Mathematics for Teachers

supplementary

A famous Polish mathematician, Hugo Steinhaus once said: “no matter what you will do in the future, after mathematics studies you will do it better”. Mathematics can teach many things of universal use like noticing patterns, realizing and examining relations e.g. reason-result, concluding, argumenting, convincing… can create proper conditions for formulating hypothesis based on inductive reasoning (in natural sense) and verifying them. It can as well create conditions for mastering the skill of reasoning by analogy, for both making generalities and examining particular cases, for learning and using both analytical and synthetic thinking.

For years the mentioned above educational aspects of mathematics have been frequently emphasised and it has been encouraged to teach via mathematics or by mathematics more than to teach mathematics itself.

he main aim of the classes is to present this general value of mathematics as well as its practical use in primary school mathematical education.

Arithmetic: numbers in Ancient Egipt and Babilon, Maya calendar, positional notation, digit and number, decimal numbers, estimation, arithmetical operations, including the use of calculator, patterns with calculator, strategy games, word problem solving strategies.

Geometry: geometrical experiments (experiments with mirror, folding a sheet of paper etc.), perpendicular and horizon, different kinds of symmetry, analogy in geometry.

Algebra: meaning and value of algebraic notation, symbolic notation as generalisation of pattern, functions as models of realistic situations.

Statistic: modes of data collection, presentations of data, parameters of data: mode, median, arithmetic mean.

Probability: random phenomena and probability games, experimental and theoretical frequency, probability thinking.

Polya G. (1954), Induction and Analogy in Mathematics. Princeton: Princeton University Press.

Polya G. (1990), Odkrycie matematyczne. Warszawa: PWN.

Polya G. (1993), Jak to rozwiązać? Warszawa: PWN.

Mason J., Burton L., Stacey K (2005), Myślenie matematyczne. Warszawa: WSiP.

Learning outcomes – student:

I. In terms of knowledge:

1. has basic knowledge of different means of recording numbers including positional notations.

2. knows some strategies of calculations.

3. knows some non-algebraic word problem solving strategies.

4. knows basic properties of geometrical solids and figures.

5. knows meaning of algebraic notation.

6. knows some modes of data presentation.

7. has basic knowledge of random phenomena.

II. In terms of skills:

1. can use some modes of recording numbers.

2. can find winning strategy in simple game.

3. can use some strategies of calculations.

4. can use some word problem solving strategies.

5. can solve simple geometrical problems.

6. can find and notice simple patterns.

7. can analyze collected data.

8. can make basic probability reasoning.

III. In terms of social competences:

1. can solve problems in group cooperation.

2. is aware of risks and dangers which low level of mathematical culture can cause in social life.

Conditions for course credition:

• Students may leave two classes, each subsequent absence must be justified by a medical certificate and credit by the student in a form agreed with the teacher

Credit is obtained by a student who:

• leaves no more than 2 classes or credit absences

• participates actively in the classes and does housework.

The evaluation covers the knowledge, skills and competencies of the selected learning outcome.