In this paper, a new weighting sum method for multi-criteria decision making is presented. The main advantage of this method is that it is easier for understanding and it can effectively be handled by a decision maker, so the obtained solution best suits his goal and his understanding of the problem.

This research aimed to determine the effectiveness of applying instructive simulation experiments (SE) to the development of deeper conceptual understanding, retention of static electricity contents, and engagement of 4th-grade students. The correlation between student achievements and engagement was examined. 76 4th graders (10–11 years) were assigned to one of the groups: direct – DI + SE (DSE) and indirect instruction – II + SE (ISE) group. The results indicate that the ISE group showed significantly better achievements on the highest cognitive level compared to the DSE group. The application of SE had a significantly greater impact on the perceived behavioral, cognitive, and agentic engagement of the ISE group compared to the DSE group. A positive correlation was observed between student engagement and achievements.

In this paper we give elementary proofs of the generating functions for the Pochhammer symbol {(i)n} ∞ i=o,nεN. .

Kurepa’s hypothesis for the left factorial has been an unsolved problem for more than 50 years. In this paper, we have proposed new equivalents for Kurepa’s hypothesis for the left factorial. The connection between the left factorial and the continued fractions is given. The new equivalent based on the properties of the integer part of real numbers is proven. Moreover, a new equivalent based on the properties of two well-known sequences is given. A new representation of the left factorial is listed. Since derangement numbers are closely related to Kurepa’s hypothesis, we made some notes about the derangement numbers and defined a new sequence of natural numbers based on the derangement numbers. In this paper, we indicate a possible direction for further research through solving quadratic equations.

The aim with this research was to examine how the implementation of the flipped classroom model (FCM) impacted the quality and durability of 4th grade students’ knowledge in the field of measuring and measures when compared to traditional teaching (TT). The research was conducted in Serbia on a sample of 135 students, divided into 3 groups. The 3 groups were a control group (C) which was taught mathematics content using the TT model, an experimental group 1 (E1) which was taught using the FCM, while the students in experimental group 2 (E2) were taught using the FCM – the teacher also provided them with feedback regarding their work and made recommendations for their further development. The results show that the students from the E2 group surpassed those from the C and E1 groups regarding the quality and durability of their knowledge in the field of measuring and measures. There was a statistically significant difference in the knowledge of students in this field at the lower cognitive level among all the groups, while the statistically significant difference at the higher cognitive level was seen between the C and the E2 and between the E1 and the E2 groups.

Thehitting time index $\mathrm{HT}\left(G\right)$ is a recently introduced topological descriptor based on expected hitting times of a random walk on a graph. In this paper, we derive a closed-form formula for $\mathrm{HT}\left(G\right)$ for broom graphs $B_{n,d}$ that holds for all parameters $2\le d\le n-1$, $\mathrm{HT}\left(B_{n,d}\right)=S_1+S_2+S_3+(n-d){\displaystyle \sum _{i=1}^{d-1}}\max \{A\left(i\right),B\left(i\right)\},$ where $S_1,S_2,S_3,A\left(i\right),B\left(i\right)$ are explicitly defined. For $d\ge 2$ and $n\ge 4d-8$ we derive a simpler cubic polynomial formula in n, $\mathrm{HT}\left(B_{n,d}\right)=n^3+a_d{n}^2+b_{d}n+c_d,$ with explicitly given coefficients $a_d,b_d,c_d$ depending only on d. We also consider quartic polynomial formulas for special cases.