planning a route for a performing trip of a music team: a group … · 2018-12-10 · a musical...

Mathematics Teaching-Research Journal On-Line

A peer-reviewed scholarly journal Editors: Anne Rothstein (Lehman College)

Bronislaw Czarnocha (Hostos Community College) Vrunda Prabhu (Bronx Community College) City University of New York

Volume 2 Issue 1 Date September 2007

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Planning a route for a performing trip of a music team: A group project in 4th grade mathematics

Grażyna Pawłowska,

Szkoła Podstawowa Nr1 im. Gustawa Morcinka w Warszawie,Poland e-mail: [email protected]

Overview

I have used a project-based approach in two 4th grade classes at a grammar school. The project entailed planning the most efficient route for a music team. The group work method used was presented in NIM and Forum of Education (Pawlowska, 2001). This was the first experience of this kind for for my students, although they had already worked with the collaborative group method in the context of an integrated approach.

I wanted all pupils to understand precisely what is expected of them in similar situations, to be clear about the principles of the cooperative work and to find the task doable as a whole. I wanted the children – also those working slower or requiring help of a teacher or classmates – to experience satisfaction and success. In order not to discourage able pupils with too simple problems, each set of them contained separate, more difficult problems designed for the members of the team and its leader. In order to accommodate children, who after initial teaching still have problems with reading, the instruction was written in larger font and tasks were discussed in front of the blackboard. The aim of the class was to use counting by memory in the practical context of calculating the length of a car route on the basis of a map of Poland. The skill of using the map is very useful in life and I wanted children to also learn map skills. Observing them, I think that the problem posed in front of them was interesting, convincing and speaking to childrens‘ imagination.

As usual with group work, pupils had to take on certain roles and perform actvities connected with them. This simple approach engages pupils imagination and reinforces their emotional attitude toward their work. During the time of the proposed game, every group became a musical team preparing a performance tour. The route commenced in Frombork through Ostróda to Mława to Płock. There were three concerts on each day in each of the cities. In order to make the problem more real I suggested that each of the music teams played well but was not famous enought to have a manager. Consequently, each member of the team had to play and also plan the route of the travel. The work had to be divided: each member of the team was supposed to plan the route on a different interval of the trip and calculate its length.






The computational part of the work consisted of adding lengths of individual pieces read off the map. After finishing its calculations, each group had to glue coordinated pieces of the map onto a poster board indicating each of the travel intervals. The groups also included tables with the intervals and their calculated length, as well as the list of villages and towns passed along the road. The presentation was designed to enhance and diversify the work of the teams. Goals and Objectives The general aims of a class period were to: --Develop the competency of applying mental calculus to daily life problem solving, and in particular to problems encountered while using car road maps. -- Develop the competency to create a simple outline showing the problem situation. -- Develop the capacity for collaborative work. The proposed design of the class will also impact: --Competency of reading with understanding. --Competency of using tables as means for organization and presentation of information. The proposed problem is also useful for the realization of wider, interdisciplinary educational aims such as: --Familiarization with geographic regions contained in the road map. --Familiarization with the history and development of the passing communities. --Familiarlization with the scale of distance in Poland. --Introduction to the art of writing ads and announcements. --Organization of the musical program of the team. Among the detailed outcomes, students will be able to: -Plan the route of the trip from given initial site to the final site using the car map. -Make a sketch of the route. -Read the distances between different cities. -Complete the form describing the route in accordance with the template; -Do simple mental calculations applied to practical problem. -notice the relationships between different details of the map. -Synthisize details and make a useful chart or table.






Materials The design involves the following didactical materials in addition to a large map of Poland:

a) three different fragment maps,limited by the horizontal lines passing through the passing and final destinations (Fig.1)

b) instructions for the leader of the team c) instructions for the team’s members d) three forms for each of the members of the

team e) one form to collect information for the

leader of the team e) a handout with information about the cities

passed along the route f) large piece of the poster board to integrate

all the elements of the work.

Method

The teacher informs the class that each of the teams is responsible for plotting the performance route for a music team, scheduled to play three concerts in three different cities on one day. In the morning the teams leave Frombork where they stayed overnight and have to go to Ostróda, where they have the first concert at 10:00am in the gymnasium. The trip to Mława follows, where they have to play at 14:00 (2 p.m.) in the Cultural Center. Finally, for the evening they have engagement for 19:00 (7 p.m.) in the discoteque in Płock.

While presenting the outline of the game/activity, the teacher shows the essential cities on the map of Poland and briefly describes their history, development, significance for the region. Next, she shows the set of materials to be received by each of the groups. She discusses the distribution of tasks for the team. The teacher reads the instructions aloud and coordinates the forms with the map. Finally, she explains the sequential activities using the demonstration map.

Each member of the team is responsible for one interval of the trip and must design the route and compute its length. The activities are:

Frombork , miasto w województwie warmi_sko -mazurskim, nad Zalewem Wi_lanym, na skraju Równiny Warmi_skiej. 2,7 tys. mieszka_ców (2000). Port rybacki, przysta_ _eglugi pasa_erskiej, regularne po__czenia z Krynic_ Morsk_. Spe_nia funkcje miejscowo_ci wypocz ynkowej. Dobrze rozwini_te zaplecze noclegowe.

Historia Prawa miejskie nadano w 1310 osadzie, która rozwin__a si_ wokó_ warowni biskupów warmi_skich. Od 1466 w granicach Polski. Miejsce pracy i _mierci M. Kopernika, który mieszka_ we Fromborku w lat ach 1512 -1516 i 1522 -1543. W XVI i XVII w. rozwój handlu, powstanie portu i huty szk_a. W okresie rozbiorów pod panowaniem pruskim. W 1945, znacznie zniszczony, powróci_ do Polski.

Zamek we Fromborku, w_a_ciwie zespó_ katedralny wraz z umocnieniami obronnymi, za_o_ony na miejscu staropruskiego grodu. Umiejscowiony na wysokim wzgórzu. Ok. 1278 kapitu_a warmi_ska przenios_a tu swoj_ siedzib_ ze zniszczonego przez Prusów Braniewa. Wówczas wybudowano tu pierwszy ko_ció_, którego wygl_d nie jest znany, przypuszczalnie by_ on otoczony umocnieniami z drewna i ziemi. Istniej_cy dzisiaj ko_ció_ katedralny zbudowano w latach 1329 -1388. Wtedy te_ prawdopodobnie zacz_to wznoszenie murowanych umo cnie_

wzgórza. W latach 1510 -1543 z czteroletni_ przerw_ pracowa_ tu i mieszka_ Miko_aj Kopernik, b_d_cy kanonikiem warmi_skim. W 1626 wojska szwedzkie pod wodz_ Gustawa Adolfa zdoby_y i ograbi_y miasto i katedr_ ze wszystkich skarbów, biblioteka katedraln a i zbiory Kopernika zosta_y wywiezione do Szwecji.

Rys. 1. Collection of team’s materials

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Planowana godzina wyjazdu

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Czas przejazdu trasy przy

pr_dko_ci 60 km na godzin_

(godziny:minuty)

Planowana godzina

przyjazdu do Ostródy –

oblicz ! (godzina:minuty)

Potrzebna ilo__ paliwa przy

zu_yciu 10 litrów na 100 km

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przejazd Frombork -Ostróda 7:00 I.

koncert w Ostródzie 10:00 10:30

przejazd: Ostróda -M_awa 11:00 II.

koncert w M_awie 14:00 14:30

przejazd: M_awa -P_ock 16:00 III>

koncert w P_ocku 19:00 20:00

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Matematyka GRA -IV, ©Paw_owscy`2002 KAPELA: Praca w grupach (dodawanie)

Instrukcja dla zespo_u i jego lidera.

Jeste_cie zespo_em muzycznym, wybieraj_ cym si_ na tras_ koncertow_. W sobot_ macie

zagra_ a_ trzy koncerty, wi_c musicie dok_adnie to zaplanowa_. Z samego rana musicie

pojecha_ swoim busem z Fromborka do Ostródy, gdzie przed po_udniem , o godzinie 10:00

gracie w miejscowym gimnazjum. Potem czeka was podró_ do M_awy , gdzie o godzinie

14:00 gracie w Domu Kultury. Na wieczór macie umówiony koncert w dyskotece w

P_ocku o godzinie 19:00 .

Wasz zespó_ gra bardzo _adnie, ale jeszcze nie zdobyli_cie s_awy, wi_c nie macie

mena_era. Ka_dy z muzyków musi nie tylko gra_, ale i planowa_ tras_ – tak jak pilot

rajdowy w rajdzie samochodowym . Lider zespo_u nadzoruje prac_ wszystkich i pomaga

tym, którzy sobie nie radz_.

Zadania dla lidera (zadania na szarym tle nie s_ obowi_zkowe) :

1. Sprawd_ , czy koledzy prawid_ow o policzyli d_ugo_ci tras.

2. Wpis z d_ugo_ci tras do tabelki zbiorczej (pola I. II. i III.)

3. Policz ca_kowit_ d_ugo__ sobotniej trasy (pole |IV. RAZEM: ).

4. Pomó_ kolegom zrozumie_ i wykona_ zadania dodatkowe.

5. Wpis z wyniki zada_ dodatkowych do tabelki zbiorczej.

6. Oblicz potrzebn_ ilo__ paliwa i jego koszt.

7. Rozplan uj rozmieszczenie mapek i tabelek na kartonie, i pomó _ kolegom je naklei_.

8. Nakle jcie razem karteczki z plakatami informuj_cymi o koncertach.

Matematyka GRA -IV, ©Paw_owscy`2002 KAPELA: Praca w grupach (dodawanie)

Instrukcja dla pilota trasy (zadania na szarym tle nie s_ obowi_zkowe):

1. Odszukaj na mapce swoje miast o pocz_tkowe i ko_cowe , i zaznacz tras_ przejazdu.

2. Naszkicuj tras_ w tabelce .

3. Wpisz do tabelki nazwy co najmniej 4 kolejnych miast mijanych na Twoim

odcinku trasiy (pola nr 1a., 2a., 3a., ....) . Cz___ pól mo_e pozosta_ pusta.

4. W polu obok ka_dego miasta, wpisz d_ugo__ drogi od miasta poprzedniego (pola nr

1b., 2b., 3b., ...) . Nie zapom nij o mie_cie ko_cowym, które ju_ jest wpisane!

5. W polu „RAZEM” tabelki podsumuj d_ugo__ ca_ej trasy.

6. Je_li potrafisz i masz czas, to wype_nij kolejne pola „Tabel i zada_ dodatkowych”.

Podpowied_: pr_dko__ 60 km na godzin_ to to samo co 1 km na minut_

7. Wytnij i naklej na karton swoj_ mapk_, dopasowuj_c j_ do mapek kolegów.

8. Naklej na karton sw oj_ tabel_ .

9. Wykonaj projekt plakatu informuj_cego o koncercie waszego zespo_u w mie_cie, do

którego prowadzi Twoja trasa. Podaj miejsce, dat_ i godzin_ .

Figure 1. Fragment of a map obtained by one of the groups/






-find the initial and final town on the map. - draw the route on the map. - make a draft of the route on the appropriate form. -wirte in at least 4 names of passing towns. -write in the distances between them. -calculate the sum of the distances for the total trip.

Team leaders have their own tasks. They are responsible for the work of the members of

the teams: they should check whether the members do their work correctly; offer suggestions; and assist where needed. They organize common activities including: naming the team; planning the composition of maps and forms on the final poster presentation; and creating the announcements. The leader also supervises filling out the final form, plans the course for the day and sums up the length of the whole route. The forms for the particular intervals of the route contain additional tasks with instructions and needed information. Understanding these instructions is part of the overall task, hence it’s not discussed by the teacher.

When all the members of the team end their activities, the team aprpoaches the construction of the final product on the poster board. Each team member cuts out their map and glues them to the board making sure all individual maps fit together. The team leader supervises the gluing and adds the handout about one of the concerts. The team continues to work on the announcements of their concerts. (The teacher demonstrated different possible arrangements of the final product using the magnetic pieces.) The lesson and project can be accomplished in about 45 minutes. After checking the group submissions it is important that the teacher display each groups work (Figure 2.).

Figure 2. Example of the work design






Outcomes The described design was realized in two 4th grades with19 and 18 pupils respectively. Pupils were informed about upcoming activity and about the car maps and their utilization one class in advance; the appointed leaders were good in mathematics. The class experienced real joy and satisfaction in both classes. I was available to help children but only after each question was directed back to the team leaders. I was reminded children about the necessity of mutual help, about the final product depending on the collaboration of every one in the team. I looked for students who needed help the most and was helping them in more difficult situations. The real difficulty was reading off real distances from the map. I had also encouraged children to organize their work better.

Figure 3. Working Group. In the background there is a blackboard with attachad materials..






Assessment and evaluation of knowledge I used the following rubric to assess pupils‘ work - the member of the team could get 5 points for basic activities, which - gave 2 pts for starting all activities - gave 2 pts for correct reading off the distances from the map - gave 1 point for correct sum of all the distances. Captain could also get 5 points for basic activities: -2 points for starting -1 point for correct writing in the data into the table; - 1 point for finding sum -1 point for good leadership of the team (averaging 4 points by team members). Both captain and the team members could get max 3 points for additional activities.

Figure 4. One of the work results.






The distribution of points for the tasks is presented Figure 5. The average was 4.05. More than 75% of students received 4 points which means that basic tasks were done correctly or at most with small corrections. The additionaL task was taken by 4 pupils in the class Ivd, including two team captains.

Histogram of teams‘ average results (Figure 6) shows that all teams, except one, averaged above 3.5 pts, and four out of nine teams averaged more than 4.5 pts. These data confirm the subjective

assessment that the lesson was able to motivate collaboration in the majority of the teams. Corrected and graded products were discussed a couple of days later. The classroom where the posters were produced was changed into a gallery of finished work. The exhibition evoked deep interest amongst the children. Every child received the grade for individual work in a team in agreement with the accepted criteria. Besides two best teams in each class received the special prize to be divided by the team members. Assessment of effectiveness

The value of the project based learning is in its effectiveness. At the same time it is difficult to assess objectively because of the individual characteristics of the pupils. One measure can be the sum of all activities undertaken by pupils. All activities are counted independently of the correctness of the result. There were 6 activities in the described lessons which can be objectively registered on the basis of the documentation. Those activities together with the percentage of activities undertaken is presented in Table 1. Activity 3 was

0.0

1.0

2.0

3.0

4.0

5.0

6.0

b1.1

b1.3

b2.1

b2.3

b3.1

b3.3

b4.1

b4.3

b5.1

b5.k

d1.2

d2.1

d2.3

d3.1

d3.3

d4.1

d4.3

Figure 5. Distributionof points

0.0

1.0

2.0

3.0

4.0

5.0

6.0

b1 b2 b3 b4 b5 d1 d2 d3 d4

Figure 6. Team Averages






not required accounting for the smaller percentage. The presented data suggest that all or almost all students intensively participated in the classroom work. This confirms my subjective assessment. Summary and discussion

The sequence of activities in grade 4 as well as the effectiveness demonstrates that the group work method worked in this case. The lesson achieved it’s outlined goals. The coefficient of difficulty was 0.8 which means that the problems were well chosen for the class. Even children from the class who usually work slower and are a less able team presented the final effect of their work.

An additional problem was done by few children so the coefficient of difficulty is not reliable as there was not much time for this problem. Pupils who had undertaken the problem demonstrated high levels of competency and work organization. More difficult problems are needed so that more able students experience have satisfaction with the work.

The class design can be easily adapted for use in mathematics, biology, language, history and music. Use of the music team performance task including characteristics of the geography, history, legend and curiosities of passing cities) worked in the case of mathematics. At the same time the children had more time for the actual task of mathematical computation of the best route. Expanding the range of subjects to be included would necessitate using additional class periods. Although for this project I didn’t plan collaboration with other teachers I think it would be interesting and useful to realize multidisciplinary project. Talking with my colleagues, I think such a collaboration is possible. References

1. G. Pawłowska. Zamawiamy sadzonki na klomby. Praca w grupach, klasa V. Nauczyciele i

Matematyka 35 (2000) 10. 2. G. Pawłowska. Płacimy podatki. Praca w grupach na temat procentów, klasa V. Nauczyciele

i Matematyka 36 (2000) 21. 3. G. Pawłowska. Witraż: Praca w grupach na przykładzie lekcji w geometrii w klasie piątej.

Nauczyciele i Matematyka 40 (2001) 21. 4. G. Pawłowska. Planujemy zakupy na wycieczkę: Praca w grupach, klasa IV. Część I. Forum

Edukacji 2/3 (2001) 70.






5. G. Pawłowska. Planujemy zakupy na wycieczkę: Praca w grupach, klasa IV. Część II. Forum Edukacji 4 (2001) 72.

planning a route for a performing trip of a music team: a group … · 2018-12-10 · a musical...

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