Catalogue Search | MBRL
Are you sure you want to remove the book from the shelf?
{{itemTitle}}
9,140
result(s) for
"Numbers, Natural"
Sort by:
On the Analysis of a System of Equations Containing a Parameter n and Describing a Special State of a Certain Table of Numbers
In this paper, we study a system of 10 equations containing a parameter—a non-negative integer n—and associated with the problem of filling a special table with natural numbers. As a result, by developing a hybrid approach—first, by proving an a priori estimate for the solution of the system, which implies a finite set of solutions, thereby significantly narrowing the search space for a solution, and second, by performing a computer calculation of all remaining vectors satisfying the a priori estimate—we established that the system is not solvable for all values of the parameter n. We also prove a criterion for (x0,x1,…,x9)∈N10 to be a solution to the system for some value of the parameter n. Furthermore, we prove a fact that, in particular, implies that the set of values of the parameter n for which the system has at least 10 solutions is countable.
Journal Article
7 ate 9 : the untold story
When 7 is accused of eating 9, worried 6 hires a detective to investigate.
Book
Is there a Gap or Congruency Effect? A Cross-Sectional Study in Students’ Fraction Comparison
Many studies have addressed the natural number bias in fraction comparison, focusing on the role of congruency. However, the congruency effect has been observed to operate in the opposite direction, suggesting that a deeper explanation must underlie students' different reasoning. We extend previous research by examining students' reasoning and by studying the effect of a gap condition in students' answers. A cross-sectional study was conducted on 438 students from 5th to 10th grade. Results showed that the gap effect could explain differences between congruent and incongruent items. Moreover, students' use of gap thinking decreased towards the end of Secondary Education.
Journal Article
Max's math
Max and his brothers drive to Shapeville and Count Town searching for problems, and are able to use their skills in arithmetic and sleuthing to help get things ready for a rocket launch.
Book
Inappropriately applying natural number properties in rational number tasks: characterizing the development of the natural number bias through primary and secondary education
The natural number bias is known to explain many difficulties learners have with understanding rational numbers. The research field distinguishes three aspects where natural number properties are sometimes inappropriately applied in rational number tasks: density, size, and operations. The overall goal of this study was to characterize the development of the natural number bias across the span between 4th and 12th grade. To achieve this goal, a comprehensive test was constructed to test 4th to 12th graders' natural number bias. This test was administered to 1343 elementary and secondary school students. Results showed that an overall natural number bias could be found. This bias appeared to be equally strong in tasks with decimal numbers and tasks with fractions. Moreover, the natural number bias was weakest in size tasks, somewhat stronger in operations tasks, and by far the strongest in density tasks. An overall decrease of the strength of the natural number bias—but no disappearance except for size tasks—could be found with grade.
Journal Article
Teaching and learning about whole numbers in primary school
This book offers a theory for the analysis of how children learn and are taught about whole numbers.
Book
Why is the learning of elementary arithmetic concepts difficult? Semiotic tools for understanding the nature of mathematical objects
The semiotic approach to mathematics education introduces the notion of \"semiotic system\" as a tool to describe mathematical activity. The semiotic system is formed by the set of signs, the production rules of signs and the underlying meaning structures. In this paper, we present the notions of system of practices and configuration of objects and processes that complement the notion of semiotic system and help to understand the complex nature of mathematical objects. We also show in what sense these notions facilitate the description and comprehension of building and communicating mathematical knowledge, by applying them to analyze semiotic systems involved in the teaching and learning of some elementary arithmetic concepts.
Journal Article
Counting with Barefoot Critters
\"What is a day of counting with Barefoot Critters? Making pancakes, helping friends, exploring, swimming, playing pirates, learning about numbers! Join this adorable cast of animal characters as they explore numbers and counting over the course of a day, having fun at all stops along the way\"--Front jacket flap.
Book
The Zahl-Anzahl Distinction in Gottlob Frege: Arithmetic of Natural Numbers with Anzahl as a Primitive Term
The starting point is Peano’s expression of the axiomatics of natural numbers in the framework of Leśniewski’s elementary ontology. The author enriches elementary ontology with the so-called Frege’s predication scheme and goes on to propose the formulations of this axiomatic, in which the original natural number (N) term is replaced by the term Anzahl (A). The functor of the successor (S) is defined in it.
Journal Article