scholarly journals LEARNING TRAJECTORY OF QUADRATIC INEQUALITY

2018 ◽  
Vol 2 (1) ◽  
pp. 12
Author(s):  
Kimura Patar Tamba ◽  
Melda Jaya Saragih ◽  
Tanti Listiani
Keyword(s):  
Learning Process ◽  
Design Research ◽  
Mathematical Thinking ◽  
Mathematics Learning ◽  
Learning Activities ◽  
Learning Goals ◽  
Learning Trajectory ◽  
Learning Trajectories ◽  
Quadratic Inequality ◽  
Trajectory Learning

<p>A learning trajectory offers a description of key aspects in planning mathematics learning. It also helps teachers follow and interpret students’ mathematical thinking, so that learning can be developed in accordance with the characteristics of students, and even become a tool for teachers to develop curriculum. There are three main components of learning trajectory: learning goals, learning activities, and hypothetical learning processes. In this article, we constructed a learning trajectory of the quadratic inequality. This qualitative study used didactical design research with 105 grade 10 students as the participants. In the prospective analysis step, didactic design, learning obstacle, and quadratic inequality system were analyzed. Based on the results of this analysis, we constructed hypothetical learning trajectories in the form of didactical design. Then, hyphothetical learning trajectories were implemented in the learning process. Student’s responses were analyzed qualitatively. Results of this analysis were used to revise the learning trajectory in order to obtain alternative trajectory learning outcomes of theoretical and empirical analysis. Finally, this article offers an alternative learning trajectory of quadratic inequalities that are different from the existing learning trajectories presented in the current textbook. The learning trajectory that is offered is the learning quadratic inequality which starts from the function approach.</p><p> <strong>BAHASA INDONESIA ABSTRACT: </strong>Learning trajectory (LT) menawarkan sebuah deskripsi akan aspek kunci dalam perencanaan pembelajaran matematika. LT juga membantu guru belajar dalam mengikuti dan menginterpretasi cara berpikir matematisnya siswa, sehingga pembelajaran dapat dikembangkan sesuai dengan karateristik siswa, bahkan menjadi alat bagi guru untuk mengembangkan kurikulum.  Ada tiga komponen utama dari learning trajectory, yaitu: tujuan pembelajaran (learning goals), kegiatan pembelajaran (learning activities) dan hipotesis proses belajar siswa (hypothetical learning process). Dalam artikel ini akan dikonstruksi sebuah LT pertidaksamaan kuadrat. Penelitian ini menggunakan pendekatan kualitatif dengan didactical design research. Adapun partisipan sebanyak 105 siswa kelas X. Pada awal penelitian ini, dilakukan analisis propektif yaitu analisis atas materi pertidaksamaan kuadrat, hambatan belajar dan tingkat berpikir siswa. Kemudian dari hasil analisis ini disusunlah Hipotetical Learning Trajectories yang berupa desain didaktis. Desain didaktis berdasarkan Hypotetical Learning Trajectories ini diimplementasikan dalam pembelajaran. Respon siswa dianalisis secara kualitatif. Hasil analisis ini digunakan untuk merevisi Learning Trajectory, sehingga diperoleh Learning Trajectory alternatif hasil analisis teoritik dan empirik. Akhirnya, artikel ini menawarkan sebuah alternatif learning trajectory pertidaksamaan kuadrat yang berbeda dengan learning trajectories yang ada pada buku pelajaran sekarang. Learning trajectory yang ditawarkan adalah pembelajaran pertidaksamaan yang dimulai dengan pendekatan fungsi. </p>

scholarly journals HYPOTHETICAL LEARNING TRAJECTORY PADA PEMBELAJARAN BILANGAN NEGATIF BERDASARKAN TEORI SITUASI DIDAKTIS DI SEKOLAH MENENGAH

2018 ◽  
Vol 6 (1) ◽  
pp. 13-24 ◽  
Author(s):  
Nyiayu Fahriza Fuadiah
Keyword(s):  
Learning Process ◽  
Teaching And Learning ◽  
Design Research ◽  
Lesson Plan ◽  
Mathematics Learning ◽  
Learning Goals ◽  
Learning Trajectory ◽  
Mathematical Activity ◽  
Negative Numbers ◽  
Hypothetical Learning Trajectory

Penelitian ini bertujuan untuk mendesain Hypothetical Learning Trajectory (HLT) pada pembelajaran bilangan negatif sebagai hasil dari tahap pertama Didactical Design Research yaitu Analisis Prospektif. HLT ini merupakan tindak lanjut dari hasil identifikasi Learning Obstacle yang yang dilakukan peneliti dalam pembelajaran bilangan negatif yang terintegrasi dalam materi Bilangan Bulat di kelas 7 sekolah menengah pertama. Observasi mendalam terhadap proses belajar mengajar di kelas yang diamati peneliti memperlihatkan kesulitan guru dalam menanamkan konsep bilangan negatif dan operasi bilangan yang melibatkan bilangan negatif serta beberapa kesalahan konstruksi konsep yang dialami oleh siswa. Istilah HLT merujuk pada rencana pembelajaran berdasarkan antisipasi belajar siswa yang mungkin dicapai dalam proses pembelajaran yang didasari pada tujuan pembelajaran matematika yang diharapkan pada siswa, pengetahuan, dan perkiraan tingkat pemahaman siswa, serta pilihan aktivitas matematika secara berurut. HLT ini disusun berdasarkan analisis terhadap Learning Obstacle, tahap berpikir siswa, dan analisis terhadap kurikulum dengan tetap berpijak pada konsep materi yang harus dipahami siswa.This research aims to design Hypothetical Learning Trajectory (HLT) on learning of negative numbers as a result of the first stage on Didactical Design Research specifically in Prospective Analysis. This HLT is a follow up of the results of the identification of the Learning Obstacle conducted by researcher in learning negative numbers that integrated in the material Integer in the 7th grade secondary school. From the observations conducted by researcher on the teaching and learning process in the classroom showed the difficulties of teachers in embedding the concept of negative numbers and arithmetic operations involving negative numbers and several construction errors of concepts that experienced by the students. Term of HLT refers to a lesson plan based on the anticipation of student learning possibly achievable in the learning process which is based on mathematics learning goals expected on students, knowledge, estimates of the level of students understanding, and the selection of mathematical activity sequentially. This HLT is compiled based on an analysis of the Learning Obstacle, level of students thinking, and analysis of the curriculum that standing on the concept that must be understood by the students.

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 BAHAN AJAR PADA MATERI GARIS SINGGUNG LINGKARAN DENGAN PENDEKATAN SAINTIFIK UNTUK SISWA SMP

2018 ◽  
Vol 3 (1) ◽  
pp. 63-80 ◽  
Author(s):  
Sowanto Sowanto
Keyword(s):  
High School Students ◽  
Junior High School ◽  
Learning Process ◽  
Design Research ◽  
Learning Activities ◽  
Learning Trajectory ◽  
Preliminary Design ◽  
Teaching Materials ◽  
School Students ◽  
Scientific Approach

This research is motivated by the lack of teaching materials on tangent topic to the circle that is able to facilitate junior high school students through a scientific approach. This research produced teaching materials so-called students' worksheets that can facilitate students. The research used the design research which includes: (1) preliminary design, in this phase the researchers conducted a theory study which followed up by making a Hypothetical Learning Trajectory (HLT); (2) experiment, in this phase, the existing design is tested to the students to investigate the learning process that related to the process of developing students' thinking in situations and learning atmosphere that formed from HLT; (3) retrospective analysis, in this phase, the researchers compare the HLT with the actual student learning process. The results show that the teaching materials that have been developed by considering obstacle learning and preliminary studies are able to facilitate students as a source of support for learning activities.

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)

scholarly journals PEMANFAATAN KONTRIBUSI SISWA SEBAGAI ALAT TRANSISI MENUJU PEMAHAMAN KONSEP OPERASI PECAHAN

2018 ◽  
Vol 9 (1) ◽  
Author(s):  
Gregorius Sebo Bito
Keyword(s):  
Retrospective Analysis ◽  
Learning Process ◽  
Design Research ◽  
Teaching Experiment ◽  
Learning Trajectory ◽  
Fourth Grade Students ◽  
Hypothetical Learning Trajectory ◽  
Three Stages ◽  
Actual Learning ◽  
Is Design

The purpose of this study was to describes the use of student’s contribution as a transition tool at each level of learning the fraction operation concept. This study involved fourth grade students of an elementary school in Ngada East Nusa Tenggara. The type of this research is Design Research with three stages, namely: initial design, teaching experiment and retrospective analysis. This research begins conduct a hypothetical learning trajectory (HLT) of fraction operations concept. The HLT has been tested before the actual learning process (ALT). The results of the retrospective analysis obtained an overview of the Actual Learning Trajectory (ALT) show that the use of various student’s contribution at each level of learning can lead to understanding the fraction operation concept.

scholarly journals DESIGN OF LEARNING MATERIALS ON CIRCLE BASED ON MATHEMATICAL COMMUNICATION

2019 ◽  
Vol 8 (1) ◽  
pp. 87
Author(s):  
Cita Dwi Rosita ◽  
Tri Nopriana ◽  
Isna Silvia
Keyword(s):  
Communication Skills ◽  
Design Research ◽  
Mathematics Learning ◽  
Research Result ◽  
Material Design ◽  
Learning Trajectory ◽  
Learning Material ◽  
Mathematical Communication ◽  
Learning Materials ◽  
Two Stages

Mathematical communication skills is an important role in mathematics learning. However, the importance of mathematical communication skills has not been fully realized in learning, especially circle material. Design a learning material based on mathematical communication is one way to develop this ability.  The preliminary study produced the findings of an epistemological learning obstacle so that students' mathematical communication skills were still in the low category. This study aimed to analyze learning obstacle and designing learning materials based on the material mathematical communication circle. This study is design research that contained two stages of Didactical Design Research (DDR), didactic situation and metapedadidactional stage. Research result obtained are students difficulties in relating the material defining elements of the circle with their own language, identifying circle elements that were known and explaining through pictures, calculating the circumference and distance of circular objects based on problems, calculating the surface area of circular objects based on the problems, and rearrange the formula which states the relationship of circle elements. To solve that learning obstacle, we recommend some learning trajectory in a circle that useful for teachers. This design of learning material is valid and practical to implement in the classroom.

Designing The Hypothetical Learning Trajectory (HLT) for Sinus Using Context of Scout Tent

2020 ◽  
Vol 1 (1) ◽  
pp. 31-40 ◽  
Author(s):  
Dinda Mahardika ◽  
Ratu Ilma Indra Putri
Keyword(s):  
Design Research ◽  
Mathematics Learning ◽  
Rule Learning ◽  
Learning Trajectory ◽  
Study Phase ◽  
Literature Study ◽  
Mathematical Concepts ◽  
Classroom Experiment ◽  
Preliminary Study ◽  
Modern Mathematics

One of the problems in modern mathematics learning is mathematical concepts presented by teachers to students such as machines. So, the concept is used by students as finished products without knowing the origin and how to reconstruct them. The effort that can be made by the teacher in overcoming this is by designing learning wherever possible starting with presenting realistic problems to arrive at an abstract idea. In this article we will discuss the design of sine rule learning in the context of scout tents, which is a type of design research. Design research has three cycles, namely preliminary design, classroom experiment, and retrospective analysis. In this article only the preliminary study phase will be discussed, which includes literature study activities, curriculum analysis, and the design early prototype. An HLT (Hypotetical Learning Trajectory) has been produced which deals with sine rules that use the context of scout tents.

scholarly journals Changes in Teachers’ Discourse About Students in a Professional Development on Learning Trajectories

2017 ◽  
Vol 54 (3) ◽  
pp. 568-604 ◽  
Author(s):  
P. Holt Wilson ◽  
Paola Sztajn ◽  
Cyndi Edgington ◽  
Jared Webb ◽  
Marrielle Myers
Keyword(s):  
Professional Development ◽  
Mixed Methods ◽  
Student Performance ◽  
Mathematics Learning ◽  
Development Program ◽  
Learning Trajectory ◽  
Learning Trajectories ◽  
Elementary Grade ◽  
Over Time ◽  
Discursive Patterns

This study examines teachers’ discussions in a professional development setting to understand the ways in which learning a mathematics learning trajectory may change aspects of their discourse about students as learners. Using mixed methods, we bring together two theoretical frames that use a Vygotskian perspective on learning to analyze professional discussions among 22 elementary-grade teachers participating in a yearlong, 60-hour mathematics professional development program. Results indicate that over time, some discursive patterns for explaining students’ academic performance changed to incorporate the trajectory, while others remained unaffected. Whereas this change transformed one of the patterns in a way that led to new explanations for student performance, another pattern changed only slightly and was still used to express the same explanations for performance.

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