Concept About Mathematics Learning Pdf

Mathematical understanding continues to be one of the major goals of mathematics education. However, what is meant by "mathematical understanding" is underspecified. How can we operationalize the idea of mathematical understanding in research? In this article, I propose particular specifications of the terms mathematical concept and mathematical conception so that they may serve as useful constructs for mathematics education research. I discuss the theoretical basis of the constructs, and I examine the usefulness of these constructs in research and instruction, challenges involved in their use, and ideas derived from our experience using them in research projects. Finally, I provide several examples of articulated mathematical concepts.

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... The use of the term Hypotetichal Learning Trajectory (HLT) was initiated and implemented in the process of mathematics learning by a mathematician, named Simon. Simon (2017) focused his attention on the ways teachers teach and present information to students how the flow of thinking about the concept of mathematics, as well as the creation of new experiences or problems that are designed to assist the processof better student understanding. The learning process and the level of thinking called HLT are somet ...

... The method used is the design research with an emphasis on the development of the HLT instrument. According to Simon (2017), HLT is defined by researchers as a goal to achieve meaningful learning according to the stage of thinking, a series of tasks to achieve goals, and predict how students think in understanding concepts by conducting retrospective analysis after learning activities. Bakker and van Eerde (2015) stated HLT design consists of three stages: the initial design, the experimental design, and the retrospective analysis. ...

... Hypothetical learning trajectory in mathematics learning bySimon (2017). ...

The relationship between spatial conceptions and students' spatial abilities is still rarely studied specifically, even though this is the basis for students to think in learning geometry. This paper aims to explore spatial abilities and the development of spatial ability theory, discusses the relationship between spatial conceptions in students' understanding, and how to develop HLT (Hypothetical Learning Trajectory)in transformation geometry learning. HLT design consists of three stages: initial design, experimental, and retrospective analysis. The results of HLT are then refined into LIT (Local Instructional Trajectory). Then this paper present the empirical results of the perceptions of twenty 9th grade students in one of Islamic private school in Kabupaten Kuningan, West Java, Indonesia, towards the corresponding geometric and math questions. Literature review analysis was used to analyze the retrieved articles. At the end of the paper, we explain and discuss how to apply mathematical conceptions in learning geometry. This research is expected to be a guidance for teachers to develop learning in accordance with the students' spatial thinking process in studying geometry.

... Concepts are the substance of mathematical knowledge (Burhanzade & Aygör, 2014;Simon, 2017). Students can make sense of mathematics only if they understand its concepts and their meanings or interpretations. ...

... Students can make sense of mathematics only if they understand its concepts and their meanings or interpretations. A mathematical concept is knowledge of the mathematical necessity of a particular mathematical relationship (Simon, 2017;Smith et al., 2018;Sukardjo & Salam, 2020). This means in order to understand knowledge that we have learned previously, a particular relationship must exist. ...

... This means in order to understand knowledge that we have learned previously, a particular relationship must exist. For example, students who can identify prime numbers understand how to find factors of numbers (Bahr & Rieth, 1989;Simon, 2017). ...

Ni Nyoman Wulan Darma Putri
I Wayan Puja Astawa
I Made Ardana

This study aims to investigate the effectiveness of GeoGebra-assisted 5E Learning Cycle model toward student's understanding of mathematical concept with control of student's prior knowledge. This study was a quasi-experiment with post-test only control group design. The population of the study was 324 ninth grader students where 81 of them were selected as sample through cluster random sampling technique. The data collected in this study were student's mathematical prior knowledge obtained by giving objective tests before starting the learning process and data of student's mathematical conceptual understanding obtained by giving an essay test at the end of learning process. The hypotheses were tested using t-test and one-way analysis of covariance test. The results showed that: the usage of GeoGebra-assisted 5E Learning Cycle Model has a positive impact toward student's understanding of mathematical concept, where t = 2,977 and p = 0,002; the usage of GeoGebra-assisted 5E Learning Cycle Model has a positive impact toward student's understanding of mathematical concept after the prior knowledge variable was controlled, where F = 31,880 and p = 0,000. The findings of this research implied that GeoGebra-assisted 5E Learning Cycle Model can be used as an alternative learning model in an effort to improve students' understanding of mathematical concepts.

... One is said to have an object of the concept if he/she is able to show the properties of the concept, while someone is said to have had a conceptual process if that he/she can discuss the concept using a mathematical object (Sfard, 1991). A concept can be learned through definition (Simon, 2017). When a student understands the definition of a concept presented in textbooks and classroom learning, the student will form an image of the concept in his mind (Viholainen, 2008). ...

... Zetterberg (1966) provides an explaination that there are three components that make up a concept, they are symbols, objects and conceptions. Conception is a model of explaining learners about a certain concept (Simon, 2017). Another explanation of conception is a form of internal representation of the concept, which is owned by students and becomes an element of a student's knowledge (Sfard, 1991). ...

This study aims to identify types of errors made by students and their conceptions related to the concept of relations and functions. This research is a descriptive study with a qualitative approach conducted in eight grades at one of Madrasah Tsanawiyah in Kabupaten Bandung Barat. The research subjects were taken from 26 students who answered incorrectly on a given test. The research instrument was in the form of a diagnostic test based on basic competencies and indicators in the Relations and Function material. In-depth interviews were conducted with students who made mistakes in answering. Based on the data analysis, the mistakes made were: 1) conceptual error type 1, 2) conceptual error type 2, 3) procedural error, 4) technical error, and 5) error in understanding the problem. One of the causes of students' mistakes is the dissimilar concept between students' and scientific conceptions.

... Teachers can use student contributions (e.g., utterances, work) to make inferences about a student's conceptions. Thus, the conceptions are the "explanatory model[s] used to explain observed abilities and limitations of mathematics learners in terms of their (inferred) ways of knowing" (Simon 2017). In that sense, teacher responding moves are subject-specific. ...

... It is because what the teacher teaches is not a mathematical concept but a mathematical procedure. Mathematical concepts consist of mathematical objects (mental) and the relationships between these objects (Simon, 2017). Students' difficulties may not involve one particular math skill, but they may construct several skills (Tambychik, Meerah, & Aziz, 2010). ...

Damianus D Samo

Mathematical connection is the ability to make connections to understanding mathematical concepts that are associated with contexts outside of mathematics. Various studies revealed that the students' mathematical connection is still low; therefore, this study aims to describe the difficulties of junior high school students in mathematical connection ability. This research is a descriptive qualitative study. The study sample was 52 students from a junior high school in East Flores Regency. The methods used in this study were tests, observations, and interviews. The study results showed that the mathematical connection ability based on the three indicators of connection ability tends to be below. Students did not understand concepts that had been studying; easy to forget concepts, principles and procedures; not used to use concepts, principles and procedures; assume mathematics has nothing to do with other sciences; not accustomed to applying mathematical concepts in everyday life; lack of understanding about the story

... Besides that, there was a need for a teacher to develop HLT (hypothetical learning trajectory) as a learning reference and a guide for students' thinking processes. With HLT, it was easier for teachers to analyze students' thinking errors and anticipate learning barriers that may occur in learning (Fuadiah, 2018;Nuraida & Amam, 2019;Prahmana & Kusumah, 2016;Simon, 2017). ...

Kreano 12 (1) (2021) : 178-188 K R E A N O J u r n a l M a t e m a t i k a K r e a t i f-I n o v a t i f Abstract This research is motivated by the low mathematical representation skills of students. Mathematics learning based on android applications is an alternative idea that can be a solution to the problems above. The results showed: (1) Mathematics learning based on android applications has a positive impact on the ability of students' mathematical representation (2) from the results of the analysis of students' answers, it is concluded that students' representation skills in solving various questions, diverse representations are a manifestation of the solution strategy In addition, there are several learning barriers, including misinterpretation of the application of concepts, the fluency of students in connecting between concepts and other mathematical concepts, as well as student difficulties in communicating mathematical ideas, (3) The solution that can be done is the use of technology that can improve skills. students 'mathematics and (4) the need for a teacher to compile HLT as a basis for students' thought processes in learning the concepts of roots, ranks and logarithms. Abstrak Penelitian ini dilatarbelakangi oleh masih rendahnya keterampilan representasi matematis siswa. Pembelajaran matematika berbasis aplikasi android adalah salah satu gagasan alter-natif yang dapat menjadi solusi permasalahan diatas. Hasil penelitian menunjukan: (1) Pembelajaran matematika berbasis aplikasi android memiliki dampak yang positif terhadap kemampuan representasi matematis siswa (2) dari hasil analisis jawaban siswa, didapatkan kesimpulan bahwa keterampilan representasi siswa dalam menyelesaikan soal beragam, representasi yang beragam merupakan perwujudan dari strategi penyelesaian yang berbeda, disamping itu ditemukan beberapa hambatan belajar diantaranya kesalahan interpretasi penerapan konsep, kelancaran siswa dalam menghubungkan anatra suatu konsep dan kon-sep matematika lainnya, serta kesulitan siswa dalam mengkomunikasin ide gagasan ma-tematis,(3) Adapun solusi yang dapat dilakukan adalah pemanfaatan teknologi yang dapat meningkatkan keterampilan matematis siswa serta (4) perlunya seorang guru menyusun HLT sebagai landasan proses berpikir siswa dalam mempelajari konsep akar, pangkat dan logaritma.

... Hypothetical Learning Trajectory (HLT) is a description of the learning process when students experience the learning process from the beginning until the learning objectives are achieved (Andrews-Larson et al., 2017;Simon & Tzur, 2004). HLT refers to the teacher's plan based on the anticipation of student learning that might be achieved in the learning process based on the expected mathematics learning objectives of students, the knowledge and estimated level of understanding of students, and the choice of mathematical activities in sequence (Simon, 2017). The HLT is used as a guide in the research implementation process. ...

... Mokyklinės matematikos kontekste tikslesniam sąvokos apibūdinimui reikalingas sąvokos supratimo būdas. Pavyzdžiui, M.A. Simon [16] siūlo tokį mokyklinės matematikos sąvokos apibūdinimą. ...

Rimas Norvaiša

We discuss different alternatives of the content of school mathematics. According to the prevalent public opinion in Lithuania school mathematics can be oriented either to the academic mathematics or to the applications of mathematics. In reality the second alternative means lowering of the level of teaching in the hope that school mathematics will be accessible to all students. While the content oriented to the academic school mathematics is accessible only to gifted students. In this article we describe a middle alternative content which we call school mathematics based on mathematical reasoning. We argue that such school mathematics serves all students and makes acquaintance with mathematical reasoning and with applications of mathematics to the real world. Reasoning makes mathematics reasonable for all.

Candas Uygan
Gülay Bozkurt

This case study examines instrumented techniques of a pre-service mathematics teacher when utilising a dynamic geometry system (DGS) for the construction of cyclic quadrilaterals. Equally, it investigates her understanding of the hierarchical relations between the constructed cyclic quadrilaterals. For this aim, the hierarchical classification and instrumental genesis constitute the theoretical framework of our study. The data was collected through task-based interviews in which the participant was asked to construct the cyclic quadrilateral without using the circle tool in DGS. Data analysis was carried out to examine the participant's development of construction strategies related to her instrumented techniques and her reasoning regarding the properties of different cyclic quadrilaterals. The analysis showed that the participant's initial instrumented techniques enabled her to construct subsets of the cyclic quadrilaterals. Also, the process of reaching the most inclusive cyclic quadrilateral affected both her instrumented techniques and her understanding about the hierarchical relations between the constructed quadrilaterals.

Sven Trenholm

A review of related research found the use of recorded lecture videos (RLVs) in undergraduate mathematics to be negatively correlated with academic performance. To investigate this correlation, an initial study found students' regular RLV use to be linked to surface approaches to learning. The present study continued this investigation and was informed by cognitive research on the use of television which suggested framing learning using RLVs as a dual process system operating within a framework of self-regulated learning. Interviews were conducted with some initial study participants focusing on students' judgements of their learning when using RLVs. A dual-process theoretical lens was used to analyse interview transcripts and determine the nature of student thinking processes. Overall, regular RLV users were found significantly more likely to exhibit judgements of learning associated with achieving 'feelings of rightness'. Across both studies, evidence suggests regular RLV use, overall, is depressing student learning.

Juan D. Godino

Some key elements for developing a theory for understanding mathematical concepts are outlined. These elements are derived from the theory of mathematical objects and their meanings developed by Godino and Batanero (1994; 1996). We shall argue for the need to complement the psychological facets of understanding - 'as a mental experience', and 'connection of internal representations in information networks'- with the sociocultural approach, that is, understanding as 'correspondence between personal and institutional meanings'. The role of situation-problems and semiotic instruments is also emphasized in both personal and institutional dimensions of understanding processes.

Martin Simon

Currently, there are more theories of learning in use in mathematics education research than ever before (Lerman & Tsatsaroni, 2004). Although this is a positive sign for the field, it also has brought with it a set of challenges. In this article, I identify some of these challenges and consider how mathematics education researchers might think about, and work with, the multiple theories available. I present alternatives to views of the competition or supersession of theories and indicate the kinds of discussions that will support effective theory use in mathematics education research. I describe the potential for mathematics education researchers to make informed, justified choices of a theory or theories to address particular research agendas.

Ernst von Glasersfeld

Growing up Constructivist - Languages and Thoughtful People Unpopular Philosophical Ideas - A History in Quotations Piaget's Constructivist Theory of Knowing The Construction of Concepts Reflection and Abstraction Constructing Agents - The Self and Others On Language, Meaning and Communication The Cybernetic Connection Units, Plurality, and Number To Encourage Students' Conceptual Constructing.

Martin Simon
Nicora Placa
Arnon Avitzur

Tzur and Simon (2004) postulated 2 stages of development in learning a mathematical concept: participatory and anticipatory. In this article, we discuss the affordances for research of this stage distinction related to data analysis, task design, and assessment as demonstrated in a 2-year teaching experiment. We describe our modifications to and further explicate and exemplify the theoretical underpinnings of these stage constructs. We introduce a representation scheme and use it to trace the development of a concept from initial activity, through the participatory stage, and to the anticipatory stage.