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Science and Maths by inquiring about the image size in a camera obscura - A. M. Criado, A. García-Carmona Universidad de Sevilla, Spain 1 Introduction and objectives Our line of research 1 is based on IBL strategies applied to practical work as part of science teacher education. The present communication describes an activity carried out by prospective primary teachers as part of the unit "How can one learn through inquiry? In the context of a school inquiry into the camera obscura, it is shown how the students are encouraged to review their hypotheses using qualitative arguments, and a proposal is made for them to go deeper into that review using more quantitative approaches. The initial goal was for them to reach a result that possibly contradicts the first hypotheses. This expressly fosters the process of reformulation and the search for new explanations that can reconcile theoretical predictions with experiment. All this takes place within an activity of school IBL about the characteristics of the projected image in a camera obscura in which the students will find that, in some cases, one does not appreciate the expected change in size of the image when the depth of the camera is increased. 2 Methodological aspects (implementation and instruments) As an example of IBL being initiated due to the existence of a question without an immediate answer, the students are grouped into teams of 4 to inquire into the following problem: "What will be the characteristics of the image seen in the camera obscura?" To delimit the problem, and focus the students' attention on the variables of interest, they were asked about the lighting, sharpness, and image size. We shall here focus on how this last variable (image size) depends on several characteristics. 210
f = 60 / 80cm Hole aperture Ø ≈0,5cm • Inner screen: White graph Figure 1: An observer, holding the camera made of black cardboard in their hands, has put their head inside. The class IBL activity consists of the following phases: I. The proposal put to the students is for them to construct a camera obscura (Figure 1) for which they are given precise instructions, (Criado et al., 2007), reinforced with the help of an educational video[2]. II. They are next asked to formulate their hypotheses in writing. This orients them towards considering factors that may affect the image's characteristics. They then consult a document on how the camera obscura works (Criado at al., 2007), revise their hypotheses, and prepare a table for data collection. III. They then make empirical observations with the camera, and log the data in a table. They are asked to include observations made outdoors, viewing nearby buildings and a classmate. IV. With the data they collected, each group writes up a report, completing the tables by relating the hypotheses to the results (both definitive and inconclusive), and ending with a summary of the conclusions. V. The groups' results and conclusions are pooled, the differences found are discussed and analysed, and a revision is proposed for those which are most divergent. VI. For the case of how the depth of the camera affects the image size, the students are provided with another document (Figure 2) as support in their revision of their hypotheses, and a new brief experimental session is proposed to make the necessary checks. 3 Results The students' hypotheses In their first response to the problem, the students' commonest beliefs about what factors will influence the size of the image were, in this order: (i) the distance of the object, (ii) the depth of the camera, and (iii) the aperture. Once 211
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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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disadvantage, as one facilitator po
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valid experiences to the discussion
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proposal. It is more likely to resu
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Joyce, B. and Showers, B., 1980,
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For this structure the Chair of Mat
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Acknowledgements This project has b
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Module 1: • Interpretation and de
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3.3 Structure & Contents The whole
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One usual name for providers of suc
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considered strong enough (e.g., a v
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This could make the situation of mu
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used for continuous adaptation of d
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M2-idea was extended and combined w
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discussed, also representatives fro
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in B Herzog-Punzenberger (ed), Nati
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KOMMS: Teacher training courses fos
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which involves ingredients which ca
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smartphones in school is increasing
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References Blomhøj, M., Jensen, T.
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Figure 1: The model of implementati
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Therefore following crucial challen
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as useful. Majority (91 %) of teach
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How to determine what teachers shou
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6.2 Track 2: Blended learning conce
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process, compared to the usual scho
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Figure 1: Elements of Activity 1 Th
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The supervision of the teacher educ
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Promoting teacher trainees’ inqui
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1.3 Tablet support Furthermore, Cas
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Figure 3. Blended-learning concept
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Measuring the distance of each step
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Figure 4: Interaction graph of the
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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,
Page 163 and 164: Figure 1: An activity from the Corn
Page 165 and 166: The PD process is illustrated in Fi
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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
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Page 187 and 188: 2.2 Blended learning and the HU uni
Page 189 and 190: At the beginning of the weekly cycl
Page 191 and 192: 3.3 Evaluation and reflection The n
Page 193 and 194: 4.2 A perspective on flexibility No
Page 195 and 196: 4.3 Experience We are going to inco
Page 197 and 198: 6.3 Track 3: Disseminating and scal
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Page 201 and 202: Figure 1: Model for studying differ
Page 203 and 204: An IBL application from the inside
Page 205 and 206: 3.1.2 The classroom management In t
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Page 209 and 210: Figure 7 3.2.3.4 Task 4 At the fina
Page 211 and 212: Moreover, they pointed out that thi
Page 213: Appendix: The activity (Worksheet)
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Page 221 and 222: pose questions, explore situations,
Page 223 and 224: Figure 1: Worksheet for the Parking
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Page 229 and 230: groups, the work of individual stud
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Page 233 and 234: equired to spend 440 hours (within
Page 235 and 236: Therefore the Steering Committee as
Page 237 and 238: References Michels, B., Kruger, J.
Page 239 and 240: 7. Development of competencies 8. E
Page 241 and 242: classroom environment or not be ver
Page 243 and 244: 4 Conclusions The project of raisin
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Page 247 and 248: were engaged in the process of defi
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Page 251 and 252: 5.1.3 PTs’ design and implementat
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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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