Methodology of Algebra Teaching

elective courses

The course intends to systematize the fundamental notions of number theory, algebra and analysis in the scope of the national curriculum in mathematics.

It will also present methods of teaching of school algebra and the good practices, at the level of an elementary school and of a high school. The course will also include topics that can inclrase the interest of students in mathematics.

The following topics will be covered:

Why do we teach mahematics?

The role of algebra within mathematics.

A review of the national curriculum in the scope of algebra and calculus.

Criteria of divisibility of natural numbers.

A construction of natural numbers. lcd and lcm. Prime numbers. Unique decomposition into prime factors.

Reasoning in number theory - which natural numbers are sums of at leas two consecutive natural numbers?

Axioms of real numbers. Dedekind sections. Why can't we divide by 0?

Euclid's algorithm, measurung of segments and continuous fractions.

Estimating number values. Percentages.

About solving text problems without equations. What is a variable?

Short multiplication formulas. Newton's binomial formula.

Viete's formulas.

Bezout theorem. Rational roots of polynomials with integer coefficients.

Solving and proving inequalities.

Operations on fractions. Rational functions.

Proporties of elementary functions. Transforming function pgraphs.

Continuous functions. The Darboux property.

Number sequences. The arythmetic and geometric progressions. Limit of a number sequence.

Derivatives of elementary functions. Intervals of monotonity and extrema of functions. Optimization problems.

The above topics will be discussed in the context of the teaching methods. Also ipical students' errors will be indicated.

(Each effect is followed by the code of the corresponding requirement of the Teachers' Education Standard)

In the scope of knowledge a graduate knows:

the national curriculum of mathematics in the scope of the school algebra, the teaching objectives and the content knowledge at different education levels (D.1/E.1.W2.);

methods of teaching of school algebra - substantive and methodical solutions, good practices, how to adapt the teaching to needs and abilities of students of divirsified learning potentials, typical students' errors, their role and how to makee use of them while teaching (D.1/E.1.W6.);

the need to build a positive attitute of students towards studying, developing their curiosity, activity and coginitive independence, logical and critical thinking, to build the motivation to learn mathematics in a systematic way, to use different knowlegde sources, incuding the Internet and to prepare students for life-long learning through self-reliant learning (D.1/E.1.W15.);

In the scope of skills a graduate can:

identify typical school exercises with teh learning objectives, in prticular with the general requirements of the national curriculum and with the key competemces (D.1/E.1.U1.);

identify the school algebra topics with other learning content topics (D.1/E.1.U3.);

addopt the communication style to the level of development of his/her students (D.1/E.1.U4.);

create didactical situations invoking students' activity and aimed at broadening of their interests and at the knowledge popularization (D.1/E.1.U5.);

recognize typical students' errors and use them in the teaching practice (D.1/E.1.U10.).

In the scope of social competences, a graduate is ready:

to popularize knowledge among students, within and outide the school (D.1/E.1.K2.);

to encourage students to research attempts (D.1/E.1.K3.);

to promote a responsible and critical use of digital media and to obey the copyright laws (D.1/E.1.K4.);

to develop students' curiosity, activity and cognitive independence as well as the logical and critical thinking (D.1/E.1.K7.);

to stimulate students to life-long learning through self-reliant learning (D.1/E.1.K9.).

The grade is based on the students's performance on the exercise sessions and on written exam. Another requirerment is to give a short presentation of a selected topic from school algebra.