SZc0059 Didactics of mathematics 3

Faculty of Education
Autumn 2024
Extent and Intensity
0/0/1.2. 4 credit(s). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
doc. RNDr. Jaroslav Beránek, CSc. (lecturer)
RNDr. Břetislav Fajmon, Ph.D. (lecturer)
Bc. Tereza Mikulášková (seminar tutor)
Guaranteed by
Mgr. Irena Budínová, Ph.D.
Department of Education – Faculty of Education
Contact Person: Mgr. Irena Budínová, Ph.D.
Supplier department: Department of Education – Faculty of Education
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
After completing the discipline, the student:
• Understands the taught content from the point of view of the context with the development of concepts in history mathematics.
• Understands the contents taught from the point of view of teaching mathematics in secondary school.
• Can connect knowledge from individual levels of mathematics education (primary, secondary, tertiary), understands their gradual development and connections.
• Reflects knowledge from practice and connects it with mathematical and didactic knowledge.
Learning outcomes
After completing the course, the student is able to:
• Describe important historical moments in the development of mathematical concepts and put them in connections with the student's concept-forming process and various difficulties in creating concepts.
• Choose math problems that are adequate to the needs of a high school student.
• Solve these tasks using methods appropriate to the grade of the high school student and his mathematical abilities.
• Reflect knowledge from practice and relate it to theoretical mathematics didactic knowledge.
• Transform didactic knowledge into mathematics teaching.
• Establish the objectives of the mathematics lesson.
Syllabus
  • History of mathematics, possibilities of using historical notes to motivate the curriculum. Historical period in the development of mathematics, significant results. Prominent philosophers and mathematicians. (1 throw.)
  • Number fields: complex numbers. (1 hour)
  • Financial Mathematics. Simple and compound interest. Use of geometric sequence at problem solving. (1 hour)
  • Middle School Equations and Inequalities: Equations and Inequalities with an Unknown in the Denominator. Quadratic equations and inequalities, different methods of solving them. Equations and inequalities with absolute value. An equation with an unknown square root. Exponential and logarithmic equations. Trigonometric equations. Graphical solution of equations. (2 hours)
  • Elementary functions in secondary school curriculum. Quadratic function. Absolute value function. Linear curve function. Exponential functions. The square root function. Exponential a logarithmic functions. Trigonometric functions, unit circle. Properties of functions. (1 hour)
  • Sequences in high school. Determination and properties of sequences, arithmetic and geometric sequence. Use in word problems. Planimetry in high school: Use of visualization in solving design problems. (1 hour)
  • Stereometric design tasks (solutions in free parallel projection, sections of bodies in a plane, off-road bars). Stereometric tasks for calculations (deviations of planes, straight lines from the plane, the radius of the circumscribed and inscribed spherical surface). (2 hours)
  • Right-angled and general triangle trigonometry. The sine and cosine theorem, other relations. Analytical geometry of linear figures and conics in high school. Analytical geometry in a plane - vectors and operations with them, analytical expression of a straight line in a plane, conic sections). (2 hours)
  • Combinatorics in high school: variations, permutations, combinations (without repetition, with repetition). Binomial theorem. Pascal's triangle. High School Probability and Statistics. A random phenomenon and its probability, probability of unification and intersection of phenomena, independence (2 hours)
  • phenomena. Basic concepts of mathematical statistics. Analysis and processing of various data representations, a statistical set and its characteristics (weighted arithmetic mean, median, mode, percentile, quartile, standard deviation, interquartile deviation). (2 hours) Odeslat zpětnou vazbu
Literature
    required literature
  • Vondrová, N. (2019). Didaktika matematiky jako nástroj zvládání kritických míst v matematice. Univerzita Karlova, Pedagogická fakulta.
  • Vondrová, N. (2020). Matematická slovní úloha: mezi matematikou, jazykem a psychologií. Charles University in Prague, Karolinum Press.
  • Budínová, I. (2018). Přístupy nadaných žáků 1. a 2. stupně základní školy k řešení některých typů úloh v matematice. Masarykova univerzita.
  • Budínová, I., & Pavlíčková, L. (2020). Konstrukční úlohy. Učební text pro studenty učitelství matematiky 2. stupně základní školy. Masarykova univerzita.
  • Stančíková, M.: Kombinatorika – webová učebnice pro žáky středních škol. https://is.muni.cz/th/ycgxr/web/index.html
Teaching methods
Lecture, explanation, workshop, independent work, consultation, portfolio creation.
Assessment methods
The following will be evaluated:
• Continuous active work.
• Solving assigned tasks.
• Creating a portfolio: creating didactic aids suitable for forming an opinion in individual parts of school mathematics.
• Oral exam on the discussed topics.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: in blocks.
Information on the extent and intensity of the course: 15 hodin.
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