Dec 23, 2008


By Marsigit
This article strives to explain philosophically on the students’ experiences on decimal numeration which were emerged in the research on The Effect of Epistemic Fidelity On Teaching Decimal Numeration With Physical Materials by Kaye Stacey et al (2001). The use of linear arithmetic blocks (LAB) was associated with more active engagement by students and deeper discussion than that of multi-base arithmetic blocks (MAB). Epistemic fidelity is critical to facilitate teaching with the models, but Stacey, K, et al (p.199-221, 2001) attributed the enhanced environment to the greater accessibility of the LAB material. This research and its results exhibits the writer to employ Greimas’ Structural Analyses, Kant’s theory of double-affection and other notions of philosophical explanation in order to uncover concepts behind the aspects of the process as well as the results of the research. The in-depth explanations of the nature of mathematical experiences, specifically about the effect of epistemic fidelity on teaching decimal numeration with physical materials, will expose not a single truth of its nature due to the fact that they will be put in the area of philosophy.
The level of philosophical discussion have their characteristics such as the need to cross-check as well as to compare with several point of views independently, to construct general theory of subject related. Mackenzie, J.S, (1917), stated that philosophy has to take account of the general results of the investigations of all sciences to endeavour or to construct a general theory. To achieve the purpose the writer employ some philosophical approaches such as interpretation, internal coherences, idealisation, comparison, analogy and description. Based on those approaches, accordingly, the writer adapts Greimas’ Hermenetics Structural Analyses to show the inter-relationship among the components of decimal numeration teaching with physical materials as it was carried out as part of the research of Kaye Stacey et al. To achieve the objective i.e the general theory of the related subject, the writer strive to implement the theory of ‘double-affection’ to the scheme of Greimas’ Hermenitics Structural Analyses with the context of the process and the results of the research, conducted by Stacey, K, et al, (2001), on the effect of epistemic fidelity and accessibility on teaching with physical material.
Greimas’ Hermenitics Structural Analyses
In that scheme, the student was put into the centre of the mathematical teaching learning activities; the teacher has a role as the ‘the sender’ as well as the ‘supporter’ in such a way that their students learn physical material as an object of learning; the ‘transaction’ between the teacher and their students happened if there is a motivation of the students to learn the objects i.e. physical material; the ‘constraints’ need to be considered and to be anticipated as well as to be found its solutions in such away that the students are able to interact with their physical material; the ‘anti-subject’ arises if there is extremely constraints such as bullying, un-expected accident etc. in such a way that the students are not able to interact with their physical material mathematical objects; the ‘receivers’ are the people or the agents that takes the benefit of the students’ interaction with their objects, therefore, the student him/herself cam be perceived as ‘receiver’.
The Myth Of Double Affection
The theory of double affection is a classical attempt to rescue Kant’s account of perceptual awareness from what is alleged to be a glaring inconsistency (Gram, S.M, in Werkmeister, W.H, 1975). According to Kant, ‘to be affected by anything ‘ is to experience the effect of an object upon the faculty of representation (ibid, p.29). Kant provides two kinds of objects which affect the subject: there are ‘thing in themselves’ which affect the self; and there are ‘appearances in themselves’ which act on our sensibility and are independent of whatever characteristics attach to our sensory receptors (Werkmeister, W.H, 1975). Facing this Kant’s notion, Gram, S.M, in Werkmeister, W.H, (1975) delivered the following argument:
“ Suppose we say that what affects our sensibility is ‘a thing in itself’. This account of what affects us, however, prevents us from distinguishing between a case in which somebody perceives an object and the quite different case in which an object exert a merely causal influence on the body of the perceiver. This can be seen by consulting an elementary fact of perception. The fact is that to perceive anything is to perceive it under ‘a certain description’. If this were not the case, then we could not distinguish between the perceiving of one object rather than another. But if we must always perceive something under a description, to say that we are affected by ‘a thing in itself’ when we perceive anything would imply that we perceive that objects satisfy certain descriptions. And this would contradict the claim that we cannot be perceptually acquainted with ‘a thing in itself’.
The above propositions were delivered to argue Kant’s description that affection as the experience of the ‘effect’ of an object on our sensory apparatus; whilst, the dilemma facing Kant’s theory has nothing to do with the quite separate issue of whether what is related to sensibility is the effect of an object rather than the object itself; and, the issue concerns the nature of the object which is immediately present to perceptual awareness rather than the casual relation in which it might stand to some further object. The notion of affection does not, however, become fully clear unless we can specify the kind of object which can stand in such a relation to our sensibility (ibid, p.29). He then erected the next dilemma as shown the following:
“If ‘a thing in itself’ can act upon our sensory organs even though we cannot perceive it to satisfy any description at all, we would not be able to distinguish between ‘the situation ‘ in which an object casually affects our bodies in certain ways and we do not perceive the effects of that action from the quite different situation in which the object exerts such as influence and we do perceive it. If the first affection is to hold between ‘a thing in itself’ and ‘an act of perceptual awareness, we would have to be able to perceive ‘thing in themselves’ under descriptions appropriate to them or obliterate the distinction between causation and perceptual awareness”.
What we can learn is that there should be any other relation between ‘thing in themselves’ and affection. Kant asserted that ‘space’ and ‘time’ are forms of our sensibility; what affects our sensibility is an object that has ‘spatial’ or ‘temporal’ characteristics i.e. a phenomenal object. If the object which affects the forms of our sensibility cannot itself have ‘spatio-temporal’ characteristics, then what affects us must, on Kant’s theory, be a thing in itself . Empirical affection does not require that the objects in our sensory field lack spatio-temporal characteristics; while, transcendental affection countenances the existence of objects which affect ego in themselves. However, the distinction between these two kinds of perception is still a myth (ibid 32-33).
Research on The Effect Of Epistemic Fidelity On Tea-ching Decimal Numeration With Physical Materials by Kaye Stacey et al (2001)
The results of the research on the effect of epistemic fidelity and accessibility on teaching with physical material (Stacey, K, et al, 2001) comes to some conclusion that: 1) the are numbers of favor differences of different model of physical material (LAB and MAB), 2) the most striking difference between the two models was their ability to model number density, with LAB found to be the superior model in this respect, 3) teaching with physical materials is an area of great difficulty for many students, 4) students did not attend to the volume relationships embedded in MAB and struggled to remember the names, rather than immediately appreciating the sense behind them, 5) MAB students experienced difficulty generalizing to numbers beyond the model due to their difficulties with volume and apparent dimensional shifts in their perceptions of the components, 6) LAB appeared to promote richer engagement in the classroom than MAB due to its greater accessibility (detail results of the research, refer to Educational Studies in Mathematics 47: 199-221, 2001).
It was acknowledged by the researchers that some manipulative materials can be distracting and open misinterpretation; teachers could overestimate the value of physical materials because they are already familiar with the concepts being presented (Ball in Kaye, et al, 2001). It also stated that, Meira (1998), the mechanical devices became ‘visible’ as things that required explanation, rather than ‘invisible’ resources for making the mathematics more accessible. Having considered those notions of the constraints in employing physical materials in teaching mathematics and having learnt the document of the process and the results of the research, the writer perceives that the research consists a lot of important critical concepts that need to be developed as the notions in the implementation of mathematics teaching as well as the notions of theoretical and or philosophical discussions. In term of theoretical concept, those important critical concepts consist of: 1) epistemic fidelity, 2) the posing problems devices, 3) the link between the features of the device and the target knowledge, 4) something objective, 5) students’ engagement, and 6) accessibility. From the explanation, it can be inferred that the objective of this paper is to investigate general theory of the aspects of mathematics teaching learning processes with the context of the process and the results of the research conducted by Stacey, K, et al, (2001), on the effect of epistemic fidelity and accessibility on teaching with physical material.
Philosophical Explanation on Mathematical Experience
In their theoretical review of the stated research, Stacey, K, et al, (2001) indicated that epistemic fidelity of the material is one of the factors influences the transparency of instructional material. They also indicated that epistemic fidelity of the material depends on the materials themselves in which the mathematical domain being represented does not depend on their use by students. Explicitly, they defined that the epistemic fidelity of an instructional material is a measure of the quality of analogical mapping between the features of the material and the target knowledge domain. Further, they stated that epistemic fidelity of a model depends on the relationship of features intrinsic in the model to target mathematical structure, and is independent of user characteristics. On the other hand, Gram, S.M. (1975) provides a clear and comprehensive statement, of the case that likely as what Stacey, K., et al infer as epistemic fidelity, that he called ‘double affection’. He claimed that what affects our sensibility is ‘a phenomenal object’; it allowing anything which has spatial or temporal characteristics to count as such an object. Further he stated that, according to Kant, sensibility is the capacity (that the researcher claimed as ‘quality’) for receiving representations through the mode in which we are affected by objects.
From those two points of view we may learn that although there similarities of the claim of the relation between subject and object of learning, although the writer could not identify what did they mean by ‘a measure of the quality of analogical mapping between the features of the material and the target knowledge domain’, except that of its category consists of excellent, good, satisfactory and unsatisfactory. If the researchers meant that epistemic fidelity is the capacity for receiving representations through the mode in which we are affected by objects, the next problem is that we need to clarify them. Kant implied that affection is to be partially defined in terms of a relation in which an object stands to certain spatio-temporal forms; and this kind of relationship is specified in terms of a connection between an object and these forms, not in term of an object exhibiting these forms and sensibility. It is important here to conclude that, according to Kant, if the object which affects the forms of our sensibility cannot itself have spatio-temporal characteristics, then what affects us must be ‘a thing in itself’(in which the researchers indicated it as ‘material in themselves’). It seemed that the researchers did not specify the affect of the different characteristics of the object in term of ‘appearances in themselves’ and ‘things in themselves’.
Next, they also indicated that the ‘accessibility’ of the materials is a collection or psychological factors that arise in the use of the materials by students but which are not specific to particular students (ibid. p. 2001); further it was stated that accessibility of a model of physical material depends on characteristics of likely users interacting with features of the model; accessibility, stands above the detailed analyses of particular tasks in particular classrooms that Meira (1998) in Stacy (2001) has traced in his quest for ‘transparency’. Accordingly, there are at least two issues (both social and psychological) that may impact of LAB and MAB. In LAB the issues consists of: 1) students’ confusing the organizer rods with the value of the component and 2) students’ confusing about the left-right positioning of the place value columns. It is clear that what the researcher infer by ‘accessibility’ is something related to the subject that what inferred by Kant as ‘sensibility’.
Differences accessibility were actually found that students in MAB group experienced confusion with remembering the new names components. There was no such confusion in the LAB group. How numbers are represented? In MAB group, the students did not understand that the components relative value is based on their volume. In term of ability to generalise beyond the model, the students were confused by the apparent dimensional shift and appeared to be looking for a forth dimension. Were the different learning outcomes related to differences in epistemic fidelity or accessibility? The LAB model was more effective on decimal numeration; the LAB model was found to more transparent model for numeration; the LAB model was more effective model of number density; the LAB model should also be better model for rounding decimal number.
In term of the differences between the group, the LAB model was more favourable and the LAB model appeared to promote richer engagement in the classroom due to greater accessibility. The Year 5 students appeared reluctant to use the MAB; it was a constant struggle to get them to use it. There was more discussion and exchange the ideas in the LAB group and there more significantly episodes of talk referring to the LAB model than the MAB model. There was evidence that LAB students spontaneously exploring new ideas, which did not occur with students using MAB. When LAB was not available, students made connections with other physical representations, such as ruler lengths and MAB; One student pointed out “LAB is another type of MAB”; “These are the exact same thing”. The LAB group scored higher than the MAB group on every measure of attitude(Likert items). In term of the attitude, the LAB group is typified by one student’s comment: ”Learning what the numbers mean –how big they were-just from length, was the best”.
The research has given the researchers an insight into the different roles of epistemic fidelity and accessibility of physical instructional material. The researchers hypothesise that epistemic fidelity is necessary for securely grounded teaching of concept with a model, whereas accessibility promotes rich classroom engagement. Epistemic fidelity and accessibility have different roles in establishment transparency. From all of those findings, the writer strives to develop the method to uncover what are there behind the concepts.
Over all, we regard to the students’ status of mathematical knowledge resulted by manipulating with physical materials, in the schema of Greimas’ Hermenetics Structural Analyses. If the distinction between the two kinds of perception is still a myth, then we can still argue it on the status of mathematical knowledge. As it was acknowledged by the researchers that some manipulative materials can be distracting and open misinterpretation; it can be explain with the theory of double-affection due to the fact that the teachers are already familiar with the concepts being presented. The writer perceives that Kant’s notion of appearance in them selves and thing in themselves are useful to explain the issues of visibility and /or invisibility of the mechanical device.
The writer emphasizes that the different context, i.e. in term of time and space as it was notified by Kant, may influence students perception of the objects. Therefore, teachers need to employ those kind of factors as supporting one in teaching learning of mathematics. The link between the features of the device and the target knowledge was very intensively to be discussed by Kant in his Critical of Pure Reason. General theory of the aspects of mathematics teaching learning processes is to pursue in term of the relation of student as a subject and physical material as an object in the schema of Greimas’ Hermenetics Structural Analyses. The effort to pursue those relationships will determine the extent of the quality of philosophical point of view.
Haryatmoko, 2004, Research Methodology, Unpublished document of his lecturing in the Post Graduate Program of Philosophy Science, Gadjah Mada University
Kant, I., 1998, Critique of Pure Reason (trans. Meiklejohn, J.M, )
Kant, I., 1998, Prolegomena to Any Future Metaphysics(trans.)
Smith, N.K., 2003, A Commentary to Kant’s Critique of Pure Reason, New York: Palgrave
Stacey K., 2001, The Effect Of Epistemic Fidelity On Teaching Decimal Numeration With
Physical Materials by Kaye Stacey
Werkmeister, W.H., 1975, Reflections on Kant’ Philosophy,Florida: University Presses of


  1. Arung Mega Ratna
    PPs PMC 2017

    Di dalam analisis Struktural dari Greimas, peserta didik menjadi pusat dalam aktivitas pembelajaran matematika sehingga peserta didik dituntut aktif, sedangkan seorang guru menjadi “pengirim” atau “pendukung” dalam proses pembelajaran. Interaksi antara guru dan peserta didik terjadi jika ada motivasi dari peserta didik untuk mempelajari suatu objek atau materi.
    Penggunaan alat peraga model linear (LAB) lebih mendorong aktivitas dan diskusi siswa dibanding dengan penggunaan alat peraga model ruang (MAB). “Epistemic fidelity” merupakan pendekatan yang dilakukan oleh peneliti untuk
    mengembangkan model alat peraga. Sedangkan Teori “Double-Affection” dari Kant merupakan usaha klasikal yang mempunyai pandangan tidak tetap. Apa yang dapat kita pelajari berhubungan dengan sesuatu yang menyangkut diri kita dan mempunyai pengaruh terhadap diri kita.
    Penjelasan tentang sesuatu hal ternyata tidak bersifat tunggal karena ruang dan waktu. Adanya ruang dan waktu tersebut mungkin akan mempengaruhi persepsi peserta didik dalam memandang suatu objek. Oleh karena itu, guru perlu menggunakan faktor yang mendukung dalam mempelajari matematika.

  2. Nama: Dian Andarwati
    NIM: 17709251063
    Kelas: Pendidikan Matematika (S2) Kelas C

    Assalamu'alaikum. Pengalaman belajar itu penting bagi siswa Sekolah Dasar, karena pada tahap sekolah dasar siswa masih berpikir berdasarkan pengalamannya. Siswa sekolah dasar masih berpikir secara kokrit maka dari itu pengalaman harus diberikan dalam memulai setiap topik baru. Guru berperan sebagai fasilitator siswa dalam memperoleh pengalaman matematikanya. Matematika siswa sekolah dasar itu relistis harus ada dalam kehidupan sehari-hari, harus dapat mereka bayangkan dan rasakan. wassalamualaikum

  3. Yusrina Wardani
    PPs PMAT C 2017
    Matematika merupakan sebuah ilmu dengan objek kajian yang bersifat abstrak. Abstrak diartikan sebagai sesuatu yang tak berwujud atau hanya gambaran pikiran. Artinya sesuatu yang abstrak,tidak berwujud dalam bentuk konkret atau nyata, hanya dapat dibayangkan dalam pikiran saja. Sehingga objek matematika tidak dapat ditanggap secara inderawi, yang dapat ditangkap hanyalah bentuk atau contoh bentuk objek matematika. Sehingga objek yang abstrak dapat dipahami dengan lebih mudah bagi siswa SD dengan dimulai dari pengenalan konsep-konsep yang konkret dan berkaitan dengan kejadian dalam kehidupan sehari-hari.

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  5. Rosnida Nurhayati
    PPs PMB 2017

    Bacaan diatas menekankan bahwa konteks hal ruang dan waktu dapat mempengaruhi persepsi siswa tentang objek. oleh karena itu, guru perlu menggunakan berbagai macap persepsi sebagai pendukung dalam pembelajaran. Bacaan diatas bisa mebantu guru dalam hal pengembangan persepsi siswa dalam pembelajaran.

  6. Anisa Safitri
    PEP B

    Metode pembelajaran adalah hal yang penting dalam suatu proses kegiatan belajar mengajar. Metode ini bisa menunjang keefektifan KBM kalau direncanakan dan dilaksanakan secara baik. Seorang guru harus pintar dalam memilih metode KBM yang sesuai dengan situasi, waktu, materi dan karakter siswa sehingga proses KBM bisa berjalan dengan baik dan siswa mengetahui materi dengan baik. Dalam mengajar guru harus dapat merancakan pembelajaran yang akan dilakukan, karena perencanaan dalam pembelajaran adlah menntukan sikap dan kepercayaan diri kita sebagai guru untuk mengajarkan dengan yakin serta dengan perencanaan yang dibuat kita dapat mengontrol kondisi didalam kelas agar tetap tenang dan aktif dalam pembelajaran, begitu juga dengan metode yang digunakan dapat mempengaruhi keefektifan pembelajaran dilakukan.

  7. I Nyoman Indhi Wiradika
    PEP B

    Pada elegi ini dipaparkan mengenai makna pengalaman matematika secara filsafat. Pengalaman merupakan hal yang penting dalam menyusun pengetahuan. Seperti contoh pada pembelajaran matematika di SD tidak akan bisa jika guru menjelaskan hanya menggunakan definisi-definisi abstrak, dibutuhkan pengalaman untuk memperkaya pemahaman siswa. Maka dari itu, dalam pembelajaran guru haruslah memahami hubungan antara siswa sebagai subjek dan materi fisik sebagai objek.

  8. Yusrina Wardani
    PPs PMAT C 2017

    Pada tingkat sekolah dasar merupakan landasan awal kemampuan yang perlu dikuasai siswa secara matang sebelum beranjak ke jenjang berikutnya yang lebih tinggi, jika landasannya sudah kokoh, maka pemahaman pada materi pembelajaran yang lebih tinggi dapat dicapai dengan mudah. Untuk itu perlu dicermati dan dikembangkan secara tepat proses pembelajarannya.

  9. Isoka Amanah Kurnia
    S2 Pendidikan Matematika 2017 Kelas C

    Pada siswa SD, matematika yang digunakan adalah matematika berwujud konkret. Hal yang paling penting adalah membuat siswa senang belajar. Matematika SD lebih difokuskan pada pemecahan masalah sederhana yang tidak membutuhkan konsep dan rumus tertentu untuk memecahkannya. Siswa dapat menyeelsaikan masalah berdasarkan pengalaman belajar nya yang terdahulu, untuk menimbulkan keyakinan pada diri siswa bahwa maetematika dapat digunakan secara terus menerus dan bukan merupakan ilmu yang bersifat hafalan.

  10. Ilania Eka Andari
    S2 pmat c 207

    Pembelajaran matematika harus mampu membentuk pola pikir yang logis, kritis, dan sistematis. Jadi matematika tidak hanya sebatas mencari hasil penyelesaian dari soal atau permasalahan yang diberikan guru. Namun yang terpenting adalah proses membentuk pola pikir anak. Pola pikir ini akan semakin matang jika didukung oleh berbagai pengalaman-pengalaman belajar siswa baik dalam merumuskan masalah ke model matematika ataupun menyelesaikannya.
    Pusat pembelajaran seharusnya adalah siswa, guru berfungsi sebagai fasilitator bagi siswa untuk mengembangkan pengetahuannya.

  11. Sofi Saifiyah
    S2 PEP B

    Tingkat diskusi filosofis memiliki karakteristik, seperti pada kebutuhan untuk memeriksa kembali serta untuk membandingkan dengan beberapa pandangan independen, yang bertujuan untuk membangun teori umum dari subjek yang terkait. Mackenzie berpendapat bahwa filsafat harus memperhitungkan hasil umum dari suatu penyelidikan ilmu untuk membangun sebuah teori umum. Untuk mencapai tujuan tersebut penulis menggunakan beberapa pendekatan filosofis diantaranya interpretasi, idelaisme koherentis, perbandingan, analogi dan deskripsi. Berdasarkan pendekatan-pendekatan tersebut, penulis memilih pendekatan dai teori Greimas Hermenetics Analisis Struktural untuk menunjukkan antar-hubungan antara komponen-komponen mengajar dengan bahan fisik seperti yang dilakukan sebagai bagian dari penelitian Kaye Stacey dkk. Untuk mencapai tujuan tersebut yaitu teori umum dari subjek yang terkait, penulis berusaha untuk menerapkan teori skema Greimas yaitu 'Analisis Hermenitics Struktural dengan konteks proses dan hasil penelitiannya pada efek dari epistemik kesetiaan dan aksesibilitas pada pengajaran dengan materi fisik.

  12. Firman Indra Pamungkas
    S2 Pendidikan Matematika 2017 Kelas C

    Assalamualaikum Warohmatullah Wabarokatuh
    Siswa bukanlah objek pembelajaran, tetapi subjek pembelajaran. Siswa lah yang belajar dan mencari ilmunya. sedangkan guru sebagai fasilitator bagi siswa dalam pembelajaran. guru yang menyiapkan perangkat pembelajaran serta merancang pembelajaran sehingga pembelajaran mampu mengarahkan pada keaktifan siswa. maka dari itu perlu adanya komunikasi antara gurudan siswa, misalnya guru mengkomunikasikan tujuan pembelajaran, sehingga terdapat kesamaan dalam pembelajaran

  13. Eka Luthfiana Lathifah
    PPs PMat C
    Pembelajaran guru haruslah memahami hubungan antara siswa sebagai subjek dan materi fisik sebagai objek. Siswa bukanlah objek pembelajaran, tetapi subjek pembelajaran
    guru berfungsi sebagai fasilitator bagi siswa untuk mengembangkan pengetahuannya.

  14. Novita Ayu Dewanti
    S2 PMat C 2017

    Pembelajaran pada tingkat SD sangatlah materi emndasar yang perlu dipahami dengan benar oleh siswa. Pembelajaran matematika SD merupakan pembelajaran matematika sekolah yang mana pendekatannya menggunakan pendekatan yang berbeda dengan pembelajaran matematika murni. Dengan melakukan pendekatan yang sesuai dengan umurnya maka siswa SD akan merasa enjoy dengan pembelajaran mat.

  15. Dewi Thufaila
    Pendidikan Matematika Pascasarjana C 2017


    menambahkan sedikit bapak, bahwa disini siswa menjadi pusat dalam kegiatan pembelajaran bukan hanya sebagai obyek namun juga berperan aktif sebagai subyek yang terlibat secara langsung dan guru hanya sebagai fasilitator dimana adanya motivasi yang didapat siswa dari mempelajari obyek-obyek nyata


  16. Dewi Thufaila
    Pendidikan Matematika Pascasarjana C 2017

    Filosofi yang didapat siswa dari pengalamannya pada penomoran desimal dalam penelitian The Effect of Epistemic Fidelity On Teaching Decimal Numeration With Physical Materials by Kaye Stacey et al (2001). mengaitkan penggunaan blok aritmatika linear (LAB) dengan keterlibatan siswa yang lebih aktif dan diskusi dari multiblok dasar aritmatika (MAB). Penulis menggunakan Analisis Struktural Greimas, dalam rangka untuk mengungkap konsep-konsep balik dari proses serta hasil penelitian.

  17. Dheni Nugroho
    PPs Pendidikan Matematika

    Matematika adalah kegiatan mencari pola untuk menemukan model matematika yang tepat untuk materi yang terkait. Oleh karena itu seharuanya siswa sekolah dasar tidak harus selalu memulai penjelasan dari model-modelmatematika yang ada, akan tetapi bisa mengenalkan matematika dari kegiatan-kegiatan atau benda-benda sekitar yang mengajarkan matematika, misalnya untuk menjelaskan bilangan kita bisa membahas benda-benda yang memiliki jumlah satu, dua, atau tiga dan seterusnya. dengan demikian siswa sekolah dasar akan lebih memungkinkan untuk menikmati pelajaran matematika dan dengan demikian pula akan tumbuh rasa ikhlas hati dan ikhlas pikir untuk belajar matematika.

  18. Arina Husna Zaini
    PEP S2 B

    Matematika selama ini dianggap sebagai mata pelajaran oaling sulit bagi siswa karena dianggap materi dalam pelajaran ini abstrak dan sulit di aplikasikan dalam kehidupan sehari-hari. Oleh karena itu, melalui artikel ini kami mencoba memahami bahwa mencari aspek filosofi dalam filsafat metematika sangat penting untuk menggali dan mencari sejatinya inti dalam pembelajaran matematika. Berdasarkan artikel diatas bahwa pengalaman merupakan hal yang penting dan diperlukan untuk mendesain pembelajaran matematika. Pengalaman yang dibentuk melalui pembelajaran matematika dapat meruntuhkan bahwa matematika tidak sekedar simbol dan hal yang abstrak. Matematika merupakan aktivitas bagi siswa dan dapat diaplikasikan dalam kehidupan sehari-hati. Terima Kasih