The paper examines the empirically verified effect (parallel group experiment) of the application of the software form of integration and individualization of teaching of natural and mathematical knowledge in relation to traditional teaching, for example, the teaching sub-themes Cultivated habitats and life communities, and Equations with addition, subtraction, multiplication and division in the set N (the natural numbers) and N0 (the natural numbers plus the neutral element 0). The sample consisted of 250 pupils aged 10 to 11 years: 125 in the experimental group and 125 in the control group. The data were processed by statistical procedures and displayed in textual and graphical ways. The statistical analysis of the data obtained from the research has been achieved by the SPSS 17.0 software package, wherein the arithmetic mean, standard deviation, a t-test. Statistical indicators have confirmed the assumptions that the software form of integration and individualization contributes to more efficient and easier acquiring of knowledge, raising the quality and quantity of students' knowledge and increasing the interest in studying content in the teaching of Knowledge of Nature and Mathematics, and as such points to a preferred model of teaching and learning.
Problem-based and inquiry-based learning, are excellent opportunities for improving, perfecting and modernizing the educational process. In this regard, the aim of the paper is to present in more detail the application of the problem-based and inquiry-based learning in the teaching of nature and society (as the subject is named in primary schools of Republic of Srpska), as well as the similarities and differences, i.e. the border that separates these two methods of acquiring knowledge, while highlighting the difficulties that may report during their implementation. The paper is of a theoretical nature, based on the findings of eminent authors who are experts in the given field of education, and it also contains examples for lessons which are self-created. The purpose of the paper is to help teachers in preparing and conducting this type of nature and society lessons and to encourage the improvement of the learning process. The differences between the models are that problem-based learning is somewhat narrower and is directed towards finding solutions according to clearly defined steps, while inquiry learning is more directed towards fulfilling the human need for discovery, and encourages students to make exploring the world around them their lifestyle. From the above, it can be seen that it is necessary to pay attention to several aspects in order to make the class as high quality as possible, so that the role of the teacher remained unsurpassed, regardless of how independent the students were in learning.
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