Middle school math education, or the first two circles of the Understanding and doing Math books series, is enough to follow these presentations about math learning.
The teaching of mathematics is dominated by the analytical approach, while the qualitative and numerical approaches are neglected. This has negative consequences for the correct mathematical development of students. It limits their access to problem-solving and limits the range of problems they can solve. Conceptually, in this kind of teaching the student does not develop a qualitative way of thinking and does not adopt essential ideas of numerical mathematics. Qualitative and numerical approaches imply appropriate software, which further emphasizes the need to introduce adequate mathematical software in mathematics teaching. In the presentation Qualitative, analytical, and numerical approach to teaching mathematics (in Croatian) the advantage of a balanced qualitative, analytical, and numerical approach is presented.
In the presentation Program Microsoft Mathematics – use and abuse in learning mathematics (in Croatian), I analyzed what characteristics good math software should have. These should support a combined qualitative- analytical-numerical approach to learning and use of mathematics. The Microsoft Mathematics software was tested against the set of criteria.
In the presentation, The concept of function in mathematical education (in Croatian), I briefly describe the importance of the concept of function in modern mathematics, as well as the importance of acquiring this concept in the process of mathematical education. The educational treatment of the concept of function in primary, secondary, and higher education is analyzed. The conclusion is that the notion of function is insufficient and inadequately treated, so suggestions for improvement were given.
In the presentation Is zero a natural number? (in Croatian) I consider some questions to which there are not good enough answers given in mathematics teaching: Is zero a natural number? Is there a difference between fractions and rational numbers? Are the vectors directional lengths? What is the similarity? Is the function f (x) = ax + b a linear or affine function? Each question illustrates one type of problem that should be approached in an appropriate way in mathematics teaching. For example, regardless of whether we assume that zero is a natural number or not, it is methodologically important not to present it to the student as some great truth about numbers, or as some educational achievement, but as a result of our modeling of the idea of numbers, a convention that ( in a given context) we need to hold. In this way, the student develops the notion of mathematics as a human activity in which he too can actively participate, and not as truths that are beyond the reach of ordinary mortals.
The notion of similarity of geometric figures and bodies is one of the basic notions of Euclidean geometry by which it differs significantly from other homogeneous and isotropic geometries, eg spherical and hyperbolic geometry. It is the properties of similarity that give Euclidean geometry its characteristic simplicity, beauty, and usability. Given such significance, I consider that the notion of similarity is not adequately represented in the mathematical education of elementary school students. The presentation The concept of similarity in elementary mathematical education (in Croatian) proposes a sketch along which the concept of similarity can be incorporated into elementary math teaching, without burdening it but, rather, making it simpler and more relevant.