Fibonacci数列与Euclidean除法

利用Fibonacci数列，给出了求最大共因数的Euclidean算法的复杂度。     

基于VCN智能技术的除法精确运算

基于智能VCN的变溢性、可拓性及压缩性等有机结合的技术,本文提出了一种新的数的智能除法精确运算.该运算结果商值的精确位数,是可以任意或无限地确定的,它可以很好地解决了计算机数值分辨率因CPU字长制约造成数字的扰动性问题,如对中国古代数学家祖冲之曾研究圆周密率π值实验数据（π=355/113）除法精确计算PC的数字扰动问题.     

和谐：小学数学教学设计的新视角——以“用字母表示数”的教学设计为例

教学设计的主旨是以学习者为中心的学习环境设计,因而,教学设计过程中,多要素、多视角的和谐是必然的诉求。从小学数学学科的视角看,丰富的"和谐"内涵应包含这样的三方面含义:学校形态和原始形态的融通,实践经验和教育理论的结合,意义建构和文化传承的并举。     

“数字“在中西文化中的应用欣赏

数字"三"、"四"、"六"、"七"、"八"、"九"和"十三"在中西文化中的习惯用法是相同相通的,是文化"共核"部分。     

Examining the relation between whole numbers and fractions: A meta-analytic structural equation modeling approach

With a Meta-Analytic Structural Equation Modeling approach, we investigated the role of whole-number knowledge on fraction performance, accounting for domain-general skills, age, and mathematics-difficulty status. We conducted analyses based on 6,096 students from 39 independent samples within 29 studies. Findings suggested conceptual whole-number knowledge emerged as a significant and stable predictor of conceptual and procedural fraction knowledge. More importantly, students experiencing mathematics difficulty demonstrated a distinct pattern of performance compared to typically-achieving students, including: conceptual whole-number knowledge had lesser impacts on conceptual fraction knowledge; procedural whole-number knowledge had greater impacts on procedural fraction knowledge; and working memory and fluid intelligence made fewer contributions to fraction knowledge.     

等幂和多项式及应用

利用递归方法引入等幂和多项式,运用组合数学相关知识,以函数的泰勒级数为工具,用等幂和多项式解决了等差数列及自然数等幂和问题.     

一致有界随机变量序列的弱律与强律

利用一致有界条件,建立了弱大数定律和强大数定律。它不仅改进了目前的相应结果,同时还获得了弱大数定律与强大数定律的本质差别。     

菲波那契数列与黄金分割的内在联系及应用

给出菲波那契数列的几种求法及其与黄金分割的内在联系,并得出其与组合数之间的一般性的结论,阐述其在日常生活中的广泛应用.     

第一及第二数学归纳原理的推广

将第一及第二数字归纳原理由自然数集N推广到全序整环Z的子集∑={ay＋b∈Z/y遍历N中诸数,而a,b为∈Z的某二数,且a≠0},得到定理I（第一数学归纳原理的推广）：设S（∈∑={a×1＋b,a×2＋b,…}）具有性质1）a×1＋b∈S;2）s∈S=〉s＋a∈S,则S=∑及定理Ⅱ（第二数字归纳原理的推广）：设S（∈∑={a×1＋b,a×2＋b…}）具有性质1）a×1＋b∈S,2）∨2≤k∈N,a×1＋b,a×2＋b,…,a×（k-1）＋b∈S=〉a×k＋b∈S,则S=∑。     

The Cognitive Predictors of Computational Skill with Whole versus Rational Numbers: An Exploratory Study

The purpose of the present study was to explore the 3rd-grade cognitive predictors of 5th-grade computational skill with rational numbers and how those are similar to and different from the cognitive predictors of whole-number computational skill. Students (n = 688) were assessed on incoming whole-number calculation skill, language, nonverbal reasoning, concept formation, processing speed, and working memory in the fall of 3rd grade. Students were followed longitudinally and assessed on calculation skill with whole numbers and with rational numbers in the spring of 5th grade. The unique predictors of skill with whole-number computation were incoming whole-number calculation skill, nonverbal reasoning, concept formation, and working memory (numerical executive control). In addition to these cognitive abilities, language emerged as a unique predictor of rational-number computational skill.