{"id":440,"date":"2012-06-24T14:18:10","date_gmt":"2012-06-24T12:18:10","guid":{"rendered":"http:\/\/revista.newprojects.org\/?p=440"},"modified":"2017-04-10T10:56:43","modified_gmt":"2017-04-10T08:56:43","slug":"proiectarea-instrumentului-de-evaluare","status":"publish","type":"post","link":"https:\/\/revista.newprojects.org\/?p=440","title":{"rendered":"Proiectarea instrumentului de evaluare"},"content":{"rendered":"
Prof. Maria Teodora Stanculete,\u00a0Liceul \u201cIon Heliade R\u0103dulescu \u201c T\u00e2rgovi\u0219te<\/h5>\n

Instrumentul de evaluare a fost proiectat pentru unitatea de \u00eenv\u0103\u0163are \u201eGrafuri neorientate\u201d, la clasa a XI-a profil real, specializarea matematic\u0103 \u2013 informatic\u0103, \u00eencadr\u00e2ndu-se \u00een categoria\u00a0 testelor de evaluare sumativ\u0103<\/strong>.<\/p>\n

\u00cen componen\u0163a instrumentelor de evaluare sunt incluse urmatoarele elemente:<\/p>\n

1. Competen\u0163ele specifice<\/strong> \u00a0pentru care se evalueaz\u0103 nivelul de realizare.<\/p>\n

2.Competen\u0163ele de evaluare <\/strong>obiectivele pedagogice opera\u0163ionale, care transpun competen\u0163a specific\u0103 \u00een ac\u0163iune pedagogic\u0103.<\/p>\n

3. Matricea de specifica\u0163ii <\/strong>\u00a0<\/em>care are rolul de a corela obiectivele pedagogice opera\u0163ionale \u015fi itemii probei, cu clasele comportamentale care se evalueaz\u0103.<\/p>\n

4. Testul elevului\u00a0 <\/strong>care trebuie s\u0103 con\u0163in\u0103:<\/p>\n

– itemii oferi\u0163i elevilor pentru rezolvare (con\u0163inutul itemilor);<\/p>\n

– punctajul maxim (PM) al fiecarui item.<\/p>\n

5. Etalonul de rezolvare<\/strong> care cuprinde:<\/p>\n

– rezolvarea corect\u0103 a fiec\u0103rui item;<\/p>\n

– modul de acordare a punctajului pentru fiecare ac\u0163iune relevant\u0103 corect\u0103 a elevului.<\/p>\n

6. Etalonul de convertire a punctajelor \u00een note \u015fcolare.<\/strong><\/p>\n

Scala de evaluare care, pentru fiecare item, prevede etalonul de rezolvare \u015fi punctare, performan\u0163a maxim\u0103, performan\u0163a minim\u0103 admis\u0103 \u015fi normalizarea procentual\u0103 a punctajelor ob\u0163inute.<\/p>\n

Scara de notare alc\u0103tuit\u0103 din etalonul de convertire a punctajelor \u00een note \u015fcolare \u015fi instrumentele de convertire (nomograma de convertire sau formulele de calcul ale convertirii).<\/p>\n

<\/p>\n

NIVELELE TAXONOMICE \u2013 DOMENIUL COGNITIV<\/strong><\/p>\n

O1 <\/sub>. Cunoa\u015fterea<\/strong> (Achizi\u0163ia informa\u0163iei) (10 %)<\/p>\n

–\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Cunoa\u015fterea no\u0163iunii de graf neorientat: defini\u0163ie, clasificare, terminolgie.<\/p>\n

–\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Cunoa\u015fterea termenilor specifici: adiacen\u0163\u0103, inciden\u0163\u0103, grad; lan\u0163, drum, ciclu, circuit; subgraf, graf par\u0163ial;<\/p>\n

O2<\/sub>. Comprehensiunea<\/strong> (\u00cen\u0163elegerea) (15%)<\/p>\n

–\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Reprezentarea grafurilor neorientate, matrice de adiacenta, liste de adiacenta.<\/p>\n

–\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Descrierea metodelor de reprezentare.<\/p>\n

O3<\/sub>. Aplicarea<\/strong> (38%)<\/p>\n

–\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Calcularea gradului nodurilor, determinarea lanturilor, drumurilor, circuitelor intr-un graf neorientat.<\/p>\n

–\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Aplicarea algoritmilor de reprezentare a grafurilor neorientate.<\/p>\n

–\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Valorizarea cuno\u015ftin\u0163elor \u00een rezolvarea exerci\u0163iilor propuse.<\/p>\n

O4<\/sub>. Analiza<\/strong> (18%)<\/p>\n

–\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Analizarea particularit\u0103\u0163ilor de rezolvare a unor tipuri de exerci\u0163ii cu grafuri<\/p>\n

–\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Analiza grafurilor neorintate cu o anumita proprietate pornind de la defini\u0163iile acestora .<\/p>\n

O5<\/sub>. Sinteza<\/strong> ( 5%)<\/p>\n

–\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Caracterizarea elementelor unei graf prin derivarea proprietatilor date in ipoteza problemelor.<\/p>\n

O6<\/sub>. Evaluarea<\/strong> ( 4%)<\/p>\n

Validarea metodelor de rezolvare alese dupa analiza tuturor cazurilor posibile.<\/p>\n

MATRICEA DE SPECIFICA\u0162II A NIVELELOR TAXONOMICE<\/strong><\/p>\n

Matricea de specifica\u0163ii const\u0103 \u00eentr-un tabel cu dou\u0103 intr\u0103ri care serve\u015fte la proiectarea \u015fi organizarea itemilor dintr-un test docimologic, \u00een care sunt precizate, pe de o parte, con\u0163inuturile care vor fi vizate, \u015fi, pe de alt\u0103 parte, nivelele taxonomice la care se plaseaz\u0103 obiectivele de evaluare.<\/p>\n

Liniile matricei de specifica\u0163ii includ elementele de con\u0163inut vizate, iar coloanele se refer\u0103 la nivelele taxonomice le care vor fi m\u0103surate performan\u0163ele elevilor \u00een raport cu aceste con\u0163inuturi.<\/p>\n

Celulele tabelului, aflate la intersec\u0163ia dintre elementele de con\u0163inut \u015fi nivelele taxonomice pentru nivelul cognitiv cuprind procentele de itemi (din totalul itemilor consacra\u0163i \u00eentregului test) ce vor fi folosi\u0163i \u00een proiectatea testului.<\/p>\n

\n\n\n\n\n\n\n\n\n
\n

Nivele<\/strong><\/p>\n

taxonomice<\/strong><\/p>\n

Continuturi<\/strong><\/p>\n<\/td>\n

\n

Cunoastere intelegere<\/strong><\/p>\n<\/td>\n

\n

Aplicare<\/strong><\/p>\n<\/td>\n

\n

Analiza<\/strong><\/p>\n

Evaluare<\/strong><\/p>\n<\/td>\n

\n

Total<\/strong><\/p>\n

%<\/strong><\/p>\n<\/td>\n<\/tr>\n

\n

No\u0163iuni specifice grafului neorientat:<\/p>\n

\n<\/td>\n

\n

A1.1;A1.2;A1.3;<\/p>\n<\/td>\n

\n

B1;<\/p>\n<\/td>\n

\n

–<\/p>\n<\/td>\n

\n

15%<\/strong><\/p>\n<\/td>\n<\/tr>\n

\n

Metode de reprezentare a grafurilor neorientate<\/p>\n<\/td>\n

<\/td>\n\n

A1.4; B2;<\/p>\n<\/td>\n

\n

B3<\/p>\n<\/td>\n

\n

30%<\/strong><\/p>\n<\/td>\n<\/tr>\n

\n

Graf partial \u0219i subgraf \u00eentrun graf neorientat<\/p>\n<\/td>\n

<\/td>\n\n

A1.5;<\/p>\n<\/td>\n

\n

B4<\/p>\n<\/td>\n

\n

30%<\/strong><\/p>\n<\/td>\n<\/tr>\n

\n

Proiectarea modular\u0103 a aplica\u021biilor<\/p>\n<\/td>\n

<\/td>\n<\/td>\n\n

C1<\/p>\n<\/td>\n

\n

25%<\/strong><\/p>\n<\/td>\n<\/tr>\n

\n

Total<\/strong><\/p>\n<\/td>\n

\n

30%<\/strong><\/p>\n<\/td>\n

\n

45 %<\/strong><\/p>\n<\/td>\n

\n

25%<\/strong><\/p>\n<\/td>\n

\n

100%<\/strong><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

TEST DE EVALUARE<\/strong><\/span><\/p>\n

CLASA A XI-A<\/p>\n

UNITATEA DE \u00ceNV\u0102\u0162ARE: GRAFURI NEORIENTATE<\/p>\n

Toate subiectele sunt obligatorii. <\/strong><\/p>\n

Timpul efectiv de lucru este de o or\u0103. Se acord\u0103 10 puncte din oficiu.<\/p>\n

\u00a0Subiectul A 20p<\/strong><\/p>\n

\u00a0<\/strong>1)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong>Pentru graful din figura al\u0103turat\u0103 stabili\u021bi valoarea de adev\u0103r a fiec\u0103reia dintre propozi\u021bii. \u00a0\"\"<\/a><\/strong><\/p>\n

 <\/p>\n

1.1.G este un graf conex.<\/p>\n

1.2.Nodurile 1 \u0219i 5 sunt adiacente.<\/p>\n

1.3.Gradul nodului 3 este 3.<\/p>\n

1.4.Matricea de adiacen\u021b\u0103 asociat\u0103 grafului G este simetric\u0103.<\/p>\n

1.5.Subgraful generat de nodurile {2,3,4} formeaz\u0103 o component\u0103 conex\u0103.<\/p>\n

Subiectul B 40p<\/strong><\/p>\n

\u00a0<\/strong>1)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong>Se consider\u0103 un graf neorientat cu 7 <\/strong>noduri, numerotate de la 1 <\/strong>la 7<\/strong>, cu proprietatea c\u0103<\/p>\n

exist\u0103 muchie cu extremit\u0103\u0163ile \u00een nodurile i <\/strong>\u015fi respectiv j <\/strong>dac\u0103 numerele i <\/strong>\u015fi j <\/strong>sunt de<\/p>\n

aceea\u015fi paritate sau dac\u0103 i <\/strong>este divizor al lui j<\/strong>. Gradul maxim al unui nod din acest graf<\/p>\n

este:<\/p>\n

a)1;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 b). 7;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 c). 4;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 d). 6;<\/strong><\/p>\n

\u00a0<\/strong>\u00a0<\/strong>2)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong>C\u00e2te grafuri neorientate, distincte, cu 3 <\/strong>v\u00e2rfuri se pot construi? Dou\u0103 grafuri se consider\u0103<\/p>\n

distincte dac\u0103 matricele lor de adiacen\u0163\u0103 sunt diferite.<\/p>\n

a)23<\/sup>;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 b). 6 ;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 c.) 32 ,\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 d) 16;<\/strong><\/p>\n

3)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong>Se consider\u0103 graful neorientat cu 5 <\/strong>noduri a c\u0103rui matrice de adiacen\u0163\u0103 are toate elementele 1<\/strong>, cu excep\u0163ia celor de pe diagonala principal\u0103, care sunt nule. Care este num\u0103rul minim <\/strong>de muchii care pot fi eliminate astfel \u00eenc\u00e2t graful par\u0163ial ob\u0163inut s\u0103 fie format din 3 <\/strong>componente conexe?<\/p>\n

 <\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong>a.) 4;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0b) 8;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 c) 6;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 d) 7;<\/strong><\/p>\n

\u00a0<\/strong>4)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong>Se consider\u0103 graful neorientat cu mul\u0163imea v\u00e2rfurilor {1,2,3,4,5,6} <\/strong>\u015fi mul\u0163imea muchiilor{[1,2],[2,3],[3,4],[3,5],[4,5],[1,3],[2,6],[2,4],[4,6]}<\/strong>. Care este num\u0103rul minim de muchii ce trebuie eliminate astfel \u00eenc\u00e2t graful par\u0163ial ob\u0163inut s\u0103 nu mai fie conex?<\/p>\n

5)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong>Care este gradul maxim <\/strong>pe care \u00eel poate avea un nod al unui graf neorientat cu 6 <\/strong>muchii \u015fi noduri dintre care exact dou\u0103 <\/strong>au gradul 0<\/strong>?<\/p>\n

 <\/p>\n

\u00a0<\/strong>Subiectul C 30 p<\/strong><\/p>\n

1)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong>Se consider\u0103 un graf neorientat cu n noduri, reprezentat prin matricea sa de adiacen\u021b\u0103. Realiza\u021bi un algoritm modular prin care se poate stabili dac\u0103 graful G, este aciclic. Detalia\u021bi un modul pe car \u00eel considera\u021bi reprezentativ scriind \u00een limbaj Pascal sau C++ subprogramul corespunz\u0103tor.<\/p>\n

BAREM DE CORECTARE \u015eI NOTARE<\/strong><\/p>\n

\u00a0TEST DE EVALUARE<\/p>\n

CLASA A XI-A<\/p>\n

UNITATEA DE \u00ceNV\u0102\u0162ARE: GRAFURI NEORIENTATE<\/p>\n