Graduate Course

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

Course title / Winter semester / Summer semester
Hours/week / ECTS credits / Hours/week / ECTS credits
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

Course title / Winter semester / Summer semester
Hours/week / ECTS credits / Hours/week / ECTS credits
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: • E:

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

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 assessment[1]
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 )

S. Kurepa: Konačnodimenzionalnivektorskiprostoriiprimjene, Sveučilišnanaklada Liber, Zagreb, 1976
H. Kraljević: Vektorski prostori, Odjel za matematiku, Sveučilište u Osijeku

1.11.Recommended literature (when proposing the program)

P. R. Halmos: Finite Dimensional Vector Spaces, Van Nostrand, New York, 1958
K. Horvatić: Linearna algebra, Golden marketing – Tehnička knjiga, Zagreb, 2004
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.

General information

Lecturer

Rene Sušanj

Course title / Linear Programming
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

COURSE DESCRIPTION

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.
1.18.Modes of instruction / 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 assessment[2]
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 )

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

1.24.Recommended literature (when proposing the program)

R.V. Benson : Euclidean Geometry and Convexity, Mc Graw - Hill, NY, 1966.
L.Lyusternik : Convex Figures and Polyhedrons, Dover publications, NY, 1963.
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
1.26.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.

General information

Lecturer

Sanja Rukavina

Course title / Mathematics education 1
Program / Graduate course in mathematics – Math. Education Specialization
Course status / Core
Year / I
Credit values and
modes of instruction / ECTS credits / student workload / 6
Hours (L+E+S) / 30 + 0 + 30

COURSE DESCRIPTION

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;
-introducingcurriculum of mathematics in the higher grades ofelementary 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.
1.31.Modes of instruction / lectures
seminars and workshops
exercises
e-learning
field work
practice
practicum / independent work
multimedia and the internet
laboratory
project strategies
tutorials
consultations
other ______
1.32.Comments
1.33.Student requirements
Students must satisfy requirements for obtaining the Signature (listed in the executive program) and to pass the final exam.
1.34.Evaluation and assessment[3]
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.
1.35.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.
1.36.Required literature(when proposing the program )

Current textbooks for elementary and secondary schools
Matematika bez suza, ed. Ilona Posokhova, Ostvarenje, Lekenik, 2000

1.37.Recommended literature (when proposing the program)

Polya,G.: Kako ćuriješitimatematičkizadatak, Školskaknjiga, Zagreb, 1984
XXX: Matematika i škola, časopis za nastavu matematike, Element, Zagreb
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 of the course
Title / Number of copies / Number of students
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.

General information

Lecturer

Sanja Rukavina

Course title / Mathematics education II
Program / Graduate course in mathematics – Math. Education Specialization
Course status / Core
Year / I
Credit values and
modes of instruction / ECTS credits / student workload / 7
Hours (L+E+S) / 30 + 0 + 30

COURSE DESCRIPTION

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.
1.42.Expected outcomes for the course
After completing this class students should be able to:
-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.
1.44.Modes of instruction / lectures
seminars and workshops
exercises
e-learning
field work
practice
practicum / independent work
multimedia and the internet
laboratory
project
tutorials
consultations
other ______
1.45.Comments
1.46.Student requirements
Students must satisfy requirements for obtaining the Signature (listed in the executive program) and to pass the final exam.
1.47.Evaluation and assessment[4]
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.
1.48.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.
1.49.Required literature(when proposing the program )

Current textbooks for elementary and secondary schools and teachers' manuals
Matematika bez suza, ed. Ilona Posokhova, Ostvarenje, Lekenik, 2000
e-literature

1.50.Recommended literature (when proposing the program)

Polya,G.: Kako ćuriješitimatematičkizadatak, Školskaknjiga, Zagreb, 1984
XXX: Matematika i škola, časopis za nastavu matematike, Element, Zagreb
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 of the course
Title / Number of copies / Number of students
Textbooks for elementary and secondary schools and teachers' manuals / 20 / 10
Matematika bez suza, ed. Ilona Posokhova, Ostvarenje, Lekenik, 2000 / 5 / 10
1.52.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.

General information

Lecturer

Course title / Educational psychology I - Psychology of learning and teaching
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 + 15 + 0

COURSE DESCRIPTION

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.
1.54.Course prerequisite
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.
1.57.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 ______
1.58.Comments
1.59.Student requirements
Students must satisfy the requirements for obtaining the signature (listed in the executive program) and to pass the final exam.
1.60.Evaluation and assessment[5]
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.
1.61.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.
1.62.Required literature (when proposing the program )

Kolić-Vehovec, S. (1999). Edukacijska psihologija. Filozofski fakultet, Rijeka
Vizek-Vidović, V., Vlahović-Štetić, V., Rijavec, M., Miljković, D. (2003). Psihologija obrazovanja. Zagreb: IEP

2.1.Recommended literature (when proposing the program)

Kroflin, L., Nola, D. (Ed.). (1987). Dijete i kreativnost. Zagreb: Globus.
Faber, A., Mazlish, E. (2000). Kako razgovarati s djecom da bi bolje učila. Zagreb: Mozaik knjiga.
Janković, J. (1996). Zločesti đaci genijalci. Zagreb: Alinea.
Neill, S. (1994). Neverbalna komunikacija u razredu. Zagreb: Educa.
Pintrich, P.R., Schunk, D.H. (1996). Motivation in education: Theory, research and application. Englewood Clifs, HJ: Prentice Hall.
Salovey, P., Sluyter, D.J. (1999). Emocionalni razvoj i emocionalna inteligencija. Pedagoške implikacije. Zagreb: Educa.
Winkel, R. (1996). Djeca koju je teško odgajati. Zagreb: Educa.

7.1.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
7.2.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.

General information