representations disappeared. This is in line with our
previous findings (Van Schaik et al., in press).
18 episodes were selected in which the students we followed for this study were
present. Most of those were around the episodes in which representations were
visible. In two episodes there were no representations.
In all episodes and in an interviews we code the utterances to the level of
integration (table 3). As with the representations, at school 1the prevalence of
utterances with some level of knowledge decreased towards the end of the
process. At school 2 however, in the final presentations students still showed
integration of knowledge. Another difference between the schools is the level of
integration. At school 1 only level 1 and level 2 utterances were found, whereas at
school 2 also level 3 integration was coded. No level 4 was found in the
observations.
Table 3
Level of integration in utterances
Martijn van Schaik | 04/27/13
School 1 School 2
Lesson type Lesson type
Week 1
Week 2
Week 3 Practice 1:09:09 4
Week 4 1:08:13 6
Week 5
Week 6 Practice 1:46:46 7 Practice 1:53:05 3
Week 7 Practice 0:57:07 5
P-lesson 0:31:21 1
Week 8
Week 9
Week 10 Practice 2:13:39 0 Practice 1:25:48 3
Week 11 Interview
Later 0:52:05 3
Total 6:37:06 19 5:20:07 13
duration of
video obs.
number of
repr.
duration of
video obs.
number of
repr.
Practice
(drawing)
Presentations
(3)
School 1 School 2
week 4 week 6 week 7 week 3 week 6
Level 1 8 8 4 4 4 1 2
Level 2 1 1 3 1
Level 3 4 2 2
Level 4
Levels of
integraon
week
10
week
10
Week
10
(intervi
ew)
Presen-
taon
Analyses of student use of representations and reasoning
The analyses of the prevalence of the utterances over the process shows that it
resembles the appearance of representations. As found in earlier studies,
representations, as tools during the design and production process, tend to
dissapear towards the end of the process. This seems also the case for utterances
that have a level of knowledge in them. Only at school 2 both drawings and
utterances with knowledge remain present in the end of the process. The turning
point in this study seems to be week 6. The majority of the representaions as well
as the utterances at all levels decreases from there.
At school 2 more level 2 utterances are found and only at that school
statements that contain both practical and subject-matter/vocational knowledge
arre found. This may be due to the fact that students at that school had to present
there final prototype, including the drawing and reflection on the process, to their
peers. In this presentation students still made statements at level 3. In the next
paragraph examples of the utterances are shown.
Examples of level 1 statements
Most utterances found in the observations are at level one. The statement vary
from very short ones about tasks, dimensions, materials, or measures as example 1
shows, to statements on what students do and have done in example 2.
Three of the four students of the subgroup are together and looking at their design.
One of them is playing with measurement tape.
Example 1
School 1 week 4
Utterance Remarks
Student These are far to small dimensions. While looking at the
measurement tape
In the final presentation for peers at school 2 the subgroup presents the prototype
and reflects on their process. One of them explaines why their design drawing is
not finished. That is, the drawing does not accurately reflects the actual product
they constructed. There is not much more than that.
Example 2
School 2 peer-presentation session
Utterance Remarks
Student So, this is the design drawing as actually built, but
it is not finished yet.
Peers are laughing and
comparing the drawing
with a map.
Examples of level 2 explanations/reasoning
There were three instances of level 2 reasoning. The examples here are typical for
the explanations at both schools when students are asked to explain the reasons
for their design an prototype. It shows that most reasons are practical or at least
are not connected to knowledge.
Martijn van Schaik | 04/27/13
Example 3
school 2 week 6
Utterance Remarks
Student When you that that, then the chair also has to
come further like this. Otherwise we can not attach
it.
Moving around with parts
of a chair for the tricycle
on the workbench.
Example 4
school 1 week 4
Utterance Remarks.
Examples of level 3 statements
Only at school 2 level 3 statements were found. Most (4) were in week 6, in the
final presentation, there were 2. In week 6 the subgroup is discussing their plans
for the construction. The talk what can be done, by whom. One of the students
states something about the rear of their design by which he uses mathematical
issues in the design that first have to be solved before the practical tasks at hand
can be carried out.
Example 5
school 2 week 6
Utterance Remarks
Student At the rear we need a triangle. I still have to decide
on the degrees to see how big the triangle will be.
While the subgroup is
sitting around the
computer with the printed
drawing in front of them.
In the same presentation as in example 4, an other student of the subgroup
explicitly refers to their drawing as a tool. With this statement he shows that he
knows what the rules for a technical design drawing are, but that theirs does not
comply to those. In other words, he shows an understanding of vocational
knowledge.
Example 6
School 2 peer-presentation session
Utterance Remarks
Student Coming back to our drawing, we were mainly
busy with our product, so the drawing has suffered
as a result. So it isn't right yet.
Referring to their design
drawing at the screen.
Martijn van Schaik | 04/27/13
Example of teacher guidance toward theoretical reasoning
In order to see how the teachers help the students to improve their knowledge
development and integration on theory and practice, we also need to look at the
teacher guidance. For every school there is one example of an interaction which
characterizes the pedagogical approach of the teacher in question.
The first example is one from school 1 in week 4 in which the teacher announces
an ad hoc instruction for the next day after a discussion with students.
Example 7
school 1 week 4
Utterance Remarks
Teacher … and then there is the the fact that we also need
to calculate this length
Pointing at the drawing on
the screen.
Teacher You can always try that. You can sketch that. But
let me come back to what I just said. This length
needs to be calculated at some point. How would
you do that?
Pointing at the diagonal
lines in the drawing of the
frame.
Student We have those here.. Looking for the papers
with the sketches
Teacher In the drawing? But can I also calculate those
using maths?
Student But its on scale [the drawing], then you only have
to....
Teacher Jaahhh, but you can't just draw everything at scale.
Suppose that I have to make a big contruction of a
bridge?
Interrupting the student
Student That has to be on scale, otherwise if you do
something wrong it collapses
Teacher But, is that on a scale of 1:2000 or of 1:200? I can
calculate that. Help me remember, then we can
discuss it next time [during a prototypelesson].
Because with Pythagoras' theorem... We will
calculate it next time, because it's calculatable.
This interaction shows that the teacher points the students to the role of
mathematics in their drawing. He asks questions an thus tries to have the student
come to mathematical operations. Subsequently he postpones the theoretical
explanation to a moment when the whole group