QR decomposition is widely used for solving the least squares problem. However, existing materials about it may be too abstract for non-mathematicians, especially STEM students, and/or require serious background in linear algebra. The paper describes theoretical background and examples of GNU Octave compatible MATLAB scripts that give relatively…

Process data from educational assessments enhance the understanding of how students answer cognitive items. However, effectively making use of these data is challenging. We propose an approach to identify solution patterns from operation sequences and response times by generating networks from process data and defining network features that…

The study focuses on the identification of relationships and/or rules between computational thinking (CT) concepts among the undergraduate students of Applied Informatics due to their attitudes towards mathematics. We analyze three CT concepts -- decomposition, pattern recognition, and algorithmic thinking. We assume that students who have a…

The mathematics associated with division is discussed, working from a theorem for the real division algorithm. Real-world, geometric, and algebraic approaches are discussed, as are related topics. (MNS)

A previously developed program for the HP-41C programmable calculator is extended to handle models of differential and difference equations with multiple eigenvalues. How to obtain difference equation solutions via the Z transform is described. (MNS)

A few examples are discussed of situations where some solution to writing a computer program for an algorithmic problem is immediately evident, but the best solution is some distance away. (MP)

This investigation concerns the repeated application of the rule "take the sum of the squares of the digits." (MP)

The article identifies five incorrect beliefs about mathematics often held by students who have difficulty with mathematics. They include: the relative size of numbers is more important than the relationships between quantities; computation problems must be solved by using a step-by-step algorithm; mathematics problems have only one correct…

Built-in data structures are the registers and memory words where binary values are stored; hard-wired algorithms are the fixed rules, embodied in electronic logic circuits, by which stored data are interpreted as instructions to be executed. Various topics related to these two basic elements of every computer program are discussed. (JN)

Two algorithms are developed for finding the square roots of numbers. One is based on the rule that x square is the sum of the first x odd numbers; the other is algebraic. (MP)

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)

Describes two experiments that investigate how "buggy algorithms" in multi-digit subtraction are used. The first experiment tested third grade students (N=110) and repeated the test two years later. The second experiment tested students in grades 3-6 (N=301). Contains 21 references. (DDR)

The forum is focused on thinking about and with algorithms as a way of unifying all one's mathematical endeavors. The lead article by Maurer presents examples and discussion of this point. Responses, often disagreeing with his views, are by Douglas, Korte, Hilton, Renz, Smorynski, Hammersley, and Halmos. (MNS)

The Euclidean algorithm for finding the greatest common divisor is presented. (MNS)

Four different types of problems from graph theory are presented and discussed. (MK)