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


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  2. Assalamu Alaikum Warohmatullahi Wabarokatuh
    Besse Rahmi Alimin
    s2 Pendidikan Matematika 2018

    Dalam artikel ini, penulis ternyata menggunakan beberapa pendekatan filosofis seperti interpretasi, koherensi internal, idealisasi, perbandingan, analogi dan deskripsi. Kemudian dianalisis secara struktural hermenetik's Greimas untuk menunjukkan hubungan antar komponen pembelajaran numerik desimal dengan materi fisik.
    Dalam skema itu, siswa dimasukkan ke pusat kegiatan belajar mengajar matematika; guru memiliki peran sebagai ‘pengirim’ serta ‘pendukung’ sedemikian rupa sehingga siswa mereka mempelajari materi fisik sebagai objek pembelajaran; 'Transaksi' antara guru dan siswa mereka terjadi jika ada motivasi siswa untuk mempelajari benda-benda itu, yaitu materi fisik; 'kendala' perlu dipertimbangkan dan diantisipasi serta dapat ditemukan solusinya sedemikian rupa sehingga siswa dapat berinteraksi dengan materi fisik mereka; 'anti-subjek' muncul jika ada kendala yang sangat besar seperti pembuliyan, kecelakaan yang tidak diharapkan, dll.
    Kant menyediakan dua jenis objek yang mempengaruhi subjek: ada 'benda dalam diri mereka sendiri' yang mempengaruhi diri; dan ada 'penampilan dalam diri mereka sendiri' yang bertindak berdasarkan kepekaan kita dan tidak bergantung pada karakteristik apa pun yang melekat pada reseptor indera kita. Kant menegaskan bahwa 'ruang' dan 'waktu' adalah bentuk kepekaan kita; apa yang memengaruhi sensibilitas kita adalah objek yang memiliki karakteristik 'spasial' atau 'temporal', yaitu objek yang fenomenal. dapat disimpulkan bahwa tujuan dari makalah ini adalah untuk menyelidiki teori umum dari aspek proses belajar mengajar matematika dengan konteks proses dan hasil penelitian. menganggap status pengetahuan matematis siswa dihasilkan dengan memanipulasi dengan materi fisik, dalam skema Analisis Struktural Hermenetik Greimas. Jika perbedaan antara dua jenis persepsi masih merupakan mitos, maka kita masih bisa membantahnya pada status pengetahuan matematika. Seperti yang diakui oleh para peneliti bahwa beberapa materi manipulatif dapat mengalihkan perhatian dan salah tafsir terbuka; itu bisa dijelaskan dengan teori kasih sayang ganda karena fakta bahwa para guru sudah akrab dengan konsep yang disajikan.

  3. Bayuk Nusantara Kr.J.T

    Para ahli dan pakar pendidikan matematika berpendapat bahwa proses pembelajaran matematika di sekolah sampai saat ini lebih cenderung berpusat kepada guru dan guru sebagai satu-satu sumber materi dan pengetahuan. Konsekuensinya, materi matematika dianggap sebagai “barang jadi” sehingga gagal menjalankan pembelajaran yang bermakna dan bermanfaat bagi siswa yang berhubungan dengan kehidupan mereka sendiri, dan juga gagal dalam membekali anak untuk memecahkan masalah dalam kehidupan jangka panjang.

  4. Rindang Maaris Aadzaar
    S2 Pendidikan Matematika 2018 (PM B 2018)

    Assalamualaikum warahmatullahi wabarakatuh
    Pada postingan di atas dapat diambil kesimpulan bahwa epistemik dan aksesibilitas memiliki peran yang berbeda dalam transparansi pendirian. Perbedaan antara dua jenis persepsi masih merupakan mitos, maka masih bisa dibantah pada status pengetahuan matematika. Beberapa materi manipulatif dapat mengalihkan perhatian dan salah tafsir terbuka dan dapat dijelaskan oleh konsep-konsep yang disajikan. Kant berpendapat tentang penampilan di dalamnya adalah sebuah ponsel dan hal-hal yang berguna untuk menjelaskan masalah visibilitas perangkat mekanis.
    Wassalamualaikum warahmatullahi wabarakatuh

  5. Fany Isti Bigo
    PPs UNY PM A 2018

    Matematika akan bermakna jika dimengerti dan dipahami siswa. Oleh karena itu, dalam pembelajaran matematika hendaknya mampu menuntun siswa untuk dapat menemukan konsep pengetahuan sendiri tanpa harus diberikan atau ditransfer terus-menerus dari guru saja sebab jika demikian siswa cenderung menghafal apa yang diajarkan oleh guru. Belajar matematika tidak ada artinya jika berupa hafalan saja. Jadi, siswa harus belajar secara bermakna, yang berarti cara belajar dengan pengertian lebih dari pada hafalan, mengerti dan memahami apa yang menjadi konsep dalam pembelajaran

  6. Elsa Apriska
    S2 PM A 2018

    Dari artikel di atas disimpulkan bahwa teori umum tentang aspek proses pembelajaran matematika adalah untuk memperoleh hubungan siswa sebagai subjek dan materi sebagai objek. Uoaya untun mengejar hubungan-hubungan itu akan menentukan sejauh mana kualitas sudut pandang. Selama ini pembelajaran yang berlangsung masih sering bersifat berpusat pada guru, murid hanya diberikan materi-materi secara langsung tanpa diminta untuk mengkonstruk pengetahuannya sendiri. Padahal seperti yang kita ketahui belajar bermakna adalah ketika siswa menjadi pusat pembelajaran itu sendiri, dimana mereka berusaha untuk menemukan dan membangun pengetahuannya sendiri.

  7. Aizza Zakkiyatul Fathin
    Pps Pendidikan Matematika A

    Matematika itu dianggap sulit oleh para siswa salah satu penyebabnya adalah cara guru memberi matematika yang kaku, abstrak, penuh rumus, asing dengan siswa dan sebagainya. Siswa kelas 5 SD masih berada pada tahap berpikir kongkrit sehingga matematika yang diberikan haruslah dekat dengan mereka. Matematik harus disajikan berdasarkan pengalaman siswa atau hal-hal kongkrit. Guru sudah seharusnya tahu matematika mana yang pantas diajarkan untuk siswa SD. Sehingga matematika yang diperoleh siswa adalah matematika yang menyenangkan dan tentunya konsep-konsep matematika akan bermakna.

  8. Diana Prastiwi
    S2 P. Mat A 2018

    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.

  9. Agnes Teresa Panjaitan 
    S2 Pendidikan Matematika A 2018

    Pemahaman saya akan tulisan ini adalah pentingnya melihat hubungan antara objek dengan afeksi yang ada didalamnya. Artinya melihat bahwa objek lebih dari apa yang terlihat dari luarnya, hal ini juga berkaian dengan ruang dan waktu yang ditempati oleh objek tersebut. Sehingga, Sehingga objek dapat memiliki karakter spasial dan temporal yang bervariasi satu dengan yang lainnya. Teori yang disampaikan oleh Kant ini memiliki kaitannya dengan sensibilitas seseorang. Hal yang dapat disimpulkan adalah pentingnya sensibilitas siswa dalam mempelajari materi-materi fisik.

  10. Yoga Prasetya
    S2 Pendidikan Matematika UNY 2018 A
    Keberhasilan dalam proses pembelajaran terletak pada guru yang mengajar. Seorang guru harus mampu menjadi seseorang yang menyenangkan bagi siswa dalam belajar matematika. Matematika bukan merupakan pelajaran yang harus dihapal, melainkan pelajaran yang harus dimengerti, dipahami dan direalisasikan. Sehingga seorang guru harus lebih kreatif dalam menyampaikan materi yang harus diberikan kepada siswa agar menyenangkan.

  11. Wilis Putri Hapsari
    S2 PEP A 2019

    This article provide a philosophical explanation that student are more assecible to understand decimal by Linear Arithmetic Block LAB than Multibase Arithmetic Block, thus research conducted by Kaye Stacey in 2001. LAB model is easy to understand because they show directly the part of the linear block fractioned and that in line with Kant preception that ‘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. Linear model is easier accepted by student sensory receptors because it simply form rahter than volume form that took the student to imagine more of rest of the decimal fractioned or unshowed in that model. The fifth grade student based on Piaget is in the trasition stage of operational concrete to operational so they need a physical objet to trigger their common sense so it can be more valuable to understand the concept.

  12. Tiara Wahyu Anggraini
    S2 Pendidikan Matematika D 2019

    Matematika dianggap sulit oleh siswa karena mereka sudah membayangkan duluan bahwa matematika itu sulit. Nah, ditambah lagi dengan gurunya yang langsung memberikan rumus dan langsung mengerjakan soal matematika. Kalaupun gurunya menjelaskan terlebih dahulu, pasti langsung abstrak atau langsung masuk rumus dan contoh soal-soalnya saja. Hal-hal inilah yang membuat siswa menjadi susah untuk enjoy dan paham ketika belajar matematika. Siswa SMP dan SMA saja masih sulit ketika diajar seperti itu, apalagi siswa SD. Hendaklah guru berpikir kreatif ketika mengajar sehingga nantinya dapat membawa siswa ke dalam kehidupan sehari-hari sehingga nantinya informasi yang masuk ke anak bisa tersampaikan. Seperti pendapat dari Piaget yang mengemukakan bahwa cara mengajarkan anak/siswa yaitu pertama dengan benda-benda konkret misalkan sebuah apel, terus kemudian semi konkret yaitu di gambar apel tersebut di buku ataupun papan tulis, kemudian semi abstrak mengatakan bahwa apel itu berjumlah 1 sehingga ditulis 1, kemudian abstrak dimana anak sudah mengetahui angka 1 tanpa harus melihat apel atau gambar apel tersebut. Nah dengan begitu, anak akan lebih paham apa yang dimaksud oleh gurunya. Hal tersebut adalah satu diantara contoh-contoh lainnya yang memudahkan siswa untuk lebih paham lagi dengan materi yang diajarkan. Selain itu, mereka akan lebih tertarik dan senang ketika belajar matematika. Dan juga, materi yang diajarkan guru bisa lebih bermakna lagi untuk siswanya.

  13. Indra Kusuma Wijayanti
    Pendidikan Matematika S2 C

    Adanya hubungan antara siswa dengan materi fisik yang digunakan ini siswa mampu mencapai tujuan pembelajaran, sehingga siswa dikatakan telah melalui proses belajar. Siswa sekolah dasar cenderung belum mampu berpikir abstrak karena siswa baru mulai berpikir secara logis terkait kejadian-kejadian konkret. Siswa SD mereka dapat belajar dengan bantuan benda-benda konkrit. seperti, ketika belajar berhitung dulu saya menggunakan permen atau membawa jagung atau korek api dari rumah. selain itu dapat menggunakan gambar-gambar seperti gambar buah-buahan untuk mempermudah siswa dalam menemukan apa yang sedang dicari.

  14. Dhamar Widya Safitri
    S2 PEP A 2019

    Pelajaran matematika sering dianggap pelajaran yang sulit bagi banyak siswa. Penyebab utamanya adalah cara guru menyampaikan materi kepada siswanya. Banyak guru yang hanya sekedar menyampaikan materi, rumus, dan proses penyelesaian soal, tanpa memperhatikan apakah siswanya sudah paham atau belum. Cara mengajar yang seperti itu juga membuat siswa merasa malas, mengantuk atau bahkan takut dengan pelajaran matematika.