The Use of Bruner’s Modes of Representations in Teaching Factoring Second-Degree Polynomials

2012 ◽  
Vol 1 (1) ◽  
Author(s):  
Jerr A. Cabahug
Keyword(s):  
Conceptual Understanding ◽  
Teaching Mathematics ◽  
Abstract Concepts ◽  
Symbolic Representations ◽  
Teaching Aids ◽  
The Common ◽  
Common Problems ◽  
Factoring Polynomials ◽  
Iconic Representations ◽  
Second Degree

In teaching mathematics, one of the common problems of teachers is how to teach unfamiliar and abstract concepts in such a way that the students would make sense of them. One of these ways is the use of the different teaching aids which are reflected in Bruner’s Theory. In his theory, Bruner argued that conceptual understanding could be enhanced if students are exposed to different representations of a concept. In particular, he identified three main types of representations: concrete, iconic, and symbolic. Bruner’s theory stipulates that all three modes can be utilized in introducing abstract concepts for students. Based on this theory, this paper discusses one possible set of activities in teaching the topic of factoring second-degree polynomials. In this set of activities, the students will be taught first to factor polynomials using algebraic tiles which constitutes concrete representation of the concept; followed by factoring polynomials using pictures as iconic representations; and lastly, the students will be taught on how to factor polynomials using algebraic patterns which are the symbolic representations.   Keywords - Bruner’s Theory; representations; teaching; factoring second-degree polynomials; conceptual understanding

Applying Possessive pronoun in Writing Sentences: Exploring Students’ Ability and Problems in a Mixed Method Study

2019 ◽  
Vol 1 (3) ◽  
pp. 79-83
Author(s):  
Eka Utami Putri ◽  
Syahdan Syahdan
Keyword(s):  
Mixed Method ◽  
Simple Random Sampling ◽  
Average Score ◽  
Mixed Method Study ◽  
Z Score ◽  
Possessive Pronoun ◽  
Efl Students ◽  
The Common ◽  
Common Problems ◽  
Essay Test

The purpose of this research was to find out the students' ability in applying Possessive pronoun in writing sentences and the problems encounter it.  This mixed method study employs an explanatory design to reveals it. 53 students out of 105 students from1st semester EFL students from one reputable University in Pekanbaru, Indonesia, were invited to this study. These 53 students were selected using simple random sampling and enrolled for an essay test and interview to see the students' ability and explaining the problems. The data analysis using SPSS showed that the average score of students was 52.98. Meanwhile for the median is 48, the mode is 20. The score of Standard Deviation is 27.93, Variance is 780.25, and Range is 84.  Z-Score was found 41.5%, which is means higher than average and 58.5% while, students' ability was indicated below the average. It showed that the students were low ability in applying possessive pronoun in writing sentences. The study also found the common problems, i.e., (1) students still mixed up between possessive pronoun and possessive adjectives. (2) students used the wrong pattern in using a possessive pronoun. (3) students did not understand clearly about a possessive pronoun, (4) experiencing difficulties in learning possessive pronoun. 

scholarly journals Is There a Place for Theoretical Frameworks in Qualitative Research?

2021 ◽  
Vol 20 ◽  
pp. 160940692098795
Author(s):  
Casey M. Garvey ◽  
Rachel Jones
Keyword(s):  
Qualitative Research ◽  
Conceptual Understanding ◽  
Inductive Reasoning ◽  
Theoretical Framework ◽  
Theoretical Frameworks ◽  
Common Sense Model ◽  
Rich Description ◽  
The Common ◽  
The Rich ◽  
Qualitative Analyses

Qualitative research proceeds from the position that there is no one observable reality. Researchers utilizing qualitative methods build findings inductively, from raw data to a conceptual understanding. Theoretical frameworks may be utilized to guide qualitative analyses by suggesting concepts and relationships to explore. The framework may provide a sense of the story emerging from the analyses. And concurrently, the rich description provided by the analyses may allow the framework to be more deeply appreciated. However, there is a risk that using a theoretical framework may stifle inductive reasoning or result in findings incongruent to the data. The following is a discussion of the application of a theoretical framework in a qualitative study. This study, guided by the Common-Sense Model, explores the choice to undergo treatment for Hepatitis C Virus among veterans. Examples from the analyses are provided to facilitate discussion on the utilization of a theoretical framework. Techniques to optimize the use of a theoretical framework, as well as mitigate risks of such use, are presented. When utilized alongside rigorous data analyses and introspection, a theoretical framework may serve as a valuable tool to navigate data in qualitative research.

scholarly journals Common issues in the hetero-epitaxial seeding on SiC substrates in the sublimation growth of AlN crystals

2021 ◽  
Vol 127 (8) ◽  
Author(s):  
R. Radhakrishnan Sumathi
Keyword(s):  
Power Electronic ◽  
Etch Pit ◽  
Micro Hole ◽  
Wet Chemical ◽  
The Common ◽  
Common Problems ◽  
Hole Defects ◽  
Sublimation Growth ◽  
Impurity Elements ◽  
Very High

AbstractAluminium nitride (AlN) is a futuristic material for efficient next-generation high-power electronic and optoelectronic applications. Sublimation growth of AlN single crystals with hetero-epitaxial approach using silicon carbide substrates is one of the two prominent approaches emerged, since the pioneering crystal growth work from 1970s. Many groups working on this hetero-epitaxial seeding have abandoned AlN growth altogether due to lot of persistently encountered problems. In this article, we focus on most of the common problems encountered in this process such as macro- and micro-hole defects, cracks, 3D-nucleation, high dislocation density, and incorporation of unintentional impurity elements due to chemical decomposition of the substrate at very high temperatures. Possible ways to successfully solve some of these issues have been discussed. Other few remaining challenges, namely low-angle grain boundaries and deep UV optical absorption, are also presented in the later part of this work. Particular attention has been devoted in this work on the coloration of the crystals with respect to chemical composition. Wet chemical etching gives etch pit density (EPD) values in the order of 105 cm-2 for yellow-coloured samples, while greenish coloration deteriorates the structural properties with EPD values of at least one order more.

scholarly journals Stimulating Mechanistic Reasoning in Physics Using Student-Constructed Stop-Motion Animations

2021 ◽  
Author(s):  
Rayendra Wahyu Bachtiar ◽  
Ralph F. G. Meulenbroeks ◽  
Wouter R. van Joolingen
Keyword(s):  
Conceptual Understanding ◽  
Physical Phenomenon ◽  
Ninth Grade ◽  
Abstract Concepts ◽  
Projectile Motion ◽  
Mechanistic Reasoning ◽  
Stop Motion ◽  
Ninth Grade Students ◽  
Scientific Phenomena

AbstractThis article reports on a case study that aims to help students develop mechanistic reasoning through constructing a model based stop-motion animation of a physical phenomenon. Mechanistic reasoning is a valuable thinking strategy for students in trying to make sense of scientific phenomena. Ten ninth-grade students used stop-motion software to create an animation of projectile motion. Retrospective think-aloud interviews were conducted to investigate how the construction of a stop-motion animation induced the students’ mechanistic reasoning. Mechanistic reasoning did occur while the students engaged in creating the animation, in particular chunking and sequencing. Moreover, all students eventually exhibited mechanistic reasoning including abstract concepts, e.g., not directly observable agents. Students who reached the highest level of mechanistic reasoning, i.e., chaining, demonstrated deeper conceptual understanding of content.

scholarly journals From the Philosophy of Cult to the Philosophy of History in the Work of Pavel Alexandrovich Florensky (* 1882 + 1937)

Religions ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 533
Author(s):  
Daniel Porubec
Keyword(s):  
Human Activities ◽  
Historical Materialism ◽  
Philosophy Of History ◽  
Abstract Concepts ◽  
Interdisciplinary Work ◽  
Primary Activity ◽  
Human Ability ◽  
The Gift ◽  
The Common ◽  
Historical Periods

P. A. Florensky dedicated nine writings of his rich interdisciplinary work to the phenomenon of cult, which were first published in a censored form in 1977. We turn our attention to one of these writings called Cult, Religion and Culture, published under the common title Philosophy of Cult, in which the author elaborates a distinctive concept of the cult as the primary activity of man and at the same time as the gift offered to him for his own sanctification. It is the sacred cult—sacra from where, according to the author, two other human activities originate: namely, the ability to create tools—instrumenta—and the ability to create abstract concepts—notiones. However, both human activities have to be understood as a process of disintegration of the cult—sacra. Thus, by prioritizing one of the three human activities mentioned above, we can recognize three historical periods in history. According to Florensky, the human ability to create tools corresponds to the era of historical materialism, the ability to create concepts corresponds to the era of ideologism, and ultimately, the primary human activity—the life of man in the cult and its culture corresponds to the sacral materialism or concrete idealism.

Way to improve efficiency of teaching linear algebra to students with health disabilities by means of enlarged didactic units

2021 ◽  
pp. 65-71
Author(s):  
A.N. Semakin ◽  
◽  
G.P. Emgusheva
Keyword(s):  
Students With Disabilities ◽  
Linear Algebra ◽  
Teaching Methods ◽  
Educational Material ◽  
Educational Process ◽  
Teaching Mathematics ◽  
Abstract Concepts ◽  
State Technical ◽  
Analytical Geometry ◽  
Time Gap

Presented is enlarged didactic units developed by P.M. Erdniev for teaching mathematics, that improves the ability of students to understand educational material. This effect is achieved as a result of organizing the educational process according to the principles of complementarity of teaching methods and the spatial and temporal combination of interrelated elements of knowledge. Among the basic mathematical disciplines taught at Bauman Moscow State Technical University for students with disabilities the most difficult discipline is Linear Algebra, which is due to its content and various problems with students’ health. Linear Algebra is largely based on the theory from Analytical Geometry that is quite well perceived by students with disabilities. A comparative analysis of these disciplines shows that the enlarged didactic units linking these disciplines together can significantly simplify the study of Linear Algebra. However, due to difficulties with scheduling the time gap between these disciplines can be up to two semesters, which makes it impossible to directly use the enlarged didactic units. To solve this problem, we introduce the supporting discipline "Cognitive technologies for supporting the discipline Linear Algebra" which runs in parallel with Linear Algebra and which is based on the material of Analytical Geometry. Forming its content in close connection with Linear Algebra in accordance with the main principles of the enlarged didactic units, we smoothly lead students to the understanding of abstract concepts of Linear Algebra, reducing the complexity of learning.

Variations of Cystic Duct and Its Clinical Significance

2021 ◽  
Vol 9 (4) ◽  
pp. 8120-8126
Author(s):  
K. Sangameswaran ◽  
Keyword(s):  
Bile Duct ◽  
Cystic Duct ◽  
Gallstone Disease ◽  
Cystic Artery ◽  
Normal Anatomy ◽  
Biliary Anatomy ◽  
Medical College ◽  
Gallbladder Surgery ◽  
The Common ◽  
Common Problems

Background: Cystic duct drains the bile from the gallbladder into the common bile duct. Gallstone disease is one of the most common problems affecting the digestive tract and may lead to many complications. To avoid the complications in these patients the gallbladder is removed surgically (Cholecystectomy). Ligation of cystic duct and cystic artery is a prerequisite procedure when cholecystectomy is done. Understanding about the normal anatomy & the possible variations in biliary ductal system is important for the surgeons for doing cholecystectomy surgery successfully. Errors during gallbladder surgery commonly result from failure to appreciate the common variations in the anatomy of the biliary system. Aim of the study: To find out the incidence of variations in the length, course, and termination of cystic duct in cadavers. Materials and Methods: Present study was done in 50 adult cadavers in the Department of Anatomy, Government Tiruvannamalai medical college, Tamilnadu. Meticulous dissection was done in the hepatobiliary system of these cadavers. Observations: During the study variations in the length of cystic duct, course and different modes of insertion of cystic duct were observed. Conclusion: Knowledge of variations in the length of cystic duct and knowing about different modes of course & insertion of cystic duct is necessary for surgeons while conducting cholecystectomy. The risk of iatrogenic injury is especially high in cases where the biliary anatomy is misidentified prior to surgery. KEY WORDS: Cystic duct, Gallbladder, Cholecystectomy.

The Management of Rescued Shipwreck Survivors

1980 ◽  
Vol 66 (2) ◽  
pp. 107-113
Author(s):  
F. St. C. Golden
Keyword(s):  
Medical Officer ◽  
The Common ◽  
Common Problems

AbstractA ship’s medical officer may be called upon at any time to attend to casualties from a shipwreck. This paper outlines some of the common problems which may be encountered in such a situation and gives advice on a possible course of procedure.

The Use of the Concrete-representational-abstract (CRA) Sequence to Improve Mathematical Outcomes for Elementary Students with Emotional Behavioral Disorders

2021 ◽  
Author(s):  
Margaret M Flores ◽  
Vanessa M Hinton
Keyword(s):  
Elementary Students ◽  
Behavioral Disorders ◽  
Conceptual Understanding ◽  
Mathematical Thinking ◽  
Emotional Behavioral Disorders ◽  
Teaching Mathematics ◽  
Teaching Sequence ◽  
Positive Effects ◽  
Students With Ebd

The concrete-representational-abstract (CRA) sequence is an explicit methodology for teaching mathematics that has been shown to have positive effects for students with EBD. This teaching sequence fosters conceptual understanding and mathematical thinking. This article describes how a teacher used explicit CRA instruction with two elementary students with EBD. Its aims are to describe and provide rationale for CRA instruction. We will describe lesson activities, methods, materials, and procedures. Finally, we will offer suggestions for implementation.

Sign in / Sign up

Export Citation Format

Share Document