In many advanced mathematics courses, comprehending theorems and proofs is an essential activity for both students and mathematicians. Such activity requires readers to draw on relevant meanings for the concepts involved; however, the ways that concept meaning may shape comprehension activity is currently undertheorized. In this paper, we share a…

Author Pam Harris argues that teaching real math--math that is free of distortions--will reach more students more effectively and result in deeper understanding and longer retention. This book is about teaching undistorted math using the kinds of mental reasoning that mathematicians do. Memorization tricks and algorithms meant to make math…

In this note we demonstrate two instances where matrix multiplication can be easily verified. In the first setting, the matrix product appears as matrix element concatenation, and in the second, the product coincides with matrix addition. General proofs for some results are provided with a more complete description for 2×2 matrices. Suggested for…

A critical part of supporting the development of students' algorithmic thinking is understanding the challenges that emerge when students engage with algorithmatizing tasks--tasks that require the creation of an algorithm. Knowledge of these challenges can serve as a basis upon which educators can build effective strategies for enhancing students'…

We report on an innovative design of algorithmic analysis that supports automatic online assessment of students' exploration of geometry propositions in a dynamic geometry environment. We hypothesized that difficulties with and misuse of terms or logic in conjectures are rooted in the early exploration stages of inquiry. We developed a generic…

Fuzzy sets have experienced multiple expansions since their conception to enhance their capacity to convey complex information. Intuitionistic fuzzy sets, image fuzzy sets, q-rung orthopair fuzzy sets, and neutrosophic sets are a few of these extensions. Researchers and academics have acquired a lot of information about their theories and methods…

The index entries generated by the Selective Listing in Combinations (SLIC) technique constitute a lattice which is a subset of the power set of the set of descriptors assigned to a document and this fact leads to an improved algorithm for generating SLIC entries. (Author/MF)

Proposes a new approach for classifying text documents into two disjoint classes. Highlights include a brief overview of document clustering; a data mining approach called the One Clause at a Time (OCAT) algorithm which is based on mathematical logic; vector space model (VSM); and comparing the OCAT to the VSM. (Author/LRW)

This report describes the initial evaluation of a text compression algorithm against computer assisted instruction (CAI) material. A review of some concepts related to statistical text compression is followed by a detailed description of a practical text compression algorithm. A simulation of the algorithm was programed and used to obtain…

Reports on a study that found people could follow instructions from flowcharts or lists more quickly and accurately than from prose. (HOD)

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)

Proper name matching schemes are reviewed and an updated version of these schemes is tested on a suburban telephone book. (Author/AB)

Examines problem-solving results among second-grade students in three schools that were all using a reformed mathematics curriculum. Except for one problem, more students used a mental procedure than the standard written algorithms, and both methods were used with approximately the same degree of accuracy. (AIM)

Discusses the fraction system developed by the ancient Egyptians. Includes puzzles and number-theory problems. (MA)

Provides a solution method for the problem of finding an optimal traffic network in its simplest form where there are no congestion costs. (Author)