Mathematics

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• Alternating phases of discussion and reflection in order to deal with one's own practice as well as with new ways of thinking and patterns of action • Target group oriented 2.4 Support Systems Current teaching of mathematics is not only based on knowledge of facts and arithmetic operations, but focuses on problem solving skills, understanding and thought processes. This new alignment of teaching mathematics is also reflected in the new final examination in mathematics, which will become mandatory for each high school student by 2015. Through the training course and the training of multipliers, it is possible to prepare teachers early on this change. Thanks to the provision of resources and the support of both the Ministry and the Bifie as well as to the good cooperation with the provincial school boards and the universities this series of continuing training courses could have been developed and be made accessible to many teachers. 3 Training Course - Competence-oriented Teaching Focussing on Educational Standards at Primary School 3.1 Objectives Primary school teachers shall: • gain knowledge of basic theoretical concepts of competence-oriented maths teaching in relation to the educational standards. • get to know ways of individual learning assessments (Lernstandserhebungen) and providing supportive feedback. • reflect on their own classroom instruction in accordance with competence-oriented learning and teaching. • be enabled to design their maths lessons competence-oriented • act as multipliers and disseminators at their schools. 3.2 Target Group It is a series of training seminars for primary school teachers. On the one hand the whole series can be attained as one complete course, on the other hand individual modules can be attained by all interested teachers. The individual course modules were held in three regions in order to ensure a comprehensive implementation of the competence-oriented teaching of mathematics in Tyrolean primary schools. In parallel to the subject-specific modules a pilot project was launched in two districts. In each of these districts the support of project groups is offered. Within these groups further development tasks can be supervised and discussed. 40% of the primary schools have already taken advantage of this special offer for themselves. 94
3.3 Structure & Contents The whole course consists of six interlinked, sequential modules, which are supplemented by phases of deepening self-study. The relatively high proportion of self-study results from • the dialogical and interactive form of the modules - knowledge is not merely taught, but developed in a dialogic process among the students. • the structure of the individual modules - phases of presence and selfstudy with collegial exchange alternate. Contents examples for each module: • competence model of education standards in mathematics for the 4 th grade. • mathematical tasks and assignments. • analysing the competence potential of assignments. • development and application of diagnostic tools. • Feedback. • development of support frameworks. • dealing with mistakes in learning situations and settings in mathematics. References Alber_E, Juen-Kretschmer_C., Mayr_W., 2010, “Tiroler Modell – Implementierung von Bildungsstandards gelingen im Zusammenspiel mit Bildungseinrichtungen“, Erziehung & Unterricht, pp.236-244. Juen_H., 2012, „ Die standardisierte kompetenzorientierte schriftliche Reifeprüfung: Entwicklungsschritte, Grundlagen und Begleitmaßnahmen“, Erziehung & Unterricht, pp. 36-43. Andre_M., Juen-Kretschmer_C., 2013, „Zentrale Fähigkeiten, Fertigkeiten, Kenntnisse aus Sicht der Fächer – Mathematik“, Fokus Bildung Schule Bd.4, pp. 87-125. 95
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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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Page 51 and 52: Building capacity: developing a cou
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Page 55 and 56: teaching of specific concepts in sc
Page 57 and 58: • The use of repetition in some p
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Page 61 and 62: the curriculum, or main part of it,
Page 63 and 64: its applicability, write a final th
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Page 73 and 74: 3.4 The facilitator Looking at the
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Page 83 and 84: 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: Module 1: • Interpretation and de
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Page 107 and 108: used for continuous adaptation of d
Page 109 and 110: M2-idea was extended and combined w
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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
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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
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Page 135 and 136: Figure 1: Elements of Activity 1 Th
Page 137 and 138: The supervision of the teacher educ
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
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Bell, T., Urhahne, D., Schanze, S.,
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Online training courses: Design mod
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about 1000 course participants, whi
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mandatory). This is followed by the
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Research project WOLF is about deve
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Positive aspects timely, content-re
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References Bruder, R. & Sonnberger,
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Figure 1: An activity from the Corn
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The PD process is illustrated in Fi
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and for students with English as an
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5 Future research The Cornerstone M
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A Virtual Mathematics Laboratory in
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informatics/IT). The synergy betwee
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than 70% would commit essential err
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computer, Theme of the month (Figur
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References Branzov, T., 2015, Viva
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Supporting the teacher role during
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worksheets and encouraged teachers
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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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Mathematics

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