Collection of effective teaching methods that focus on active and cooperative learning
Methodology: Learning Caroussel Aims: -To let students study a new topic by self-direted learning - To activate students' prior knowledg e of a topic or topics through movement and conversation. - to have all students active at the same time and during a long period of work TWhat kind of stations in the learning croussel? While working in a leraning croussel work on small groups or in pairs on different stations. These stations consists of worksheets with introdiction into a new topic or tasks, hands-out activities (it depends on the topic), check-lists, tasks with using maths software or online exercises, tasks to make a poster, …. It is important that there are different activties, stations to learn a new topic, more creative ones, stations with problems from real life, hands-on or experiments, acoustic stations (listen to a report or a description), drafting own texercises, more graphic orientated stations (using a comic, …) so that all learning types are included. How to organise? - A learning caroussel consists of 4-8 or more stations (it depends on the topic), all have to be prepared before the start of the learning caroussel in the classroom. - You make a copy of all stations for each student or you have 4-5 stations (laminated) for parallel groups that work on a special station. - It is good to have solutions of important stations. students can go to the teacher’s desk to check their solution. -You organize groups of 3-4 students (by chance or you decidede before or students decide themselves) who work together. - For some stations I prepared hints – sheets of paper that are on the teacher’s desk. - Students have to know before starting to work that they have to document their work accurately.
- I advice to make a list of all stations so that students can mark what they have done. I also add an evaluation of each station by using smilies to see what they like and how difficult it was for them. - Normally students can choose the order of tasks. If the stations are not independent I tell them before. - It is important to give a time span before starting to work. - I also prepared 1-2 additional stations that are not compulsory e.g. for more gifted students or those who finshed their work earlier. - Before leaving the final station, each group has select the top 3 ideas from their station to share with the entire class (a sort of revision). .
Which topics are suitable for this learning method? -all topics that should be revided - topics that are not so difficult and can be learned without the help a teacher (if the material is drafted for self-directed learning) - learning new topics like solving linear equations, perecentages, simplifying terms with variables, graphs and equations of quadratic functions, rules of derivatives, ... - revisions of topics: fractions, decimal numbers, properties of quadrilaterals, solving systems of linear equations, linear functions, solving quadratic equations, zeros of polynomials, ‌.
Monika Schwarze, Unna 2013
Die Placemat Activity belongs to group-working methods and is a special form of cooperative learning. The group of students is divided in small groups of 3 -5 members. Each group gets a paper, a so-called “placemate” that has been prepared as you see it in the picture below, containing 3-5 fields plus one in the middle of the sheet. The format of the paper is DIN A4 or DIN A5.
Each group gets an exercise, a question or a problem that hast to be solved by each member of the group. This method can also be good for having the students (indirectly) practice on formulating questions. It works in three periods: 1. Think (thinking and writing): Each student thinks about the given task and writes down his thoughts, answers and explanations according to the task. (about 5 min.) 2. Pair (comparing without words): Each student reads the notes of the others, comments it and asks only questions if he/she could not understand it. (about 5 min.) 3. Share (sharing and finding an agreement): the group decides commonly, what should be noticed in the middle of the sheet (about 5 min.). At the end – if there are different tasks- each group presents the results of group work. Examples for effective use in the classroom: a) Revision of a topic – theory, formulas b) A task at the end of training exercises for a special topic- e.g. the problem of World Rope Challenge from UK c) A problem that allows different ways to solve it, e.g. how to determine the area of a given polygon d) Good for having the students (indirectly) practice on formulating questions e) Writing down open questions at the end of teaching a topic; questions can be answered by the others in the group or whole-class working. f) Giving some data on an extra sheet: students have to find suitable questions and answer these questions (or the neighbor right to him/her has to do so). g) … Advantage of this method: highly cooperative, improving social and communicative skills, mix of individual and group work, all students in the classroom are active at the same time (some parts are translated from a German Wikipedia page)
by Monika Schwarze, 26.1.2014
(This article is copied from the website: http://uways.net/genialcurriculum/genialcd/genial_main_p012.htm) ================================================================= Cooperative learning methods: Jiigsaw puzzle =Gruppenpuzzle (jigsaw learning technique) The organisational principle that SOL is based on is the jigsaw learning technique, a procedure in which students split up the work they have to do. The jigsaw classroom is a specific cooperative learning technique in which – just as in a jigsaw puzzle each piece (each student’s part) is essential for the completion and full understanding of the final product. The class is divided into jigsaw groups (basic groups). They receive a task that consists of several aspects/segments (see also advance organiser , figure 1). Each member of the group chooses one of the aspects/segments and prepares it individually and then assembles with the students of the other jigsaw groups that have chosen the same aspect. In these temporary expert groups (which should preferably not be larger than 5 students) each theme is acquired, discussed and a presentation is prepared. The experts return to their jigsaw group and inform each other about the aspects unknown to the others (see figure 2). The working materials (e.g. working sheets, literature, the internet) have to be chosen according to the ability, knowledge and experience of the students. Inexperienced students will need more instruction, guidance, monitoring and assistance from the teacher and time for preparing a presentation and the subsequent peer coaching. The members of the jigsaw groups may have to be reminded to take notes and encouraged to ask questions for clarification. In the beginning students might also need a timetable that leads them through the jigsaw classroom. The jigsaw technique is an efficient way to enforce the students to learn less teacher guidance. Furthermore the jigsaw technique supports skills like time management, preparing an oral report, presentation-techniques and soft skills. It encourages listening, engagement and empathy by giving each member of the group an essential part to play in the academic activity.
Figure 2: Jigsaw learning technique for a topic divided into three segments (HEROLD and LANDHERR 2001c) o o o
dividing students into jigsaw and expert groups working on the segments in the expert groups presentation of segments in jigsaw groups
My Comments:
It depends on the topic and the group if students like this way of learning or not The responsibility of every student for the progress in learning of every member of his group must be clear! If the topic is new the problems should not be too hard. The work order must be very clear (sometimes very detailed). It must be clear that all students have to make notes or get a worksheet with notes after the presentation of each “student teacher” or “teacher student.” Students normally write down teachers’ notes from the blackboard, but they don’t create notes for the classmates. To ensure the success in the first period for each group and every student who becomes teacher in the next period I took a bright student in each expert group. After the two period (expert group, then jiigsaw (=mixed groups) I contninue whole class working, asking questions about the different topics to be sure that all have really understood the stuff I like this method very much because all students are active. Expaining to others means to be clear of the topic (normally). If more than one student is ill in period 2, there is a problem because in one group there is a teacher missing. In one group it is me who replaces an ill student. I use this method one or two times a school year. I have to admit that this takes about 30% (or more) more time than whole class working Example 1: pythagorean theorem: group one:
h 2 p q finding this and proof
group two:
b 2 c q finding and proof
group three: special proof pythagorean theorem Example 2: graphs of quadradratic functions: group 1:
f ( x) ax 2 exploration using GeoGebra
group 2:
f ( x) x 2 c exploration using GeoGebra
group 3:
f ( x) ( x d ) 2 exploration using GeoGebra
group 4:
f ( x) ( x x1 )( x x2 )
group 5:
f ( x) ax bx
Example 3: for revision of percentages before a clastest: 3 - 4 groups for the different types of calculation, formula and a short example
Monika Schwarze, PGU Unna
Methodology: learning cooperati ely ith „secret cards“ What about this method? A team of three or four students get some cards with short information belonging to a task of a topic. Each student gets 2-4 different information. These information has to be exchanged within the team and then the team has to make conclusions concerning the task and solve the problem. Are there rules? Each member of the group is only allowed to read the information on the card load. The cards are not lyed on the table. This improves communication and fosters mathematical argumentation. You may enhance this by adding information that is not really necessary for for solving the problem. Why in this way? Furthermore this approach to solve a problem cooperatively allows a formal and a more logical content-orientated solution (logical thinking, combination) and differentation so that brighter and weaker students will be sucessful in solving the task. Different test show that students see their work as a challenge and are highly motivated. Suitable in which part of a learning unit? It depends on the topic. It may introduce in a topic to find a formal way to solve different problems in the same way (e.g. same algorithm) or a motivating way of training. Then different groups can solve different problems (different sets of cards) and present it later to the whole lass or he k their solutio y aski g a solutio ard fro the tea her. For which topics can this method be used? - systems or linear equations (see example) - application of trigometry - determing equations of quadratic or exponential functions - applied calculus: zeros, maxima or minima - word problems around measuring units or with negative numbers or fractions - calculating surfaces, volume and mass of cylindes, cones, ‌ How can this method be variated? - cards without any questions - one card may contain a variation of the task - one extra-card that targets the way of calculation - stude ts draft a set of se ret ards y splitti g a ew pro le
i differe t i for ation.
Evaluation? I have used this method several times in different groups. The topics were trigonometry, calculus, surface, volume and mass of buoy (cone). The students have to get aqquainted with this method, then it worked well. Students lived it because it was a challenge and an alter atio to or al tasks. I hope that so e part ers try it out a d report a out their experiences in the class room. Monika Schwarze, PGU Unna, 8/2014
Mister Mayer pays 153 € in total for all entrances into the thema park “Fun City”.
Mrs. Miller is looking forward to visiting the theme park with her family next weekend.
Jonathan, his sister and his parents visit “Fun City” sunday morning.
If there is a group of more than 10 persons an adult up gets a reduction of 2 € of the normal prize for adults.
Mister Mayer makes a class outing to the students’ favorite theme park “Fun City”.
[Geben Sie ein Zitat aus dem Dokument oder die Zusammenfassung eines interessanten Punktes ein. Sie können das Textfeld an einer beliebigen Stelle im Dokument positionieren. Verwenden Sie die Registerkarte 'Textfeldtools', wenn Sie das Format
Mrs. Bank visits “Fun
Claire is Jonathan’s sister.
Mrs. Bank is a pensioner. Pensioners pays for the theme park the same price than children.
Monika Schwarze, PGU Unna, 8/2014
City” alone.
€
In this lesson students work on a real-life problem: calculating the volume of buoys Author : Monika Schwarze, Hamm, Germany and Bianca Gouterney, M端nster Grade Level/Subject : (9-12), Math or Science Overview : In this lesson students have use the learned formulas for calculating surface and volume of cones and globes in a sort of game. I used a special teaching method (from the teacher's point of view) and a special learning method that is highly motivating, enhancing co-operative work of gifted and of weaker students as well. The students are given some information to solve a problem, but they have to find out the questions of the problem before. Purpose : Having a high amount of self-guided learning and improving problem-solving skills. Resources/Materials : worksheet 1, worksheet 2, cut into parts (whorksheets should perhaps be laminated before cutting into cards) Activities and Procedures : So it worked in my lesson: Students work in groups of 4 students. They get one common problem. But the difficulty is that the information for the task is split up on 12-16 individual cards. Each student gets 3-4 cards. They are allowed to look at the information on their hands, and are allowed to talk about it, but they mustn't put it down on the table. That way they are forced to share information by talking about it (this is especially difficult by describing pictures or tables). Another difficulty is to actually find out what the task is. They can take notes and are supposed to solve the given task in a certain amount of time, and be able to present their solution to the rest of the class at the end of the lesson (e.g. on a transparency). There are two options for this: A: each group has a different task to work on and all groups present at the end (takes a long time) B: all groups work on the same task and only one group is picked for a presentation
of the solution and the rest of the class contributes to it. For a group that hasn't worked with a method like that I'd suggest option B. I explained the way of working to the students. Then they got the cards and tried to find some questions and answers. Before I had given them them the hint that there is more than one single question and one caculation of volume in the problem. It takes a little bit more than 45 minutes ( a lesson in Germany normally has 45 minutes) as I had expected before.. In the next lesson they finished their work and prepared a presentation via blackboard. Because of more than one questions and answer (sewe below) in the problem all groups had contributed to the solution of the whole problem. I put attention on their explanations how (!) they solved the problem because my intention is to broaden the student's problem solving competencies whenever possible. Evaluation: It was highly motivating for almost all students. Weaker ones feel more integrated because they really contribute to steps of the solution and got more self-confidence (as some of them said). All students were active at the same time in comparision of working whole-class. The first time the students need more time to get comfortable with this learning method. If you use this method the second, third time the students don't have these problem to start with their work. All classes in which I introduced this method like it very much because it is somewhat indifferent to "normal" teaching. This puzzle-method can be transferred to almost all topics when you work with real-life problems or more complex problems. it takes only a few time to "cut" a problem of a maths textbook into differents parts/information. It doe not matter if 1-3 of them are not relevant for the solution. Questions that the students may find while working on the problem? 1. What about the volume and weight of the buoy on the picture? 2. What about the surface and the weight of the shell? 3. Calculate the weight of a sphere of styrofoam which has the same radius as the buoy. Compare the weights! 4. Calculate the weight of buoys made of cork! 5. What's about the volume of a buoy that consits of two equal cones and has a diameter?
The math topic: calculations of volumes and mass of solids buoy 2
The total height of all buoys is 1,20 m.
density of cork: 0,2 g /cm³ density of iron: 7,86g/cm³ density of styrofoam: 0,05 g/cm³
Is it possible to carry a buoy like buoy 1 (same measurements) that is made of cork?
The shell of the buoys is made of a sheet of iron.
Optional: Calculate mass of the shell of a buoy that is covered with a sheet of iron.
The diameter of all mentionned boys is 6 dm.
What’s about the volume of buoy 1 that consists of two equal cones and a total height of 1,2 m?
alculate the mass of a sphere of styrofoam which has the same radius like all buoys. Compare the weights!
4 V r 3 3
The sheet of iron is 3mm thick.
All buoys are yellow.
optional task: Calculate the mass of buoy 1.
What about the surface of buoy 1?
The task has to do with solids that are existing in real life.
“Invent� a buoy of another form, choose realistic measurements and calculate its volume.
Methodology: Self-Directed Learning Online On www.blendspace.com teacher can create a lesson with videos, pictures, tasks and e.g. worksheets. example: www.blendspace.com/lessons/rcIeNbRur2-yXQ/maths-bridges
Methodology: writing a textbook for other students What about this method? This method fosters self-learning activities for the students. Students cn use – besides their normal textbooks – a lot of different textbooks from other publishers to work a new topic out. They work in pairs – if possible - students of the same ability level. They have to write a textbook that contains an introduction, some introducing activties for each chapter, an example and the rules e.g. for calculation and some interesting exercises with detailed solutions at the end of the book. Are there rules? Two students work on one textbook. The amount of work must be rather the same for each student (can be seen on their handwriting). The book must contain all chapters – the table of contents had been fixed before - whole class working. Students have to do most of the ork i their aths lesso s, the ooks re ai i s hool. The ay of assess e t is also fixed before starting – design and amount of exercises are assessed besides correctness, comprehensibility and completeness. After the assessment of all books by the teacher the books are given back, a small exhibition follows and then a small test for each student individually to check of the really have understood the topic and are able to solve problems related to the topic that they have worked out. Why in this way? In each grade there are math topics that are rather easy for the students and appropriate for this learning method. As students work as pairs there is a huge communication and ooperatio he de idi g ho to rite do hat they ha e orked out. “o the tea her’s role is reduced to give advice and help if both students have different meanings. Mostly students are eager to really work alone without the teachers. Most questions concern the layout. For which topics can this method be used? -
How to calculate with decimals methods how to solve systems of linear equations volume and surface of cylinders, prism rules for calculating with powers ways of simplyfying terms with variables …
How many time does it take? It depends on the topic. I tried it out 3 times, last time 2014 in grade 6 with decimals. Division of decimals divided by decimals was taught whole-class working (I feared too many misunderstandings in the side of the weaker ones when the worked alone). It takes 11 lessons à 45 min., class test included. It takes more time than teaching in a more traditional way, I estimate about 20-25%. Monika Schwarze, PGU Unna, 8/2014
Evaluation? The students liked this way of self-guided learning. They really felt as book publishers. Most of them learned rather quick how how to allot the time. As they knew from the beginning that a wonderful layout only counts 10% they put most attention on correctness and a lot of different tasks. The parents had been informed before because this book and the test replace a big full classtest (one of three a in a half-term), 50% of the points was for the book – each of the two pu lishers got the sa e a ou t of poi ts- and 50% for the test. A lot of parents attested that they liked this unusal way of working and assessment. The results of the test are comparable to the results in traditional ways of teachĂng, one time a little bit better. I add some scans of 4 math books (quality is not no good because of blue ink) in another document to give an impression how the books look like. I attached also letter for the parents by using google translation with a few corrections.
Monika Schwarze, PGU Unna, 8/2014
Dear parents of 6b, dear students,
as I promised I give you some information about the replacement of the second class test, about issues and mode of assessment.Two students of class 6b write a "textbook" about "decimals". The composition of the pairs who work together was such that I took into account students’ wishes as well as a similar math grades. The structure of the book has been prepared commonly. For the six topics students various textbooks of different publishers are available to work out rules and exercises. Of course students may ask me questions that can not be cleared within their group. The students know that each chapter should contain intorducing exercises, examples, explanations, rules and exercises for training. The exercises, as they are present in each textbook must be solved at the end of the book. Students may use occasionally small images from the Internet for illustrations and a beautiful visual design. The assessment of the "math books" (each group writes usually only one) works according to the following criteria: property, accuracy 50%, tasks correctly solved 15%, understandibility 10%, creativity 10%, presentation 10%, additional hints and tricks 5%. There is a mark for the book, which is the same for both partners. Learners are encouraged to divide the work so that each partner works rather the same. The students are allowed to have a short look into written math books that were written by other sic grades two year ago.
It is planned that the students use the entire class time to develop and (pre) formulating entries, and e.g. draft tasks for each chapter or entering text by arrangement with each other at home without your help, of course. I have planned about 8 lessons for completiton. The deadline is will be announced in time.
After assement with marks the books are given back to the students,then each students has to write a classtest with tasks from all chapters. The final mark of each is calculated as the average of the grade for the book and the test. This note counts as a mark of one of 3 classtests in this half-term. The school management has agreed to this procedure.
Topics: Introduction Chapter 1: What are decimals? Why would you need it? Where do they appear? ... Chapter 1: We add and subtract Chapter 2: We multiply and divide by 10, 100, 1000, ... Chapter 3: We multiply, decimal numbers with natural numbers, decimals together Chapter 4: We divide decimals by a natural number Chapter 5: We divide decimals by decimals (done whole class working) 6 We convert decimals into fractions and vice versa 7 solutions
With kind regards
Monika Schwarze, PGU Unna, 8/2014
bzi rno-Lz..h[ma
§;trIl
k&n7
\R-roano\gn uÄr sre- lrn nqhiliöpn -t-
DeP.6ry
zur Det\nratxdrru{nA
Dezirmq,,ollln rrqrn{
rno.n duo ?qhhn ,
Ltorrt 8ciupiel
otr
?, 8
O,
tn demn dn llorrrrra roorLarrrn }
q) UL S'ld&n Köts
Der.iura\stetbn Oiq qrsb. lkü\rornrnrshkq skrh{
uorn
trr
lhlrrnq renn{ r,lqD
dr.r
aehnleß r cl^b.
ttn^k- Stohl {,r.ir }trnAr\sfrg, dis diiltt [ü. euesd$a( und ss upib.
^=
§r=
Ä23,q63,,( ,' t §,9 32,S
,1. trb \Eruen&§\ 6ir 0ezirrp0ahhn irn
hrr knuks, edfrq0tcrhlon b{.^ &r fe.h*nx \ron dH §Enn r^tis z.B. sag,,,,
/rt, i2 {."
S
+.ß.
hqba-
ltörnhr t^xro.rrch sogn,r,llhr hqben / SA («rt.
^
RtLhg x
q \
-
"ffi ..1S,-
^tu,j*>.
i
-
/4f,2 <
)\,
N
t,l, *rpcLqn posi{iy unt nWV* &aimoted,lBn ilnd windth s/! Lrt f"id, ///n t. Deirrrd.tohlan uer{uch rrrrn irn qrurda
Sind q§so d,.o di-o
?üh\en s<sr dern
&ynlel Sind
!r.s.ts.
-
r€chur\
d,ts
--()16
S
G"\s na}ürLiüu ?d.tan
3
6rd",s 'rcrc$$ch[ rnan u.il ttu.,*"shft t, q d
i
1rö§Ter'{^}qrttl"^e,. {
tra& .,i:t
t}r}
der
kö8"
rxrch
H"*
nrr,itdErn t,:s"rrstn
qg i q06 i qt ; 0,§5 i 0,q+§ / C,S§ i '{5 i Ü,3 ; Ä- i CI,gg
I
Ci,
J. Se{:«-- ei.n a)016
35
E.{,2 trs
c)q,3
zg
dq',.s.t
l--
( ,)
0t6 v3 4g.Lt b
- iJ J v
.*)
*
ij
-, r.t-)/ 0 L
-,1 e/J
* ,1,2 Lts *,$Z tt I
-'tn ;Q 6 *är;l') \ d ),
\r$*3
g\
ä,Bs.t
'^l
l, Y .."t !-
h}r,, rprr*1sL(n
rtrre-i-*ritls.
:
r\-.i\Elfl l ''' f. On{ne-
.
c$ojc|t,^Er}q gs Grof!,rAl- rnon
&rirnalülün Lst ts snu-l ilqs #iäo.
u\nn rrrqn {.8 ü, ü ,§ .:, ur*l -v
lbrnr.pr
drqse. .oiüor.^-
t&^neqOh,rerr
$rus
(üro*f i
hodet rrmo des "Uc{naa pnnl}*.lm Rekh usre
QmA *§trhrd rdns
ü,lL
U.,-
€r6ebds se{a+ *on;
lqrrrra um so §&te
St&t
trlrrt
rgb t^nks,
rr*t4{tlt\ercndq OceuraL?oh[n ÄJoötrcroaosklfrn t-ntk.
DoS eükrüs hn[, uq,nriÄlig
\hür\§rnrärldfr,
ffüräi!
r»t
t*, *is &timota!(
dq ro["sl irrmar so
*d"
L.' dgr fur
ßdryHa-: 3.5 ' 5:-:t ?,S 3,36 . J - Zts.oE
,p
n*Sübö'/. 2,3s.
{g'? )
?
,lltr '9
3q,Z 'q
1,6?,E '$
.(8r3 '3
ttt,+'q
5Q,6'8 33,+
-.t
Zg,?- Z
J-fr.kqs pu* €taksuhr,. €r rnr§§ J'mo§. drl. .S,ekdoda lur a. q 8€ s L-nuq die ]t';&J^ tÄr O, 89 + t,t-rd
l,\3 € trrl .t/t-(na0- 6]up fu^r o,8.re Lcqrlhn . Lü ü \rol. t^b[ tr tnsgisfn] c\r$. {rq kiSe-tl"-
ead/.re-
q6nqrl
.
r
tt'
L
l&tp;&S W;r mub;pl;gbqn b.;rvtzalien
mite,.tnqol€r
fuL$wrsädt;"v-t Lanr* C,, xvo\ Mir,aLh&en r»,* bziwniwiren vnodtipiiz*er*.r . i)"ü J,^s 15i gg.nz €;{r 6. }e;,n frwäkzn ,Jr Stetkn h;nfu, b- V.anv,o ^ux* sl, n,)n axtr d;e 5*-t{en Jer hV krj*sirhrigenr(hie
e, nrß*; pi,'Z;€ft- vvird. I-n fo;5ppL r€cl.p5 sir6t es -*rnie
insgtv,nnt
,Ä
Sei€rr , d;e ot,,
bÄ
Srgpn;s' voh a:nbn *str€klen
Bz,sp&a
,
,tli 25 oo
o,*!
? 50
L2S
o34?s ri
ird6§r
f, f
t
l-ieAwrc{s ,^d'g Veiq Vom*q, *t
z.ähte
fu
qk ffiteqa
Prlül*/- h.',r&r iaa Uor*+a*q (h*A) S.tsöl/€ i,'r €rgsüaü
ersqe*nd *;€
,tqs{ir-.'o\ Std,{en ,&n hiq&^ 45 lQro A
6-1,3
d) ii,
zs -tgs
$ u12.3 ' l,zs
bq - o,?-5
el zq,Ls- 3,zt
hl z? gz-*toLr
q2 - O,§ü
$ ilq,a.§q{
;l
g.{st . 0, t"f
-8-
Sbkql
hpitei o W;, $;viÄeen
j*euu
tr\it gil€r ,ttt.,r-i;n,n *irr-
gr;#*t..tr
{rrr1t fu
(r-r>
O*}B,'rrU.
,*tn^}.t tJryt "l;i;*W"
tJf f;§".r-cn ir( *P i*ortff: -jqa1 :{,,:n .tct\ ,,#* Lvr","rra tri;a! irriü.rgn. ig,l?fr;1.-, ,lrf{ jU * filu.tc:rurlr| .rrr*
'iäg"rrr€ gaae
.r!
/tgrirg sl;r n,tr, Lfgnn ,;lt ]rgJ"a'i3{ i,,:r,
fu ir
an Je-,;eg,,e'ks
i,ä9c J,t ;tic;.,5
pq-ry,r.ritq
tJ;n rryt =rgCZoU
;t*e:
&,*4' 'i
28,q2:i7 lL { ii
Ir
rt/\11 fUtt
,ja
ilz i,,
zü ,,Y 0o r_.
t? t3
t9'r &*ut ;g f,ä""* 2inF&,.a,ien ttt:l .,,,öe,i€ *),. {W,grry-, elre ,izi@t€ {a*xe ?'tb,e'€en trvwwni \te* z, zs Ltr eiagzüa**. Zre 'vkr. {;slh b}n:,n*i @e. ,kst- *d den t*ier
!
-S-
F Zu
Yqp;H-
r
2-
r
i
i I
i
.-/-lon v*Ale,io\t
Dazirrrz Ly-ahbn gem-usa
zje r,,q.n
n*{Ürt;Äe *al"*n rniveiyg,rd* wgdei.ßf, §;hd
bae Z,Jrte* vo, Jery korrrrrr.r g{u;& i&f, 1,2 1,3} so uergle;obt yrr&n Jg Satntut. §;nC JW- ,Lrderurrl ß&,.& Sü ugrgcirr# rr)ü.n J;e l*unCerastet {8sp i,zz i,zi )
Qcnh pos.
urd nq. Teziw.,.{z*bten i.arn r,crh vsr-
g.feArÄar
§A üqgLt;"gn .}rlz.iotqL?Rh*h st e)*.n, t i+J,e
neä.
rrt*Jrtiüen ?;;lnün ü+ Jen, 7.,hlenst-alrl {."&s \€r ub- ,Ut:i. t - ,rl ,S
-12
-
Hqst
dt es vq**en3.
).
Ao{*g,,U,
Sohte;ba S ledeuLuqph von &az lvnqLzaLll4n i"n täg1.ir)*n
&bve;be
4.;
62L5
,§anvne
13, tr{S =
23*ä*ä
"t
C sz,Be
d
2r,got
c) JS.
zg3
ll +3, z'l C"*aab.
FCJ"4
d
&
2,3oü i
..r|,,ß2 nrotrr:
2,23;
6) 7,üS$ot 7,tto3
*)re;U
2tflt;
; 8,bX;
2r3;
6]
;,2* ;,«
O,ur
Jl
o) L3,g+ o,?u
ii
ß,§o+ c,qe
ü,te
c!tra,
- ?3,q
"§
cP- tä.q
aI
ZqA
r]"1, §3gl
; ?tt'l?l; 8,3§
s3,& + it,Q
e) i,5;i+
ä
81 OO.Q
t,,{,;ereirzader urcJ e&tne-
c',
{o
@,i'r',e 'ni* Jer L&-,ioan 2,1 ; ZP§; 2,2111 2,3
- 3t, üF
iüQ,a*
t
t),$ ,i2-
i3,&g- t,{
l.I ß3,üq -31,1
- l]-
bUn
o'ttt
'
-. .1:"
{\.'l..
l+
j ;i-rf .r
i r{trrf
*.t,
rV'i-t,r
:;e1,, r.l{,r::t,-l
A r,5 I
-s^&
reP%"d s&
,
.\ i
34 i
, u}{*'rsLt
/ i,3
,
,t Ei?,
;''; #*ü
t,
ro,*ä&ii.,
iltr:fur. §*it -*,ra '(. *Ctü rrru)J>h Tnqrrt- dja., § ru+ lltu, L tr--u[srn. lirlrruY, .ebq €,c, ?, tr#s{$t Ä A;Mff d$Y' froW /'§Jhri,F-r &, nh$L tü.ty 1:
u *lo
q.e td..
'
i. t nttet
.-l
.,i*Je tCtu
!L
,=f
i#{J-
r .Lt, plr-
dia»!- arr4,(tEur1.S*t rj
l)
&9* lÄrl- j{,""L. ,{x,*'
- '.jic
,* sol* *rlt{ix,, ,u- "g1§4ri .: rL ,i*. I
l:
*-*L*
l"{"3
dJ*
'1.
tt4§/,,'ilr,srtr*
r'hjli wrv
: I rltu eq
A-<i} .1
. F
;1 it' " ila 3 r--
ffirrL
ri
ts,-.
g.'rJbrhfrU-
'l#hd natuli e"&. &qÄ -!{tf ,t'1 ],*-'.,r--U^*' +eprfirr4t 'il1,0, ru /{irr.t_
';5,':r-ti jc*t ,iruril* r-
Ce:r-""
.
,i*.
,rr-i',J*1
i. -g- i
.
/ .r
{.1
"- j-r tu _r;tli-t
-.-"J -L§, I-.(1.5. t:,+- -!' i*!l,