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Figure 2: Elements of activities 2 and 3 Activity 3 consisted in the experimentation of the participants’ own design of the teaching activity with a group of students. The participants had to individually assume the role of the teacher and implement the initial phases of the lesson plan proposed in Activity 2. With this purpose in mind, they had to elaborate a more detailed design, a more in-depth a priori analysis (phase 1), experiment their proposal (phase 2), finish with the a posteriori analysis (phase 3) and prepare a brief ‘experimentation report’ (phase 4). Finally, Activity 4 was devoted to a joint analysis and final revision of the lesson plan with the aim of proposing a new version taking into account both their own experience and the experience of their teammates. In particular, the difficulties found in the implementation of the modelling activity (a posteriori analysis) were supposed to highlight the constraints related to the normal implementation of this kind of teaching proposals and the possible ways to overcome them (see figure 3). Figure 3. Elements of activity 4 132
The supervision of the teacher educators during the SRP-TE consisted of the following. By way of feedback to the team discussions in the forum and to the activities (reports, lesson plans, etc.) submitted, the course staff progressively introduced some didactic tools to support the mathematical analysis of activity 1: notions of model and system, criteria and ways to characterise the models provided, ways of comparing them, etc. At the end of activity 2, as a means to carry out the didactic analysis of the spontaneous teaching proposals, some publications about SRP were provided: Serrano et al. (2010) and Chevallard (2012). Between activities 3 and 4, the educators prepared a guideline with the main sections of the a posteriori analysis of a SRP, including some examples of its mathematical description, some criteria to describe the didactic organisation and some elements of the conditions produced, the constraints faced and the global evaluation of the teaching process. They also provided an assessment grid for the final report and a questionnaire about the development of the course to be answered individually at the very end of the course. All the material produced by the students was gathered during the course, especially the students’ discussions in the forums (including the teacher educators’ interventions), the students’ questions raised (in the forums or by mail), the partial and final reports and their answers to the questionnaire. Acknowledgements This research has been funded by the Spanish ‘Ministerio de Economía y Competitividad’ under research project EDU2012-39312-C03-01. References Barquero B., M. Bosch and J. Gascón, 2008, “Using Research and Study Courses for Teaching Mathematical Modelling at University Level”, In D. Pitta- Pantazi, & G. Pilippou (Eds.), Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (pp. 2050-2059). Larnaca: University of Cyprus. Barquero B., M. Bosch and A. Romo, to appear, “A study and research path on mathematical modelling for teacher education”, In Proceedings of CERME9. Barquero B., L. Serrano and V. Serrano, 2013, “Creating necessary conditions for mathematical modelling at university level”, In B. Ubuz, Ç. Haser & M. A. Mariotti (Eds.), Proceedings of the Eighth Congress of the European Society for Research in Mathematics Education (pp. 950-960). Ankara: Middle East Technical University. Burkhardt H., 2008, “Making mathematical literacy a reality in classrooms”, In D. Pitta-Pantazi, & G. Pilippou (Eds.), Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (pp. 2090-2100). Larnaca: University of Cyprus. 133
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Editors: Katja Maaß Bärbel Barzel
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Conference Proceedings in Mathemati
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Contents 1 Conference: Educating th
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Inquiry based biology education in
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1 Conference: Educating the educato
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and at the same time, as profession
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In addition to exemplary, high qual
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2 Conference outcomes and conclusio
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One of the most significant develop
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2.5 Trends and needs in Europe to s
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necessary to delve even deeper into
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Strategies that effectively support
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• Common research question: In re
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3.2 DZLM - German Centre for Mathem
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4 Keynotes: Abstracts and Speaker I
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Teacher professional development in
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aspects of science education and ed
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EU countries (www.edumatics.eu). Al
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For several years, Manuela Welzel-B
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6 Papers 6.1 Track 1: Scaling-up wi
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3.1 The mathematical culture of cla
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literature and of a distributed fly
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proportional magnitudes - asking fo
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surface. Alternately two persons A
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subsets? Explain!” and “Write a
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Building capacity: developing a cou
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provision of professional developme
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teaching of specific concepts in sc
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• The use of repetition in some p
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Even, R. and Ball, D. eds., 2008, T
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the curriculum, or main part of it,
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its applicability, write a final th
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professional life. That is why she
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“The meeting closed with a reques
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set-up. PRIMAS courses offered mult
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Figure 1: Extended Interconnected M
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3.4 The facilitator Looking at the
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Penuel, W., B. J. Fishman, et al. (
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a means of ensuring that students a
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environment and attitude that all w
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tended to end with phrases such as
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3.2.4 Feelings reported Teachers de
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Page 93 and 94: For this structure the Chair of Mat
Page 95 and 96: Acknowledgements This project has b
Page 97 and 98: Module 1: • Interpretation and de
Page 99 and 100: 3.3 Structure & Contents The whole
Page 101 and 102: One usual name for providers of suc
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Page 105 and 106: This could make the situation of mu
Page 107 and 108: used for continuous adaptation of d
Page 109 and 110: M2-idea was extended and combined w
Page 111 and 112: discussed, also representatives fro
Page 113 and 114: in B Herzog-Punzenberger (ed), Nati
Page 115 and 116: KOMMS: Teacher training courses fos
Page 117 and 118: which involves ingredients which ca
Page 119 and 120: smartphones in school is increasing
Page 121 and 122: References Blomhøj, M., Jensen, T.
Page 123 and 124: Figure 1: The model of implementati
Page 125 and 126: Therefore following crucial challen
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Page 129 and 130: How to determine what teachers shou
Page 131 and 132: 6.2 Track 2: Blended learning conce
Page 133 and 134: process, compared to the usual scho
Page 135: Figure 1: Elements of Activity 1 Th
Page 139 and 140: Promoting teacher trainees’ inqui
Page 141 and 142: 1.3 Tablet support Furthermore, Cas
Page 143 and 144: Figure 3. Blended-learning concept
Page 145 and 146: Measuring the distance of each step
Page 147 and 148: Figure 4: Interaction graph of the
Page 149 and 150: Bell, T., Urhahne, D., Schanze, S.,
Page 151 and 152: Online training courses: Design mod
Page 153 and 154: about 1000 course participants, whi
Page 155 and 156: mandatory). This is followed by the
Page 157 and 158: Research project WOLF is about deve
Page 159 and 160: Positive aspects timely, content-re
Page 161 and 162: References Bruder, R. & Sonnberger,
Page 163 and 164: Figure 1: An activity from the Corn
Page 165 and 166: The PD process is illustrated in Fi
Page 167 and 168: and for students with English as an
Page 169 and 170: 5 Future research The Cornerstone M
Page 171 and 172: A Virtual Mathematics Laboratory in
Page 173 and 174: informatics/IT). The synergy betwee
Page 175 and 176: than 70% would commit essential err
Page 177 and 178: computer, Theme of the month (Figur
Page 179 and 180: References Branzov, T., 2015, Viva
Page 181 and 182: Supporting the teacher role during
Page 183 and 184: worksheets and encouraged teachers
Page 185 and 186: Using Blended Learning in a Math Pe
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2.2 Blended learning and the HU uni
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At the beginning of the weekly cycl
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3.3 Evaluation and reflection The n
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4.2 A perspective on flexibility No
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4.3 Experience We are going to inco
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6.3 Track 3: Disseminating and scal
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processes and on important science
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Figure 1: Model for studying differ
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An IBL application from the inside
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3.1.2 The classroom management In t
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and what part it plays in the cover
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Figure 7 3.2.3.4 Task 4 At the fina
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Moreover, they pointed out that thi
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Appendix: The activity (Worksheet)
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f = 60 / 80cm Hole aperture Ø ≈0
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a) The image size in a camera obscu
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D(m) h(m) h(m) Image height when f
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pose questions, explore situations,
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Figure 1: Worksheet for the Parking
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mathematical domains and related to
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5 minutes 10 minutes 5 minutes 25 m
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groups, the work of individual stud
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(Retrieved at January 9 th , 2015 f
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equired to spend 440 hours (within
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Therefore the Steering Committee as
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References Michels, B., Kruger, J.
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7. Development of competencies 8. E
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classroom environment or not be ver
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4 Conclusions The project of raisin
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(Settlage 2007, p. 204), that is to
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were engaged in the process of defi
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emerging. The students are expected
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5.1.3 PTs’ design and implementat
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eflected on their experience and in
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a designer to the students. This is
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throughout their studies. The use o
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6.4 Track 4: Professional learning
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2.1 Objectives and areas of experti
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Teacher PD in the Czech Republic an
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• and last but not least the call
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3 Teacher training in the Czech Rep
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Samples of course topics for primar
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Professional qualification of teach
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Three practical work phases Phase 1
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All courses are evaluated by the DZ
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Competencies in Mathematics and Sci
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up to upper secondary level. The pr
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materials and interim reports are e
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Professional Learning Communities:
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presentation of professional develo
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and included participants from Spec
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In each intake participants exhibit
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Figure 1: The course content has be
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Figure 3: There have been sufficien
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Professional Learning Communities -
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Lesson study Observation classroom
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studying their response to particul
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Learning on three levels In the kno
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study as one form of clinical resea
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A study of collaboration between ma
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4 Towards an effective community of
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students and providing professional
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Figure 1: The structure of the JCU
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JCU learning community and (2) a gr
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At the moment this paper is written
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In 2014, 144 students were selected
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Van der Valk T., 2014b, “Connecti
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Figure 1: Lesson study cycle (adapt
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Work experience in Degree + extra i
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I learned that… from.. IMTPG Alan
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References Batanero, C., et al. (19
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Content focused peer coaching and t
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group simultaneously receives an in
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Wanzare, Z.O. (2007) The Transition
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