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Modelling across the disciplines in simulated workplaces at school

Modelling across the Disciplines in Simulated Workplaces in
A Report of a Design-Based Research Project.
Dr. Martijn VAN SCHAIK1, VU University Amsterdam, ,
Prof. Dr. Jan TERWEL, VU University Amsterdam
Prof Dr. Bert VAN OERS, VU University Amsterdam
This article is a report of a design-based research project that consisted of three phases: a case study
(n=20), a first experiment (n=65) and a second experiment (n-84). In every phase students worked on
an integrated assignment: design and built a tandem tricycle. Main question of the overall project was:
are the learning results of students participating in a process of guided-co-construction with peers and
experts better than the results of students that have ready-made models provided by the teachers? The
tricycle assignment proved to be knowledge-rich and the results of the posttests showed positive effects
of student learning on mathematics and science. There are clues to suppose that the strategy of 'guided-
co-construction' can support students to acquire codified knowledge and understanding of modelling.
Keywords: modelling, vocation education, disciplined perception
1Address for correspondence:Van Abbestraat 58, 1064 WV Amsterdam (e-mail: ,
phone: +31 (0) 6 48466407)
This paper reports on a design based research project conducted between 2006 and
2009 in pre-vocational secondary education(VMBO2) in which students follow a general
curriculum with a vocational perspective.
The overall research question of this design-based project was the following: do
students, who participate as model designers in a process of guided co-construction with an
expert (teacher) and peers, show better learning outcomes than students who learn to work
with ready-made models provided by the teacher? The general, working hypothesis is that
collaboratively learning to design and use models in vocational education has positive effects
on learning outcomes, compared to providing ready-made models to the students. The basic
idea underlying the hypothesis is that students will develop knowledge and skills in
modelling along with codified knowledge in mathematics and science as a result of
constructive involvement and dialogic inquiry under teacher guidance. In all three
interventions the students were to design and construct a technical product in the form of a
tandem tricycle (in the first case study a bicycle racing game was the second product). The
overall research project was divided into three phases: a case study, and two experiments in a
pre-test post-test control group design. These interventions resulted in four studies (see
In the first section below the theoretical framework and a methodological overview of the
project is given. In the next sections those questions are addressed by providing a
chronological summary of the findings of each study. We will end with some remarks on
educational theory and practice and propose some suggestions for further research.
Theoretical framework
Within the European Union and elsewhere it is recognised that in order to prepare
students for the demands of the future, they should obtain competencies that cover both broad
general knowledge as well as technical skills (Cedefop, 2009; Commission of the European
Communities, 2008). However, there is an ongoing debate on how to connect formal learning
and learning in the workplace (Billett, 2004; Griffiths & Guile, 2003; Guile & Griffiths,
2001; Tuomi-Gröhm & Engeström, 2003). At the same time, little research has been
conducted into the learning environments in vocational education that are expected to
promote this kind of learning (Koopman, Teune & Beijaard, in press). For example, a query
in the ERIC database with the keywords “workplace learning”, “formal” and “informal”
returned 44 journal articles of which 14 concerned vocational education. None of them were
empirical studies investigating the learning environment. Another search on pre-vocational
2VMBO is preparatory senior secondary education. It is secondary education for students 12-16 years that prepares them for senior secondary vocational education. About 60% of all Dutch
students 12-16 years attend VMBO (Maes, 2004).
education journal articles at the secondary level returned 15 hits, three of which concerned
the learning environment.
As an attempt to improve the relevance of the knowledge and the effectiveness of transfer
to the workplace, reforms are taking place in Dutch pre-vocational schools (De Bruijn, 2004;
Guile & Young, 2003; Seezink, Poell & Kirschner, 2009), as in other countries. One of the
proposed reforms envisions the teaching-learning process as an activity embedded in a
simulation of real world practices, whereby students, guided by teachers, work on products
for 'real' customers, in the meantime acquiring new knowledge and skills. The basic
assumption behind this approach is that the learning of codified knowledge and vocational
skills can be integrated into authentic workshop practices. The pedagogical approach is what
Tynjälä labels “integrative pedagogics”, which is more of a principle integrating theory and
practice than a specific teaching method (2008, p. 144). However, working on a (practical)
problem is not enough to motivate students to learn (Guile & Young, 2003), and participating
in real life situations is not sufficient to develop expertise on a higher level (Tynjälä, 2008).
Explicitly taught knowledge, for example knowledge about modelling or knowledge gained
in mathematics education classes, is not automatically used for problem solving in a
workshop setting, and vice versa. Students simply do not recognise the connection between
theory and practice. This may result in reduced learning outcomes and lack of motivation on
the part of students. The challenge for schools is to provide assignments that are meaningful
for students and realistic with regard to their future work (Terwel, Van Oers, Van Dijk & Van
den Eeden, 2009; Tuomi-Gröhm & Engeström, 2003; Volman, 2006). At the same time, those
assignments should also result in highly qualified learning outcomes that enable students to
recontextualise their knowledge and skills acquired in the classroom to the workplace.
Teaching should support students in relating practical problem solving to codified curriculum
knowledge (Guile & Young, 2003; Van der Sanden, Terwel & Vosniadou, 2000). It follows
therefore that students, when solving real life problems, need to be supported by “conceptual
and pedagogical tools which make it possible for them to integrate theoretical knowledge
with their practical experiences.” (Tynjälä, 2008, p.145).
Real workshop activities could increase the need for specific knowledge and skills, and
subsequently provide opportunities for learning. Following Guile & Young (2003), such
workplaces can be characterised as a “knowledge-rich workplace” (p.73). They are assumed
to engage students in meaningful activities while at the same time promoting subject matter
learning (including mathematics, see Kent, Noss, Guile, Hoyles & Bakker, 2007).
Models as tools
In vocational education, students are sometimes involved in such knowledge-rich
workplaces while designing and constructing real products. In the design process as well as in
the actual construction issues arise that need to be solved. To anticipate possible problems
and their solutions models may be used. Although drawings and models are important in the
design of technology and serve both to communicate and generate ideas, MacDonald &
Gustafson (2004) claim that in classrooms the emphasis is on their mere representational
function. Students have to draw correctly, while their models are only used for teacher
diagnostics. If in these types of environment student drawing were related to orientation in
the problem situation as well as to an exploration of ideas, modelling might turn into action-
cum-learning strategies by which students could gain deeper understanding of problems and
their possible solutions.
Following Van Oers (Van Oers, 1988), a model is defined in this paper as “... any
material, materialised (for example a graphical display) or mentally pictured construction,
built up from identifiable elements and relations, which structures the user's action ...”
(p.127). These models function as tools in activities for orientation and communication, in
ways similar as described by Tuomi-Gröhn and Engeström (2003). For example, a model
may allow the designer to calculate angles in a drawing in advance, for example to correctly
saw steel in a single process rather than by trial and error. Here the mathematical formula
functions as an orientation tool. When the drawing is then used by students to negotiate the
design, it becomes in addition a tool for communication. Hence, orientation and
communication are both functions of a model, and a model can serve both at the same time.
From a sociocultural point of view models have two core functions: orientation and
communication. These functions are not mutually exclusive. Orientation, according to
Gal'perin, is essentially the psychological process of human action that constitutes awareness
in human activity. Through education this process acquires a cultural form which is
characteristic for a certain practice, leading to what we usually call 'disciplined perception'
(Stevens & Hall, 1998). Models play a particularly important role in this process: a model is a
cultivated tool for orientation towards future actions (Van Oers, 2006), providing direction to
someone's activities. Orientation includes valuation, produces information, and functions as a
basis for plans and predictions. As tools for communication, models foster the distribution of
individual ideas and meaning across the community. When students work together, as in our
case on the construction of a tricycle, they utilise drawings and ideas to plan and predict the
process, and to discuss the final design. The models provide direction not only to the actual
design and the planning of the activities but also to the coordination of ideas and actions
among the participants. In other words, the models assist in anticipating the outcomes and
meaning distribution in a community (Gal'perin 1969; 1979 in Van Oers, 2006).
Modelling in the practical workshops in vocational education can serve both students'
technical codified knowledge as well as the more general type of knowledge in subjects such
as mathematics and science. In contrast to simply looking at a technical artefact or making a
practical construction, by collaboratively designing models during the construction process
students are faced with a newly emerging dimension, by which the basic structure of the
construction is uncovered. The new dimension provides insight into how elements relate to
each other and how technical artefacts work, for example a tricycle (cf. Verkerk, Hoogland,
Van der Stoep & de Vries, 2007). As a result, the student is not only able to see the tricycle as
a working means of transport, but also to conceive of it as a concrete specimen for the
transmission of forces.
Guided co-construction
Introducing students to certain sociocultural practices (e.g., workplace as well as
mathematical practice) is best described as a process of legitimate peripheral participation
(Lave & Wenger, 1991; Mercer, 1995). In such a context learning may be seen as a process of
qualitative change in activities, resulting in enhanced possibilities of sociocultural
participation (Van Oers & Wardekker, 2000). When learning takes place in a workplace
setting the agents involved (students and teacher) may be characterised as a community of
practice (Lave & Wenger, 2005). In these communities the participants share basic
assumptions about rules and purposes. As learners they are actively involved in meaning-
making activities, as well as in problem solving with the support of tools and artefacts, while
communicating with each other as well as with others outside the community.
Furthermore, empirical analysis has shown that in the accomplishment of activities new
goals and needs may emerge which drive participants to construct or adopt new tools
(Kozulin, Gindis, Agayev & Miller, 2003; Saxe & Guberman, 1998). Hence, by participating
in communities, students may be compelled to aim for new goals that encourage them to
adopt appropriate new practice-related tools, including concepts, symbols and models
(Gravemeijer, Lehrer, Van Oers & Verschaffel, 2002). In guiding the participation process
teachers help their students understand the use and meaning of the concepts, symbols and
models as tools in a range of similar practices. At the same time the teachers themselves are
participants in the same community, as much involved in the co-construction process as the
students. It is important to remember that the teacher is not just a guide in this process of
meaning making, but also a genuine participant (Van Oers, 2001). For example, the teacher
may help students create a construction plan by asking questions while referring to both
domain specific drawing rules as well as the relevant mathematical concepts. In other words
teachers participate in the teams not only as guides but also as experts.
Guile and Young (2003), however, argue that for knowledge acquisition in a 'community
of practice' participation alone is not sufficient. Teachers should explicitly focus on relating
both situated and more general knowledge as codified in the curriculum subjects. In our
intervention the curriculum project was aimed precisely at this objective: moving from
practical problems to modelling, and, eventually, to an understanding of the relevant domain-
specific concepts.
The important role of the teacher, as a guide to knowledge acquisition and
understanding in practical environments, also includes introducing students to the practice of
modelling with the aid of mathematical tools. The teacher's role is to identify what is
'mathematical' in the workplace practice, to recognise the students’ emergent need for
mathematical tools, and to relate such recognition to the practice of (mathematical) modelling
(Van Oers, 2001). In other words: to help students become familiar with the modes of thought
that prevail in the discipline (Stevens & Hall, 1998). The discipline is in this case both
vocational and academic. However, simply providing models is not sufficient for
understanding the use of models as tools; in addition, conditions should be created which
focus “ … on the hidden rules and assumptions in the tools.” (Van Oers, 2001, p.81). Teacher
guidance should therefore promote such understanding by helping students to co-construct
the models.
One of the major issues in theories of learning to model involves the question: Are
models to be provided or generated? We have theoretical reasons and empirical evidence
from earlier research projects in the mathematical domain to the effect that guided co-
construction – as a third way in this dilemma - is an effective teaching and learning approach
compared to the simple provision of ready-made models by the teacher (Poland, 2007;
Terwel, 2004; Van Dijk, 2002). However, questions for further research remain. The
outcomes of a number of other studies into the design and use of models in mathematical
problem solving show that self-constructed models do not always have the intended effect
(De Bock, Verschaffel, Janssens, Van Dooren & Claes, 2003; Perkins & Unger, 1999). In
addition, as mentioned earlier, little is known about modelling in the vocational (technical)
domain. It was against this background that the present study was planned and conducted.
Research questions
The theoretical background sketched above leads to the following overall research
question: do students, who participate as model designers in a process of guided co-
construction with an expert (teacher) and peers, show better learning outcomes than students
who learn to work with ready-made models provided by the teacher?
The general working hypothesis for this study is that collaborative learning to design and
use models in vocational education has positive effects on learning outcomes, as compared to
providing ready-made models to the students. The basic idea underlying the hypothesis is that
students will develop knowledge and skills in modelling along with codified knowledge in
mathematics and science as a result of constructive involvement and dialogic inquiry under
teacher guidance.
The project is a design based research project with three phases or iterations (The design
based research collective, 2003). Based on findings from a case study (Study 1) and a first
intervention (Study 2), we re-designed an educational programme for students in vocational
education aimed at modelling for a second intervention (Study 3 and 4) (Van Schaik, Terwel
& Van Oers, in preparation a, in preparation b). All together six schools, about 150 students
and 27 teachers participated in the project.
As a design research project, we wanted to study the interventions in authentic contexts.
An appropriate way to characterise our interventions would be to place it in the tradition of
formative intervention (Engeström, 2007, 2009).
In all phases of the project video was used for observations and interviews. With a three-
camera approach teaching practices were recorded, two cameras capturing an overview of the
classroom and a third camera was handheld. The handheld camera was operated by one of the
researchers and recorded interactions between teachers and students following a protocol
(more information in Van Schaik, 2009, 2010). Analyses were conducted over the merged
recordings of the three cameras. The video data played a crucial role in the research. First, the
video data helped determining the redesign of the interventions. Second, also the method of
design based research could be reviewed and adjusted to the typicalities of VMBO. Finally, in
hindsight the development of the theory became visible: the perspective changed in the
course of the project on the basis of the subsequent findings in the interventions.
In Study 1 we used a qualitative approach and conducted a pattern analyses on video data.
In the subsequent interventions both pre- and post-tests as video observations were used in an
experiment (trial) with a control group.
A narrative of the design-based research
Case study (Study 1)
In a case study (Van Schaik, van Oers & Terwel, 2011) we explored the implementation
of two assignments and the subsequent teacher guidance at one school and tested whether or
not the learning environments became knowledge-rich (Guile & Young, 2003) as a result.
Knowledge-rich workplaces are assumed to engage students in meaningful activities and at
the same time promote subject matter learning (including mathematics, see Kent, Noss,
Guile, Hoyles & Bakker, 2007). In other words, the learning environment has the potential
for students to acquire knowledge that is codified or disciplinary.
For this first phase of the project, one school in the middle of the Netherlands was
selected that had been working with assignments like the ones described above. Students first
received an assignment to design (on paper) a tandem tricycle or a bicycle race game.
Second, the team with the best design, chosen by a teacher jury, was allowed to build the
product. The designing took place during a series of four mathematics lessons in the open
learning centre next to the workshop. Students were able to use computers to search for
information and to ask the mathematics teacher for help. After that, the construction of the
products was done during the vocational lessons in the workshop under the guidance of the
vocational teacher. The total duration of the project for the school was 12 weeks.
Most of the data we gathered came from observing two practice lessons a week during
seven weeks with the three video cameras (thus a total of 14 lessons of 45 minutes).The video
data was subjected to multiple viewings to explore the footage for patterns. We used this
method, known as pattern analysis (Erickson, 2006; Terwel, 2005), to allow the observers
watching the videos to detect patterns in the data. These patterns are called a posteriori
patterns. A pattern is a formal description of a repeating structure in interviews and in
interactions. Patterns can be mentioned by the participants in interviews or can be noticed by
the researcher during observation. Analysis was performed on the video data and the
materials that the students created in their projects (such as drafts, designs, drawings and
calculations. See figure 1.) exploring only the a posteriori patterns. This resulted in three
Figure 1. Design drawing of a tandem tricycle drawn by students
1. “Let your mind work” outside the workplace, because time is scarce.
In one of the first weeks of the curriculum project, Mr Williams, the technology teacher,
was heard saying: “Let your mind work,” three times in one lesson. It seemed to be an
encouragement for the students to think. However, the students were given a task they had to
perform at home, or in the mathematics classes. Hence, some deeper thinking in the practice
workshop can occur, but when students did not come up with solutions or answers fast
enough, they had to find them elsewhere. Moreover, we can see that the teacher made an
effort in teaching the students more than just the situated knowledge needed for the solution
of a particular problem. In the beginning of the construction process, the teacher often
referred to mathematics or he explained rules and possibilities in general. However, as the
actual construction process proceeded and the teacher and students had less time, and the
more situated and tacit the knowledge remained for the students, the less the teacher
explained and tended to ‘give away’ or provide the solution to the students. This means that
the students received increasingly tailored solutions and ‘tips & tricks’. In the workplace,
time is scarce, so deeper thinking that takes more time has to be done outside the workplace,
or, later on in the process, solutions are simply provided by the teacher.
2. Problem solving starts with modelling, but solutions are often provided.
As we focus on the students' problem solving, it appears that two different activities
occur. First, students design situational models themselves when they are drawing the design
or are planning their client interview. Second, canonical models, like models for technical
drawing or mathematical rules, are provided by the teacher (see figure 2). As a result, no
reinvention of these models occurs. The guidance teachers give on the canonical tools is one
of providing students with answers or instructing students how the models should be used,
whereas the guidance on the drafts and drawings of the students themselves helps students to
transform drawings into the construction of a working model.
Figure 2: Construction drawing by the teacher
3. A workplace simulation is stimulating
Once the students realize that what they are designing and engineering can be
constructed, they take more responsibility for their design, ideas and plans. Hence, they see it
as a challenge and they develop ‘ownership’ of their design, whereas the teacher acts as a co-
designer. As a result of this ownership, the problems they encounter in the realisation process
are meaningful and authentic. The solutions become their solutions that they are proud of.
These results showed that designing a tandem tricycle did, in fact, create opportunities for
teaching students’ codified knowledge and modelling. The teachers, however, tended to
simply provide ready-made models while for the students the knowledge involved remained
situated. That is, as solutions to problems, mathematical and scientific concepts and models
tended to be bound to the (practical) situation in which they were constructed. Although the
assignment itself was potentially knowledge-rich from the teachers' perspective, students
could not relate the provided problem solving models to more general codified knowledge.
Our assumption is that if the models had been designed by the students under teacher
guidance, the role of models as tools would have become clear and the relation between
theory and practice might have become more transparent in the process.
We also learned from the case study that student design processes should not be
disconnected from actual construction; not only for motivational reasons (students who did
not construct their designs were disappointed), but also because the transitions from design to
construction turned out to be the most interesting. Moreover, the verisimilitude of the
situation was also important for student motivation: “Clients should not be teachers playing
the client”, as the students put it. Interestingly in this connection, the students that had a
primary school as client proved more motivated than the others.
First experiment (Study 2)
Next, for Study 2, two conditions were shaped in a pre-and post-test control group design:
a 'providing' condition (control group) and a 'guided co-constructing' condition
(experimental). This first experiment was an intervention at two schools following the case
study. A programme based on the tricycle assignment was designed and teachers were trained
to guide the students either in a co-constructive or in a providing way (Van Schaik et al.,
2010). In the subsequent experiment the two conditions, providing (control group) versus
guided co-construction (experimental), differed in the way models were used in the
classroom. In the control condition models were drawn by the teacher and functioned only as
a fixed representation of the product, as opposed to a developing tool for orientation and
communication. In the guided-co-construction condition models evolved into thinking tools
for students to help them orientate towards the situation, and communicate with each other
and the teacher on their plans and ideas.
Important change in the intervention for students was that they had to design a prototype
of a tandem tricycle in a competition (see figure 3 for the winner). Instead of creating just a
single product, now the students also had to think about the production process in the light of
their final presentation for a jury. In turn this created opportunities to further discover general
Figure 3: Winning prototype tandem tricycle
For the students the intervention took about 10 weeks. 65 students participated. Using
existing knowledge tests pre- and post-knowledge was measured (see figure 4 for an example
item). Pre- and post tests were almost identical. The tests also contained a modelling item
asking the students to draw a motor in a cart (see figure 5).
Figure 4: Test item from pre- and post-test
Figure 5: Modelling item from pre- and post-test
Next to the tests final drawings of every subgroup were assessed by design professionals
according to criteria for design based on diSessa (2002). The interrater agreement was
determined by Cohen's kappa (.86). Video observations and interviews as well as sketches,
drawings and products of students and teachers were incorporated in the analyses.
It turned out that although the experimental group outperformed the control group on the
knowledge-test (see Table 1), the two groups did not differ significantly when controlled for
initial differences. With regard to modelling as measured in the tests, a trend was found that,
adjusted for other co-variables, students in the experimental condition produced better models
than students in the control condition.
Table 1: Scores on pre- and posttests.
M SD Min Max
Control group (n=15)
Age (in months) 199.6 6.42 190 210
Vocabulary 64.73 13.66 40 84
Pre-knowledge 15.25 8.95 2 30
Pre-modelling 2.61 2.48 1 8
Post-knowledge 16.83 6.53 5 24
Post-modelling 2.31 2.39 1 8
Experimental group (n=50)
Age (in months) 186.1 6.60 176 206
Vocabulary 64.96 12.45 41 101
Pre-knowledge 13.02 5.44 4 29
Pre-modelling 3.69 3.49 1 12
Post-knowledge 14.40 5.22 3 24
Post-modelling 4.69 3.28 1 12
A regression analysis showed that a model that predicted the scores on the product-
models by condition was significant (see Table 2). However, an interaction effect was found
between age and condition. Younger students in the experimental condition scored better.
Table 2: Regression analysis for variables predicting the scores on the dependent variable modelling of
the product.
Model R Square Std Error of the
R Square change F
Sign. F Change
1 .55110.50 .55 33.83 .000
2 .6329.64 .08 7.22 .011
1 Predictors: (constant), age in months
2 Predictors: (constant), age in months, interaction age*condition.
# Group scores
These results of the intervention showed that there was no difference between the
conditions with respect to scores on the posttests on codified disciplinary knowledge.
However, the students in the experimental condition produced better models of their
products. At the same time younger students scored better than older students. This could
mean that younger students benefited more from the intervention due to the fact that the older
students were the weaker students (they could be the ones that stayed back in class for
From the analyses of the qualitative data the models in the experimental condition indeed
functioned as tools in the design and construction process. However, the models in the
control condition remained visible longer during the process. Therefore the conclusion was
that guided co-construction with explicit attention for modelling could lead to acquisition of
knowledge and understanding of modelling.
Final experiment (Study 3 and 4)
Phase 3 consisted of two studies (3 and 4) in which the intervention was further
developed and implemented at four schools. Main adjustment of the intervention was the
incorporation of 'prototype lessons' to maintain explicit attention for modelling. In those
lessons students were guided in reflection on the process of designing and construction. Pre-
and posttests measuring knowledge and modelling were conducted as in the previous
experiment. In addition vocabulary and the g-factor of intelligence were measured (J. Raven,
J. C. Raven & Court, 2000). Again video observations and interviews were conducted. In
total 87 students divided over 4 schools participated in this final experiment. The analyses are
divided over two studies.
Quantitative study 3
The study based on quantitative data, showed that two schools, one from each condition,
scored better on the posttests (see Table 3). Consequently, explanation of the differences on
the knowledge tests – after controlling for initial differences – had to be found at school level.
Keeping constant the other variables, both School 2 and 4 scored higher on the knowledge
test (Table 4). However this was not significant.
Table 3: Descriptives of pre- and post- measures
N M SD Min Max
Overall 87
Age (in months) 87 192.72 7.56 168 212
Vocabulary 76 67.34 12.31 39 101
SPM 80 42.50 8.21 0 54
Pretest* 82 18.17 8.30 4 35
Posttest* 73 20.45 7.74 4 35
Control condition 38
Age (in months) 38 192.95 7.32 180 212
Vocabulary 32 62.41 11.51 39 81
SPM 34 43.38 9.07 0 53
Pretest* 35 18.40 8.03 4 33
Posttest* 31 20.81 7.66 5 35
Experimental condition 49
Age (in months) 49 192.55 7.82 168 205
Vocabulary 44 70.93 11.73 39 101
SPM 46 41.85 7.55 17 54
Pretest* 47 18.00 8.58 5 35
Posttest* 42 20.19 7.88 4 33
* Maximum score on pre- and posttest is 47
Table 4: Initial average scores and adjusted means on post-test scores at school level
SPM Pre-test Adjusted post-
School 1 69.03 38.83 13.81 18.50
School 2 75.00 47.50 26.93 21.15
Control group
School 3 64.81 42.32 14.07 19.30
School 4 57.82 44.73 23.33 22.96
Our hypothesis that students in the experimental condition would outperform their
counterparts in the control conditions, had to be rejected. It needs to be noted that students at
School 2 scored high on all pre-measures, whereas students at School 4 scored low on
vocabulary. In average students scored 50 per cent on the knowledge tests.
A first analyses of qualitative data showed that these schools explicitly connected
modelling to the general subject matter, such as mathematics and physics. Moreover these
schools had a smaller student/teacher ratio. Better performing school had less students per
teacher (see Table 5).
Table 5: Student/teacher ratio
Teacher: student Ratio
School 1
School 2
School 3
School 4
* At School 3 there was a change of the second teacher during the project, therefore most of the time only one
teacher was present.
Qualitative study 4
For the second part of the final experiment, Study 4, we continued our analyses by an in-
depth qualitative study to find the determinants that might explain differences in learning
outcome at school level. First of all, in Study 4, the goal was to examine precisely how the
design was enacted at each school. Next, we aimed to establish how the activity of modelling
developed with the process of constructing a tandem tricycle. Moreover, we sought to find
out if modelling actually brought together practical experiences and the codified theories of
the general curriculum. The main focus of this analysis was to find the key determinants of a
microlevel pedagogy that supports students' use of representations as tools. We mainly used
the observational and interview data. All products, drawings and other artefacts were
considered in the context in which they appeared. The representations that appeared in the
observations were classified according to three categories, initial sketches, elaborated and
refining drawings, and final and presentation drawings. According to MacDonalds and
Gustafson (2004) these are the types of drawings professionals use in their design process.
Table 6 shows the categories and the clues by which they were established. We used the clues
and categories for the representations we found in the observations.
Table 6: Categories and clues for drawings (from MacDonalds & Gustafson, 2004)
Based on the analyses of the interactions with models, a vignette was made for every
school, especially focussing on the process of modelling.
School 1
Drawings and models are little in-between-assignments with hardly any reference to the
actual construction. Teachers in the practice workspace helped the students with practical
problems, without explicitly referring to mathematics, science or other codified knowledge.
General subject matter is disconnect from the vocational practice.
School 2
The drawings and representations created by the students develop continuously from initial
sketches to final drawings, and are used by the students themselves as well as by the teachers
as a tool on which to reflect. General knowledge is implicitly referred to.
School 3
Drawings and models are almost non existent in the workshop, only internet pictures or the
initial computer drawing were used as reference. Hardly any relations to curriculum subjects
were mentioned. The prototype lesson was an introduction to the practical problems of
tricycle construction.
School 4
Drawings and models remain visible during the whole process. By drawing and questioning,
the teacher relates the practical issue of construction to the theoretical concepts of
Category 1: Initial sketches
A sketch is made at the beginning of a project
The sketch indicates the pupil's initial thoughts/key ideas about the project.
The sketch is exploratory and conceptual rather than representational.
The sketch is made quickly and spontaneously.
The sketch includes images and words.
Category 2: Elaborate and refining drawings
A series of freehand and hard-line drawings are made during the project.
The drawings are shared with other members of the design team.
The drawings transform the ideas expressed in the initial sketch.
The drawings elaborate, refine, expand, and develop the pupil's initial ideas.
The drawings show increasing accuracy and detail, including dimensionally.
Category 3: Final and presentation drawings
The drawing is made at the end of the project.
The drawing is a recognizable representation of the finished product.
The drawing can be used by those outside the design process as a guide to making.
The drawing is hard-line, finished, precise, and detailed.
The drawing is labeled and measured.
transmission, speed and ratio, as well as to other practical examples. General subject matter
is disconnect from the vocational practice.
The conclusion was that the use of models at two schools resembled the practice of
professional designers more than at the other schools (MacDonald & Gustafson, 2004).
Teachers and students used their models as tools for orientation and communication, which
engaged the students more authentically in the reality of the workplace. As a result, the
students were presumably better supported at these schools in approaching problems in a
vocational as well as an academic fashion (Van Schaik et al., in preparation).
All in all, the question whether or not students show better learning outcomes when they
are the model designers in knowledge-rich simulated workplaces in a process of guided-co-
construction remains unresolved. Based on the tests in the two experiments, the conclusion is
that there is hardly or no difference in learning outcomes compared to students who had
ready-made models provided. However, two findings lead us to believe that guided-co-
construction might improve the students' understanding of modelling and codified
knowledge. First, the students in the experimental condition in the first experiment produced
better models. This may have been due to the fact that the teachers used their models as
communication and orientation tools. Secondly, at two schools in the final experiment more
interactions on models were found, while models were part of the process for a longer time.
Moreover, the models were in a more finalised state. We therefore concluded that the
students' design process at those schools resembled that of professional designers more than
that of the students at the other schools. Our impression was that disciplined perception is
better supported at schools where designing is integrated into the activities of the simulated
workplaces. As a consequence students' understanding and knowledge are enhanced. This
leads to our overall conclusion that the use of models as tools for communication and
orientation in product-oriented vocational practice resembling that of professional designers,
help students develop better understanding, while codified knowledge of both academic and
vocational disciplines is enhanced.
In addition to addressing the overall research question the four studies also resulted in a
closer analysis of the research process and, in particular, the use of video in design-based
research. In retrospect we can see that the extensive use of video data co-determined the
course of the research trajectory in ways that would not have been possible with quantitative
data alone. On the basis of the quantitative data we would have concluded that the research
conditions in the project (providing versus co-constructing models) did not work out as
predicted in our context of knowledge-rich environments. On the basis of our workplace
observations we were able to refine the guiding principles of the design and conduct a
replication study which resulted in basically the same outcome as the answers to our main
research questions. Through the use of video data from workplace activities of students and
teachers the redesigned project enabled us to determine that the use of the models differed at
the different schools. We were even able to speculate about conditions that might be
conducive to such situations. As a result, our attempts to find an answer to questions on the
learning of codified knowledge in simulated, knowledge-rich vocational education obviously
needed a new theoretical refinement that no longer focused on examining the possible value
of broadly defined conditions such as ‘guided co-construction’, but concentrated on actual
microgenetic learning trajectories in the use of modelling (as a tool for orientation and
communication). A decade of studies on the issue of providing versus co-construction has
reached a new stage with the help of detailed video-analysis, which can be defined as a study
of providing in the context of guided co-construction and ways of supporting the meaningful
use of tools and codified knowledge in students’ problem solving during the processes of
construction and design.
Among the first few empirical studies of Dutch pre-vocational education (e.g. Boersma,
ten Dam, Volman & Wardekker, 2009; Koopman et al., in press; Van de Pol, Volman &
Beishuizen, 2011) this study is the only one that combines the perspective of the students and
the role of the teachers by using an intervention that incorporates process data (e.g. video)
and output measures (knowledge tests). It resulted in findings that are in line with the other
studies. With Boersma et al. (2009) we agree that students are motivated by 'real'
assignments. That is, tasks which, as Koopman et al. (in press) argued, should be oriented
towards delivering a 'product'. The fact that we observed only two schools at which teachers
were able to link students' practical problems to theory, concurs with the results in Van de Pol
et al. 2011), in which observed teachers showed few examples of guidance that were
contingent on student capabilities.
Given that we only found minor statistical differences, further study of the complex
environment will have to be considered. Strict control of the conditions proved impossible,
while a fidelity approach would have been counterproductive in this rather loosely organised
school sector. As a consequence the design implementation differed considerably among
schools. Since student groups and teacher teams are especially unstable in pre-vocational
education, a larger sample could only partly solve that problem. We also know from our logs,
observations and interviews that adaptation to the local school context does not ensure
implementation of the intervention as intended. The concept of mutual appropriation may
therefore be the correct one to gain insights into the dynamics of interventions in (pre-
vocational) education, with the researcher(s) on one side and teacher(s) on the other
(Downing-Wilson, Lecusay, & Cole, in press).
Taking the conclusions of the four studies in this paper together with the analyses in
chapter 2 of the development of the intervention, we propose three suggestions for the
modelling curriculum in (pre)vocational education. The first suggestion addresses the content
of teaching; the second suggestion, on how the teaching-learning processes could be shaped,
is more pedagogical in nature; the third suggestion describes the assignments.
With regard to the content of modelling teaching in vocational education, the focus of
teacher guidance should be on the process of designing. Since we learned that those schools
performed best at which the enacted curriculum project resembled the practice of professional
designers, the suggestion is that when students act as designers they learn better how to use
models and reach acceptable levels of knowledge. Moreover, models that are used as tools for
orientation and communication and utilised in combination with teacher guidance, can
support student understanding as well as enhance the knowledge codified in academic and
vocational disciplines.
It follows from the above considerations that teacher guidance is crucial. Two main
characteristics can be formulated from our studies. First, teachers who are capable of
explicitly integrating theory and practice through their academic background guided students
to better (use of) models. Teams of teachers should therefore be composed in such a way that
at least one of the teachers has an academic background and is able to connect that to the
workplace. This way, students can be guided towards concepts, rules and principles of
academic and vocational disciplines by working on practical assignments. Secondly, as we
saw, when students work on their own design and draw models themselves their own models
are more elaborate, and they perform better on modelling tests. Hence, teacher guidance
should have a student’s’ own design as its starting point.
Finally, for the assignment it proved important that it was 'real' and complex. Students
were motivated to work on products that could be used as real products. Although the
assignment in the two experiments had no clients, the prototype competition was real enough.
In addition, to promote understanding and codified knowledge, assignments need to be
complex, though not too difficult. The tricycle assignment had the right balance in this
respect. It was complex enough to connect practical problems to academic as well as
vocational disciplines, such as are, for example, manifested in the concepts of transmission
and the principles of designing and modelling. At the same time the assignment proved not
too difficult, since most students were able to finish the product.
In light of the above, the discussion about providing versus guided co-construction
can be taken a step further by specifying in greater detail what teachers really do, where,
when, and finally how their activities are related to learning outcomes. In other words, the
proposed focus for future research consists in the further elaboration of the different forms of
guidance (by instruction, discussion, etc.) in workplace contexts and how such forms could
support students’ development towards expertise in the vocational practice. More detailed
studies are required into the development of disciplined perception and into ways in which
such development could be stimulated in workplace settings.
Further research should also explore a teaching/learning strategy that incorporates
actual school practice. In ideal practical situations students design and construct complex
'real' products, guided by teachers who are able to connect practical problems to disciplinary
theory, while the students' own designs form the basis for guidance. Only approximations to
such situations could explain what guided co-constructing means for teaching and learning in
general, with specific reference to (pre)vocational education.
At this stage the empirical relevance of these practical implications to educational theory
needs to be addressed. First of all, in the course of the three interventions we developed the
concept of a knowledge-rich learning environment in vocational education. We started by
stating that it should be an environment in which students acquire more than just practical
skills. Codified knowledge should also be imparted in such an environment. Our final
impression is that if the concepts of both Guile and Young (2003) and Stevens and Hall
(1998) are connected, the learning environment has the potential for students to acquire
codified or disciplinary knowledge. Furthermore, the results of the two experiments have led
to an improved understanding of how models work as tools in vocational education and that
the use of such tools may result in acceptable knowledge levels (i.e. scores above 50 per cent
on posttests). Our view of models as tools for orientation and communication was enriched
by the way models work in a design process in school practice (MacDonalds & Gustafson,
2004). Finally, we now have additional proof that guided co-construction as a teaching-
learning strategy works in pre-vocational education. Furthermore, the nature of what
constitutes relevant guidance has been further elaborated (see for example the suggestions
above). While working on real products VMBO students need the type of guidance that leads
them from their own designs and models to the knowledge codified in vocational and
academic disciplines. Such guidance must explicitly connect theory to practical problems.
Only in that way will students be able to learn to recontextualise their practical knowledge
within the system of codified disciplinary knowledge. Such recontextualisation will improve
their practical skills as well as their theoretical knowledge. In short, our theory of modelling
in vocational education has now been connected to VMBO practice.
Billett, S. (2004). Learning through work. Workplace participatory practices. In: H. Rainbird,
H. Fuller, & A. Munro (Eds.), Workplace learning in context (pp. 109-125). London:
Boersma, A., ten Dam, G., Volman, M., & Wardekker, W. (2009). “This baby…it isn’t alive.”
Towards a community of learners for vocational orientation. British Educational
Research Journal, 36(1), 1-23.
Cedefop (2009). Future skill supply in Europe. Medium-term forecast up to 2020.
Luxembourg: Office for Official publications of the European Communities.
Retrieved from
Commission of the European Communities (2008). Improving competences for the 21st
century: An Agenda for European cooperation on schools (Communication from the
commission to the European parliament, the council, the European economic and
social committee and the committee of the regions No. SEC (2008) 2177). Brussels:
Commission of the European communities. Retrieved from http://eur-
De Bock, D., Verschaffel, L., Janssens, D., Van Dooren, W., & Claes, K. (2003). Do realistic
contexts and graphical representations always have a beneficial impact on students’
performance? Negative evidence from a study on modelling non-linear geometry
problems. Learning and Instruction, 13(4), 441-463. doi: doi: DOI: 10.1016/S0959-
De Bruijn, E. (2004). Changing pedagogic and didactic approaches in vocational education in
the Netherlands. From institutional interests to ambitions of students. European
Journal of Vocational Training, 31(1), 27-37.
diSessa, A. (2002). Students criteria for representational adequacy. In: K. Gravemeijer, R.
Lehrer, B. Van Oers, & L. Verschaffel (Eds.), Symbolizing, modelling and Tool use in
mathematics education, Mathematics Education Library (pp. 105-129). Dordrecht:
Kluwer academics publishers.
Downing-Wilson, D., Lecusay, R., & Cole, M. (in press). Design experiments and mutual
appropriation: two strategies for university/community collaboration after school
interventions. Theory & Psychology.
Engeström, Y. (2007). Enriching the Theory of Expansive Learning: Lessons From Journeys
Toward Coconfiguration. Mind, Culture, and Activity, 14(1-2), 23-39.
Engeström, Y. (2009). The future of activity theory; a rough draft. In: A. Sannino, H. Daniels,
& K. D. Gutiérrez (Eds.), Learning and expanding with activity theory (pp. 303-328).
New York: Cambridge University Press.
Erickson, F. (2006). Definition and analysis of data from videotape: some research procedures
and their rationales. In: J. L. Green, G. Camilli, & P. B. Elmore (Eds.), Handbook of
complementary methods in education research (pp. 177-192). Mahwah, New Jersey:
Lawrence Erlbaum associates, Inc. Publishers American Educational Research
Gravemeijer, K., Lehrer, R., Van Oers, B., & Verschaffel, L. (2002). Symbolizing, modelling
and tool use in mathematics education. Mathematics Education Library. Dordrecht:
Kluwer academic publishers.
Griffiths, T., & Guile, D. (2003). A connective model of learning: the implications for work
process knowledge. European educational research journal, 2(1), 56-73.
Guile, D., & Griffiths, T. (2001). Learning Through Work Experience. Journal of Education
and Work, 14(1), 113-131.
Guile, D., & Young, M. (2003). Transfer and transition in vocational education: some
theoretical considerations. In: T. Tuomi-Gröhn & Y. Engestrom (Eds.), Between
school and work: new perspectives on transfer and boundary crossing (pp. 63-84).
Amsterdam: Pergamon An imprint of Elsevier Science.
Kent, P., Noss, R., Guile, D., Hoyles, C., & Bakker, A. (2007). Characterizing the Use of
Mathematical Knowledge in Boundary-Crossing Situations at Work. Mind, Culture,
and Activity, 14(1-2), 64-82.
Koopman, M., Teune,, P., & Beijaard, D. (in press). Development of student knowledge in
competence-based pre-vocational education. Learning Environments Research.
Kozulin, A., Gindis, B., Agayev, V. S., & Miller, S. M. (2003). Introduction: Sociocultural
theory and education: students, teachers, and knowledge. In: B. Gindis, V. S. Ageyev,
S. M. Miller, & A. Kozulin (Eds.), Vygotsky’s educational theory in cultural context
(pp. 1-14). Cambridge: Cambridge University Press.
Lave, J., & Wenger, E. (2005). Practice, person, social world. In: H. Daniels (Ed.), An
introduction to Vygotsky (Vol. 2, pp. 149-156). East Sussex: Routledge.
Lave, J., & Wenger, E. (1991). Situated learning: legitimate peripheral participation (Vol.
repr.). Cambridge: Cambridge University Press.
MacDonald, D., & Gustafson, B. (2004). The role of design drawing among children engaged
in parachute building activity. Journal of Technology Education, 16(1), 55-71.
Maes, M. (2004). Vocational education and training in the Netherlands. Cedefop Panorama
series (Revised Edition.). Luxembourg: CEDEFOP (European Centre for the
Development of Vocational Training). Retrieved from
Mercer, N. (1995). The guided construction of knowledge: talk amongst teachers and
learners. Clevedon: Multilingual matters.
Perkins, D. N., & Unger, C. (1999). Teaching and Learning for understanding. In: C. M.
Reigeluth (Ed.), Instructional-design theories and models. (pp. 91-114). II: Lawrence
Erlbaum associates.
Poland, M. (2007). The treasures of schematising. The effects of schematising in early
childhood on the learning processes and outcomes in later mathematical
understanding. Amsterdam: Vrije Universiteit.
Raven, J., Raven, J. C., & Court, J. H. (2000). Standard progressive matrices. Manual for
Raven’s progressive matrices and vocabulary scales. Oxford Psychologists.
Saxe, G. B., & Guberman, S. R. (1998). Studying mathematics learning in collective activity.
Learning and Instruction, 8(6), 489-501.
Seezink, A., Poell, R., & Kirschner, P. (2009). Teachers’ individual action theories about
competence-based education: the value of the cognitive apprenticeship model.
Journal of Vocational Education & Training, 61(2), 203-215. doi:
Stevens, R., & Hall, R. (1998). Disciplined perception: learning to see in technoscience. In:
M. Lampert & M. L. Blunk (Eds.), Talking mathematics in school. Studies of teaching
and learning (pp. 107-149). Cambridge: Cambridge University press. Retrieved from
Terwel, J. (2004). Curriculum and curriculum differentiation. Curriculum as a Shaping
Force. New York: Nova.
Terwel, J. (2005). Analyse van kwalitatieve data: Patronenanalyse en de critical incident
methode [Analysis of qualitative data: Pattern analysis and critical incidents method].
VU University Amsterdam.
Terwel, J., Van Oers, B., Van Dijk, I., & Van den Eeden, P. (2009). Are representations to be
provided or generated in primary mathematics education? Effects on transfer.
Educational research and Evaluation, 15(1), 25-44.
The design based research collective. (2003). Design based research: an emerging paradigm
for educational inquiry. Educational researcher, 32(1), 5-8.
Tuomi-Gröhm, T., & Engeström, Y. (2003). Conceptualizing transfer: form standard notions
to developmental perspectives. In: T. Tuomi-Gröhn & Y. Engeström (Eds.), Between
school and work New perspectives on transfer and boundary crossing, Advances in
learning and instruction series (pp. 19-38). Bingley: Emerald Group publishing
Tynjälä, P. (2008). Perspectives into learning at the workplace. Educational Research Review,
3(2), 130-154. doi: 10.1016/j.edurev.2007.12.001
Van Dijk, I. (2002). The learner as designer: processes and effects of an experimental
programme in modelling in primary mathematics education. Vrije Universiteit,
Van Oers, B. (1988). Modellen en de ontwikkeling van het (natuur-) wetenschappelijk denken
van leerlingen.[Models and the development of (natural) scientific thinking of
students]. Tijdschrift voor Didactiek de Beta-wetenschappen [Journal of didactics for
the beta-sciences], 6(2), 115-143.
Van Oers, B. (2001). Educational forms of initiation in mathematical culture. Educational
Studies in Mathematics, 46(1), 59-85.
Van Oers, B. (2006). An activity theory approach to the formation of mathematical cognition:
developing topics through predication in a mathematical community. In: J. Maasz &
W. Schloeglman (Eds.), New mathematics education research and practice (pp. 97-
141). Rotterdam: Sense Publishers.
Van Oers, B., & Wardekker, W. (2000). De cultuurhistorische school in de pedagogiek [The
cultural historical school in pedagogy]. In: S. Miedema (Ed.), Pedagogiek in
meervoud [Pedagogy in plural] (pp. 171-213). Houten/Diegem: Bohn Stafleu Van
Van Schaik, M. (2009). Looking at learning in practice - Classroom observation with Noldus
Observer XT. Noldus. Retrieved from
Van Schaik, M. (2010). Let the video be your guide: a case study of video-based design
research. Co-constructing models as tools in vocational practice. Learning in a
knowledge-rich environment. Amsterdam: Free Musketeers.
Van Schaik, M., Van Oers, B., & Terwel, J. (2010). Learning in the school workplace:
knowledge acquisition and modelling in preparatory vocational secondary education.
Journal of Vocational Education & Training, 62(2), 163-181. doi:
Van Schaik, M., van Oers, B., & Terwel, J. (2011). Towards a knowledge-rich learning
environment in preparatory secondary education. British Educational Research
Journal, 37(1), 61-81. doi: 10.1080/01411920903420008
Van Schaik, M., Terwel, J., & Van Oers, B. (in preparation). Tools for learning in the
workplace at school: results of an intervention in vocational education.
Van Schaik, M., Terwel, J., & Van Oers, B. (in preparation). Representations in simulated
workplaces. Journal of Engineering Education.
Van de Pol, J., Volman, & Beishuizen, J. (2011). Patterns of contingent teaching in teacher-
student interaction. Learning and Instruction, 21(1), 46-57. doi:
Van der Sanden, J. M. M., Terwel, J., & Vosniadou, S. (2000). New learning in science and
technology. In: P. Simons, J. Van der Linden, & T. Duffy (Eds.), New Learning: three
ways to learn in a new balance (pp. 119-140). Dordrecht: Kluwer Academic
Verkerk, M. J., Hoogland, J., Van der Stoep, J., & de Vries, M. J. (2007). Denken, ontwerpen,
maken- Basisboek techniekfilosofie [Thinking, designing, making - Handbook
philosophy of technology]. Amsterdam: Boom.
Volman, M. (2006). Jongleren tussen traditie en toekomst [Juggling between tradition and
future] Inaugural lecture. Centre for Education Training, Assessment and Research,
VU University Amsterdam.
ResearchGate has not been able to resolve any citations for this publication.
Full-text available
What are the differences among American, German, and Japanese classrooms? If we take as a cue the anecdote told by Stiegler and Hiebert (1999) in their book The Teaching Gap, in a Japanese classroom there are students and there is knowledge and the teacher serves as a mediator between them. In a German classroom there are also knowledge and students, but teachers perceive this knowledge as their property and dispense it to students as they think best. In the American classroom there are teachers and there are students, but the status of knowledge is uncertain. In this book we are offering a perspective that is different from those mentioned, yet poses the same fundamental question of the relationships among students, teachers, and knowledge. Our perspective is grounded in the theory of Lev Vygotsky (1896–1934), whose ideas turned out to be instrumental in shaping the learning processes in a growing number of classrooms in Russia, Europe, and the United States. At the heart of Vygotsky's theory lies the understanding of human cognition and learning as social and cultural rather than individual phenomena. During his tragically short lifetime Vygotsky developed this central thesis in a variety of areas including the theory of child development and educational psychology. He explored relationships between language and thought, instruction and development, everyday and academic concept formation, and a host of others. For a number of decades his theory inspired only a relatively small group of followers in Russia and Eastern Europe.
A review of literature shows that during the history of mathematics education at school the answer of what counts as ‘real mathematics’ varies. An argument will be given here that defines as ‘real mathematics’ any activity of participating in a mathematical practice. The acknowledgement of the discursive nature of school practices requires an indepth analysis of the notion of classroom discourse. For a further analysis of this problem Bakhtin’s notion of speech genre is used. The genre particularly functions as a means for the interlocutors for evaluating utterances as a legitimate part of an ongoing mathematical discourse. The notion of speech genre brings a cultural historical dimension in the discourse that is supposed to be acted out by the teacher who demonstrates the tools, rules, and norms that are passed on by a mathematical community. This has several consequences for the role of the teacher. His or her mathematical attitude acts out tendencies emerging from the history of the mathematical community (like systemacy, non-contradiction etc.) that subsequently can be imitated and appropriated by pupils in a discourse. Mathematical attitude is the link between the cultural historical dimension of mathematical practices and individual mathematical thinking.
In prior work we1 observed that, while designing representations, students employed an iterative process of innovating, critiquing, selecting, refining, and combining representations. Prior work also cataloged a rich set of ideas for representational innovation. This chapter focuses on the ability to judge and critique the quality of representations. In a study of high school students’ critical abilities, we investigated three main hypotheses: (1) Students’ ability to critique representations is rich and generative. (2) Students’ critical capabilities are, by and large, relatively reactive and inarticulate. (3) Students’ critical capabilities are design-linked; that is, competence does not appear equally in all contexts, but shines particularly in the context of design. Data from our study support all these hypotheses, with qualifications. Most unequivocally, students seem to have a strong, uninstructed, yet scientifically cogent competence to judge the quality of representations.