scholarly journals Proposal Of a Hypothetical Learning Trajectory Line for The Assimilation of The Concept Of Height Of A Triangle By Using GeoGebra

2021 ◽  
Vol 12 ◽  
pp. 1-11
Author(s):  
Armando Morales Carballo ◽  
Angie Damián Mojica ◽  
Jessica Maldonado Morales
Keyword(s):  
Problem Solving ◽  
Learning Trajectory ◽  
Learning Trajectories ◽  
Methodological Basis ◽  
Visual Activity ◽  
Hypothetical Learning Trajectory ◽  
Technological Tool

A hypothetical learning trajectory line is described for the assimilation and fixation of the concept of height of a triangle for its treatment in pre-university. The theoretical and methodological basis is based on the processes of assimilation, learning trajectories, problem solving and the use of GeoGebra software. This work provides a didactic proposal aimed at the teacher, different from the classic presentation for the treatment of the concept of height, highlighting that the use of the software favors the processes of assimilation of this concept through the dynamic-visual activity, use of the geometric and numerical resource that this technological tool makes possible.

scholarly journals Acquiring the notion of learning hypotheses in mathematics teacher education

2018 ◽  
Vol 32 (61) ◽  
pp. 459-479
Author(s):  
Pedro Gómez ◽  
María C. Cañadas ◽  
María A. Suavita
Keyword(s):  
Teacher Education ◽  
Secondary School ◽  
Mathematics Teachers ◽  
Education Program ◽  
Teaching Practice ◽  
Teacher Education Program ◽  
Mathematics Teacher Education ◽  
Learning Trajectory ◽  
Learning Trajectories ◽  
Hypothetical Learning Trajectory

Abstract The notion of hypothetical learning trajectory has generated much interest among experts in mathematics education. It is proposed that this notion is a useful tool in teachers’ teaching practice and that it is necessary to prepare teachers in their capacity to formulate hypothetical learning trajectories about specific mathematics school topics. It is therefore also necessary to explore the learning processes that teachers undergo when learning this notion in their education. In this article, we introduce the notion of learning hypotheses as an adaptation of the idea of hypothetical learning trajectory (SIMON, 1995). We describe how the groups of secondary-school mathematics teachers that participated in a teacher education program understood and used this notion in order to determine the contribution of a set of tasks to a learning goal previously established. We found that the groups developed their knowledge of the notion of learning hypotheses and used it in a heterogeneous way, and that the education program was partly successful in its goal to make the groups of teachers learn and perceive the notion’s utility.

scholarly journals Kajian Hypothetical Learning Trajectories dalam Pembelajaran Matematika di Tingkat SMP

2020 ◽  
Vol 1 (1) ◽  
pp. 1-11
Author(s):  
Agnes Ivana Hendrik ◽  
Christine K Ekowati ◽  
Damianus D Samo
Keyword(s):  
Student Learning ◽  
Mathematics Learning ◽  
Student Thinking ◽  
Learning Activities ◽  
Learning Trajectory ◽  
Learning Trajectories ◽  
Hypothetical Learning Trajectory ◽  
Main Components ◽  
Learning Flow ◽  
Improve Student Learning

Mathematics learning in this era requires teachers to be able to develop learning models that pay attention to the characteristics of students, so it is important for teachers to know learning trajectory. This study aims to describe the conception of learning trajectory and hypothetical learning trajectory, as well as presenting the design of hypothetical learning trajectories in mathematics learning. Based on the theories studied, it is concluded that hypothetical learning trajectory is a learning design in the form of allegations on student learning activities based on initial understanding and characteristics of students to achieve higher understanding. HLT has three main components namely learning objectives, learning activities, and hypotheses of the learning process. HLT is used by teachers as a guide to predict and prepare learning flow designs that are appropriate to the stages of student thinking and can improve student learning outcomes. The findings of previous studies show that to design HLT in mathematics learning, educators need to consider student obstacle learning, a hierarchy of material, and learning support capacity, so that learning activities to be hypothesized are built based on these things. It is recommended that future researchers can use the existing HLT, and also develop HLT in other materials that have not been tested by further studying HLT and whatever affects it, research with different differences can be used.

scholarly journals Study of Hypothetical Learning Trajectories in Mathematics Learning

2020 ◽  
Vol 9 (3) ◽  
Author(s):  
Agnes Ivana Hendrik ◽  
Yuanda Oktrin Lay ◽  
Yohanes Sanca Nele Amuntoda
Keyword(s):  
Student Learning ◽  
Mathematics Learning ◽  
Student Thinking ◽  
Learning Activities ◽  
Learning Trajectory ◽  
Learning Trajectories ◽  
Hypothetical Learning Trajectory ◽  
Main Components ◽  
Learning Flow ◽  
Improve Student Learning

Mathematics learning in this era requires teachers to be able to develop learning models that pay attention to the characteristics of students, so it is important for teachers to know the learning trajectory. This study aims to describe the conception of learning trajectory and hypothetical learning trajectory, as well as presenting the design of hypothetical learning trajectories in mathematics learning. Based on the theories studied, it is concluded that a hypothetical learning trajectory is a learning design in the form of allegations on student learning activities based on initial understanding and characteristics of students to achieve higher understanding. HLT has three main components namely learning objectives, learning activities, and hypotheses of the learning process. HLT is used by teachers as a guide to predict and prepare learning flow designs that are appropriate to the stages of student thinking and can improve student learning outcomes. The findings of previous studies show that to design HLT in mathematics learning, educators need to consider student obstacle learning, a hierarchy of material, and learning support capacity, so that learning activities to be hypothesized are built based on these things.

scholarly journals THE CONTEXT OF ARCHIPELAGO TRADITIONAL CAKE TO EXPLORE STUDENTS’ UNDERSTANDING IN INTEGERS DIVISION CLASS VII

2019 ◽  
Vol 14 (1) ◽  
pp. 91-100 ◽  
Author(s):  
Elis Muslimah Nuraida ◽  
Ratu Ilma Indra Putri
Keyword(s):  
Junior High School ◽  
Design Research ◽  
Mathematics Learning ◽  
Learning Trajectory ◽  
Mathematics Problems ◽  
Learning Path ◽  
Starting Point ◽  
Hypothetical Learning Trajectory ◽  
Integer Division ◽  
Division Operation

This study aims to explore the students’ mathematical understanding in integer division operation through the context of archipelago traditional cakes in class VII. This research is related to the Indonesian Realistic Mathematics Approach (PMRI) as a learning approach used. The methodology used in this study is Design Research consisting of three stages: preliminary design, experimental design, and retrospective analysis. The study was conducted on VII grade students of Palembang 1 Junior High School. The learning path (Hypothetical Learning Trajectory) in design research plays an important role as a research design and instrument. The Hypothetical Learning Trajectory (HLT) was developed together with a series of activities using the context of archipelago traditional cakes such as: omelette roll, bakpia, milk pie, etc. The medium used in this study was the Students’ Activity Sheet. The results of this study indicate that exploration using the context of traditional archipelago cakes can help students understanding in multiplication and division of integers. The conclusion of this study is the use of archipelago traditional cakes as starting point in mathematics learning in integer division operation material helps the students to explore their understanding in solving mathematics problems.

scholarly journals Designing professional learning tasks for mathematics learning trajectories

2013 ◽  
Vol 7 (4) ◽  
pp. 135-143
Author(s):  
P. Holt Wilson ◽  
Paola Sztajn ◽  
Cyndi Edgington
Keyword(s):  
Elementary Teachers ◽  
Teacher Learning ◽  
Teacher Knowledge ◽  
Professional Learning ◽  
Mathematics Learning ◽  
Theoretical Perspective ◽  
Learning Task ◽  
Learning Trajectory ◽  
Learning Trajectories ◽  
Learning Tasks

In this paper, we present an emerging set of learning conjectures and design principles to be used in the development of professional learning tasks that support elementary teachers’ learning of mathematics learning trajectories. We outline our theoretical perspective on teacher knowledge of learning trajectories, review the literature concerning mathematics professional learning tasks, offer a set of initial conjectures about teacher learning of learning trajectories, and articulate a set of principles to guide the design of tasks. We conclude with an example of one learning trajectory professional learning task taken from our current research project.Diseño de tareas de aprendizaje profesional para trayectorias de aprendizaje de matemáticasEn este artículo, presentamos un conjunto emergente de conjeturas de aprendizaje y de principios de diseño para ser empleados en el desarrollo de tareas de aprendizaje profesional que apoyan el aprendizaje de trayectorias de aprendizaje de matemáticas de maestros de primaria. Describimos brevemente nuestra perspectiva teórica sobre el conocimiento del profesor acerca de trayectorias de aprendizaje; revisamos la literatura sobre tareas de aprendizaje profesional, presentamos un conjunto de conjeturas iniciales acerca del aprendizaje del profesor sobre trayectorias de aprendizaje; y articulamos un conjunto de principios para guiar el diseño de tareas. Concluimos con un ejemplo de una tarea de aprendizaje profesional que ha sido tomada de nuestro proyecto de investigación actual.Handle: http://hdl.handle.net/10481/24791Nº de citas en WOS (2017): 3 (Citas de 2º orden, 2)Nº de citas en SCOPUS (2017): 3 (Citas de 2º orden, 1)

From High School to Higher Education

2021 ◽  
Vol 12 (4) ◽  
pp. 36-51
Author(s):  
Francesco Maiorana
Keyword(s):  
Higher Education ◽  
High School ◽  
Computer Science ◽  
Curriculum Design ◽  
Research Effort ◽  
Learning Trajectory ◽  
Lifelong Education ◽  
Learning Trajectories ◽  
Loop Invariant ◽  
Key Concepts

The vision of introducing computing as a literacy taught from primary school to higher and lifelong education is producing a worldwide new curriculum design and adoption. A strong research effort has involved researchers and educators to find the best ways to prepare teachers and their students for computing with an emphasis on core computer science concepts. This paper, starting from a previously developed curriculum, aims to present and discuss learning trajectories for a first course on computing aiming to presenting key concepts first, such as functions and their use. This learning trajectory is compared with a second learning trajectory presenting loop and loop invariant first and a third one presenting variable first.

Sign in / Sign up

Export Citation Format

Share Document