This study examined 11 U.S. textbooks written for prospective teachers to investigate how standard decimal multiplication and division algorithms are presented, especially the rationale of both algorithms. Analytical frameworks of various methods used in different textbooks were developed. The findings suggest that half of the textbooks do not…

The aim of this paper is to present a teaching proposal for the theoretical part relating to the first- and second-order linear difference equations with constant coefficients suitable for the first-year students at various types of universities. In contradistinction to the methods often applied (memorization of algorithms without a proper…

Multiple choice questions are traditionally expensive to produce. Recent advances in large language models (LLMs) have led to fine-tuned LLMs that generate questions competitive with human-authored questions. However, the relative capabilities of ChatGPT-family models have not yet been established for this task. We present a carefully-controlled…

Purpose: This study sought to 1) identify linguistic features important for Chinese text complexity with a theory-based and systematic approach, and 2) address how feature sets and algorithms affect the performance of Chinese text complexity models. Method: Texts from Chinese language arts textbooks from Grades 1 to 6 (N = 1,478) in Mainland China…

The first books in Polish about the Pascal programming language appeared in the late 1970s, and were soon followed by a Polish translation of Niklaus Wirth's book "Algorithms + Data Structures = Programs." At that time, many efforts were made to prepare teachers to teach informatics in schools, and Pascal was one of the topics taught,…

This study investigates how utilizing student-invented strategies in the classroom can inform teachers' pedagogical content knowledge. Two elementary school teachers participated in professional development discussing the benefits of invented strategies. Data was then gathered as the participants implemented this practice in their classrooms. Data…

This text contains material designed for about 18 weeks of study at grades 11 or 12. Use of a computer with the course is highly recommended. Developing an understanding of the relationship between mathematics, computers, and problem solving is the main objective of this book. The following chapters are included in the book: (1) Algorithms,…

This is the student's textbook for Algorithms, Computation, and Mathematics (Algol Supplement). This computer language supplement is split off from the main text to enable a school to choose the computer language desired, and also to make it easier to modify the course as languages change. The chapters in the text are designed to add language…

This is the student's textbook for Algorithms, Computation, and Mathematics (Fortran Supplement). This computer language supplement is split off from the main text to enable a school to choose the computer language desired, and also to make it easier to modify the course as languages change. The chapters in the text are designed to add language…

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…

Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…

This is the second unit in a series of 14 SMSG texts designed to cover mathematical concepts which the general population should know. One chapter of the unit discusses algorithms, flow charts, and computers; the second chapter tackles problem formulation procedures (not actual problem solving) and briefly covers mathematical models. For a special…

PRODUCED AS PART OF A PROJECT FOR THE IMPROVEMENT OF CLASSROOM TEACHING, THIS BOOK DISCUSSES THE BASIC CONCEPTS AND OPERATIONS OF ARITHMETIC WHICH ARE TAUGHT TO ELEMENTARY SCHOOL STUDENTS. THE CONCEPT OF A SET IS USED THROUGHOUT AS A BASIS FOR EXPLANATION, AND THE DISCUSSION STRESSES WAYS BY WHICH STUDENTS CAN BE BROUGHT TO UNDERSTAND THE…

Chapters 1-3 of the special materials written for low achieving students in grades 7-8 by SMSG include flow charting, elementary coordinate geometry, and functions. Included for student use are many tables which are to be used to shorten computational processes. Each chapter also includes pretest exercises, instructional lessons and exercises, and…

This is the second unit of a 15-unit School Mathematics Study Group (SMSG) mathematics text for high school students. Topics presented in the first chapter (Informal Algorithms and Flow Charts) include: changing a flat tire; algorithms, flow charts, and computers; assignment and variables; input and output; using a variable as a counter; decisions…