Text mining in the trend of education 4.0: A study on clustering mathematical terms of algebra textbooks in Vietnamese high schools

In the context of Educational Revolution 4.0, text mining with digital tools plays an important role. Various techniques and softwares have been employed in text mining, among which the clustering technique using Atlas.ti, a German software, is widely used thanks to its versatility and open access. This article presents the results of clustering Mathematical terms in Algebra textbook in Vietnamese high schools with the support of Atlas.ti. Initial research results can yield the insight into the relationship among Mathematical terms in the curriculum, thereby, aiming for a better teaching process.

Equations as Unruly Objects

Specialized notation, complexity, and sheer length contributed to the unruly nature of 18th-century equations, whether in manuscript or printed form. By close examination of early modern material texts, this essay compares constraints and affordances of the pen and the composing stick for setting boundaries and imposing order on algebraic expressions. Drawing on French and British mathematical works, it considers typesetting practices and advice to readers in influential algebra textbooks, compares mathematical manuscripts prepared for print and the printed results, unpacks oversize pages brimming with derivations and multiple cases, and reflects on practices of mise-en-page in the Mémoires of the Paris Academy of Sciences and the Philosophical Transactions. It thus invites attention to the tools, gestures, and traces of amateur, expert, reader, writer, and typesetter in 18th-century algebra.

On Subnomials

Summary While discussing the sum of consecutive powers as a result of division of two binomials W.W. Sawyer [12] observes “It is a curious fact that most algebra textbooks give our ast result twice. It appears in two different chapters and usually there is no mention in either of these that it also occurs in the other. The first chapter, of course, is that on factors. The second is that on geometrical progressions. Geometrical progressions are involved in nearly all financial questions involving compound interest – mortgages, annuities, etc.” It’s worth noticing that the first issue involves a simple arithmetical division of 99...9 by 9. While the above notion seems not have changed over the last 50 years, it reflects only a special case of a broader class of problems involving two variables. It seems strange, that while binomial formula is discussed and studied widely [7], [8], little research is done on its counterpart with all coefficients equal to one, which we will call here the subnomial. The study focuses on its basic properties and applies it to some simple problems usually proven by induction [6].

Brief Report: A Comparison of Symbol-Precedence View in Investigative and Conventional Textbooks Used in Algebra Courses

Recent reform movements have emphasized students making meaning of algebraic relationships; however, research on student thinking and learning often remains disconnected from the design of widely used curricular materials. Although a previous examination of algebra textbooks (Nathan, Long, & Alibali, 2002) demonstrated a preference for a symbols-first approach, research has demonstrated that Algebra I students' performance on verbally presented problems is better than on symbolic equations, consistent with cognitive theories suggesting the value of concreteness fading. The present study investigates whether current textbooks used in Algebra I courses demonstrate a formalisms-first approach using five different analyses. Results show that despite nearly 2 decades of research on student learning, the conventional textbooks used in most classrooms have been resistant to change and emphasize manipulation with symbols prior to making sense of verbal scenarios.