Examinando por Materia "Matemáticas"

Mostrando 1 - 18 de 18

Acceso abierto
Aplicación de herramientas de aprendizaje en ambientes virtuales para fortalecer el pensamiento geométrico en estudiantes de primaria de Barrancabermeja, Colombia- 2019
(Universidad Privada Norbert Wiener, 2021-06-25) Santos, María Carolina; Huaita Acha, Delsi Mariela
The low results achieved by Colombian students in national and international tests in mathematics are known, therefore, and as an improvement plan, all educational institutions have set out to improve the quality of the provision of educational services. That is why this research seeks to determine to what extent the application of learning tools in virtual environments strengthens Geometric Thinking in fifth grade students of the Jhon F. Kennedy Educational Institution in Barrancabermeja, Colombia in 2019. The research had a quantitative approach, with a quasiexperimental design, which set the objective of measuring the incidence of one variable under study under the effect of another in a school context. It was used in a survey by means of a questionnaire to collect information on the teaching-learning process of mathematics, which took into account the informational and practical dimensions, use of didactic resources, evaluation and accompaniment, and attitudinal; and a knowledge test that included the first three levels of the Van Hiele model. Statistical methods were used for data analysis, and Student's t-test for hypothesis tests. Finally, as a result, it was possible to determine that the application of learning tools in virtual environments favorably affects the development of geoometric thinking of fifth-grade primary school students at the John F. Kenendy educational institution, and as a conclusion it was established that the The application of learning tools in virtual environments improved the level of performance of the development of geometric thinking in the fifth grade students of the John F. Kenendy Institution in the two experimental groups, since according to the post-test tests, a significant difference was found of means for the control and experimental groups, thereby accepting the general alternative hypothesis raised.
Acceso abierto
Aplicación de la herramienta digital Geogebra en el proceso de aprendizaje de la función lineal en el grado noveno del Colegio Nuestra Señora de la Candelaria de Cimitarra Santander 2017
(Universidad Privada Norbert Wiener, 2018-12-10) Salazar Barrera, Jorge Hernán; Rivera Arellano, Edith Gissela
The objective of this research was to determine the extent to which the use of the GeoGebra tool influences the understanding of the linear function in ninth grade students of the Colegio Nuestra Señora de la Candelaria in Cimitarra Santander. The study was framed in an experimental design of quasi-experimental level. We worked with a population of 138 students of ninth grade, of which 70 students were selected as sample, so that an experimental group was established (formed by the ninth grade "C", with 36 students, who interacted with the digital tool GeoGebra) and a control group (Ninth Grade "A" with 34 students that was used as a witness), which were selected naturally as constituted in the institution. A pre-test was applied to the two groups in order to take a baseline and use it as a reference. Then the two groups were subjected for 13 sessions to the study of the linear function, with the difference that the experimental group (9ºC) was exposed to the influence of the GeoGebra digital tool and the control group to the traditional methodology, to develop this theme. Finally, a knowledge test on the aforementioned subject was applied again, in order to verify the fulfillment of the objectives and to check or reject the hypotheses. As a result, it was obtained that 100% of the students in the experimental group passed the test with a grade equal to or higher than 55 points, the average of this group was 78.19, which turned out to be 22.9 points higher than that obtained by the group. control that was of 55.29 and in addition half of the experimental group obtained notes superior to 80; 25 points more than the control group in this same indicator that was 55. It was evident that the continuous exposure to the digital tool Geogebra allowed to understand the concept and the different forms of expression of the linear function and were able to solve problems of their school environment , on this subject in a more easy and practical way.
Acceso abierto
Evaluación de estrategias didácticas y su relación con la compresión de lectura matemática en estudiantes del Instituto Integrado San Bernardo de Floridablanca - Colombia
(Universidad Privada Norbert Wiener, 2018-06-15) Caballero Vargas, Ramiro; Puente Saldaña, Rosa Ernestina
Mathematics has, like most sciences and other disciplines of knowledge, a specific, specific language, which simplifies, in some cases, communication, and on the other hand clarifies and designates in an exact manner, without possible confusion, its contents ... Ignorance of mathematical language produces errors of construction, of interpretation, and ultimately makes communication impossible. (Ortega, 2001). The objective of the present investigation was to establish the relationship that exists between the teaching strategies with the comprehension of mathematical reading in students of the Integrated San Bernardo Institute of Floridablanca Colombia. It is a research of applied type and non-experimental design. We worked with a population and sample of 47 students. For the data collection, the survey was used, and the questionnaire was used as an instrument. The results obtained show that the evaluation of strategies is directly related to reading comprehension in students of the Integrated San Bernardo Institute of Floridablanca - Colombia.
Acceso abierto
Implementación de un blog educativo para el mejoramiento de las habilidades del pensamiento crítico en el área lógico-matemáticas de los estudiantes del grado 11 de la Institución Guillermo Martinez Nuñez, Tulua, Colombia 2017
(Universidad Privada Norbert Wiener, 2018-07-18) Barrera Tejedor, Pascual; Méndez Toledo, Heimer Ali
The main objective of this research is to determine to what extent the implementation of an educational blog influences the skills of critical thinking in the logical-mathematical area of the students of the 11th grade of the Guillermo Martínez Núñez Institution of the Municipality of Tuluá del Valle del Cauca - Colombia year 2017. The development of the research is of applied type, explanatory level, quasi-experimental design, quantitative approach and the T-Sudent statistic. With a population of 282 students attending the 11th grade of the institution and a non-probabilistic sample of 60 students, it was used as a means of collecting information directly as pre-test and post-test. According to the results of the T test in the relation of the pre and posttest in the experimental group, it gives a significance of 0.00003, which when being less than 0.05 rejects the null hypothesis that says there is no significant difference between the results of the pre and posttest of the GE, confirming the assumption that there is a significant difference between tests in said group
Acceso abierto
Influencia de las TIC en el aprendizaje del área de geometría en los estudiantes de la institución educativa “Francisco José de Caldas”, ciudad de Manizales – 2015
(Universidad Privada Norbert Wiener, 2018-02-20) Echeverry Cárdenas, Giovanny Octavio; Méndez Toledo, Heimer Ali
Objective: Determine the influence that the use of TIC in the learning of the area of geometry of the students of the educational institution "Francisco José de Caldas" of the city of Manizales, Colombia in the year 2015. Methodology: Quasi-experimental research applying pre-test and post test to two homogeneous population groups of grade 9, keeping in one of them the traditional teaching scheme 9 with 30 students, and in the other 9b with 34 students, a didactic strategy mediated by ICT, such as internet, specialized software, video tutorials and multimedia tools, for 10 weeks. Results: It confirms the general hypothesis that ICT significantly influence the learning of the area of geometry in students of the educational institution "Francisco José de Caldas" of the city of Manizales, which was validated statistically through the realization of t test for paired or related samples from the non-parametric approach, ie a Wilcoxon rank test. Conclusions: The use of ICT in teaching geometry positively influences students' performance by allowing a better understanding of concepts and problem solving with greater easy, facilitating meaningful learning through a technological environment that motivates and brings knowledge
Acceso abierto
Influencia del diseño e implementación de entornos virtuales de aprendizaje de la matemática de los estudiantes del grado sexto de bachillerato del distrito de Buenaventura departamento del Valle en el año 2016
(Universidad Privada Norbert Wiener, 2017-11-21) Velasco Ortega, Aldemar; Tafur Portilla, Raúl Arturo
Faced with the concern of teachers and parents for the low academic performance of students in the area of mathematics; several evaluations show that Colombian children do not get satisfactory results. This panorama motivated the interest to find out the causes of the problem because the results will allow to design educational programs using Virtual learning environments that allow to overcome the learning difficulties observed. In this sense, the present study aims to determine how the design and implementation of virtual learning environments influences the learning of mathematics in the students of the sixth grade baccalaureate of the industrial technical educational institution Gerardo Valencia Cano; tries to answer the question How does the use of virtual environments of learning in the learning of mathematics in the students of the sixth grade of the baccalaureate of the industrial technical educational institution Gerardo Valencia Cano Influence? It was assumed that the use of virtual learning environments significantly improves math learning in students in the sixth grade students of the industrial technical education institution Gerardo Valencia Cano. The population was made up of sixth grade students, and the sample of 22 students. The research design is experimental. The instruments applied were the pretest evaluation of math learning and the posttest test through the use of virtual learning environments. The instrument was validated by expert judgment with an average rating of 90% and with the reliability coefficient of Küder Richardson, the instrument was found to be reliable (f = 0.65). The results show that the use of virtual learning environments significantly influences math learning; Student's t-test calculated a difference of -15,870, significant at .000 (** p <.01). In theoretical terms, to establish the basic definitions of the research is that they favor the development of pedagogical practices in the classroom with support of Virtual Learning Environments. This research has been based on the contributions of the authors: Hernández, R. and others (2003), Marquès P. (2010), Orantes (1980), Herrera (2006), Olguín (2010), Asencio (2008).
Acceso abierto
Influencia del software educativo Geogebra en el aprendizaje de las cónicas en los estudiantes de 10º de la Intitucion Educativa Simón Araujo. Año 2014
(Universidad Privada Norbert Wiener, 2017-09-28) Ruiz Medina, Carlos Antonio; Gómez Mongua, Pedro Jesús; Alzamora de los Godos Urcia, Luis Alex
The present research is centered in the determination of the effect of the use of the GeoGebra dynamic software in the assimilation of concepts of conics with students of the tenth grade of secondary education of the Institution Educative Simón Araujo. With the purpose of determining whether or not there is influence in the learning, of the conic sections, with the use of GeoGebra software, a diagnosis was made through the application of a pre-test and post-test. For this purpose, a group of 23 students, randomly selected from a universe of 140 students, was used to implement class environments with GeoGebra and a control group of 23 students with which classes were developed as they were working in a traditional way. The work was done during the first quarter of the year 2014, in which classroom environments were implemented that included activities with GeoGebra software to develop conic concepts. We worked as follows: Introduction to the knowledge and management of software GeoGebra, construction and identification of elements and characteristics of conics using GeoGebra, analytical deduction of concept of conics and their properties. The analysis of the results obtained by the students of the experimental group in the entrance and exit tests in each competition were found significant differences (p <0.05) in favor of the results in the exit test. This is because when using class environments with GeoGebra dynamic software, students can manipulate shapes, deform them, and they maintain the properties that define them, allowing them to infer, experiment, conjecture, discover and generally improve the acquisition of concepts and important results of mathematics.
Acceso abierto
Influencia del software Winplot sobre el pensamiento variacional en estudiantes de grado décimo de la Institución Educativa José María Carbonell en el municipio de San Antonio (Tolima), 2016
(Universidad Privada Norbert Wiener, 2018-05-11) Tovar Perdomo, Javier Enrique; Santodomingo Saurith, Carlos Mario; Pérez Mamani, Rubens Houson
The present research was entitled "Influence of Winplot software on the variational thinking in tenth grade students of the educational institution José MaríaCarbonell in the municipality of San Antonio (Tolima), 2016" aimed to determine the influence of Winplot software on thinking Variation in IE tenth grade students José MaríaCarbonell of the municipality of San Antonio (Tolima); Was based on an applied type study with experimental design. The PROBLEM was studied. At what level does the Winplot software influence on the variational thinking in 10th grade students of the I.E. José MaríaCarbonell of the municipality of San Antonio (Tolima), 2016? This research was carried out in order to determine the influence of winplot software on variational thinking. For this research we worked with a sample of 70 students between 14 and 17. Of the sample indicated, 35 students were part of the control group and the other 35 were part of the experimental group. In the first test that was applied to the experimental group there were a total of 57 correctly answered questions. In the second test, the number increased to 141. After applying the pre-test and the posttest to both groups, it was concluded that the hypothesis proposed for this thesis was accepted since the expected results were obtained In the second test.
Acceso abierto
Los juegos didácticos y su influencia en el pensamiento lógico matemático en niños de preescolar de la Institución Educativa el Jardín de Ibagué – 2015
(Universidad Privada Norbert Wiener, 2016) Arias Tovar, Claudia Milena; García Mendoza, Lisandro; García Huamantumba, Camilo Fermín
This research had as main objective, to determine how educational games influence the mathematical logical thinking in preschoolers Technical Educational Institution Garden Ibague - 2015; also it aims to provide teachers at this level, different alternatives in the use of educational games, so that the formulation of plans and encourage innovative teaching strategies and foster meaningful learning. The population is 60 preschool grade students of the Technical Educational Institution Garden of Ibague, with similar socioeconomic characteristics. The sample is census, due to easy access to students and to the fact that the amount of research subjects is manageable. It is an applied research and its level is explanatory. The design of the research is experimental, using an observation instrument designed by the researchers, which was applied to the control and experimental group. Once we collected the data, hypothesis testing was performed using the statistical test Mann - Whitney, with which it was concluded that educational games actually positively influence the development of mathematical logical thinking.
Acceso abierto
Mapas mentales como propuesta didactica para la enseñanza de los numeros fraccionarios en el grado cuarto de basica en la Institucion Educativa Jorge Eliecer Gaitan de Ibague
(Universidad Privada Norbert Wiener, 2018-04-17) Moncaleano Ospina, Ilse Tahiza; Valbuena Pedreros, Nohemí; Pizarro Arancibia, Lily Marisol
Conceptual maps have recently acquired great importance to achieve effectiveness in learning. Thus, the objective of this research is to know the impact that the use of mathematics has on the teaching of mathematics, comparing the traditional model with the cognitive model given to the use of the tool. Supported in the study of Buzan in his book mental maps and seeking to develop the mathematical competencies established in the basic standards of competencies in five dimensions that are: formulation and resolution of problems, modeling, communication, logical reasoning and formula, compare and I exercise procedures and algorithms. In the description of the problematic reality is that the Educational Institution Jorge Eliecer Gaitán in recent years has low results in the area of mathematics. In this sense, the methodology used in this work is a non-probabilistic design of an intentional or convenience type, with a simple random sampling for the 74 students of 4th grade of primary school. Moreover, it seeks to identify influences the strategy of mental maps in the learning of fractional numbers, validating by means of the test T student. The results show that the ordered programming of mental maps allows the development of other proposed activities with greater solidification of mathematical competences within the framework of solving problems; the activities involved in this research were workshops and a knowledge-type test.
Acceso abierto
Programa JCLIC y el pensamiento crítico y lógico matemático en niños y niñas de grado primero de la Institución Educativa Distrital República de México, Bogotá 2015
(Universidad Privada Norbert Wiener, 2016) Calle Misas, Angela María; Albarrán Gil, Jorge Luis
The present research refers to the use of the JClic Program and to the critical and logical-mathematical thinking carried out students of the first degree of the Educational Institution District Republic of Mexico, Bogota 2,015 It was determined that the use of the JClic program has a correlation directly high and significant with the level of development of critical thinking and mathematical logic, evidencing that greater use of the JClic program by the first grade students of the educational institution I.E.D. Republic of Mexico, the higher the level of development of critical thinking and logical mathematics. In addition, according to the descriptive information of the data, it was observed that, in the majority of the obtained scores, either the maximum scores in both instruments are obtained, or the scores obtained in the mathematical logical thinking or for the critical mathematical thinking are greater Scores obtained in the use of the JClic program. The purpose of this study was to evaluate the correlation between the two variables: the development of critical thinking and mathematical logic and the impact of the JClic program as a favorable tool in the construction of knowledge. A non-experimental design was used because the variables were not manipulated and only the phenomena were observed in their natural environment and then analyzed. It is transectional or transverse because it allowed to observe the variables in a determined time.
Acceso abierto
El software MATLAB en el rendimiento académico de los estudiantes de Cálculo II de tercer ciclo de la EAP de Ingenierías de la Universidad Privada Norbert Wiener - 2018
(Universidad Privada Norbert Wiener, 2019-06-12) Delgado Cotrina, Gwendolyn Aurora; Carbonell Paredes, Helmer Angélica
The investigation entitled “The MATLAB software in the academic performance of students of the Calculus II – third cycle – EAP Engineering at Norbert Wiener Private University- 2018” was designed with the aim to establish how the MATLAB software influences on the academic performance of the undergraduate students of Calculus II along the academic term 2018-II. This allowed us to pose the following hypothesis: “The use of the mathematical software influences positively on the academic performance of the undergraduate students of Calculus II EAP- Engineering at Norbert Wiener Private University – 2018”. This hypothesis was proven true as per the results obtained. This is a semi experimental quantitative applied research. The sample was the Calculus II students, morning and evening schedules. Having 52 students in each schedule. The sample was divided in two groups. The control group and the experimental group. The evaluation test was applied twice - the pre-test and the post-test- to both groups, which allowed us to measure the academic performance in each one of the students. Through the obtained results it was proven that the use of the MATLAB software does influence positively on the academic performance of the Calculus II undergraduate students – third cycle – engineering school at Norbert Wiener Private university.
Acceso abierto
Uso de la herramienta Geogebra y su influencia en la comprensión de la construcción del triángulo de Sierpinski en estudiantes de 8° del Instituto Técnico Industrial Pascual Bravo, Medellín 2016
(Universidad Privada Norbert Wiener, 2017) Cano Lopera, Lina Janeth; Giraldo Duque, Diana Alejandra; Rivera Arellano, Edith Gissela
The main objective of this research is to determine in which measure the use of the GeoGebra tool affects the comprehension of the characteristics of the construction of Sierpinski's Triangle. The research matches a pre-experimental design within the quantitative explicative design, of applicative type; a non probabilistic sample of 40 8th grade students, taken from a populace of 123 students of the Instituto Técnico Industrial Pascual Bravo on Medellín on year 2016. For the use of GeoGebra, 9 sessions of 3 hours each took place and the data were gathered through a standardized test under the model based on evidences, a tool that allowed the recollection of the data before and after (pre and post test) the use of GeoGebra and was validated by 3 experts. The used method was the Kuder-Richarson 20 test, where the reliability of the tool (test), thrown the high value of 0,68401464. The Wilson statistic was used, which thrown the value of 19,5 for a signification of 0,05, concluding that the use of the GeoGebra intervention shows that it had a significant influence in the comprehension of the characteristics of Sierpinski's Triangle while comparing the group before and after its use. The results were significant for the comprehension of the characteristics of auto similarity (4,5), zero area and infinite perimeters of Sierpinski's Triangle (14,5), however for the fractal dimension characteristic it can't be concluded that it was significant, as seen in the test's results.
Acceso abierto
Uso de la plataforma Moodle para el desarrollo de competencias matemáticas del pensamiento espacial y sistema geométrico con estudiantes de preescolar y primero de la institución educativa San José de las Cuchillas sede el Carmín 2016
(Universidad Privada Norbert Wiener, 2017-08-24) Alvarez Tabares, Dora Luz; Garzón Gallego, Lina Marcela; Meza Balvin, Sandra Jeannet
This research entitled moodle platform and the development of mathematical skills in spatial thinking and geometric system with preschool students and fifth of the school San José De Las Cuchillas sede Carmín, was developed With the objective of verifying the effectiveness of the use Moodle platform in the development of mathematical skills in spatial thinking and geometric system of preschool students and fifth school San José De Las Cuchillas sede Carmín of Rionegro. By which a type study was designed quasi-experimental, descriptive and mixed approach, with a population of 34 students between preschool grade with 18 students and fifth grade with 16 students, because the research was conducted within the curriculum the sample was equal to the population, was divided randomly into two groups of equal numbers of students, the control group and the experimental, taking into account the inclusion criteria. The development of research allowed to test hypotheses and left main conclusion using the moodle platform is effective to the development of mathematical skills of students.
Acceso abierto
El uso del Blended Learning y el desarrollo del pensamiento matemático en los estudiantes de 11° grado del Colegio Técnico Industrial José Elías Puyana, Colombia (2015)
(Universidad Privada Norbert Wiener, 2017-09-15) Córdoba Buitrago, Yolvi Adriana; Méndez Toledo, Heimer Ali
The present research called "Blended learning and the development of mathematical thinking in the 11th grade of the José Elias Puyana Industrial Technical College, Colombia (2015), aimed to determine the relationship between blended learning from its pedagogical and technological application and The mathematical thinking analyzed from the mathematical communication, mathematical reasoning and problem solving in a group of 32 students of the mentioned institution. We worked with the whole population because it is small, it is a non-probabilistic sampling, the study carried out is a basic research of descriptive correlational type, we wanted to establish how the two variables are related in a given moment, through a survey that Uses the Likert scale with 30 items that evaluates the blended learning variable and 21 items that measured the mathematical thinking variable from its dimensions. The survey was validated by three experts and the reliability of the instrument was estimated Coefficient V of Aiken applying a pilot test To 15 respondents and yielding a result of 0.901 which indicates that the reliability was very high. After the analysis of data, it can be affirmed that there is a positive and significant relationship between blended learning and mathematical thinking in 11th grade students at the José Elias Puyana Industrial Technical College in Floridablanca Santander by 2015, as demonstrated by the coefficient of Rho Spearman correlation equivalent to 0.714 with a value of p = 0.000.
Acceso abierto
Uso del calendario matemático como material didáctico para fortalecer la resolución de problemas geométricos en estudiantes de cuarto grado de primaria de la institución educativa reina de la paz, Floridablanca, Santander, 2018
(Universidad Privada Norbert Wiener, 2019-11-20) Tristancho Arguello, Claudia Johanna; Tristancho Arguello, Luz Genny; Venegas Mejía, Valia Luz
The results of a colombian internal evaluation, Prueba Saber, show the advances and difficulties that the students of the Reina de la Paz School have in the different competences and mathematical components; these results allow to design improvement alternatives in the mathematics subject, specifically in the resolution of geometric problems where the difficulties in fifth grade students have reoccurred. Due to this, the use of the Mathematical Calendar with the problem solving approach of the colombian project Colombia Aprendiendo was implemented, this with the objective to determine the extent to which the use of the Calendario Matemático (CalMat) as didactic material strengthens the resolution of geometric problems in fourth grade students of the educational institution Reina de la Paz (Floridablanca, Santander). The experimental quantitative research with explanatory scope measures and explains the effect of two treatments (traditional and CalMat) on the learning of geometry. The experimental design was adjusted to the qualities of a pure experiment consisting of a one-way treatment structure and a completely randomized design structure. The number of replicas used per treatment under the parameters: error type 1 (α = 0,5),sensitivity of the hypothesistest (1-β) = 0,9, significant difference between scores δ = 15 and standard deviation σ = 12 was approximately 10. After analyzing the data collected by means of Parametric ANOVA and Non-parametric ANOVA, the general hypothesis is accepted under a significance level of 0.05: "The use of the Mathematical Calendar as teaching material strengthens the resolution of geometric problems in fourth grade students of primary the educational institution Reina de la Paz of Floridablanca, Santander, in 2018”.
Acceso abierto
Uso didáctico de los dispositivos móviles y su influencia en el aprendizaje de las matemáticas en el grado 11º de la institución educativa tricentenario del municipio de Medellín – Colombia, año 2015
(Universidad Privada Norbert Wiener, 2017) Ayala Audiverth, Willie; Renteria Palacios, Luz Milena; Meza Balvin, Sandra Jeannet
The purpose of this research was to determine the influence didactic use of mobile devices in learning area mathematics student’s 11th grade of the school tercentenary of the municipality of Medellin - Colombia in 2015. It is a research applied type, of pre experimental design, with a quantitative approach. The techniques and instruments used for data collection for this research were questionnaire and personal observation –directly, sample size group with which he worked was 70 high school students; and the Wilcoxon test was used for the contrast of the hypotheses. In this study, it was concluded from the results the educational use of mobile devices influenced learning area mathematics student’s 11th grade of the school tercentenary of the municipality of Medellin - Colombia in 2015 (value of Z = - 6,950 and value of p = 0,000), showing improvements in learning processes of concepts, application concept and attitudinal part.
Acceso abierto
Utilización de la hoja de cálculo excel en el rendimiento académico del área de matemáticas en estudiantes del grado noveno, Institución Educativa Juvenil Nuevo Futuro; Medellin-2014
(Universidad Privada Norbert Wiener, 2016) Perez Carmona, Fredy De Jesus; Rivera Arellano, Edith Gissela
The purpose of this research is to determine if the use of the Excel spreadsheet influences the academic performance of the mathematics area of the ninth grade students of the Nuevo Futuro Juvenile Educational Institution; Medellín-2014. It is an investigation of explanatory type, pre-experimental design, with pre-test / posttest, with a single group. This population is composed of 67 students and the sample is census. In the data collection a test instrument was used, standardized, validated by expert judgment and with a high reliability. In the obtained results it was verified that, the academic performance of the mathematics area, improved after the treatment was applied. In addition, it was evidenced that the numerical-variational and geometric-metric dimensions are the most difficult and easiest to learn, respectively, for grade level students. It is concluded, therefore, that the area of mathematics improves its academic performance by 76.12%, the dimension of the numerical-variational area improves the academic performance by 70.78%, the dimension of the geometric-metric area improves the Academic performance by 86.05% and the dimension of the random area by 80.01%.