In mathematics classrooms, it is common practice to work through a series of comparable tasks provided in a textbook. A central question in mathematics education is if tasks should be accompanied with solution methods, or if students should construct the solutions themselves. To explore the impact of these two task designs on student behavior…

The number and variety of educational mathematics mobile applications (EMMAs) make it difficult to select mobile applications for mathematics learning and teaching. Therefore, in this study, multi-criteria decision-making (MCDM) techniques, which are effectively used in a wide variety of disciplines, were applied to choose among alternative…

The new method of teaching the problems with a parameter was designed based on the identification of the reasons for the low success rate of the kids in solving the problems. In order to identify these causes and to find ways of their elimination, pedagogical research was carried out in two phases at selected universities of Slovakia (126…

This study aims to design case-based learning with lesson study learning trajectory with the help of teaching aids to make students understand Prim's, Cruscal's, and Djiksra's Algorithms. The validation study was selected because it is a suitable method for this research. The research subjects were 41 Mathematics Education Study Program Students…

A brief history of the development of our present day Gregorian calendar is given. Methods are then given, based on congruences, to determine such things as the week-day for any given date and the date for Easter in any year. (LS)

Discusses an algorithm from Vedic mathematics that has similarities to FOIL and the standard algorithm for multiplication. (Author/NB)

Reports on two types of unsolvability in mathematics. One is an instance of impossibility and the second is a judgment of undecidability. Presents a number of examples of undecidable propositions. (GS)

Identifying the larger (L), smaller (S) and difference (D) of two real numbers, and then selecting the appropriate relationship between L, D, and S can help students solve algebra word problems. (SD)

Two mathematical topics are interpreted from the viewpoints of traditional (performing algorithms) and contemporary (creating algorithms and thinking in terms of them for solving problems and developing theory) algorithmic mathematics. The two topics are Horner's method for evaluating polynomials and Gauss's method for solving systems of linear…

A history of perfect numbers is presented, which briefly covers the 27 values known at this time. (MP)

Teaching which does not in any significant way address the genesis of mathematical ideas hides the fact that mathematics is created by people; that it involves intuition, exploring, conjecturing, and reasoning; and that it is purposeful. Such teaching can give students appearance that much of mathematics is very arbitrary; it just falls from the…

Examines 250 sixth-grade students' understanding of arithmetic average by assessing their understanding of the computational algorithm. Results indicate that the majority of the students knew the "add-them-all-up-and-divide" averaging algorithm, but only half of the students were able to correctly apply the algorithm to solve a…

Analyzes a didactical sequence for the teaching of addition and subtraction procedures and algorithms. Uses didactical procedures by children in problem solving activities in order to gain a better understanding of the interaction between numbers, numeration, and operations knowledge which are involved in the construction of addition and…

Reviews the mathematical properties of algorithms and problems which can not be resolved by present methods in mathematics. (SL)