GRADUATE COURSE IN MATHEMATICS – MATH. EDUCATION ... · Mathematics education II 2 + 0 + 2 7 Educational psychology 1 2 + 1 + 0 5 Developmental psychology 2 + 1 + 0 5 Educational

GRADUATE COURSE

IN MATHEMATICS –

MATH. EDUCATION SPECIALIZATION

INDEX: Core courses TM – 30 ECTS Professional courses TM Methodical courses NOTICE: Students must take at least 20 ECTS in Professional courses.

Year I

Course title

Winter semester

Summer semester

Hours/week (L + E + S)

ECTS credits

Hours/week (L + E + S)

ECTS credits

Vector Spaces I 2 + 2 + 0 5

Elective course M1 2 + 2 + 0 6

Linear Programming 2 + 2 + 0 5

Mathematics education I 2 + 0 + 2 6

Mathematics education II 2 + 0 + 2 7

Educational psychology 1

2 + 1 + 0 5

Developmental psychology

2 + 1 + 0 5

Educational psychology 2

2 + 1 + 0 4

Didactics 1

2 + 1 + 0 5

General pedagogy

2 + 0 + 1 5

Elective course TM

2 3

Seminar III

0 + 0 + 2 4

Using computers in teaching mathematics

1 + 1 + 0 3

Total:

20 30 21 30

Year II

Course title

Winter semester

Ljetni semester

Hours/week

ECTS credits

Hours/week

ECTS credits

History of Mathematics

1 + 0 + 2 4

Elective course M2 8 12

Elective course M3 (7) 8 12

Selected lectures from teaching mathematics

2 + 2 + 0 5

Additional teaching of mathematics

2 + 2 + 0 5

Didactics 2

2 + 1 + 0 4

Teaching pupils with special needs 2 + 0 + 0 4

Elective course TM 2 + 0 + 0 3

Methodical practice in mathematics I 0 + 3 + 0 3

Methodical practice in mathematics II 0 + 3 + 0 3

Seminar / M.Sc. thesis

0 + 0 + 2 4

Graduation 2

Total:

22 30 19 (20) 30

Graduation requirements: All study commitments fulfilled and positively graded dissertation.

ELECTIVE COURSES

Elective courses M1

Course title Winter semester Summer semester

Hours/week ECTS credits Hours/week ECTS credits

Vector Spaces II 2 + 2 + 0 6

Descriptive Geometry 2 + 2 + 0 6

Basis of the philosophy of mathematics 2 + 2 + 0 6

Elective courses M2



Measure and Integral 2 + 2 + 0 7

Algebra I 2 + 2 + 0 7

Elective course NM 2 3

Topics in contemporary mathematics 1 + 0 + 1 4

Elective courses M3



Designing of educational system 2 + 0 + 2 6

Intoduction to Optimization 2 + 0 + 2 6

Algebra II 2 + 2 + 0 6

Probability Theory 2 + 2 + 0 6

Coding theory and cryptography 2 + 0 + 1 6

Sveučilište u Rijeci • University of Rijeka Trg braće Mažuranića 10 • 51 000 Rijeka • Croatia

T: (051) 406-500 • F: (051) 216-671; 216-091 W: www.uniri.hr • E: [email protected]

General information Lecturer Neven Grbac

Course title Vector spaces I

Program Graduate course in mathematics – Math. Education Specialization

Course status Core

Year I Credit values and modes of instruction

ECTS credits / student workload 5 Hours (L+E+S) 30 + 30 + 0

1. COURSE DESCRIPTION

1.1. Course objectives - acquisition of the notions and basic properties of vector spaces - acquisition of the notion of an algebra - acquisition of the basic properties of linear operators and their matrix representations - definition of the invariant subspaces and operator eigenvalues - acquisition of the basic properties of unitary spaces 1.2. Course prerequisite

None.

1.3. Expected outcomes for the course After completing this course students should be able to:

- describe various examples of vector spaces, linear operators and unitary spaces - understand the fundamental concepts and techniques of the theory of vector spaces - understand the relationship between linear operators and their matrix representations - apply theoretical knowledge in problem solving (such as finding the rank of a matrix, minimal polynomial,

determinant and matrix eigenvalues) 1.4. Course content

The notion of a vector space. Linear dependence. Subspace. Direct sum of subspaces. Quotient space. Basis of a vector space. Linear operators. The space (X,Y). Matrix of an operator in the given basis. Dependence of the matrix of an operator on the given basis. Limit in the space (X,Y). The notion of an algebra. Minimal polynomial. Invertible operator. Resolvent. Adjoint space and adjoint operator. Rank of an operator. Determinant and trace of an operator. Invariant subspaces and eigenvalues. Reduction of operators on finite dimensional vector spaces. Jordan matrix of an operator. Unitary spaces. Gram-Schmidt method of orthogonalization.

1.5. Modes of instruction

lectures seminars and workshops exercises e-learning field work practise practicum

independent work multimedia and the internet laboratory project strategies tutorials consultations other ___________________

1.6. Comments

1.7. Student requirements Students must satisfy requirements for obtaining the Signature (listed in the executive program) and to pass the final exam.



1.8. Evaluation and assessment1 Class attendance & class participation 1.1 Seminar paper Experiment Written exam 2 Oral exam 1.3 Essay Research work Project Continuous assessment 0.6 Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.

1.9. Assessment and evaluation of students' work during the semester and in the final exam Students' work will be evaluated and assessed during the semester and in the final exam. Total number of points student can achieve during the semester is 70 (to assess the activities listed in the table), while in the final exam student can achieve 30 points. The detailed work out of monitoring and evaluation of students' work will appear in the executive program.

1.10. Required literature (when proposing the program ) 1. S. Kurepa: Konačno dimenzionalni vektorski prostori i primjene, Sveučilišna naklada Liber, Zagreb, 1976 2. H. Kraljević: Vektorski prostori, Odjel za matematiku, Sveučilište u Osijeku

1.11. Recommended literature (when proposing the program) 1. P. R. Halmos: Finite Dimensional Vector Spaces, Van Nostrand, New York, 1958 2. K. Horvatić: Linearna algebra, Golden marketing – Tehnička knjiga, Zagreb, 2004 3. S. Lang: Linear algebra, Springer Verlang, Berlin, 1987

1.12. Number of copies of required literature in relation to the number of students currently attending classes of the course

Title Number of copies Number of students

1.13. Quality assurance wich ensure acquisition of knoxledge, skills and competencies In the last week of the semester students will evaluate the quality of the lectures. At the end of each semester (March 1 and September 30 of the current academic year) results of the exams will be analyzed.

1 IMPORTANT: Fill in the appropriate number of points for each of the chosen categories so that the sum of the allocated points corresponds to the course credit value. Add new categories, if necessary.



General information Lecturer Rene Sušanj

Course title Linear Programming


Course status Core


ECTS credits / student workload 5 Hours (L+E+S) 30 +30 +0


1.14. Course objectives Course objective is acquisition of basic types of the linear programming problems, basic algorithms for optimization problem solving, basic notions of duality, basic notions of the matrix game theory, basis of convex and integer programming.

1.15. Course prerequisite

None.

1.16. Expected outcomes for the course After completing this course students will be able to solve different problems concerning linear programming. They will know and understand the notions of convex sets, linear (affine) function, concepts of the matrix games, concepts of duality and basis of convex programming. Student will be able to apply various algorithms for finding the extreme values of function on the convex set.

1.17. Course content Polyhedral sets. Solvability of linear programming problem. Gauss-Jordan method. Basic linear programming problems. Fourier-Motzkin method. Simplex method (simplex schemata). Degeneracy case. Dual simplex method. Parametric linear programming. Duality. Integer programming. Transportation problems. Basis of matrix game theory. Convex programming.


lectures seminars and workshops exercises e-learning field work practice praktikumska nastava

independent work multimedia and the internet laboratory projektna nastava tutorials consultations other ___________________

1.19. Comments

1.20. Student requirements

Students must satisfy requirements for obtaining the Signature (listed in the lesson plan) and to pass the final exam.



1.21. Evaluation and assessment2

Class attendance & class participation 1 Seminar paper Experiment Written exam 1 Oral exam 1.5 Essay Research work Project Continuous assessment 1.5 Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.

1.22. Assessment and evaluation of students' work during the semester and in the final exam Students' work will be evaluated and assessed during the semester and in the final exam. Total number of points student can achieve during the semester is 70 (to assess the activities listed in the table), while in the final exam student can achieve 30 points. The detailed work out of monitoring and evaluation of students' work will appear in the lesson plan.

1.23. Required literature (when proposing the program ) 1. N.Linić, H.Pašagić, Č.Rnjak : Linearno i nelinearno programiranje, Informator, Zgb, 1978. 2. K.Murty : Linear and Combinatorial Programming, John Wiley and Sons, NY, 1976. 1.24. Recommended literature (when proposing the program) 1. R.V. Benson : Euclidean Geometry and Convexity, Mc Graw - Hill, NY, 1966. 2. L.Lyusternik : Convex Figures and Polyhedrons, Dover publications, NY, 1963. 3. M.Radić : Linearno programiranje, Školska knjiga, Zgb, 1974. 1.25. Number of copies of required literature in relation to the number of students currently attending classes

of the course Title Number of copies Number of students

N.Linić, H.Pašagić, Č.Rnjak : Linearno i nelinearno programiranje, Informator, Zgb, 1978 5 10 K.Murty : Linear and Combinatorial Programming, John Wiley and Sons, NY, 1976 1 10





General information Lecturer Sanja Rukavina

Course title Mathematics education 1


Course status Core




1.27. Course objectives - acquisition of basic theories of teaching mathematics; - acquisition of special theories of teaching mathematics in the elementary school (5th to 8th grade) and in the

secondary school; - acquisition of mathematical knowledge necessary for successful teaching of mathematics in the higher grades of

elementary school; - introducing curriculum of mathematics in the higher grades of elementary school; - preparing students for teaching of mathematics based on the principles of mathematics education. 1.28. Course prerequisite

None.

1.29. Expected outcomes for the course After completing this class students should be able to:

- quote principles of mathematics education and their basic properties and introduce examples; - know several forms of defining mathematics' terms and their advantages and deficiencies in school mathematics; - know different ways of proving mathematical theorems; - have mathematical knowledge necessary for successful teaching in elementary school (5th to 8th grade) 1.30. Course content

The subject of teaching mathematics. The objectives and tasks of teaching mathematics. Principles of teaching mathematics – scientific approach (axiom, mathematical definition, the definition of the term, theorem, proof), activity, independence and awareness (formalism in mathematics class), motivation (games in teaching mathematics, mathematical billboard), individualization, visualization, suitability (factors that affect the process of learning mathematics, degrees of knowing the mathematics, mathematical personality), systematicity, stability (remembering mathematical facts and procedures). In seminars, students will become familiar with the curriculum of mathematics in the higher grades of elementary school and expose the selected topics in mathematics that are processed in the higher grades of elementary school.


lectures seminars and workshops exercises e-learning field work practice practicum


1.32. Comments




Students must satisfy requirements for obtaining the Signature (listed in the executive program) and to pass the final exam.

1.34. Evaluation and assessment3 Class attendance & class participation 2 Seminar paper 0.5 Experiment Written exam 0.5 Oral exam 1 Essay Research work Project Continuous assessment 2 Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.


1.36. Required literature (when proposing the program ) 1. Current textbooks for elementary and secondary schools 2. Matematika bez suza, ed. Ilona Posokhova, Ostvarenje, Lekenik, 2000 1.37. Recommended literature (when proposing the program) 1. Polya,G.: Kako ću riješiti matematički zadatak, Školska knjiga, Zagreb, 1984 2. XXX: Matematika i škola, časopis za nastavu matematike, Element, Zagreb 3. XXX: Matka, časopis za mlade matematičare, Hrvatsko matematičko društvo 1.38. Number of copies of required literature in relation to the number of students currently attending classes


1.39. Quality assurance wich ensure acquisition of knowledge, skills and competencies In the last week of the semester students will evaluate the quality of the lectures. At the end of each semester (March 1 and September 30 of the current academic year) results of the exams will be analyzed.





Course title Mathematics education II


Course status Core




1.40. Course objectives - acquisition of basic theories of teaching mathematics; - acquisition of special theories of teaching mathematics in elementary school (5th to 8th grade) and secondary

school; - acquisition of mathematical knowledge necessary for successful teaching of mathematics in secondary school; - introducing the secondary school mathematical curriculum; - preparing students for choosing the appropriate methods in teaching of mathematics. 1.41. Course prerequisite

Mathematics education I.


- differ and distinguish methods of teaching mathematics, especially methods accordind to the subject ; - recognize the type of mathematical problem and adjust problem-solving methods to pupil's age; - know the secondary school mathematical curriculum and to have the knowledge necessary for successful

teaching of mathematics in secondary school. 1.43. Course content

Methods of teaching (methods according to the source of knowledge and methods upon the mathematical content). Empirical methods, induction, deduction, analysis and synthesis, generalization, abstraction, concretization, problem-solving methods, analogy and comparison, special mathematical cases. Methods for specific mathematical content. In the seminars, students will become familiar with the education curriculum of mathematics in high school and vocational schools. Students will present selected topics in mathematics that are processed in economic and other vocational schools and which are not part of the basic mathematicians' education.



independent work multimedia and the internet laboratory project tutorials consultations other ___________________

1.45. Comments





Class attendance & class participation 2 Seminar paper 1 Experiment Written exam 1 Oral exam 2 Essay Research work Project Continuous assessment 1 Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.


1.49. Required literature (when proposing the program ) 1. Current textbooks for elementary and secondary schools and teachers' manuals 2. Matematika bez suza, ed. Ilona Posokhova, Ostvarenje, Lekenik, 2000 3. e-literature 1.50. Recommended literature (when proposing the program) 1. Polya,G.: Kako ću riješiti matematički zadatak, Školska knjiga, Zagreb, 1984 2. XXX: Matematika i škola, časopis za nastavu matematike, Element, Zagreb 3. Methodical and popular magazines (printed or on line) 1.51. Number of copies of required literature in relation to the number of students currently attending classes


Textbooks for elementary and secondary schools and teachers' manuals 20 10 Matematika bez suza, ed. Ilona Posokhova, Ostvarenje, Lekenik, 2000 5 10





General information Lecturer

Course title Educational psychology I - Psychology of learning and teaching


Course status Core




1.53. Course objectives The objective of this course is to apply the findings of psychology of learning to school practices. The students will acquire knowledge about main factors that contribute to successful learning, including students' characteristics and motivation for learning. The effect of social interaction on classroom learning will also be considered.


Developmental psychology.

1.55. Expected outcomes for the course Students will be able to: - describe and understand learning through classical conditioning in schools - apply principles of operant conditioning in clasroom - describe and understand theory of information processing - distinguish between different learning styles - apply effective learning strategies (mnemonic strategies, summarising, questioning) - explain intelligence and its effect on school achievement - explain relationship between self-concept and school achievement - describe and compare different theories about relation between motivation and school achievement - differentiate categories of social status in classroom and plan methods for social status improvement - understand components on student-teacher relationship - apply social skills in order to establish positive social interactions in classroom and change undesirable students'

behaviours - understand different approaches to discipline management

1.56. Course content Classical conditioning in classroom; Operant conditioning; Modeling; Self-regulation of behavior and mentoring; Information processing theory; Cognitive and metacognitive strategies; Intelligence and learning; Students' personality characteristics and learning; Motivation and learning; Interactions among students in classroom; Interaction between teachers and students; Different approaches to discipline management.




1.58. Comments




Students must satisfy the requirements for obtaining the signature (listed in the executive program) and to pass the final exam.

1.60. Evaluation and assessment5 Class attendance & class participation 2.2 Seminar paper Experiment Written exam Oral exam 1.3 Essay Research work Project Continuous assessment 1.5 Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.


1.62. Required literature (when proposing the program ) 1. Kolić-Vehovec, S. (1999). Edukacijska psihologija. Filozofski fakultet, Rijeka 2. Vizek-Vidović, V., Vlahović-Štetić, V., Rijavec, M., Miljković, D. (2003). Psihologija obrazovanja. Zagreb: IEP

2.1. Recommended literature (when proposing the program) 1. Kroflin, L., Nola, D. (Ed.). (1987). Dijete i kreativnost. Zagreb: Globus. 2. Faber, A., Mazlish, E. (2000). Kako razgovarati s djecom da bi bolje učila. Zagreb: Mozaik knjiga. 3. Janković, J. (1996). Zločesti đaci genijalci. Zagreb: Alinea. 4. Neill, S. (1994). Neverbalna komunikacija u razredu. Zagreb: Educa. 5. Pintrich, P.R., Schunk, D.H. (1996). Motivation in education: Theory, research and application. Englewood Clifs, HJ:

Prentice Hall. 6. Salovey, P., Sluyter, D.J. (1999). Emocionalni razvoj i emocionalna inteligencija. Pedagoške implikacije. Zagreb:

Educa. 7. Winkel, R. (1996). Djeca koju je teško odgajati. Zagreb: Educa.








Course title Developmental psychology


Course status Core




1.63. Course objectives The main aim of the course is to familiarise students with the basic concepts of the development necessary for the understanding of the legality of upbringing and education. On the basis of perceptions regarding the psychological development of children and adolescence, to enable the understanding of applied educational procedures, as well as their appropriateness for a child’s specific age. The sensitivity of students for specific functioning of children of various ages as well as the understanding of individual differences. The acquiring of assessment skills and critical judgement of the appropriateness regarding the upbringing-educational work with children and adolescence.


None.

1.65. Expected outcomes for the course Upon completing the course, the students will be able to:

1. understand specifics of development of mid-childhood and adolescence 2. recognise normal development and understand specifics of individual development and are sensitive to the

individual differences among children 3. understand the role of the family and school in the development of the child in mid-childhood and the

importance of the interaction these factors 4. develop skills of assessment and critical judgement of the appropriateness regarding the upbringing-

educational work with children of various ages. 1.66. Course content

Developmental theories. Puberty and biological theories. Cognitive development. Concrete and abstract opinion. Intellectual development and achievement. Moral development. Self concept. Identity development. Growing up within a family. Relations with parents. The role of the school. Relations with peers. Peer groups. Violence in school. Sexuality. The role of the media in development. Stress in children and adolescents. Abuse. The problem of adjustment during adolescence (eating disorders, loneliness, suicidal tendencies, delinquent behaviour, drug consumption).




1.68. Comments





1.70. Evaluation and assessment6 Class attendance & class participation 1.2 Seminar paper Experiment Written exam 0.5 Oral exam 0.5 Essay 0.8 Research work Project Continuous assessment 1 Presentation 0.5 Practical work Portfolio Report with the exercise 0.5 Comment: ECTS distribution from above is made for studies and/or modules with courses which have ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.


1.72. Required literature (when proposing the program ) 1. Vasta, R., Haith, M.M., Miller, S.A. (1998). Dječja psihologija. Jastrebarsko, Slap. 2. Lacković-Grgin, K. (2000.). Stres u djece i adolescenata, Jastrebarsko, Slap. 3. Vizek Vidović, V., Rijavec, M., Vlahović-Štetić, V., Miljković 2.2. Recommended literature (when proposing the program)

1. Bastašić, Z., Pubertet i adolescencija, Školska knjiga, Zagreb, 1995 2. Buljan-Flander, G., Kocijan-Hercigonja, D. (2003). Zlostavljanje i zanemarivanje djece, Marko.M., Zagreb 3. Jaffe, M.L. (1998). Adolescence. New York: Wiley & Sons Inc 4. Kimmel, D. C., Weiner, I.B.(1995) Adolescence-developmental transition, J. Wiley & Sons, inc. 5. Lacković-Grgin, K. (1993). Samopoimanje mladih, Jastrebarsko, Slap. 6. Olweus (1998). Nasilje među djecom u školi. Zagreb. Školska knjiga 7. Raboteg-Šarić, Z. (1995). Psihologija altruizma, Alinea








Course title Educational psychology II - Individual differences and classroom interaction


Course status Core




1.73. Course objectives The objective of this course is to apply the findings of psychology of learning to school practices. The students will acquire knowledge about main factors that contribute to successful learning, including students' characteristics and motivation for learning. The effect of social interaction on classroom learning will also be considered.


Developmental psychology.

1.75. Expected outcomes for the course Students will be able to: - describe and understand learning through classical conditioning in schools - apply principles of operant conditioning in clasroom - describe and understand theory of information processing - distinguish between different learning styles - apply effective learning strategies (mnemonic strategies, summarising, questioning) - explain intelligence and its effect on school achievement - explain relationship between self-concept and school achievement - describe and compare different theories about relation between motivation and school achievement - differentiate categories of social status in classroom and plan methods for social status improvement - understand components on student-teacher relationship - apply social skills in order to establish positive social interactions in classroom and change undesirable students'

behaviours - understand different approaches to discipline management

1.76. Course content Classical conditioning in classroom; Operant conditioning; Modeling; Self-regulation of behavior and mentoring; Information processing theory; Cognitive and metacognitive strategies; Intelligence and learning; Students' personality characteristics and learning; Motivation and learning; Interactions among students in classroom; Interaction between teachers and students; Different approaches to discipline management.




1.78. Comments





1.80. Evaluation and assessment7 Class attendance & class participation 2 Seminar paper Experiment Written exam Oral exam 0.6 Essay Research work Project Continuous assessment 1.4 Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.


1.82. Required literature (when proposing the program ) 1. Kolić-Vehovec, S. (1999). Edukacijska psihologija. Filozofski fakultet, Rijeka 2. Vizek-Vidović, V., Vlahović-Štetić, V., Rijavec, M., Miljković, D. (2003). Psihologija obrazovanja. Zagreb: IEP

2.1. Recommended literature (when proposing the program) 1. Kroflin, L., Nola, D. (Ed.). (1987). Dijete i kreativnost. Zagreb: Globus. 2. Faber, A., Mazlish, E. (2000). Kako razgovarati s djecom da bi bolje učila. Zagreb: Mozaik knjiga. 3. Janković, J. (1996). Zločesti đaci genijalci. Zagreb: Alinea. 4. Neill, S. (1994). Neverbalna komunikacija u razredu. Zagreb: Educa. 5. Pintrich, P.R., Schunk, D.H. (1996). Motivation in education: Theory, research and application. Englewood Clifs, HJ:

Prentice Hall. 6. Salovey, P., Sluyter, D.J. (1999). Emocionalni razvoj i emocionalna inteligencija. Pedagoške implikacije. Zagreb:

Educa. 7. Winkel, R. (1996). Djeca koju je teško odgajati. Zagreb: Educa.








Course title Didactics I


Course status Core




1.83. Course objectives The objectives of this course are:

- to get students acquainted with variety of didactical choices in teaching practice and their adequate use in teaching practice;

- to enhance students for continiouos educational development and development of their teaching practice, - to motivate students for nurturing positive climate and team work in teaching; - to encourage students for basic research skills and constant inovation of their teaching practice. 1.84. Course prerequisite

None.

1.85. Expected outcomes for the course In order to fulfill his/her student requirements, students are expected to develope several competencies:

- To interprete and analyse fundamental didactical concepts and theories; - To give critical interpretation of various didactical theories, schools of thoughts and models; - To analyse and use various didactical and methodical choices in actual educational and teaching practice; - To analyse and use adequately various didactical knowledge and skills (curriculum design; micro and macro

organisation of teaching; using educational technology; assessment procedures; professional staff development of teachers etc.);

- To carry out and interprete simple research projects in the field of didactics and to suggest possible improvements and innovations of teaching practice.

1.86. Course content Methodological and epistemiological foundations of didactics. Terminology and didactical system. Education and teaching (aims, objectives and contents; regulations in teaching; didactical principles; factors, media and social forms). Theories and models of teaching and education. Didactical theories and schools of thoughts. Curriculum design. Theories of curricula. Educational and teaching situations. Didactical cycle and phases (preparation, realisation and evaluation). Educational technology. Macro and micro organisation of teaching. Trends in educational staff development.




1.88. Comments




Students are expected to come to class prepared to take active part in group discussions, to make a set of assignements in written form, to make individual or team work and to pass oral and written exam. Studies and researching of actual didactical problems will be rewarded. Students are expected to study required literature and choose at least two sources from the list of recommended literature. As a prerequisite for approaching to the exam, all written assignments should be accomplished and they should proove they are familiar with the actual problems and trends in the field of didactics. Oral exam is organised at the end of the term. Students are expected to read required literature continuously during the term (to prepare for the group discussion).

1.90. Evaluation and assessment8 Class attendance & class participation 1.5 Seminar paper 0.5 Experiment Written exam 1 Oral exam 1 Essay 0.5 Research work Project Continuous assessment 0.5 Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.


1.92. Required literature (when proposing the program ) 1. Jelavić, F. (2003). Didaktika. Jastrebarsko: Naklada Slap 2. Bognar, L. (2002). Didaktika. Zagreb: Školska knjiga 3. Poljak, V. (1991). Didaktika. Zagreb: Školska knjiga 4. Lavrnja, I (1998). Poglavlja iz didaktike. Rijeka: Pedagoški fakultet u Rijeci 5. Lavrnja, I.(2000). Vježbe iz didaktike. Rijeka: Pedagoški fakultet u Rijeci.

2.3. Recommended literature (when proposing the program) 1. Bežan, A., Jelavić, F., Kujundžić, N. i Pletenac, V. (1991). Osnove didaktike. Zagreb: Školske novine 2. Stevanović, M. (2003). Didaktika. Rijeka: Digital Point 3. Jensen, E. (2003). Super-nastava. Nastavne strategije za kvalitetnu školu i uspješno učenje. Zagreb: Educa 4. Kyriacu, C. (2001). Temeljna nastavna umijeća. Zagreb: Educa 5. Terhat,E. (2001). Metode poučavanja i učenja. Zagreb: Educa







General information Lecturer Vedrana Mikulić Crnković

Course title Using computers in teaching mathematics


Course status Core




1.93. Course objectives

Course objective is student's preparation for ICT application in the teaching mathematics.


None.


- choose appropriate methods and ICT tools for teaching, - create, prepare and present teaching contents with the use of ICT. 1.96. Course content

E-learning. Computer programs in teaching mathematics. Pupils' motivation with the ICT use. Independent learning with the use of ICT. Examination with the use of ICT. Planning and teaching with the use of ICT in mathematics. ICT application in teaching contents: elementary and secondary school.




1.98. Comments

1.99. Student requirements Students must satisfy the requirements for obtaining the signature (listed in the executive program) and to pass the final exam.

1.100. Evaluation and assessment9 Class attendance & class participation 1 Seminar paper Experiment Written exam Oral exam Essay Research work Project Continuous assessment 1 Presentation Practical work 1 Portfolio




Comment: ECTS distribution from above is made for studies and/or modules with courses which have ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.


1.102. Required literature (when proposing the program )

A.J.Oldknow, R. Taylor, Teaching Mathematics with ICT, Continuum, London, 2002

1.103. Recommended literature (when proposing the program) 1. M. Serra, Discovering Geometry: An Inductive Approach, Quizzes, Tests and Exams, Key Curriculum Press,

2001 2. M. Serra, Discovering Geometry: An Inductive Approach, Teacher's Resource Book, Key Curriculum Press, 2002 3. J. Murdock, E. Kamischke, E. Kamischke, Discovering Algebra: An Investigative Approach, Teaching and

Worksheet Masters, Key Curriculum Press, 2000 4. J. Murdock, E. Kamischke, E. Kamischke, Advanced Algebra Through Data Exploration, Constructive

Assessment in Maths: Practical Steps for Classroom Teachers, Key Curriculum Press, 2001 5. T. D. Gray, J. Glynn, Exploring Mathematics with Mathematica, Addison-Wesley, New York, 1991 6. E. Don, Schaum’s Outline of Theory and Problems of Mathematica, McGraw-Hill,New York, 2001 7. E. W. Johnson: Linear algebra with Matematica, Books/Cole Publishing Company, 1995 8. Original handbooks and other didactical material for concrete softwares and grafical calculators. 1.104. Number of copies of required literature in relation to the number of students currently attending

classes of the course Title Number of copies Number of students




General information Lecturer Majda Trobok

Course title Seminar III – Foundations of mathematics


Course status Core




1.106. Course objectives The course objective is to introduce the basic concepts of the Foundations of mathematics, ie. to describe axiomatic method and reasons for its introduction to mathematics, to describe and analyze Euclidean geometry, to know the paradoxes introduced in mathematics at the beginning of the 20th century and their influence in development of mathematics, to describe Hilbert axiomatic system, Principia Mathematica, Gödel theorem and category theory


None.

1.108. Expected outcomes for the course It is expected that students will learn and understand the basic problems that the foundations of mathematics concentrates on (axiomatic system, Principia Mathematica, 20th century paradoxes, category theory, etc.), as well as how they are linked to the standard mathematical practice.

1.109. Course content Historical background: Ancient Greek mathematics, Hilbert, Wittgenstein, Frege. The ZFC System of Axioms and the Theory of Categories.




1.111. Comments


Writing and presenting a seminar paper as well as the final (oral) exam are compulsory for students.

1.113. Evaluation and assessment10 Class attendance & class participation 1 Seminar paper 1.3 Experiment Written exam Oral exam Essay Research work 0.7 Project Continuous assessment 1 Presentation Practical work 10 IMPORTANT: Fill in the appropriate number of points for each of the chosen categories so that the sum of the allocated points corresponds to the course credit value. Add new categories, if necessary.



Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.

1.114. Assessment and evaluation of students' work during the semester and in the final exam Students' work will be evaluated and assessed during the semester. Total number of points student can achieve during the semester is 100 (to assess the activities listed in the table). The detailed work out of monitoring and evaluation of students' work will appear in the executive program.

1.115. Required literature (when proposing the program ) 1. Frege, G., 1995, Osnove Aritmetike i drugi spisi, Kruzak, Zagreb 2. Moore, A.W., 1990, The Infinite, Routledge, London 1.116. Recommended literature (when proposing the program)

1. Wittgenstein, L., 1937-44/1972, Remarks on the Foundations of Mathematics, The M.I.T. Press, Cambridge. 2. Benacerraf, P. i Putnam, H., 1983, Philosophy of Mathematics- Selected Readings, second edition, Cambridge

University Press, Cambridge. 3. Boolos, G., 1998, Logic, Logic and Logic, Harvard University Press. 4. Nagel, E.&Newman, J.R., 2001, Godelov dokaz, Kruzak, prevedeno iz Nagel, Newman, 1993, Godel's Proof,

Routledge 1.117. Number of copies of required literature in relation to the number of students currently attending






Course title Vector spaces II


Course status Elective




1.119. Course objectives - acquisition of basic notions and properties of topological vector spaces, - definition of normed space and examples, - definition and analysis of local convexity, metrizability and complete spaces, - acquisition of basic properties of linear functionals 1.120. Course prerequisite

Vector spaces I


- describe various examples of topological vector spaces, - understand basic relationships between mathematical objects that will be elaborated in this course, - understand the relationship between topological and linear structure in topological vector spaces 1.122. Course content

Topological vector spaces. Normed vector space. Local convexity. Metrizability. Completeness. Linear functionals and the Hahn-Banach theorem. Weak topologies. Dual spaces.




1.124. Comments






Class attendance & class participation 1.8 Seminar paper Experiment Written exam 2 Oral exam 1.4 Essay Research work

Project Continuous assessment 0.8 Presentation Practical work



1.128. Required literature (when proposing the program ) 1. S. Kurepa: Funkcionalna analiza, Školska knjiga, Zagreb, 1984 2. W. Rudin: Functional analysis, McGraw-Hill,1972 1.129. Recommended literature (when proposing the program)

K. Yosida: Functional analysis, Springer-Verlag, New York, 1985. 1.130. Number of copies of required literature in relation to the number of students currently attending






Course title Descriptive Geometry






1.132. Course objectives - development of spatial visualization, - acquisition of Monge's projection, - acquisition of a construction of intersection of a plane and an object in the space, - acquisition of projection methods - acquisition of a breach


1.134. Expected outcomes for the course After completing this course students will be able to understand and apply basics of descriptive geometry, e.g. projection and a construction of intersection of a plane and an object in the space.

1.135. Course content Introduction. Foundations of geometrical constructions. Parallel and orthogonal projection. Central projection. Invariant of those projections. Two-line projection. Locations and metric tasks. Representation of shapes in the general plane. Representation of objects in the space. Regular polyhedron. Intersections. Intersection of a plane and a prism. Intersection of prisms. Intersection of a prism and a pyramid. Intersection of cone and prism. Intersection of two cylinders. Intersection of a cylinder and a cone. Constructions of tangents on the intersection curves. Breach. Constructions of breach polygon and curves. Constructions of tangent on the space curves degree four. Axonometric methods. Pohlec's theorem. Representation of objects with axonometric methods. Skew algorithms. Orthogonal axonometry. Perspective. The elementary tasks.




1.137. Comments

1.138. Student requirements Students must satisfy requirements for obtaining the signature (listed in the executive program) and to pass the final exam.




Class attendance & class participation 1.2 Seminar paper 0.8 Experiment Written exam 1.4 Oral exam 1.4 Essay Research work

Project Continuous assessment 1.2 Presentation Practical work




V. Niče: Deskriptivna geometrija I i II, Školska knjiga, Zagreb, 1992

1.142. Recommended literature (when proposing the program)

H. Brauner: Lehrbuch der Konstruktiven Geometrie, Springer - Verlag, Wien, 1986 1.143. Number of copies of required literature in relation to the number of students currently attending






General information Lecturer Majda Trobok

Course title Basis of the philosophy of mathematics






1.145. Course objectives The objective of the course is to introduce the students to the basic concepts in philosophy of mathematics; mathematical and philosophical reasons for the emergence of philosophy of mathematics, introduction of realism (Platonism, Modal Realism and “Faint-of-heart” Realism) and anti-realism (Intuitionism, Nominalism, Formalism) in mathematics, epistemological and ontological questions in the philosophy of mathematics and historical examples.


None.

1.147. Expected outcomes for the course It is expected that students will learn and understand the basic problems that philosophy of mathematics concentrates on, as well as how they are linked to the standard mathematical practice. After completing this course students will be able to state reasons for nascency of philosophy of mathematics, to compare basis of realism and anti-realism, to analyze philosophical thesis in mathematical systems development.

1.148. Course content Semantical, epistemological and ontological questions in the philosophy of mathematics. Realism vs. Anti-realism. Realism: Platonism, Modal Realism and “Faint-of-heart” Realism. Anti-realism: Intuitionism, Nominalism, Formalism. The importance of the philosophical theories in philosophy of mathematics and their influence on the mathematical practice. Some Historical Examples: The “Elements”, Gödel’s theorems, the Concept of Infinity ecc. Intuinionistic Mathematics and Logic.




1.150. Comments

1.151. Student requirements Students must satisfy the requirements for obtaining the signature (listed in the executive program) and to pass the final exam.




Class attendance & class participation 2 Seminar paper 1.7 Experiment Written exam Oral exam Essay Research work 1.3 Project Continuous assessment 1 Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.

1.153. Assessment and evaluation of students' work during the semester and in the final exam Students' activities are continuously monitored, especially their presentation on seminar paper. The total number of points student can get during the class is 100 (activities assessed are indicated in the table above). The detailed work out of monitoring and evaluation of students' work will appear in the executive program.

1.154. Required literature (when proposing the program ) 1. Benacerraf, Putnam, 1983, Philosophy of Mathematics – Selected Readings (Second ed.), Cambridge University

Press. 2. Šikić, Z., 1995, Filozofija matematke, Školska knjiga, Zagreb. 1.155. Recommended literature (when proposing the program) 1. Jacuette, D. (ed.), 2002, Philosophy of Mathematics – An Anthology, Blackwell, Oxford. 2. George, A., i Velleman, D. J., 2002, Philosophies of Mathematics, Blackwell, Oxford. 3. Hintikka, J., (ed.), 1969, The Philosophy of Mathematics, Oxford University Press, Oxford. 4. Shapiro, S., 2002, Thinking about Mathematics – The Philosophy of Mathematics, Oxford University Press,

Oxford. 5. Brown, J. R., 1999, An Introduction to the World of Proof and Pictures, Routledge, London. 6. Trobok, M., 2006, Platonism in the Philosophy of Mathematics, Filozofski fakultet u Rijeci 1.156. Number of copies of required literature in relation to the number of students currently attending






General information Lecturer Tajana Ban Kirigin

Course title History of Mathematics


Course status Core

Year II Credit values and modes of instruction



1.158. Course objectives Introduction to development of mathematical theories and to the work of some important mathematicians. Studying history of some branches of mathematics will contribute to better understanding of these mathematical theories.


1.160. Expected outcomes for the course After completing this course students will know some basic facts about the history of mathematics. Students will be able to analyze ideas and facts from the mathematical history, to define fields of mathematics and to know and understand basic notions of this course.

1.161. Course content Ancient mathematics. Greek mathematics (Pythagoras, Euclid, Archimedes). Chinese mathematics. Islamic and Indian mathematics. Medieval mathematics. Mathematics since the 16th century. Current mathematics.




1.163. Comments



1.165. Evaluation and assessment14 Class attendance & class participation 1 Seminar paper 2 Experiment Written exam 0.5 Oral exam 0.5 Essay Research work Project Continuous assessment Presentation Practical work Portfolio






1.167. Required literature (when proposing the program ) 1. Dadić, Žarko: Razvoj matematike. Ideje i metode egzatnih znanosti u njihovu povijesnom razvoju, Školska knjiga, Zagreb,1975. 2. Dadić, Žarko: Povijest ideja i metoda u matematici i fizici, Školska knjiga, zagreb,1992.

1.168. Recommended literature (when proposing the program) 1. Dunham, William: The mathematical Universe: An Alphabetic Journal Through the great Proofs,Problems, and Personalities (John Wieley and Sons,Inc.), 1994 Hogben, 2. Lancelot: Sve o matematici, Mladost, Zagreb,1970 3. Devide, Vladimir: Matematika kroz kulture i epohe, Školska knjiga, Zagreb, 1979 4. Znam, Štefan et.al.: Pogled u povijest matematike, Tehnička knjiga, Zagreb,1989


Title Number of copies Number of students Dadić, Žarko: Razvoj matematike. Ideje i metode egzatnih znanosti u njihovu povijesnom razvoju 3 2

Dadić, Žarko: Povijest ideja i metoda u matematici i fizici 4 2





Course title Selected lectures from teaching mathematics


Course status Core


ECTS credits / student workload 5 Hours (L+E+S) 30+30+0


1.171. Course objectives - acquisition of procedures for assessment and evaluation of pupils' knowledge in mathematics, - introduction to school documentation, - introduction to selected topics in teaching mathematics


None.

1.173. Expected outcomes for the course After completing this course students will be able to: - know the regulations for teachers of mathematics, - know the evaluation methods and to be able to create exams and evaluate them, - know actual topics in mathematics education.

1.174. Course content Evaluation of pupils (regulations, pupils' assessment, creating exams). Outer tests for knowledge examination (national tests, international tests). The regulations for teachers of mathematics.




1.176. Comments


Students must satisfy requirements for obtaining the Signature (listed in the executive program).

1.178. Evaluation and assessment15 Class attendance & class participation 2 Seminar paper 1 Experiment Written exam 0.5 Oral exam 0.5 Essay Research work Project Continuous assessment 1 Presentation Practical work Portfolio







e-literature

1.181. Recommended literature (when proposing the program) 1. Popular and methodical magazines (printed or on line) 2. Regulations for teachers of mathematics (available on line) 1.182. Number of copies of required literature in relation to the number of students currently attending





General information Lecturer Ana Jurasić

Course title Additional Mathematics


Course status Core




1.184. Course objectives - acquisition of theory on gifted pupils, - identification and work with gifted pupils, - introduction to mathematics competitions, - acquisition of mathematical knowledge for additional classes in elementary and secondary schools 1.185. Course prerequisite

None.

1.186. Expected outcomes for the course After completing the course students will be able to state the characteristics of the gifted pupils, to identify and know the methods of teaching those pupils and to posses knowledge for additional class realization.

1.187. Course content Definition of basic notions. Characteristics of gifted pupils. Identification of gifted pupils. Methods of working with gifted pupils. Curriculum expansion. Mathematics competitions.




1.189. Comments



1.191. Evaluation and assessment16 Class attendance & class participation 2.2 Seminar paper Experiment Written exam 0.5 Oral exam 0.7 Essay Research work Project Continuous assessment 1.6 Presentation Practical work Portfolio 16 IMPORTANT: Fill in the appropriate number of points for each of the chosen categories so that the sum of the allocated points corresponds to the course credit value. Add new categories, if necessary.





1.193. Required literature (when proposing the program ) 1. George, D.: Obrazovanje darovitih: kako identificirati i obrazovati darovite i talentirane učenike, Educa, Zagreb, 2005 2. e - literature 3. mathematics competition exercises

3.1. Recommended literature (when proposing the program) 1. Vlahović-Štetić, V.: Daroviti učenici: teorijski pristup i primjena u školi, IDIZ, Zagreb, 2005 2. Lukač, N. i dr.: Matematičko natjecanje Klokan bez granica 1999.-2004., HMD, Zagreb, 2005 3. Pavleković, M.: Matematika i nadareni učenici, Element, Zagreb, 2009 4. Kurnik. Z.: Zabavna matematika u nastavi matematike, Element, Zagreb, 2009 5. Methodical and popular magazines


Title Number of copies Number of students George, D.: Obrazovanje darovitih: kako identificirati i obrazovati darovite i talentirane učenike,Educa, Zagreb, 2005 1 10





Course title Didactics II


Course status Core




1.194. Course objectives The objectives of this course are:

- to get students acquainted with variety of didactical choices in teaching practice and their adequate use in teaching practice;

- to enhance students for continiouos educational development and development of their teaching practice, - to motivate students for nurturing positive climate and team work in teaching; - to encourage students for basic research skills and constant inovation of their teaching practice. 1.195. Course prerequisite

Didactics I

1.196. Expected outcomes for the course In order to fulfill his/her student requirements, students are expected to develope several competencies:

- To interprete and analyse fundamental didactical concepts and theories; - To give critical interpretation of various didactical theories, schools of thoughts and models; - To analyse and use various didactical and methodical choices in actual educational and teaching practice; - To analyse and use adequately various didactical knowledge and skills (curriculum design; micro and macro

organisation of teaching; using educational technology; assessment procedures; professional staff development of teachers etc.);

- To carry out and interprete simple research projects in the field of didactics and to suggest possible improvements and innovations of teaching practice.

1.197. Course content Methodological and epistemiological foundations of didactics. Terminology and didactical system. Education and teaching (aims, objectives and contents; regulations in teaching; didactical principles; factors, media and social forms). Theories and models of teaching and education. Didactical theories and schools of thoughts. Curriculum design. Theories of curricula. Educational and teaching situations. Didactical cycle and phases (preparation, realisation and evaluation). Educational technology. Macro and micro organisation of teaching. Trends in educational staff development.




1.199. Comments




Students are expected to come to class prepared to take active part in group discussions, to make a set of assignements in written form, to make individual or team work and to pass oral and written exam. Studies and researching of actual didactical problems will be rewarded. Students are expected to study required literature and choose at least two sources from the list of recommended literature. As a prerequisite for approaching to the exam, all written assignments should be accomplished and they should proove they are familiar with the actual problems and trends in the field of didactics. Oral exam is organised at the end of the term. Students are expected to read required literature continuously during the term (to prepare for the group discussion).

1.201. Evaluation and assessment17 Class attendance & class participation 1.5 Seminar paper Experiment Written exam 0.5 Oral exam 0.5 Essay Research work Project Continuous assessment 1.5 Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.


1.203. Required literature (when proposing the program ) 1. Jelavić, F. (2003). Didaktika. Jastrebarsko: Naklada Slap 2. Bognar, L. (2002). Didaktika. Zagreb: Školska knjiga 3. Poljak, V. (1991). Didaktika. Zagreb: Školska knjiga 4. Lavrnja, I (1998). Poglavlja iz didaktike. Rijeka: Pedagoški fakultet u Rijeci 5. Lavrnja, I.(2000). Vježbe iz didaktike. Rijeka: Pedagoški fakultet u Rijeci.

5.1. Recommended literature (when proposing the program) 1. Bežan, A., Jelavić, F., Kujundžić, N. i Pletenac, V. (1991). Osnove didaktike. Zagreb: Školske

novine 2. Stevanović, M. (2003). Didaktika. Rijeka: Digital Point 3. Jensen, E. (2003). Super-nastava. Nastavne strategije za kvalitetnu školu i uspješno učenje.

Zagreb: Educa 4. Kyriacu, C. (2001). Temeljna nastavna umijeća. Zagreb: Educa 5. Terhat,E. (2001). Metode poučavanja i učenja. Zagreb: Educa








Course title Teaching pupils with special needs


Course status Core




1.204. Course objectives Acquiring knowledge regarding various entities of interferences in the psychophysical development on the level of primary damage and lack of various aetiologies. The emphasis is on the developing of a thwarted state, psychological consequences of various damages, and specifics of the functioning of pupils with special needs. The students are trained for a professional approach to pupils with special needs and their families, as well as for the collaboration with experts of various profiles with whom they will necessarily collaborate with in work with this special population.


None.

1.206. Expected outcomes for the course Recognise and differentiate various categories of pupils with special needs. Compare features of psychological functioning at various groups and recognise the specific problems pupils with special needs are faced with. Differentiate pupils according to the courses of learning difficulties, and knowing the specifics of work with gifted pupils. Create individualised educational problems. Know the forms of collaboration with parents through which they can indirectly encourage the learning of the pupil with learning difficulties.

1.207. Course content The concept of individuals with special needs, classification, prevalence. Attitudes towards people with special needs, the process of stigmatisation and their effects on the psychological functioning of an individual with special needs. Problems within the family. Network of social care with individuals with special needs. Sensor damages. Physical damages. Speaking and language disorders. Learning difficulties. Insufficient mental development. Behavioural and emotional difficulties. Specifics of teaching pupils with difficulties. Gifted children. Teaching gifted children. Aetiology of entity, diagnostics and prediction. Visiting various institutions as well as lectures by experts from the practice is scheduled.




1.209. Comments


Students are required to write a seminar paper and take the examination.




Class attendance & class participation 1.2 Seminar paper Experiment Written exam 1 Oral exam Essay Research work Project Continuous assessment 1.8 Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.


1.213. Required literature (when proposing the program ) 1. Dulčić, A., Kondić, Lj. (2001). Djeca oštećena sluha – priručnik za roditelje i udomitelje. Zagreb: Alinea. 2. Kocijan-Hercigonja, D. (2000). Mentalna retardacija – biologijske osnove, klasifikacija i mentalno zdravstveni

problemi. Jastrebarsko: Naklada Slap. 3. Ribić, K. (1991). Psihofizičke razvojne teškoće. Zadar: ITP Forum. 4. Vizek Vidović, V., Vlahović-Štetić, V., Rijavec, M., Miljković, D. (2003). Psihologija obrazovanja.(poglavlja: Učenici s

posebnim potrebama; Daroviti učenici) Zagreb: Udžbenici Sveučilišta u Zagrebu. 5.2. Recommended literature (when proposing the program)

1. Davis, R.D., Braun, E.M. (2001). Dar disleksije: zašto neki od najpametnijih ljudi ne znaju čitati i kako mogu naučiti. Zagreb: Alinea.

2. Cvetković-Lay, J., Sekulić-Majurec, A. (1998). Darovito je, što ću s njim? Zagreb: Alinea. 3. Čuturić, N. (1995). Zabrinjava me moje dijete: ponašanje djece od 2. do 6. godine. Zagreb: Školska knjiga. 4. Kocijan-Hercigonja, D., Buljan-Flander, G., Vučković, D. (2002). Hiperaktivno dijete uznemireni roditelji i odgajatelji.

Jastrebarsko: Naklada Slap. 5. Wenar, C. (2003). Razvojna psihologija i psihijatrija od dojenačke dobi do adolescencije. Jastrebarsko: Naklada Slap.








Course title Methodical practice in mathematics I


Course status Core




1.214. Course objectives - students learn to prepare, execute and analyze teaching methods in core, elective and additional class in

elementary and secondary schools; - training students for mathematics lifelong learning 1.215. Course prerequisite

Mathematics education I and Mathematics education II.

1.216. Expected outcomes for the course After completing this course students will be able to:

- write lesson plan and to organize lesson in accordance with the principles of teaching mathematics; - know lesson types and specific lesson structures. 1.217. Course content

Pre-performance and lesson organization in elementary and secondary school (lesson types, pupils' and teachers' literature, teaching aids, lesson plan). Methodology of teaching mathematics in elementary and secondary school. Teaching labs.




1.219. Comments



1.221. Evaluation and assessment19 Class attendance & class participation 2 Seminar paper Experiment Written exam Oral exam Essay Research work Project Continuous assessment Presentation Practical work Portfolio School practice 1






1.223. Required literature (when proposing the program ) 1. Current textbooks in mathematics for elementary and secondary schools and teachers' manuals 2. e-literature 1.224. Recommended literature (when proposing the program) 1. Curricula 2. popular and methodological magazines 3. proffesional and methodological literature 1.225. Number of copies of required literature in relation to the number of students currently attending


Textbooks for elementary and secondary schools and teachers' manuals 20 10





Course title Methodical practice in mathematics II


Course status Core




1.227. Course objectives - students learn to prepare, execute and analyze teaching methods in core, elective and additional class in

elementary and secondary schools; - training students for mathematics lifelong learning 1.228. Course prerequisite

Mathematics education I and Mathematics education II.


- write lesson plan and to organize lesson in accordance with the principles of teaching mathematics; - know lesson types and specific lesson structures. 1.230. Course content

Pre-performance and lesson organization in elementary and secondary school. Methodology of teaching mathematics in elementary and secondary school. Teaching labs.




1.232. Comments



1.234. Evaluation and assessment20 Class attendance & class participation 2 Seminar paper Experiment Written exam Oral exam Essay Research work Project Continuous assessment Presentation Practical work Portfolio School practice 1 Comment: ECTS distribution from above is made for studies and/or modules with courses which have ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.




1.235. Assessment and evaluation of students' work during the semester and in the final exam

Students' work will be evaluated and assessed during the semester and in the final exam. Total number of points student can achieve during the semester is 70 (to assess the activities listed in the table), while in the final exam student can achieve 30 points. The detailed work out of monitoring and evaluation of students' work will appear in the executive program.

1.236. Required literature (when proposing the program ) 1. Current textbooks in mathematics for elementary and secondary schools and teachers' manuals 2. e-literature 1.237. Recommended literature (when proposing the program) 1. Curricula 2. popular and methodological magazines 3. proffesional and methodological literature 1.238. Number of copies of required literature in relation to the number of students currently attending


Textbooks for elementary and secondary schools and teachers' manuals 20 10





Course title Seminar / M.Sc. thesis


Course status Core




1.240. Course objectives This seminar is the first step towards elaboration of graduate thesis. The seminar objective is to enable students for independent research and work with mathematical reading and also for presentation of mathematical contents.


None.

1.242. Expected outcomes for the course This seminar will enable students to do independent research and work with mathematical reading and presentation of mathematical contents.

1.243. Course content All lecturers will participate in determining the content of this seminar by proposing the themes for the seminars. Every student will present the theme in public and hand over the work in written form to the mentor. The work will present the basis for the graduate thesis which will be elaborated in conjunction with the mentor.




1.245. Comments

1.246. Student requirements Students must prepare the seminar, hand over the work in written form and present the work in public. Students have to attend ¾ of all other public presentations. Students will be evaluated on the basis of written work, public presentation, attendence of the seminar and participation in discussions.

1.247. Evaluation and assessment21 Class attendance & class participation 1.5 Seminar paper 2.5 Experiment Written exam Oral exam Essay Research work Project Continuous assessment Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.







To be assigned by the mentor on the basis of theme of the work.


5.5. Number of copies of required literature in relation to the number of students currently attending classes






Course title Measure and Integral






1.250. Course objectives Understanding and accepting

- definition of measure and examples, - definition of measurable sets and functions, - definition of Lebesgue measure and property analysis, - definition of integral on the measure space, - statement and proof of Lebesgue's monotone and dominated convergence theorem and

Fatou's lemma, - definition of product measure; statement and proof of Fubini's theorem, - definition of absolute continuity, - statement and proof of Radon – Nikodym theorem, - connection between Riemann and Legesgue integral


None.

1.252. Expected outcomes for the course After completion of the course students will be able to: use the properties of measures and integrals, use the theorems on convergence and Fubini's theorem in problem solving, differ Riemann and Lebesque integral.

1.253. Course content Ring, algebra, σ-algebra of sets, Borel sets. Measure, outer measure. Lebesgue measure. Theorems of Levy, Fatou; The dominated convergence theorem. Product of measures. Theorems of Tonelli, Fubini. Absolutely continuous measure, singular measure. Lebesgue decomposition of measure. Radon-Nikodym theorem. Computation of Lebesgue integral by means of Riemann one.



independent work multimedia and the internet laboratory Project strategies tutorials consultations other ___________________

1.255. Comments




Students must satisfy requirements for obtaining the signature (listed in the lesson plan) and to pass the final exam.

1.257. Evaluation and assessment22 Class attendance & class participation 2 Seminar paper Experiment Written exam 2 Oral exam 1.5 Essay Research work Project Continuous assessment 1.5 Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.


1.259. Required literature (when proposing the program ) 1. S.Mardešić: Matematička analiza II, Školska knjiga, Zagreb, 1977 2. Donald L. Cohn: Measure theory, Birkhäuser Boston, 1994

2.1. Recommended literature (when proposing the program) 1. P. Halmos, Measure Theory, Springer-Verlag, New York, 1974 2. N. Antonić, M. Vrdoljak: Mjera i integral, PMF-Matematički odjel, Zagreb 2001


Title Number of copies Number of students Sibe Mardešić: Matematička analiza II, Školska knjiga , Zagreb, (više izdanja) 5 10 Donald L.Cohn: Measure theory, Birkhäuser Boston, 1994. 1 10






Course title Algebra I






1.260. Course objectives - acquisition of basic notions of algebraic structures, - acquisition of basic notions of relation structures, - acquisition of basic notions of group theory, - possibilities of counting the number of elements in the set


None.

1.262. Expected outcomes for the course By the end of this course students will be able to:

- deal with basic algebraic and relation structures, - differ algebraic structures, - know and understand the notion of set, - apply Sylow theorems in problem solving.

1.263. Course content Groups. Factor groups. Isomorphism theorems. Lattices. Group actions. Sylow theorems. Direct products and Abelian groups. Nilpotent groups. Solvable groups.



independent work multimedia and the internet laboratory project class tutorials consultations other ___________________

1.265. Comments


Students must satisfy requirements to obtain signature (listed in the lesson plan) and to pass the final exam.




Class attendance & class participation 2 Seminar paper Experiment Written exam 2 Oral exam 1.6 Essay Research work Project Continuous assessment 1.4 Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.


1.269. Required literature (when proposing the program ) 1. T.W. Hungerford : Algebra, Reinhart and Winston, NY, 1989. 2. V. Perić : Algebra I, II, Svjetlost, Sarajevo, 1980. 3. A. Kostrikin : Vvedenie v algebru, Nauka, Moskva, 1986.

1.270. Recommended literature (when proposing the program) 1. I. Stewart : Galois Theory, Chapmann and Hall, London, 1973. 2. H. Kurzweil, B. Stellmacher: Theorie der endlichen Gruppen, Springer, Berlin, 1998. 3. Đ. Kurepa : Viša algebra, Građevinska knjiga, Beograd, 1979.







General information Lecturer Dean Crnković

Course title Topics in contemporary mathematics






1.273. Course objectives

Objective of this course is to familiarize students with selected topics and current problems of contemporary mathematics.


None.

1.275. Expected outcomes of the course After completing this course students will be prepared for independent research, for working with professional literature and research papers and for mathematical topics presentation.

1.276. Course content



independant work multimedia and the internet laboratory project strategies tutorials consultations other ___________________

1.278. Comments

1.279. Student requirements Students must satisfy requirements for obtaining the Signature (listed in the executive program) and to pass the final (oral) exam.

1.280. Evaluation and assessment24 Class attendance & class participation 1 Seminar paper 1 Experiment Written exam Oral exam 1 Essay Research work Project Continuous assessment 1 Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.






1.282. Required literature (when proposing the program ) 1. P. J. Davis, R. Hersh, E. A. Marchisotto, Doživljaj matematike, Golden marketing - Tehnička knjiga, Zagreb, 2004 2. literature for each seminar will be determined by the theme of the seminar


2.2. Number of copies of required literature in relation to the number of students currently attending classes





General information Lecturer Božidar Kovačić

Course title Designing of educational system






1.283. Course objectives - introduce students with basic concept in designing of Educational systems - acceptance knowledge about basic concept of designing Educational systems and evaluation of such systems - acceptance knowledge about proper election of media, structure of user interface and integrated artificial intelligence in

chosen software tools 1.284. Course prerequisite

None.

1.285. Expected outcomes of the course After completing the course and meeting requirements, students are expected to be capable of:

1. understand principles and methods in design of educational system 2. adopt nowledge included in "Course content". 3. make simple educational system

1.286. Course content




1.288. Comments


Students must satisfy requirements for obtaining the sgnature (listed in the executive program) and to pass the final exam.

1.290. Evaluation and assessment25 Class attendance & class participation 1.5 Seminar paper 2.5 Experiment Written exam 1 Oral exam 1 Essay Research work Project Continuous assessment Presentation Practical work Portfolio 25 IMPORTANT: Fill in the appropriate number of points for each of the chosen categories so that the sum of the allocated points corresponds to the course credit value. Add new categories, if necessary.





1.292. Required literature (when proposing the program ) 1. Dills, C.R., Ramiszovski, T., ed., Instructional Development Paradigms, Educational Technology Publications,

Englewood Cliffs, NJ, 1997. 2. Jonnasen, D.H., Computers in the Classroom: Mindtools for Critical Thinking, Merill, Englewood Cliffs, NJ, 1996.

2.4. Recommended literature (when proposing the program) 1. Gery, G.J., Electronic Performance Support Systems-How and Why to remake the Workspace Through the strategic

application of Technology, Weiengarten Publication, Boston, MA, 1991. 2. Collins, D., Designing object-oriented user interfaces, Benjamin Cummings, Redwood City, CA, 1995.







Course title Introduction to optimization






1.293. Course objectives To introduce students with the problems of optimization, the mathematics’ theory of optimization, applications and optimization methods for problem-solving.


Linear programming.

1.295. Expected outcomes for the course After completing this class, students are expected to know the basis of the problems of optimization and the mathematics’ theory of optimization. Students have to be able to use learned material for doing exercises. They will be able to: define and differ convex sets, convex functions and the notions of convex programming, classify optimization problems, analyze the common features of unconditional optimization methods and apply them, to solve the nonlinear programming problems using the unconditional optimization methods.

1.296. Course content Elements of Convex Analysis: convex sets, Farkas’ lemma, convex functions. Theory of nonlinear programming: problem of convex programming. Lagrange function, conditions of optimals, duals. Methods of unconditional optimization: common characters of methods, Cauchy’s method, Newton’s method, methods of conjugate gradients, methods of variable metric. Unconditional optimization without count derivatives, optimization of one variable functions. Methods for cunt problems nonlinear programming with unconditional optimization: method of Lagrange’s factors. Method for direct count problems nonlinear programming: Franke-Wolf’s method, Rosen’s method, Zountendijk’s method. Some applications methods of optimization in technical and economy science.




1.298. Comments

Attendance and active class participation, making a seminar paper and a number of tasks that accompany the lectures and exercises is expected from students. Students must pass a written exam that consists of two tests as a prerequisite for the oral exam on which the overall knowledge of the student is checked.


Students must participate actively in all forms of work, make the seminar paper and pass written and oral exam.




Class attendance & class participation 1.5 Seminar paper 1 Experiment Written exam 2 Oral exam 1.5 Essay Research work Project Continuous assessment Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.


1.302. Required literature (when proposing the program ) 1. Chiang, A. C. : Osnovne metode matematičke ekonomije, MATE, Zagreb,1994 2. Limić, N., Pašagić, H., Rnjak, Č. : Linearno i nelinearno programiranje, Informator, Zagreb, 1978


1. Martić, Lj. : Nelinearno programiranje, Informator, Zagreb, 1973 2.2. Number of copies of required literature in relation to the number of students currently attending classes







Course title Algebra II






2.1. Course objectives - acquisition of basic notions of field theory, - acquisition of basic notions of Galois theory, - acquisition of basic notions and principles of group actions


None.

2.3. Expected outcomes for the course By the end of this course students will be able to:

- define basic algebraic structures and introduce examples, - apply normal field extension, - mathematically prove polynomial minimality, - know basis of Galois theory, - solve Galois group determination problems.

2.4. Course content Groups. Quotient groups. Group action. Lattice. Sylow theorems. Direct product and Abel groups. Nilpotent groups. Solvable group. Field extensions (simple, finite, normal, radical). Finite fields. Galois group of a polynomial. Fundamental theorem of Galois theory. Solvability of Galois group as a condition of solvability of an algebraic equation.




2.6. Comments


Students must satisfy requirements listed in the lesson plan to obtain signature and to pass the final exam.




Class attendance & class participation 2 Seminar paper Experiment Written exam 1.4 Oral exam 1.6 Essay Research work Project Continuous assessment 1 Presentation Practical work Portfolio



2.10. Required literature (when proposing the program ) 1. T.W. Hungerford : Algebra, Reinhart and Winston, NY, 1989. 2. V. Perić : Algebra I, II, Svjetlost, Sarajevo, 1980. 3. A. Kostrikin : Vvedenie v algebru, Nauka, Moskva, 1986.

2.11. Recommended literature (when proposing the program) 1. I. Stewart : Galois Theory, Chapmann and Hall, London, 1973. 2. H. Kurzweil, B. Stellmacher: Theorie der endlichen Gruppen, Springer, Berlin, 1998. 3. Đ. Kurepa : Viša algebra, Građevinska knjiga, Beograd, 1979.








Course title Probability theory






1.303. Course objectives - acquisition of martingale theory, - description of convergence of sequences of random variables, - proving the laws of large numbers, - definition of characteristic functions and their properties, - proving the central limit theorem 1.304. Course prerequisite

None.


- know the laws of large numbers, - apply the central limit theorem, - know the basic properties of martingales, - apply properties of characteristic functions, - prove mathematically procedures and statements introduced within this course 1.306. Course content

Infinitely divisible distributions. Sequences of random variables. Laws of large numbers. Central limit theorems. Martingales. Characteristic functions.




1.308. Comments





Class attendance & class participation 1.6 Seminar paper Experiment Written exam 2.2 Oral exam 1.6 Essay Research work Project Continuous assessment 0.6 Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.


1.312. Required literature (when proposing the program ) 1. N.Sarapa: Teorija vjerojatnosti, Školska knjiga, Zagreb, 1992 2. B.V. Gnedenko, Kurs teorije vjerojatnosti, Nauka, Moskva, 1969 (Russian)

2.1. Recommended literature (when proposing the program) 1. Ž. Pauše: Vjerojatnost. Informacija. Stohastički proces., Školska knjiga, Zagreb, 1978 2. W. Feller, An Introduction to Probability Theory and Application I, II, J. Wiley, New York, 1966








Course title Coding theory and Cryptography






1.313. Course objectives Objective of this coures is to introduce, describe and analyze basic cryptosystms and basic coding theory methods, i.e.:

- to describe, compere and apply different cryptosystms, - to introduce basic principles of cryptoanalysis, - to introduce basic principles of coding theory, - to describe, compere and apply different coding methods, - to describe and analyse different error detecting methods, - to describe and analyse different error correcting methods. 1.314. Course prerequisite


- analyse and distinguish between different cryptosystms, - analyse and distinguish between different codes, - analyse and distinguish between different error detecting methods, - analyse and distinguish between different error correcting methods, - apply proper procedures in order to solve given problem, - prove all claims introduce in this course. 1.316. Course content

Introduction to cryptography. Classical cryptography. Data Encryption Standard. International Data Encrpytion Algorithm. Advanced Encryption Standard. Public key cryptography. RSA and applications. Introduction to coding theory. Golay codes. Cyclic codes. BCH codes. Hadamard codes. Reed-Solomon codes and CD.




1.318. Comments


Every student is obliged to fulfill conditions for signature and to pass the finale exam.




Class attendance & class participation 1.5 Seminar paper 1.5 Experiment Written exam 0.5 Oral exam 1 Essay Research work Project Continuous assessment 1.5 Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.


1.322. Required literature (when proposing the program ) 1. J.H. van Lint, Introduction to Coding Theory, Springer-Verlag, Berlin, 1982. 2. D.R.Stinson, Cryptography. Theory and Practice, CRC Press, Boca Raton, 1996. 1.323. Recommended literature (when proposing the program) 1. Assmus, J.D. Key, Designs and their codes, Cambridge University Press, London, 1992. 2. A.Dujella, M. Maretić, Kriptografija, Element, Zagreb, 2007. 3. N. Koblitz, A Course in Number Theory and Cryptography, Springer Verlag, New York, 1994. 4. F.J. MacWilliams, N.J.A. Sloane, The theory of error-correcting codes, North-Holland, 1977. 5. B.Schneiner, Applied Cryptography, Wiley, NY 1995. 6. J. Seberry, J. Pieprzyk, Cryptography: an introduction to computer security, Prentice-Hall, 1989. 7. D. Welsh, Codes and cryptography, Oxford: Clarendon Press, 1988. 1.324. Number of copies of required literature in relation to the number of students currently attending


J.H. van Lint, Introduction to Coding Theory, Springer-Verlag, Berlin, 1982 0 D.R.Stinson, Cryptography. Theory and Practice, CRC Press, Boca Raton, 1996 0



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