scholarly journals Un Acercamiento A La Relación Pitagórica A Través Del Cálculo De Ternas

2018 ◽  
Vol 14 (6) ◽  
pp. 58
Author(s):  
Carlos Rondero Guerrero ◽  
Marcos Campos Nava ◽  
Agustín Alfredo Torres Rodríguez ◽  
Juan Alberto Acosta Hernández

The Pythagorean Theorem and more formally the Pythagorean Relationship (PR), is one of the most well-known and used results in the context of school mathematics, given that it is an axis of conceptual articulation between different areas of Mathematics. However, in the school context it is common for a Didactic Reductionism to be presented, only enunciating it and presenting the algebraic expression that relates the squares of the sides of a right triangle, leaving aside its great historical and epistemological significance. In view of this problem, this documentary research aims to design an alternative proposal to broaden the understanding of the Pythagorean Relationship, which is based on the calculation of Pythagorean Ternas. Three different methods are proposed to generate positive integers, that satisfy the Pythagorean Theorem and suggest questions that can guide learning activities to promote the understanding of some important elements within Mathematics, particularly in reference to the identification of numerical patterns.

2019 ◽  
Vol 4 (3) ◽  
pp. 17-19
Author(s):  
Edy Mastoni

Research Highlights The study proposed two focus studies and results indicated there is a conformity between Brain Based Learning (BBL) and students' intrapersonal intelligence toward characteristics of junior high school mathematics learning. Implementation of Brain Based Learning (BBL) and intrapersonal intelligence in junior high school mathematics learning can improve student’s learning outcomes.   Research Objectives This research aims to knowing activities of junior high school mathematics learning and to knowing conformity of characteristics between Brain Based Learning (BBL) and intrapersonal intelligence with junior high school mathematics learning. BBL as a learning strategies and intrapersonal intelligence as an internal factors of students must be the main consideration in learning activities, including in this case mathematics learning. Learning is more directed at construction than instruction, which has implications for the role of teachers and students (Reigeluth and Carr-Chellman, 2009). Learning strategies concept is a various types of plans used by the teacher to achieve goals (Silver et al., 2012). In simple terms, this view states that learning strategies are ways to do something in achieving goals. Learning mathematics is learning about the concepts and structure of mathematics and looking for relationships between the two on the material being studied (Bruner, 2009). In the learning activities, learning materials must be adapted to the abilities and cognitive structures of students. Learning material must be related to the concepts that are already owned so that new ideas can be fully absorbed by students (Ausubel, 2012). Learning activities must be gradual, sequential and always based on past learning experiences.   Methodology This type of research is qualitative descriptive. The approach used is qualitative with descriptive methods and literature studies. Data collection uses documentation studies, observations, and interviews with teachers and students. Data collection was conducted in junior high school of SMP Assahil Lampung Timur in the 2018/2019 academic year. The mathematics teachers and students were included in this study as a respondents. In this study the data analysis used was quantitative descriptive and qualitative descriptive analysis. Quantitative descriptive analysis is used to present and analyze data relating to mathematics learning outcomes over the past three years. Qualitative descriptive analysis is used to interpret and analyze data regarding the learning process of mathematics that has taken place.   Results The study indicate that mathematics teachers have only used expository learning strategies in learning activities. The expository learning strategy is a form of teacher-centered learning approach. Mathematical learning outcomes are not satisfactory. The Mathematics learning is a learning process that involves active students building mathematical knowledge (Cobb, 2013). In mathematics learning there is a process of developing students' creativity to improve their abilities and beliefs in building knowledge and mastering good mathematics subject matter. The Characteristics of Brain Based Learning (BBL) emphasizes students to play an active role in building the concepts learned (Ulger, 2018). The steps in the BBL learning strategy include creating a learning environment that challenges students' thinking skills (regulated immersion), creates a relaxed learning environment, and creates actual and meaningful learning situations for students (active processing). Intrapersonal intelligence is self-knowledge as intelligence that involves self-awareness or self-sensitivity, thought processes, realizing changes that occur in oneself, involving skills of cooperation and communication both verbally and nonverbally (Alder, 2001). The characteristics of intrapersonal intelligence consist of three main aspects that can be used as benchmarks, namely recognizing oneself, knowing one's own desires, and knowing what is necessary for oneself.   Findings The results of data analysis, it was found that the learning activities that had taken place so far only used expository learning strategies. The teacher does not apply learning strategies that are in accordance with the internal factors of students in learning mathematics. The literature review show that there is a match between the characteristics of junior high school mathematics material, the characteristics of BBL learning strategies and the characteristics of intrapersonal intelligence. Therefore, the implementation of BBL learning strategies and intrapersonal intelligence in junior high school mathematics learning is very well done to improve student learning outcomes.   Acknowledgement This study was supported by Universitas Negeri Jakarta and SMP Assahil Lampung Timur, for which thanks to 1) Doctoral Program in Educational Technology, Postgraduate Program at Universitas Negeri Jakarta; 2) SMP Assahil Lampung Timur; 3) Prof. Dr. M. Syarif Sumantri, M.Pd. as the promoter and Prof. Dr. Nurdin Ibrahim, M.Pd. as the co. promoter who has provided guidance to the author.    


2018 ◽  
Vol 111 (5) ◽  
pp. 400 ◽  
Author(s):  
Arsalan Wares

One of the most well-known theorems in mathematics, the Pythagorean theorem and its proof are a standard part of the school mathematics curriculum. The theorem is named for Pythagoras, a Greek mathematician and philosopher, born around 570 BCE. More than 400 proofs of the theorem exist, and this number continues to grow (Maor 2007). A future American president, James Garfield, generated an original proof five years before being elected; another proof is credited to twelve-year-old Einstein.


2017 ◽  
Vol 53 (3) ◽  
pp. 365-408 ◽  
Author(s):  
Ruth van Veelen ◽  
Peter J. C. Sleegers ◽  
Maaike D. Endedijk

Purpose: School leadership is fundamental in efforts to successfully implement school reform and improve student and teacher learning. Although there is an abundant amount of research on school leaders’ formal training, assessment, and practice, little is known about their informal professional learning. In other words, how do school leaders learn at the workplace? To answer this question, we took an interactionist approach and argued that school leadership learning is based on the interplay between the school environment and the person. Specifically, we investigated the effect of school context (learning climate, social support), task (task variation), and the personal factor self-efficacy on both individual (reflection and career awareness) and social (asking for feedback and challenging groupthink) learning activities. Method: A questionnaire was administered among 1,150 school leaders in Dutch secondary education. Structural equation modeling was used to test the proposed relationships between our model variables. Findings: Self-efficacy positively predicted all four learning activities. Task variation positively predicted asking for feedback and reflection. Learning climate positively predicted asking for feedback, reflection, and career awareness. Interestingly, the effect of social support was twofold: It positively predicted social learning, but it negatively predicted individual learning. Finally, self-efficacy was an important mediator in the relationship between school context and professional learning. Conclusions: This study demonstrates how personal, task, and school context factors affect school leaders’ professional learning. These insights help develop tools and conditions for leaders to reflect and discuss on their practice, and to set an example for lifelong learning in schools.


2018 ◽  
Vol 2 (3) ◽  
pp. 266
Author(s):  
Ni made Sri mulyani ◽  
I made Suarjana ◽  
Ndara Tanggu renda

This study aims to describe the abilities and difficulties who experienced by students on solving the problem of addition and reduction of integer class IV. The research was held in XIV group which consist of three elementary schools, which is SD Negeri 1 Tukadmungga, SD Negeri 2 Tukadmungga, and SD Negeri 2 Pemaron. The number of population in Gugus XIV counted 67 students and used sample consist of 34 students or 50% the population joined from SD Negeri 1 Tukadmungga, SD Negeri 2 Tukadmungga, and SD Negeri 2 Pemaron. The data are collected using test methods, interviews, observations, and documentation. The results showed that teacher facilitated learning activities belong to proper kategory. Teachers present the lessons on interesting way so that the learning process is not boring. Discussion methods was used during the learning process to encourage students to ask and discuss so students can share their ideas.. Students experience difficulty solving problems between positive integers and negative integers in story form. Students experience difficulty because students understood the concept of integers contextually yet. It can be solved by using learning media and contextual emphasis on the concept of learning and observing student development using the results of evaluation at the end of class.


2016 ◽  
Vol 3 (3) ◽  
pp. 143-169 ◽  
Author(s):  
Scot McRobert Sutherland ◽  
Tobin F White

The development of the constraint-referenced analytics tool for monitoring algebra learning activities presented here came from the desire to firstly, take a more quantitative look at student responses in collaborative algebra activities, and secondly, to situate those activities in a more traditional introductory algebra setting focusing on procedural understanding. Procedural skill was analyzed by modeling the complexity of attempts to make equivalent transformations of algebraic expressions. The constraint-referenced analytics system uses log files of student inputs on a classroom network of handheld devices to measure success rate as students make attempts to replace one algebraic expression with another equivalent expression.  The analytics engine produced psychometrically verifiable results. Moving averages of student performance revealed that when students experienced a period of struggle and persisted in attempting similar transformations, an apparent conceptual shift led to subsequent success. Students also responded to periods of struggle by switching to familiar tasks or choosing non-participation.


1932 ◽  
Vol 25 (2) ◽  
pp. 84
Author(s):  
Norman Anning

The student who is preparing to discuss such a topic in mathematics club will find plenty of suggestions in F. C. Boon's Companion to Elementary School Mathematics, Longmans, Green and Co., 1924. Mention is made, as it is in any good textbook, of the bilateral symmetry of the coefficients of the expansion of (a+b)n where n is any positive integer. It is the purpose of this note to suggest that this fact is a member of a hierarchy of facts which an interested student would find easy to explore and to explain. The restriction of the exponent n to positive integers remains throughout.


2008 ◽  
Vol 14 (4) ◽  
pp. 202-207
Author(s):  
Jeong Oak Yun ◽  
Alfinio Flores

principles and standards for school mathematics advocates an experimentation approach to middle-grades geometry study (nctm 2000). Students are asked to explore and examine a variety of geometric shapes and discover their characteristics and properties using hands-on materials. They also create inductive arguments about the pythagorean relationship. This empirical approach to the pythagorean theorem, for example, will lay the foundation for analytical proofs.


2012 ◽  
Vol 20 ◽  
pp. 14 ◽  
Author(s):  
Motoko Akiba

Based on a statewide survey of professional learning activities among 577 middle school mathematics teachers in Missouri, this study examined two questions: 1) What professional learning activities do middle school math teachers participate in and how much time do they spend in these activities?, and 2) How are teacher qualifications and contextual characteristics associated with the amount of their professional learning activities? The study examined seven types of formal and informal professional learning activities: 1) professional development programs, 2) teacher collaboration, 3) university courses, 4) professional conferences, 5) mentoring/coaching, 6) informal communications, and 7) individual learning activities. The study found that middle school mathematics teachers spend the greatest amount of time involved in teacher collaboration, professional development programs, and individual learning activities. In addition, mathematics teachers in high-poverty and ethnically diverse districts tend to spend more time in formal learning activities such as professional development programs, teacher collaboration, and mentoring/coaching than do mathematics teachers in wealthier and less diverse districts. To promote a greater level of teachers’ participation in shared learning activities, it is important for district and school administrators to offer professional learning activities that meet mathematics teachers’ learning needs for understanding students’ mathematical knowledge and thinking.


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