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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Reflective Pedagogical Practice on and in Introduction to Programming and Software Engineering</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Steffen Becker</string-name>
          <email>steffen.becker@informatik.uni-</email>
          <email>steffen.becker@informatik.unistuttgart.de</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Christine Bescherer</string-name>
          <email>bescherer@ph-ludwigsburg.de</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Andreas Fest</string-name>
          <email>fest@ph-ludwigsburg.de</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Institute for Mathematics and Computer</institution>
          ,
          <addr-line>Science</addr-line>
          ,
          <institution>University of Education Ludwigsburg</institution>
          ,
          <addr-line>Ludwigsburg</addr-line>
          ,
          <country country="DE">Germany</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Institute of Software Technology</institution>
          ,
          <addr-line>(ISTE)</addr-line>
          ,
          <institution>University of Stuttgart</institution>
          ,
          <addr-line>Stuttgart</addr-line>
          ,
          <country country="DE">Germany</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2020</year>
      </pub-date>
      <fpage>7</fpage>
      <lpage>10</lpage>
      <abstract>
        <p>In an educational project aimed at introducing reflective pedagogical practice to improve the situation of preservice teachers in computer science at the University of Stuttgart, the need to restructure the introductory 'Programming and Software Engineering' course for all computer science students arose. So, the reflective pedagogical practice - by the lecturers - led to changes in the course. The first steps of the educational re-design - following a design-based research approach - are describe here.</p>
      </abstract>
      <kwd-group>
        <kwd>pre-service teachers in computer science</kwd>
        <kwd>reflective pedagogical practice</kwd>
        <kwd>introduction to programming and software engineering</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>I. INTRODUCTION</title>
      <p>Pre-service teachers1 in computer science at the University
of Stuttgart have to take the introductory “Programming and
Software Engineering” course (PSE) in their 1st semester
together with all the other computer science students. For most
of these students, especially the ones from
BadenWürttemberg, this is the first contact with concepts and
strategies for programming.2</p>
      <p>
        So, we wanted to use this opportunity, when these future
teachers make their own learning experiences with
programming, to introduce them to a reflective pedagogical
practice [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ], [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ].
      </p>
      <p>We believe that the pre-service teachers’ problems with
their first experiences using – formal – programming and
software engineering concepts and strategies will be similar to
the ones their students will face in the future when they teach
at school. So, this point in time at the beginning of the
university program is a good opportunity for the pre-service
teachers to reflect on their own learning experiences. When
they will have finished their university degree in Computer
Science Education and will start their work in schools, they
will be advanced computer scientists themselves. So, it will
probably be much harder for them to remember their first steps
into programming including the problems they had.</p>
      <p>
        In a project funded by the Ministry for Science, Research,
and Art, Baden-Württemberg the group combined of a
software engineer, a computer science educator, a
1 ‚Pre-service teacher‘ means students in pre-graduate or
graduate teacher programs compared to
‚in-serviceteachers‘, who are already working in schools.
2 In the state of Baden-Württemberg computer science as a
compulsory subject in secondary schools only started
recently and with only one hour a week in 7th grade.
mathematics educator and an experienced PSE tutor, who is
also an advanced pre-service teacher, works in a design-based
research approach [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ] to address this issue.
      </p>
    </sec>
    <sec id="sec-2">
      <title>II. THEORETICAL BACKGROUND</title>
      <sec id="sec-2-1">
        <title>A. Reflective Pedagogical Practice</title>
        <p>
          Reflective pedagogical practice was the most important of
the concepts, we used to design our intervention. Reflective
practice in teacher education means on one hand that
preservice teachers reflect on their in-school-experience in an
internship [
          <xref ref-type="bibr" rid="ref2">2</xref>
          ]. “Reflective practice is considered necessary if
teachers are to learn from their own teaching experiences and
the experiences of others.” [1 p. 482]. But it can also refer to
reflection of one’s own learning experiences [
          <xref ref-type="bibr" rid="ref5">4</xref>
          ] to identify
e.g. what were the obstacles in understanding some topics and
what supported the understanding process.
        </p>
      </sec>
      <sec id="sec-2-2">
        <title>B. Similarities in pre-service mathematics teachers’ programs</title>
        <p>
          There is a similar problem for pre-service mathematics
teachers called the “double discontinuity” [
          <xref ref-type="bibr" rid="ref6">5</xref>
          ] which describes
the conceptual changes students face in the transition from
high school mathematics to university mathematics, which is
much more formal and abstract than school mathematics.
After their university degree in mathematics education, when
going back to school as teachers they face the second
discontinuity: They have to break down their mathematical
knowledge to the level in the classroom. In Germany several
projects and initiatives aimed to improve these situations ( [
          <xref ref-type="bibr" rid="ref7">6</xref>
          ],
[
          <xref ref-type="bibr" rid="ref8">7</xref>
          ], [
          <xref ref-type="bibr" rid="ref9">8</xref>
          ]). Further, in most German universities there are no
special lectures in mathematics for pre-service teachers but
they attend the same Calculus or Analytical Geometry courses
as (future) research mathematicians.
        </p>
        <p>
          Some of the recommendations of the above-mentioned
initiatives to deal with the problems arising out of the double
discontinuity are to group the pre-service teachers in special
groups for the tutorials 3 and to substitute one of the
mathematics problems on the weekly worksheets by special
learning or teaching related problems [
          <xref ref-type="bibr" rid="ref8">7</xref>
          ]. According to
Ableitinger [
          <xref ref-type="bibr" rid="ref8">7</xref>
          ] these pre-service-teacher oriented task could
either use typical school problems as a way to connect the
3 In Germany mathematics lectures are usually accompanied
by small group tutorials, where students work on or present
their solutions of the weekly worksheets.
        </p>
        <p>
          Fig 1: Example of pre-service-specific math problem [
          <xref ref-type="bibr" rid="ref10">9</xref>
          ]
available mathematical knowledge to issues in university
mathematics. Figure 1 shows an example of this approach.
There the necessity to prove the theorem given in the last part
is “grounded” in a typical math problem from high school. On
the other hand, these pre-service specific tasks can use the
university mathematics viewpoint e.g. to better understand the
different levels of abstraction or the coherence of different
mathematical topics. For example, while discussing the
characteristics of – abstract – vector spaces, the pre-service
teachers could identify examples of this mathematical
structure used in school mathematics like the 3-dimensional
coordinate space, the complex numbers or even function
space.
        </p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>III. REALIZATIONS</title>
      <p>The aim of the project is to improve the situation of the
pre-service computer science teachers in the PSE course. So,
we planned these measures:
•
•
•
all pre-service teachers are gathered in two extra
tutorial groups4
these tutorials are conducted by an advanced
preservice teacher
in each worksheet there is one dedicated extra task
asking for a reflective pedagogical practice</p>
      <p>In the discussions while preparing these tasks, the project
group realized that it is not enough to change one task per
worksheet, but that the structure of the course and the content
of the different lectures were also not very supportive to
learning programming and software engineering regardless
whether the students were pre-service teachers or not. So, we
went through all the lectures to identify and name the learning
aims, to sort the prerequisites and the necessary definitions for
the students to understand the topics.</p>
      <p>Examples of these changes include that we added explicit
learning objectives at the beginning of each lecture focusing
on the programming related concepts and definitions. These
learning objectives play the role of a table of contents of the
lecture which makes it easier for the students to get an idea of
the extend of concepts taught in the lecture. Following that
information, we now provide insights into the didactical5 idea
of the lecture in order to make it transparent to the students.
For example, we use the Hamster simulator by D. Bohles
(http://boles.de/hamster/simulator.html) to start with a
miniature language and a miniature world to mitigate the
effect of being overwhelmed by the sheer number of concepts
used in programming. Also, it adds a gamification aspect to
the exercises on the worksheets to increase the students’
motivation to explore programming on their own.</p>
      <p>
        We also apply the objects-first teaching [
        <xref ref-type="bibr" rid="ref13">12</xref>
        ] approach
which focuses in the first lectures on using and creating
objects. This shifts the usual algorithmic topics some weeks
towards the lecture’s end. Students who have prior experience
in programming often have algorithmic experience. We
explain to the students, why we do not start with algorithms:
The reason is that concepts like branches or loops are not as
important in OOP as students usually think - based on their
prior knowledge and experience.
      </p>
      <p>However, already in the previous year we learnt that the
students do not see why teaching objects-first is of relevance.
In the lecture feedback forms they said the course is not
teaching what they believed is of most importance. Explaining
in detail why objects are taught first and why this has some
advantages aims at increasing the acceptance within the
students. As a first effect, it has already increased the
acceptance of this didactical method among the tutors which
start to favor it now. In the meantime, also the student
evaluation of the second instance of the lecture has taken
place. In the feedback forms we can see a significant trend that
the students understood much better why teaching objects first
is an interesting and useful didactical approach. The number
of students complaining about object firsts has decreased to
outliers (less than 5 students in a group of almost 200). Their
main reason for rejecting the approach is often based on
insufficient tooling support (BlueJ as IDE in contrast to
Eclipse or IntelliJ). We consider this not as fundamental issues
with the objects first approach, but rather with its
implementation.</p>
      <p>Finally, the lectures have been enhanced with a
competence-oriented list of skills and capabilities the students
should have once they fully understood the contents of the
lecture. In the last semester, we observed that a large number
of students learned a concept’s definition but were unsure
about what level of application they should be able to do in</p>
    </sec>
    <sec id="sec-4">
      <title>4 Usually there are less than 20 pre-service teachers</title>
      <p>
        attending PSE and about 400 students of computer science
plus 100-200 students taking PSE as imported subject.
5 ‚Didactical‘ is used here in the European understanding
and is similar to the concept of Shulman’s ‘pedagogical
content knowledge’ [
        <xref ref-type="bibr" rid="ref11">10</xref>
        ].
exams. For example, a large number of students was able to
define what a type of a variable is conceptually, but were
unable to derive the types of variables in a given small
program fragment. The newly structured lecture content now
is very explicit in this by naming the expected learned
competences and the level of competence we expect for
passing the course.
      </p>
      <p>The following examples give an idea of the of the pre-service
teacher specific tasks in the worksheets from wintersemester
2019/20:</p>
      <p>As stated above - beside adding information about
educational aspects to the lectures - we designed exclusive
tasks for pre-service teachers. As this is still an ongoing
process we give some highlights of the tasks we added to the
worksheets of this lecture’s instance. At the time of writing
roughly 60% of all worksheets of the semester have been
designed and used. One task focused on our “challenging
assignments”. Challenges have been added to all worksheets
to offer some interesting tasks also for those students who
already have prior programming experience as they complete
the worksheet in half the time of the beginners. This is a
common challenge in teaching programming as often teachers
will face students who learned programming before, e.g., in a
self-taught manner. In the pre-service teachers’ worksheet, we
make the future teachers aware of this problem by making
them reflect on their own different levels of experience and
discuss the pros and cons of this approach.</p>
      <p>In the following worksheets, the pre-service teachers are
supposed to reflect the gamification approach using the
Hamster simulator and the objects-first approach. They will
have to discuss how they experienced their own learning using
these didactical elements of the lecture. They can base their
discussions on our explicit information about the designed
didactical concept of each lecture. One specific task was to
reflect on the differences between the Hamster simulator mini
world and Kara the ladybug’s mini world 6 . There are
differences in the complexity, the number of supported
languages, and also in the objects first vs. algorithms first way
of teaching. We expected the pre-service teachers to identify
and analyze those differences.</p>
      <p>Finally, in even further worksheets we had the pre-service
teachers reflect on algorithmic problem solving vs.
objectoriented problem solving. They should list the pros and cons
of using the objects-first vs. the algorithms-first approach at
school and make up their mind which approach they would
like most based on their own experiences.</p>
      <p>As part of the latter, we had a task for the pre-service
teachers to discuss the pros- and cons of using a simplified
IDE for objects first (BlueJ in our case). They had to contrast
it to using another simple IDE, a more complex IDE or no IDE
at all. This task was supposed to make the pre-service teachers
explicitly reflect on the role IDEs play in learning to program.
The idea was to contrast hiding a lot of technical details in the
IDE vs. seeing and potentially understanding them when using
no IDE or a complex IDE.</p>
      <p>Another task for the pre-service teachers was to compare
their experience in learning a computer science topic to the
experiences they had in learning other, but related topics
(math, physics, etc.). The idea was to identify and utilize the
6 https://www.swisseduc.ch/informatik/karatojava/kara/
positive aspects in teaching computer science and to mitigate
the negative aspects of it.</p>
      <p>Contracts and design-by-contract are important aspects of
the objects first teaching approach. Hence, we made the
preservice teachers to reflect on the use of contracts in a
(potentially more advanced) course at school. The objective of
the task was for them to come up with ideas how to teach a
rather complex topic in such an advanced course in school. In
detail, the pre-service teachers were asked how they would
find an abstraction of the concept or how they would design
simple examples which convey the motivation of contracts in
programming.</p>
      <p>As we used the hamster simulator’s mini world to
introduce gamification in our exercises, we asked the
preservice teachers to reflect on their experiences in doing
gamebased exercises. In addition, they were asked to survey other
game-based teaching methods which already exist and can be
used in schools (like writing games in Scratch, using teaching
related smartphone apps, etc.)</p>
      <p>As part of teaching OOP, the pre-service teachers had to
learn the concept of inheritance. As this is another more
advanced topic, we made them again reflect on their
experiences in understanding inheritance. Based on this, we
asked them again to come up with ideas whether and how to
introduce inheritance in the context of a school’s course. In
addition, we asked them to design small tasks and exercises
which potentially could be used in such a course.</p>
      <p>In the last exercise designed so far, we added a task about
how to introduce and illustrate the usefulness of debugging.
As debugging is often a task which involves many and often
overwhelming features of an IDE, the main objective was how
to illustrate debugging to students. The hamster and ladybug
mini worlds provide already partial answers in their integrated
IDEs. These approaches make the idea and usefulness of
debugging much more tangible.</p>
    </sec>
    <sec id="sec-5">
      <title>IV. FIRST RESULTS</title>
      <p>As the course is still ongoing with the redesigns sketched
above it is too early for an objective assessment. However,
from a subjective point of view based on observations made
in the lecture and tutorial groups the implemented
improvements have a positive impact. Students are more
motivated and seem to be less lost in the large amount of
information a lecture at a university is able to provide. The
pre-service teachers’ tutorial groups find the additional
exercises interesting. Before, they were treated as any other
student in the course Programming and Software
Development, the question how to teach the subject has not
been addressed and remained implicit. Because of this they
also did not develop an identity as a group and complained a
lot that they were confronted with teaching related questions
only from the third semester onwards – and then it was
disconnected from their own experiences. Now they get a
preservice teacher related view on the topics right from the first
lecture in their computer science topic.</p>
      <p>V. FURTHER STEPS IN THE DESIGN-BASED RESEARCH PROCESS</p>
      <p>
        The whole project is an example of design-based
educational research [
        <xref ref-type="bibr" rid="ref12">11</xref>
        ]. After identifying the ‘problem’ – in
our case the difficulties especially the pre-service teachers
have with the course Introduction to Programming and
Software Engineering – some theoretical input is collected.
Then the design-based research cycle (s. fig 2) will be
followed through.
Diagramm according to Nando Stöcklin: http://educationaldesignresearch.de/wasistedr/
Fig. 2: Design-based Educational Research Cycle to develop new
learning scenarios.
      </p>
      <p>
        Some of the theoretical inputs are described above and the
first implantation of the course is taking place during the
winter semester 2019/20. Beside the detailed comparison of
the evaluation results (s. above) we will ask students to give a
formative feedback on the improvements using the Teaching
Analysis Poll method [
        <xref ref-type="bibr" rid="ref14">13</xref>
        ], questionnaire. Additional
interviews with a few pre-service teachers and the tutors will
be conducted. According to the results of these feedbacks the
redesign of the course Introduction to Programming and
Software Engineering will take place and be run again. If the
evaluation results of this run will be satisfying, the whole
concept will be described in detail and disseminated further.
      </p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          [1]
          <string-name>
            <surname>Lane</surname>
            ,
            <given-names>R.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>McMaster</surname>
            ,
            <given-names>H.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Adnum</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Cavanagh</surname>
            ,
            <given-names>M.</given-names>
          </string-name>
          (
          <year>2014</year>
          ).
          <article-title>Quality reflective practice in teacher education: A journey towards shared understanding</article-title>
          .
          <source>Reflective Practice</source>
          ,
          <volume>15</volume>
          (
          <issue>4</issue>
          ),
          <fpage>481</fpage>
          -
          <lpage>494</lpage>
          . DOI:
          <volume>10</volume>
          .1080/14623943.
          <year>2014</year>
          .900022
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          [2]
          <string-name>
            <surname>Power</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Clarke</surname>
            ,
            <given-names>M.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Hine</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          (
          <year>2002</year>
          ).
          <article-title>Internship learning connects the dots: The theory and practice of reflection</article-title>
          . Online at https://www.aare.edu.au/data/publications/2002/cla02481.pdf
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          [3]
          <string-name>
            <surname>Easterday</surname>
            ,
            <given-names>M. W.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Lewis</surname>
            ,
            <given-names>D. R.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Gerber</surname>
            ,
            <given-names>E. M.</given-names>
          </string-name>
          (
          <year>2014</year>
          ).
          <article-title>Design-Based Research Process: Problems, Phases, and Applications</article-title>
          . In: Polman,
          <string-name>
            <given-names>J.</given-names>
            ,
            <surname>Kyza</surname>
          </string-name>
          , E.,
          <string-name>
            <surname>O'Neill</surname>
            ,
            <given-names>D.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Tabak</surname>
            ,
            <given-names>I.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Penuel</surname>
            ,
            <given-names>W.</given-names>
          </string-name>
          <string-name>
            <surname>Jurow</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>O'Connor</surname>
            ,
            <given-names>K.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Lee</surname>
            ,
            <given-names>T.</given-names>
          </string-name>
          &amp;
          <string-name>
            <surname>D'Amico</surname>
            ,
            <given-names>L</given-names>
          </string-name>
          . (eds.).
          <source>International Conference of the Learning Sciences (ICLS)</source>
          <year>2014</year>
          , (
          <issue>1</issue>
          ),
          <fpage>317</fpage>
          -
          <lpage>324</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          https://doi.dx.
          <source>org/10</source>
          .22318/icls2014.317
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          [4]
          <string-name>
            <surname>Graham</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          &amp;
          <string-name>
            <surname>Phelps</surname>
            ,
            <given-names>R.</given-names>
          </string-name>
          (
          <year>2003</year>
          ).
          <article-title>Being a teacher: developing teacher identity and enhancing practice through metacognitive and reflective learning processes</article-title>
          ,
          <source>Australian Journal of Teacher Education</source>
          , vol.
          <volume>27</volume>
          , no.
          <issue>2</issue>
          , pp.
          <fpage>11</fpage>
          -
          <lpage>24</lpage>
          . Online at https://ro.ecu.edu.au/ajte/vol27/iss2/2/
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          [5]
          <string-name>
            <surname>Kilpatrick</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          (
          <year>2019</year>
          ).
          <article-title>A Double Discontinuity and a Triple Approach: Felix Klein's Perspective on Mathematics Teacher Education</article-title>
          . In: H.- G. Weigand,
          <string-name>
            <given-names>W.</given-names>
            <surname>McCallum</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Menghini</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Neubrand</surname>
          </string-name>
          , G. Schubring (Eds.).
          <source>The Legacy of Felix Klein</source>
          . Springer, Cham,
          <fpage>215</fpage>
          -
          <lpage>226</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          [6]
          <string-name>
            <surname>Buchholtz</surname>
            ,
            <given-names>N.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Kaiser</surname>
            ,
            <given-names>G.</given-names>
          </string-name>
          (
          <year>2013</year>
          ).
          <article-title>Improving mathematics teacher education in Germany: Empirical results from a longitudinal evaluation of innovative programs</article-title>
          .
          <source>International Journal of Science and Mathematics Education</source>
          ,
          <volume>11</volume>
          (
          <issue>4</issue>
          ),
          <fpage>949</fpage>
          -
          <lpage>977</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          [7]
          <string-name>
            <surname>Ableitinger</surname>
            ,
            <given-names>C.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Hefendehl-Hebeker</surname>
            ,
            <given-names>L.</given-names>
          </string-name>
          &amp;
          <string-name>
            <surname>Herrmann</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          (
          <year>2013</year>
          ).
          <article-title>Aufgaben zur Vernetzung von Schul- und Hochschulmathematik</article-title>
          . In: H.
          <string-name>
            <surname>Allmendinger</surname>
            ,
            <given-names>K.</given-names>
          </string-name>
          <string-name>
            <surname>Lengnink</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          <string-name>
            <surname>Vohns</surname>
          </string-name>
          , G. Wickel (Eds.).
          <article-title>Mathematik verständlich unterrichten. Perspektiven für den Unterricht und Lehrerbildung</article-title>
          . Wiesbaden: Springer Spektrum,
          <volume>217</volume>
          -
          <fpage>233</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          [8]
          <string-name>
            <surname>Beutelspacher</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Danckwerts</surname>
            ,
            <given-names>R.</given-names>
          </string-name>
          &amp;
          <string-name>
            <surname>Nickel</surname>
            ,
            <given-names>G.</given-names>
          </string-name>
          (
          <year>2011</year>
          ).
          <article-title>Mathematik Neu Denken</article-title>
          .
          <article-title>Empfehlungen zur Neuorientierung der universitären Lehrerbildung im Fach Mathematik für das gymnasiale Lehramt</article-title>
          . Online at https://www.uni-siegen.de/fb6/didaktik/personen/rainerdanckwerts/resources/empfehlungen_mathematik_neu_denken.pdf,
          <source>last retrieved 10/11/2019</source>
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          [9]
          <string-name>
            <surname>Isaev</surname>
            ,
            <given-names>V.</given-names>
          </string-name>
          &amp;
          <string-name>
            <surname>Eichler</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          (
          <year>2017</year>
          ).
          <article-title>Measuring beliefs concerning the double discontinuity in secondary teacher education</article-title>
          .
          <source>CERME 10</source>
          ,
          <year>Feb 2017</year>
          , Dublin, Ireland. hal-
          <volume>01949039</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation>
          [10]
          <string-name>
            <surname>Berry</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Friedrichsen</surname>
            ,
            <given-names>P.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Loughran</surname>
            ,
            <given-names>J</given-names>
          </string-name>
          . (Eds.). (
          <year>2015</year>
          ).
          <article-title>Reexamining pedagogical content knowledge in science education</article-title>
          .
          <source>Routledge.</source>
        </mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation>
          [11]
          <string-name>
            <surname>Van den Akker</surname>
          </string-name>
          , J.,
          <string-name>
            <surname>Gravemeijer</surname>
            ,
            <given-names>K.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>McKenney</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Nieveen</surname>
            ,
            <given-names>N.</given-names>
          </string-name>
          (
          <year>2006</year>
          ).
          <article-title>Introducing education design research</article-title>
          . In J. V. D.
          <string-name>
            <surname>Akker</surname>
            ,
            <given-names>K.</given-names>
          </string-name>
          <string-name>
            <surname>Gravemeijer</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          <string-name>
            <surname>McKenney &amp; N. Nieveen</surname>
          </string-name>
          (Eds.),
          <source>Educational design research</source>
          . New York: Routledge. 3-
          <fpage>7</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref13">
        <mixed-citation>
          [12]
          <string-name>
            <given-names>B.</given-names>
            <surname>Meyer</surname>
          </string-name>
          (
          <year>2013</year>
          ).
          <source>Touch of Class</source>
          , Springer Verlag
        </mixed-citation>
      </ref>
      <ref id="ref14">
        <mixed-citation>
          [13]
          <string-name>
            <surname>Frank</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          &amp;
          <string-name>
            <surname>Kaduk</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          (
          <year>2017</year>
          ).
          <article-title>Lehrveranstaltungsevaluation als Ausgangspunkt für Reflexion und Veränderung. Teaching Analysis Poll (TAP) und Bielefelder Lernzielorientierte Evaluation (BiLOE). In Arbeitskreis Evaluation und Qualitätssicherung der Berliner und Brandenburger Hochschulen und Freie Universität Berlin (Hrsg.), QMSysteme in Entwicklung: Change (or) Management? Tagungsband der 15</article-title>
          .
          <article-title>Jahrestagung des Arbeitskreises Evaluation und Qualitätssicherung der Berliner und Brandenburger Hochschulen am 2</article-title>
          ./3. März 2015, Freie Universität Berlin.
          <fpage>29</fpage>
          -
          <lpage>51</lpage>
          .
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>