ISSUES IN DIDACTIC OF MATHEMATICS: PROBLEM SOLVING

Course Information
TitleΘΕΜΑΤΑ ΔΙΔΑΚΤΙΚΗΣ ΤΩΝ ΜΑΘΗΜΑΤΙΚΩΝ: ΕΠΙΛΥΣΗ ΠΡΟΒΛΗΜΑΤΟΣ / ISSUES IN DIDACTIC OF MATHEMATICS: PROBLEM SOLVING
CodeΕΜ70
FacultyEducation
SchoolPrimary Education
Cycle / Level1st / Undergraduate
Teaching PeriodWinter/Spring
CoordinatorIoannis Papadopoulos
CommonNo
StatusActive
Course ID600017625

Programme of Study: PPS Tmīmatos Dīmotikīs Ekpaídeusīs (2019-sīmera)

Registered students: 15
OrientationAttendance TypeSemesterYearECTS
KORMOSElective Courses634

Class Information
Academic Year2021 – 2022
Class PeriodSpring
Faculty Instructors
Weekly Hours3
Total Hours39
Class ID
600205318
Course Type 2016-2020
  • Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
  • Face to face
Language of Instruction
  • Greek (Instruction, Examination)
Learning Outcomes
At the end the students will be able to • Understand the theory of problem solving developed by Polya • Select and apply problem solving techniques • Make and check conjectures • Develop skills in mathematical reasoning • Combine all the above-mentioned elements to create their own problem • Nurture the tendency to their students to discover mathematics through suitably designed problems
General Competences
  • Apply knowledge in practice
  • Retrieve, analyse and synthesise data and information, with the use of necessary technologies
  • Make decisions
  • Work in teams
  • Generate new research ideas
  • Advance free, creative and causative thinking
Course Content (Syllabus)
• What is problem. Categorization of problems. exercises vs problems. • Closed vs open-ended problems. • Polya's four steps. • Problem solving heuristics. • Mental argumentation. • Mathematical modeling. • Mathematical reasoning - proof. • Experimentation in problem solving. • The issue of control in problem solving. • Problem Posing.
Educational Material Types
  • Slide presentations
  • Book
Use of Information and Communication Technologies
Use of ICT
  • Use of ICT in Course Teaching
  • Use of ICT in Communication with Students
Description
ICT is used (a) for presenting the content of the course, and (b) for acquiring certain skills in relation to certain software used for teaching mathematics. The whole material is accessible through the e-learning platform. E-learning is also used for communicating with the students who attend the course
Course Organization
ActivitiesWorkloadECTSIndividualTeamworkErasmus
Lectures782.6
Reading Assigment230.8
Field trips and participation in conferences / seminars / activities80.3
Written assigments80.3
Exams30.1
Total1204
Student Assessment
Description
The students’ evaluation is summative through written exams. They are asked to complete multiple choice questions, answer questions with short answers and solve problems. They know the way and criteria of the exam through both the lectures and the website of the course
Student Assessment methods
  • Written Exam with Multiple Choice Questions (Summative)
  • Written Exam with Short Answer Questions (Summative)
  • Written Exam with Problem Solving (Summative)
Bibliography
Course Bibliography (Eudoxus)
Επίλυση Προβλήματος στα Μαθηματικά (Γ. Μαμωνά-Downs & I. Παπαδόπουλος), Πανεπιστημιακές Εκδόσεις Κρήτης, 2017, Ηράκλειο. ISBN: 978-960-524-483-5
Additional bibliography for study
Aufmann, R. N., Lockwood, J., Nation, R. D., &Clegg, D. K. (2012).Mathematical Excursions. Brooks/Cole Publishing Company. Bello, I., Britton, J. R., & Kaul, A. (2009). Topics in contemporary mathematics. Brooks/Cole Publishing Company. Brodie, K. (2010). Teaching mathematical reasoning in secondary schools. New York: Springer. Brown, S. & Walter, M. (2005, 3rd edition). The Art of Problem Posing. Mahwah, NJ: Lawrence Erlbaum Associates Publishers. Fosnot, C. T., & Dolk, M. (2002). Young Mathematicians at Work: Constructing Fractions, Decimals and Percents. Portsmouth, N. H.: Heinemann Press. Hopkins, C., Pope, S., & Pepperell, S. (2006). Understanding primary mathematics. London: David Fulton Publishers. Kaur, B., & Har, Y. B. (2009). Mathematical Problem Solving Yearbook 2009, Association of Mathematics Educators. Singapura: World Scientific Publishing Co. Pte. Ltd. Kennedy, L. M., Tipps, S., & Johnson, A. (2008). Guiding children’s learning of mathematics. Wadsworth Publishing Company. Koshy, V., Ernest, P., & Casey, R. (Eds.) (2000). Mathematics for primary teachers. New York: Routlege. Krantz, S. G. (1997). Techniques of problem solving. Providence, Rhode Island: American Mathematical Society. Mason, J., Burton, L., & Stacey, K. (1982). Thinking Mathematically. London: Addison Wesley. Mink, D., & Earlene, J. (2009). Strategies for Teaching Mathematics. Shell EducationPub. Polya, G. (1945). How to solve it. Princeton University Press. Polya, G. (1981). Mathematical Discovery: on understanding, learning, and teaching problem solving. Academic Press: New York. Polya, G. (1990). Mathematics and plausible reasoning, Volume 1: Induction and analogy in mathematics. Princeton University Press. Polya, G. (1990). Mathematics and plausible reasoning, Volume 2: Patterns of Plausible Inference. Princeton University Press. Smith, K. (2012, 12thedition). The Nature of Mathematics. CA: Brooks/Cole, Thomson Learning Inc. Silver, E. A. (1985). Teaching and learning problem solving: Multiple research perspectives. L. Erlbaum Associates. Wickelgren, W. A. (1995). How to solve mathematical problems. New York: Dover Publications. Zeits, P. (1999). The art and craft of problem solving. New York: John Wiley Συναφήεπιστημονικάπεριοδικά: Educational Studies in Mathematics Journal for Research in Mathematics Education Journal of Mathematical Behavior Mathematics Education Research Journal Mathematical Thinking and Learning International Journal of Mathematical Education in Science and Technology International Journal of Science and Mathematics Education Journal of Mathematics Teacher Education Science & Education Mediterranean Journal for Research in Mathematics Education For the Learning of Mathematics The International Journal for Technology in Mathematics Education ZDM Technology, Knowledge and learning
Last Update
04-06-2021