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Course, academic year 2023/2024
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Mathematics education II: Part-whole relation in the mathematical education of 5-12-year-old pupils - OD0310005
Title: Didaktika matematiky II: Vztah celku a části v matematickém vzdělávání 5-12 letých žáků
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2013
Semester: both
E-Credits: 0
Hours per week, examination: 0/0, other [HT]
Capacity: winter:unknown / unknown (unknown)
summer:unknown / unknown (unknown)
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Note: course is intended for doctoral students only
priority enrollment if the course is part of the study plan
can be fulfilled in the future
you can enroll for the course in winter and in summer semester
Guarantor: Mgr. Marie Tichá, CSc.
Annotation -
Last update: JANCARIK/PEDF.CUNI.CZ (28.11.2013)
The question of part-whole relation is connected to different mathematical structures. It plays an important role in the concept development process. Basic concepts of elementary mathematics (the notion of natural number and rational number and also geometric concepts) are connected to the creation and division of wholes. The course is aimed for PhD students who graduated from teaching at the elementary school.
Aim of the course -
Last update: JANCARIK/PEDF.CUNI.CZ (28.11.2013)

Clarify

  • The nature and importance of understanding the part - whole relationship for creation ideas related to the concept of fraction
  • Different interpretations and representations of fraction
  • Critical points with regard to both teachers and pupils

Literature -
Last update: JANCARIK/PEDF.CUNI.CZ (28.11.2013)

There is expected the study of some items

English, N.D. & Halford, G.S. (1995). Mathematics Education: Models and Processes. Mahwah, NJ: LEA.

Griesel, H. (1981). Der quasikardinale Aspekt in der Bruchrechnung. Der Mathematikunterricht. Wiesbaden: Akademische Verlagsgesselschaft, 87-95.

Hejný, M. (2004) Zlomek. Dvacet pět kapitol z didaktiky matematiky. Praha: UK PedF.

Charalambos Y. Charalambous, & Demetra Pitta-Pantazzi (2006). Drawing on a theoretical model to study students’ understandings of Fractions. Educational Studies in Mathematics. vol. 64, 293-316.

Lesh, R., Post, T. &. Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In: C. Janvier (Ed.) Problems of representation in the teaching and learning of mathematics. Hillsdalle: LEA, 33-40.

Lamon, S. L. (2006). Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers. Mahwah, NJ: LEA.

Littwiller, B., Bright, G. (Eds.) (2002). Making Sense of Fractions, Ratios, and Proportions. Yearbook 2002. Reston: NCTM.

Streefland, L. (1991). Fractions in Realistic Mathematics Education. Dordrecht: Kluwer.

Tichá, M. (2003).Following the path of discovering fractions. In: J. Novotná (Ed.) SEMT ’03 - International Symposium, Elementary Maths Teaching, plenary lectures. Praha: UK PedF, 17-27.

Tichá, M. & Hošpesová, A. (2005). Einige Episoden von der Reise zur Entdeckung und zum Verständnis des Bruchbegriffes. In: Ch. Kaune, I. Schwank, J. Sjuts. (Eds.) Mathematikdidaktik im Wissenschaftsgefüge: Zum Verstehen und Unterrichten mathematischen Denkens. Osnabrück: Schriftenreihe des Forschungsinstituts für Mathematikdidaktik, Nr. 40,2, s.139 - 154.

Tichá, M. & Macháčková, J. (2006). Rozvoj pojmu zlomek ve vyučování matematice (Cesty k porozumění zlomkům). Studijní materiály k projektu CZ.04.1.03/3.1.15.1/0237. Praha: JČMF.

Vergnaud, G. (1988). Multiplicative Structures. In: J. Hiebert & M. Behr (Eds.) Number concepts and operations in the middle grades. Reston, VA, NCTM, 141 - 161.

Teaching methods -
Last update: JANCARIK/PEDF.CUNI.CZ (28.11.2013)

Introducing into individual areas through brief lectures of the surveillance

Consultation on the review of the literature

Seminar work

Requirements to the exam -
Last update: JANCARIK/PEDF.CUNI.CZ (28.11.2013)

Common reflection according to the requirements:

theoretical everview, introduction

methodology

design and implementation of the experiment

characteristics of interventions

Syllabus -
Last update: JANCARIK/PEDF.CUNI.CZ (28.11.2013)

Attention will be placed on

various modes of representation and their transformations,

possibilities of expressing part-whole relation, the role of pre-concepts,

possibilities of the interpretation of fractions,

problem posing and its importance as an educational and diagnostic tool,

identification of typical mistakes, their sources and reeducation.

 
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