Mathematics

Recommendations

Info

The analysis involved several stages. The data were structured and paraphrased in order to make these accessible. Teachers’ written answers were marked by condensed statements representing what was learned and from what was learned. The ’what was learned’ statements were categorized in aspects of mathematics teaching methods: ‘not working’, ‘formulas - without student understanding’, ‘focus on one single context’ and ‘focus on different contexts’. The ’from what was learned’ statements were categorized in preparation, teaching, observation, discussion and evaluation. The researchers summarized these results in: “What was learned” and “From what was it learned”. 4 Results Table 2 reports ‘what’ and ‘from what’ the teachers learned in the Lesson Study cycles in phases. The first column holds teachers. The second column reveals ‘what’ the teachers learned. The third column holds ‘from what’ the teachers learned in phases: preparation (P) continued by teaching (T1) or observation with discussion including preparation (O1) in the first Lesson Study cycle, and teaching (T2) or observation with discussion (O2) continued by final evaluation (E) in the second Lesson Study cycle. The fourth column shows aspects of teachers’ growth network in terms of IMTPG domains. 320
I learned that… from.. IMTPG Alan … my students, with me being unaware, apply tricks and a difference between choosing and P PD ordering … when students see numbers in an exercise starting multiplying, without any meaning O1 DC … students learn from acting out a counting problem O2 DC … visualizations are important for student understanding E PD Bill … I should enrich lessons with pictures / systematic notes P ED … the teacher should help students tackling counting problems showing practical applications O1 DC Cody … student need to count systematically as a basis to learn combinatorics P ED … the supposed importance of imagining instead of drawing pictures O1 DP … enthusiast students have no idea whether their approach is correct O2 DC … visualizations and plays are important tools to understand counting problems E PD Don … certain approaches need to be developed far for (students) to see that the chosen approach P ED does not work … it is hard to teach students by letting them discover O1 DP … students are uncertain, unable to explain what they did T2 DC … suitable practical examples are hard to find E ED Eli … students are not capable yet to systematically write out P PD … students first try to work everything out in mind before writing out any part and continue O1 DC Fred … there are many ways to look at a counting problem, students should be made aware - no more problems E ED … the importance of systematic counting and the way to write this out, I will give more attention to P ED that … acting out a situation really helps students to understand the counting problem and the O1 DC differences … students need to systematically write out all possibilities to feel certain: solution is correct O2 DC … students should be able to switch the point of view, too different problems are not helpful E PD Gus … it is hard to predict student reaction on open questions P PD … open questions are helpful to reveal thinking processes, hard to relate concrete problems T1 DP … different students learn completely other things O2 DC … students should be able a visualization by situations E ED Table 2: Teachers’ learning activities in the two Lesson Study cycles on counting problems At the preparations the teachers decided to start with thirteen different counting problems, asking the student groups to order them and explain their ordering (Batanero, Navarro-Pelayo and Godino’s 1997). It proved hard to predict what difficulties students would encounter when dealing with counting problems. The students’ arguments provided the teachers a lot of insight regarding their own view on what their students are capable of and how they can investigate student thinking processes in terms of ordering and 321
Page 1 and 2:
Editors: Katja Maaß Bärbel Barzel
Page 3 and 4:
Conference Proceedings in Mathemati
Page 5 and 6:
Contents 1 Conference: Educating th
Page 7 and 8:
Inquiry based biology education in
Page 9 and 10:
1 Conference: Educating the educato
Page 11 and 12:
and at the same time, as profession
Page 13 and 14:
In addition to exemplary, high qual
Page 15 and 16:
2 Conference outcomes and conclusio
Page 17 and 18:
One of the most significant develop
Page 19 and 20:
2.5 Trends and needs in Europe to s
Page 21 and 22:
necessary to delve even deeper into
Page 23 and 24:
Strategies that effectively support
Page 25 and 26:
• Common research question: In re
Page 27 and 28:
3.2 DZLM - German Centre for Mathem
Page 29 and 30:
4 Keynotes: Abstracts and Speaker I
Page 31 and 32:
Teacher professional development in
Page 33 and 34:
aspects of science education and ed
Page 35 and 36:
EU countries (www.edumatics.eu). Al
Page 37 and 38:
For several years, Manuela Welzel-B
Page 39 and 40:
6 Papers 6.1 Track 1: Scaling-up wi
Page 41 and 42:
3.1 The mathematical culture of cla
Page 43 and 44:
literature and of a distributed fly
Page 45 and 46:
proportional magnitudes - asking fo
Page 47 and 48:
surface. Alternately two persons A
Page 49 and 50:
subsets? Explain!” and “Write a
Page 51 and 52:
Building capacity: developing a cou
Page 53 and 54:
provision of professional developme
Page 55 and 56:
teaching of specific concepts in sc
Page 57 and 58:
• The use of repetition in some p
Page 59 and 60:
Even, R. and Ball, D. eds., 2008, T
Page 61 and 62:
the curriculum, or main part of it,
Page 63 and 64:
its applicability, write a final th
Page 65 and 66:
professional life. That is why she
Page 67 and 68:
“The meeting closed with a reques
Page 69 and 70:
set-up. PRIMAS courses offered mult
Page 71 and 72:
Figure 1: Extended Interconnected M
Page 73 and 74:
3.4 The facilitator Looking at the
Page 75 and 76:
Penuel, W., B. J. Fishman, et al. (
Page 77 and 78:
a means of ensuring that students a
Page 79 and 80:
environment and attitude that all w
Page 81 and 82:
tended to end with phrases such as
Page 83 and 84:
3.2.4 Feelings reported Teachers de
Page 85 and 86:
disadvantage, as one facilitator po
Page 87 and 88:
valid experiences to the discussion
Page 89 and 90:
proposal. It is more likely to resu
Page 91 and 92:
Joyce, B. and Showers, B., 1980,
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
Page 103 and 104:
considered strong enough (e.g., a v
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
Page 127 and 128:
as useful. Majority (91 %) of teach
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 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
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
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
Page 199 and 200:
processes and on important science
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
Page 207 and 208:
and what part it plays in the cover
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 and 214:
Appendix: The activity (Worksheet)
Page 215 and 216:
f = 60 / 80cm Hole aperture Ø ≈0
Page 217 and 218:
a) The image size in a camera obscu
Page 219 and 220:
D(m) h(m) h(m) Image height when f
Page 221 and 222:
pose questions, explore situations,
Page 223 and 224:
Figure 1: Worksheet for the Parking
Page 225 and 226:
mathematical domains and related to
Page 227 and 228:
5 minutes 10 minutes 5 minutes 25 m
Page 229 and 230:
groups, the work of individual stud
Page 231 and 232:
(Retrieved at January 9 th , 2015 f
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
Page 245 and 246:
(Settlage 2007, p. 204), that is to
Page 247 and 248:
were engaged in the process of defi
Page 249 and 250:
emerging. The students are expected
Page 251 and 252:
5.1.3 PTs’ design and implementat
Page 253 and 254:
eflected on their experience and in
Page 255 and 256:
a designer to the students. This is
Page 257 and 258:
throughout their studies. The use o
Page 259 and 260:
6.4 Track 4: Professional learning
Page 261 and 262:
2.1 Objectives and areas of experti
Page 263 and 264:
Teacher PD in the Czech Republic an
Page 265 and 266:
• and last but not least the call
Page 267 and 268:
3 Teacher training in the Czech Rep
Page 269 and 270:
Samples of course topics for primar
Page 271 and 272:
Professional qualification of teach
Page 273 and 274: Three practical work phases Phase 1
Page 275 and 276: All courses are evaluated by the DZ
Page 277 and 278: Competencies in Mathematics and Sci
Page 279 and 280: up to upper secondary level. The pr
Page 281 and 282: materials and interim reports are e
Page 283 and 284: Professional Learning Communities:
Page 285 and 286: presentation of professional develo
Page 287 and 288: and included participants from Spec
Page 289 and 290: In each intake participants exhibit
Page 291 and 292: Figure 1: The course content has be
Page 293 and 294: Figure 3: There have been sufficien
Page 295 and 296: Professional Learning Communities -
Page 297 and 298: Lesson study Observation classroom
Page 299 and 300: studying their response to particul
Page 301 and 302: Learning on three levels In the kno
Page 303 and 304: study as one form of clinical resea
Page 305 and 306: A study of collaboration between ma
Page 307 and 308: 4 Towards an effective community of
Page 309 and 310: students and providing professional
Page 311 and 312: Figure 1: The structure of the JCU
Page 313 and 314: JCU learning community and (2) a gr
Page 315 and 316: At the moment this paper is written
Page 317 and 318: In 2014, 144 students were selected
Page 319 and 320: Van der Valk T., 2014b, “Connecti
Page 321 and 322: Figure 1: Lesson study cycle (adapt
Page 323: Work experience in Degree + extra i
Page 327 and 328: References Batanero, C., et al. (19
Page 329 and 330: Content focused peer coaching and t
Page 331 and 332: group simultaneously receives an in
Page 333: Wanzare, Z.O. (2007) The Transition
show all

Mathematics

Create successful ePaper yourself

Delete template?

Save as template?