CALCULUS TEACHER’S COMPETENCIES AS CORRELATES OF STUDENTS’ LEARNING EXPERIENCES

The good qualities of a calculus teacher are an asset in producing great results for students and themselves. This study aimed to investigate the different competencies of a calculus teacher as correlates of students' experiences in learning at Visayas State University, Philippines. The study employed selected secondary data from the existing study in literature such as competencies in teaching calculus subjects and different types of learning experiences of students. The study used some descriptive statistical measures to summarize the selected data and employed Spearman rho correlation to predict significant factors (teacher's competencies) that might influence the student's learning experiences. Results showed that teachers' competencies such as "prepared", "knowledgeable", "mastery", "organized", "decent", and "approachable" are highly correlated to the different learning experiences of students at a 1% level of significance. Hence, calculus teachers must be always knowledgeable in a class through rigorous preparation and studying. It is also concluded that teachers must develop a mastery of calculus subjects and apply an organized routine during class discussions to obtain desired academic performance for students. In addition, a well-groomed and professional may be integrated in front of students as well as open-mindedness and good personality to make interactive and stimulating class discussions. It is recommended that calculus teachers may undergo some rigorous training for calculus teaching to become a knowledgeable and competitive educators. Furthermore, teachers who will teach college calculus must be holding at least a master's degree in line with mathematics education or pure mathematics

Some New Notes on Mersenne Primes and Perfect Numbers

Mersenne primes are specific type of prime numbers that can be derived using the formula , where is a prime number. A perfect number is a positive integer of the form where is prime and is a Mersenne prime, and that can be written as the sum of its proper divisor, that is, a number that is half the sum of all of its positive divisor. In this note, some concepts relating to Mersenne primes and perfect numbers were revisited. Further, Mersenne primes and perfect numbers were evaluated using triangular numbers. This note also discussed how to partition perfect numbers into odd cubes for odd prime . Also, the formula that partition perfect numbers in terms of its proper divisors were constructed and determine the number of primes in the partition and discuss some concepts. The results of this study is useful to better understand the mathematical structure of Mersenne primes and perfect numbers

ON EVEN-TO-ODD MEAN LABELING OF SOME TREES

Let G=(V(G), E(G)) be a connected graph with order |V(G)|=p and size |E(G)|=q. A graph G is said to be even-to-odd mean graph if there exists a bijection function phi:V(G) to {2, 4, ..., 2p}  such that the induced mapping phi^*:E(G) to {3, 5, ..., 2p-1} defined by phi^*(uv)=[phi(u)+phi(v)]/2 for all uv element of E(G) is also bijective. The function  is called an even-to-odd mean labeling of graph . This paper aimed to introduce a new technique in graph labeling. Hence, the concepts of even-to-odd mean labeling has been evaluated for some trees. In addition, we examined some properties of tree graphs that admits even-to-odd mean labeling and discussed some important results

A CLOSER LOOK AT A PATH DOMINATION NUMBER IN GRID GRAPHS

This article exposes the combinatorial formula that determines the pathdomination number in a grid graph and discusses some of its properties. Seven propertiesare derived regarding the path domination number of grid graphs. Furthermore, some additional properties as direct consequences of the derived main properties are alsodiscussed

QUADRATIC POLYNOMIAL OF POWER SUMS AND ALTERNATING POWER SUMS

This study aims to construct quadratic polynomials in n for power sums and alternating power sums of consecutive positive integers. In addition, this paper evaluated the said quadratic polynomials under odd and even terms of the series

A SHORT NOTE ON FIBONACCI NUMBERS IN A GENERALIZED PYTHAGOREAN TRIPLES

This paper aims to construct a new formula that generates a Fibonacci numbers in a generalized Pythagorean triples. In addition, the paper formulates some Fibonacci identities and discuss some important findings

NEW COUNTING FORMULA FOR DOMINATING SETS IN PATH AND CYCLE GRAPHS

Let G=(V(G), E(G)) be a path or cycle graph. A subset D of V(G) is a dominating set of G if for every u element of V(G)\D, there exists v element of D such that uv element of E(G), that is, N[D]=V(G). The domination number of G, denoted by gamma(G), is the smallest cardinality of a dominating set of G. A set D_1 subset of V(G) is a set containing dominating vertices of degree 2, that is, each vertex is internally stable. A set D_2 subset of V(G) is a set containing dominating vertices where one of the element say a element of D_2,  and the rest are of degree 2. A set  D_3 subset of V(G) is a set containing dominating vertices in which two of the elements say b, c element of D_3, deg(b)=deg(c)=1. This paper developed a new combinatorial formula that determines the number of ways of putting a dominating set in a path and cycle graphs of order n>=1 and n>=3, respectively. Further, a combinatorial function P^1_G(n),  P^2_G(n) and P^3_G(n) that determines the probability of getting the set D_1, D_2, and D_3, respectively in graph G of order n were constructed

A Note on Full and Complete Binary Planar Graphs

Let G=(V(G), E(G)) be a connected graph where V(G) is a finite nonempty set called vertex-set of G, and  E(G) is a set of unordered pairs {u, v} of distinct elements from  V(G) called the edge-set of G. If  is a connected acyclic graph or a connected graph with no cycles, then it is called a tree graph. A binary tree Tl with l levels is complete if all levels except possibly the last are completely full, and the last level has all its nodes to the left side. If we form a path on each level of a full and complete binary tree, then the graph is now called full and complete binary planar graph and it is denoted as Bn, where n is the level of the graph. This paper introduced a new planar graph which is derived from binary tree graphs. In addition, a combinatorial formula for counting its vertices, faces, and edges that depends on the level of the graph was developed

ON THE DARK SIDE OF LEARNING CALCULUS: EVIDENCE FROM AGRIBUSINESS STUDENTS

This study focused on evaluating the agribusiness students negative experiences in learning Calculus. The study employed 121 agribusiness students in the first semester of school year 2019-2020 in Visayas State University, Baybay City, Leyte, Philippines. A selected secondary data from the study of Casinillo and Casinillo (2020a) was utilized in this study. With the aid of correlational research approach, this study stresses to explain the nature and characteristics of negative effects of learning calculus which is very helpful for improving the level of achievement of students and modifying the strategy of mathematics teachers. Results showed that most of the agribusiness students dont have enough background in pre-calculus topics since there are only 9% of them took a STEM strand during senior high school. Seemingly, it is revealed that students are experiencing extreme stress, natural emotional exhaustion and frustration, and average absenteeism, somatic burden and laziness in learning Calculus. It is found out that the negative experiences of these agribusiness students are significantly related to each other. This suggest that these negative experiences are inter-correlated and dependent to each other which is wearisome to their studies and leads to poor academic performance. However, these students are driven to pursue studying calculus since its part to their requirements in their degree program. Hence, by proper motivation and appropriate teaching strategy in Calculus, these students can progress their level of achievement

Which is better, non-fermented or fermented diets?: The case of production of broilers

The broilers food was provided from  fermented and non-fermented of the raw materials. Fermentation utilizes microorganisms to transform raw materials into useful products, resulting in the production of nutritionally enriched, very stable food products from low-value carbohydrate and protein substrates. Therefore, this study aimed to assess the growth performance, return above feed cost and mortality of broilers given a non-fermented (control) and fermented feeds using plain water, water+15 ml coco vinegar and water +15 ml RPL8+AKE probiotic as fermenting agents. The fermentation process lasted for 72 hours inside tightly covered container in a dark room at room temperature. A total of 120 broiler chicks were randomly assigned to four treatment diets and were replicated three times with ten birds per replication following a Complete Randomized Design set-up. Data on cumulative weekly weight gain (CWWG), average daily gain (ADG), and feed conversion ratio (FCR) were subjected to one-way Analysis of Variance (ANOVA) and comparison between treatment means was done by Honestly Significant Difference test using the SPSS version 20.0. Results revealed a better growth performance of broilers under non-fermented diet compared with fermented diets. Significantly (p0.01) highest ADG on broilers fed with non-fermented ration (m=0.397g, sd=0.0086g), followed by water+15 ml coco vinegar (0.365g), water+15 ml RPL8+AKE probiotic (m=0.343g, sd=0.0114g) and plain water  (m=0.314g, sd=0.0057g). Although below the Philippine average (2.0) and standard (1.9) FCR, broilers fed with non-fermented diet had the better FCR (2.3) than those fed with fermented rations. The lowest feed cost and positive return above feed cost on broilers given fermented diets imply a negative impact on the expected profit in poultry production instead of non-fermented ration. However, no mortality was recorded for broilers given a fermented diets which implies that it produces vigorous broilers