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Purpose - This study aimed to develop video-based e-module for Mathematics in Nature lessons and documented students' learning experiences in using the e-modules in a flipped classroom model. Method - The participants of this study were 113 first year college students and 10 randomly selected students for an in-depth interview. The research instruments were document analysis guide and interview guide. Qualitative data analysis techniques employed were document analysis and thematic analysis. Findings - The study revealed that there were lessons in the subject Mathematics in the Modern World that were relevant to the topic Mathematics in Nature. The developed video-based e-modules for the lessons on Mathematics in Nature have the following parts: title, learning objectives, overview, discussion, references, evaluation activity and answer key. Moreover, it has two distinct features namely the checkpoint and key to correction. Furthermore, the students, based on their learning experiences with the video-based e-modules, found it to be unique and interesting, has immediate feedback with rich examples, flexible and efficient, effective and easy to understand in learning the concepts of mathematics in nature. Significance - Students appreciate the concepts of mathematics in nature when hybridized with videos as revealed by their learning experiences with the e-modules implemented in a flipped classroom set up. It stimulates their interest and makes learning effective, efficient, and flexible. Thus, the developed video-based e-module indeed served its purpose as a unique and student-friendly instructional material integrating technology which would facilitate 21st century students' learning at home through videos and maximise classroom time for more productive activities. This would also enrich their understanding of the concepts of Mathematics in Nature as reinforced by the developed video-based emodule with the use of technology. [ABSTRACT FROM AUTHOR]

Harmony issues are widespread in human society and nature. To analyze these issues, harmony theory has been proposed as the main theoretical approach for the study of interpersonal relationships and relationships between humans and nature. Therefore, it is of great importance to study harmony theory. After briefly introducing the basic concepts of harmony theory, this paper expounds the five elements that are essential for the quantitative description of harmony issues in water resources management: harmony participant, harmony objective, harmony regulation, harmony factor, and harmony action. A basic mathematical equation for the harmony degree, that is, a quantitative expression of harmony issues, is introduced in the paper: HD=ai − bj, where a is the uniform degree, b is the difference degree, i is the harmony coefficient, and j is the disharmony coefficient. This paper also discusses harmony assessment and harmony regulation and introduces some application examples. [ABSTRACT FROM AUTHOR]

The article focuses on the association of mathematics education in sustainability. It explores the Sterling's model of educational responses and Edwards' model of organizational approaches to sustainability and mentions its use as abstraction for mathematics toward sustainability. It says that mathematical approach for sustainability can be made by using the notion of sensing large numbers and chaos, which can empower and give metaphors for the nonlinear dynamics of environment to students.

The article offers the author's account on the gardening activities participated by Australian students who have applied mathematics in the activities. According to the author, some schools participated in the Australian School Innovation in Science Technology and Mathematics projects supported by the Federal Government. He reveals that according to the teachers, students were able to experience mathematics to give solution to real problems in their environment.

The article offers information on Ontario's provincial floral emblem, white trillion, which is used as springboard for teaching mathematical concepts. It notes that a problem scenario that uses the white trillion as subject of the study is presented to the students. The problem relates the color and the foliage arrangement of the perennial herb to growing patterns. Moreover, the teacher has established questions using the problem scenario. It notes that the teacher must let the students understand the concept of growing patterns to analyze mathematical change. It suggests that students have to create new patterns by themselves so that they can feel and touch the recursive nature of the sequence. The patterns that they create will also foster their predictive power.

In this Article, we discuss the problem of the relationship between brain, mathematics, and cognition. In the first part, we present some elements concerning the anatomy of the brain and its growth. Against this background and drawing on current neuroscience research, we offer a summary of the cerebral parts usually associated with arithmetic thinking and the transition from perceptual arithmetic (common to several species) to symbolic arithmetic (specific to the human species only). Our discussion then turns around brain research and algebra. The literature review offers a general panorama that points out the multimodal nature of cognition in general and mathematical cognition in particular. This multimodal nature of cognition is compatible at different levels with the ontogenetic development of the brain --a development that turns out to be strongly related to the cultural context. In the conclusions we suggest some problems and questions that may be useful contact points for a research program between educators and neuroscientists. [ABSTRACT FROM AUTHOR]

The interesting thing about mathematical concepts is that we can trace their development or discoveries throughout history. Most cultures of the ancient world had some form of mathematics, and these basic skills developed into what we now call modern mathematics. The divine ratio is similar in that it was used in many different sections of history. The divine ratio, sometimes called the golden ratio or golden section, has been found in very diverse areas. The mathematical concepts of the golden ration have been found throughout nature, in architecture, music as well as in art. Phi is an astonishing number because it has inspired thinkers in many disciplines, more-so than any other number has in the history of mathematics. This paper investigates how the golden ratio has influenced civilizations throughout history and has intrigued mathematicians and others by its prevalence. [ABSTRACT FROM AUTHOR]

The article contends that there are alternative interpretation of Galileo's idealized claims about falling bodies. The paradox of heavy bodies and continuous motion in accelerated fall was the original question motivating Galileo's work. It argues that Galileo's 1604 hypothesis of the sameness of ratios of speeds and spaces is fully compatible with his previous analysis of accelerated motion. Grappling with the paradox, he realized that weight cannot be the cause of a body's speed of fall, and that all bodies somehow become "weightless" while falling in the void. The resolution of the paradox could lead to a "new science of motion". Galileo applied proportional reasoning based on Euclid's Elements.

The availability of powerful and affordable 3D PC graphics boards has made the rendering of rich immersive environments possible at interactive speeds. The scene update rate and the appropriate behaviour of objects within the world are central to this immersive feeling. This paper is concerned with the behaviour computations involved in the flocking algorithm, which has been used extensively to emulate the flocking behaviour of creatures found in nature. The main contribution of this paper is a new method for hierarchically combining portions of the flocks into groups to reduce the cost of the behavioural computation, allowing far larger flocks to be updated in real–time in the world. [ABSTRACT FROM AUTHOR]

The Nautilus pompilius is an exquisite example of a planar logarithmic spiral in organic nature, yet many artists and designers claim that its shape is ordained by the Golden Section, symbolically represented by ϕ, where ϕ=( [ABSTRACT FROM AUTHOR]

This paper shows the competitive exclusion principle of theoretical ecology to be mathematically identical to the criterion most commonly used for assessing yield advantage in intercrop situations — a "land equivalent ratio" greater than unity. Thus, an intercrop may show an advantage over its associated monocultures for the same ecological reasons that two species coexist in a given area. (Accepted for publication 2 December 1980) [ABSTRACT FROM AUTHOR]

The article discusses quantum nonlocality in nature, which are quantum systems, spatially separated, that exhibit nonlocal correlations. According to the author, this system has led to experiments that attempt to understand the tension that exists between quantum physics and relativity. An example is given of how quantum nonlocality works in the form of two persons. Both individuals control spatially separated quantum systems, perform the same measurements on their respective systems, and collect the same results. When the two persons obtain probability distribution data, they can share it and it will tell them what correlations exists between the experiments. Topics include an in-depth discussion on what correlations tell an experimenter about nonlocality.

The article reports on mathematics as an unpopular subject both in Great Britain and other countries. This is because less people continue with it into post-compulsory education and if ever there are those who continue, it is because they need the subject rather than they actively enjoy it. A research also shows that people find it hard to blend their personalities with mathematics because of the subject's image. The research was the first of its kind to be made within mathematics education that will focus on unpopular representations of the subject and attempts to map their effects.

The article presents the "Math by the Month" topic, using birds to apply math to elementary-school students' natural curiosity about their world. Designed to engage students to think as mathematicians, the activities develop number sense, measurement skills, and data collection through the exploration of birds. Kindergarten through grade 2 students' activities include comparing the height of penguins to each other and to students, and how much cracked corn wild turkeys could eat in a given time. Activities for older students include migration patterns, eagle nests, and flight speed of peregrine falcons.