VISUALIZATION OF ALGEBRARY IDENTIFICATIONS IN RXR=R2 (PLANE) AT SECONDARY LEVEL
Yıl: 2023 Cilt: 14 Sayı: 51 Sayfa Aralığı: 410 - 432 Metin Dili: İngilizce DOI: 10.35826/ijoess.3254 İndeks Tarihi: 24-05-2023
VISUALIZATION OF ALGEBRARY IDENTIFICATIONS IN RXR=R2 (PLANE) AT SECONDARY LEVEL
Öz: It is known that mathematics has an important effect on the development of science and technology. Identities, which are widely used in many branches of science, form the basis of some mathematics courses such as algebra. However, it appears as one of the learning areas of secondary school 7th grade mathematics and is seen as one of the difficult subjects to learn. The fact that there are many and abstract formulas about identities is difficult for students to remember. Therefore, visualization is important in teaching abstract concepts in a meaningful way and in associating concepts with daily life. Visualization is the use of mathematical and geometric symbols, shapes, diagrams, etc. to make something unseen imaginable. It is the drawing or showing of the shape and picture of an abstract concept with the help of pencil and computer. Visualization and visual proof are central to mathematics. The visualization approach is used in mathematics and mathematics education as a tool, not as a goal in the lessons. Identities are seen as one of the learning areas that we encounter in the solution of problems that we encounter in our daily lives and that are difficult to learn. In this direction, the visual proofs of the identities in R2 are shown in detail to the researchers thanks to the visualization approach, so that the algebraic identities can be learned more easily. Although identities are an important learning area in mathematics and algebra lessons, they are thought to be difficult to understand and learn by students. In line with this idea, students have difficulty in understanding identities as the visual models from which identities are obtained are not adequately expressed by the teachers and are not associated with daily life. For this reason, it is suggested by mathematics teachers that as a solution to this problem, visualizing abstract mathematical concepts in lessons or showing algebraic and visual proofs of some theorems may be beneficial. In this study, which was planned as a theoretical study, Within the scope of descriptive scanning model, document analysis technique was used. Visual proofs of basic algebraic identities are shown to researchers in detail by using geometric figures. In line with this purpose, some suggestions have been made to shed light on this issue for interested researchers.
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- Abate, A., Atnafu, M., & Michael, K. (2022). Visualization and problem-based learning approaches and students’ attitude toward learning mathematics. Pedagogical Research, 7(2), em0119. https://doi.org/10.29333/pr/11725.
- Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215-241 https://doi.org/10.1023/A:1.024.312.321.077.
- Bagni, G. T. (1998). Visualization and didactics of mathematics ın high school: An Experimental Reseach. Scientia Paedogogica Experimentalis, 1, 161-180.
- Barth, J. L., & Demirtaş, A. (1997). İlköğretim sosyal bilgiler öğretimi[Primary education social studies teaching], YÖK/Dünya Bankası[YÖK/ World Bank], Milli Eğitimi Geliştirme Projesi Yayınları[National Education Development Project Publications].
- Battista, M. T. (2007). The development of geometric and spatial thinking. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843-908). National Council of Teachers of Mathematics.
- Birgin, O., & Demirören, K. (2020). Sekizinci sınıf öğrencilerinin basit görsel ve cebirsel ıfadeler konusundaki hata ve kavram yanılgılarının ıncelenmesi[Investigation of the preservice science teachers’ views and suggestions on the application of the cooperative learning model in distance education environments]. Uluslararası Sosyal ve Eğitim Bilimleri Dergisi [International Journal of Social and Educational Sciences], 7(14), 233-247.
- Boaler, J., Chen, L., Williams, C., & Cordero, M. (2016).Seeing as understanding: The Importance of visual mathematics for our brain and learning. J Appl Computat Math 5: 325. doi: 10.4172/2168-9679,1000325.https://www.youcubed.org/wp-content/uploads/2017/03/Visual-Math-Paper-vF.pdf.
- Borwein, P., & Jörgenson, L. (1997). Visible Structures In Number Theory. https://doi.org/10.1080/00029890.2001.11919824.
- Budanur T. (2004). Coğrafya öğretiminde görsel araçlardan grafiklerin etkili ve yerinde kullanımı[Effective and appropriate use of graphics, one of the visual tools, in geography teaching]. [Unpublished Master Thesis]. Gazi University.
- Cirillo, M., & May, H. (2020, 12th ‒19th July). Decomposing proof in secondary classrooms: A promising intervention for school geometry. In The 14th International Congress on Mathematical Education. Shanghai, China.
- Dede, Y. (2013). Matematikte Ispat[Proof in mathematics]: Önemi, çeşitleri ve tarihsel gelişimi[ Importance, types and historical development],Pegem Akademi[Pegem Academy].
- Demirel, M. (1996). Bilgilendirici metin türünün ve okuduğunu kavrama becerisinin altıncı sınıf öğrencilerinin öğrenme düzeyine etkisi[The effect of informative text type and reading comprehension skills on the learning level of sixth grade students], [Unpublished Master Thesis]. Hacettepe University.
- Demircioğlu, H., & Polat, K. (2015). Ortaöğretim matematik öğretmen adaylarının “sözsüz ıspat” yöntemine yönelik görüşleri[Opinions of pre-service secondary school mathematics teachers on the "non-verbal proof" method],The journal of academic social science studies, 31(2), 233-254.
- Dexter, D. D., & Hughes, C. A. (2011). Graphic organizers and students with learning disabilities: A meta-analysis. Learning Disability Quarterly, 34, 51-72.
- Dogan, M. F., & Williams-Pierce, C. (2021). The role of generic examples in teachers’ proving activities. Educational Studies in Mathematics,106, 133–150. https://doi.org/10.1007/s10649-020-10002-3.
- Doyuran, G. (2014). Secondary school students’ misconceptions on basic terms in geometry [Published Master’s Thesis].Dokuz Eylul University.
- Dörfler, W. (1991). Forms and means of generalization in mathematics. In A. J. Bishop (Ed.), Mathematical knowledge: Its growth through teaching (pp. 63-85). Dordrecht: Kluwer Academic Publishers.
- Dufour-Janvier, B., Bednarz, N., & Belanger, M. (1987). Pedagogical considerations concerning the problem of representation. In C. Janvier (Ed.) Problems of Representation in the Teaching and Learning of Mathematics (pp. 109-122). Lawrence Erlbaum Associates: Hillsade, New Jersey.
- Eleftherios, K., & Theodosios, Z. (2007). Students’ beliefs and attitudes concerning mathematics and their effect on mathematical ability. CERME, 5, 258-267.
- Eritici, B. B. (2005). Lise ikinci sınıf biyoloji dersinde okutulan ‚boşaltım sistemi‛ konusunun öğretilmesinde görsel araçların ve geleneksel öğretimin öğrenmeye etkisinin karşılaştırılması[Comparison of the effects of visual aids and traditional teaching on learning in teaching the subject of 'excretory system' taught in high school second grade biology course]. [Unpublished Master Thesis].Selçuk University.
- Eroğlu, S. (2006). Görsel ve işitsel materyal kullanımının ortaöğretim 3. sınıf öğrencilerinin biyoteknoloji ile ilgili kavramları öğrenmeleri ve tutumları üzerine etkisi [The effect of the use of audio and visual materials on secondary school 3rd grade students' learning about biotechnology concepts and their attitudes].[ Yayınlanmamış Yüksek Lisans Tezi, Gazi Üniversitesi[Unpublished Master Thesis].Gazi University.
- Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P., & Flojo, J. (2009). Mathematics instruction for students with learning disabilities: A Meta-Analysis of Instructional Components. Review of Educational Research, 79, 1202-1242.
- Gierdien, F. (2007). From “Proofs without words” to “proofs that explain” in secondary mathematics. Pythagoras, 65, 53-62.
- Hanna, G. (2000). Proof, explanation and exploration. Special Issue on “Proof In Dynamic Geometry Environments”, Educational Studies In Mathematics, 44(1-2), 5-23.
- Hanna, G. & Barbeau, E. (2002). What Is Proof? In Baigrie, B. (Ed.), History of Modern Science and Mathematics, 1, 36- 48, Charles Scribner's Sons.
- Hanna, G. & Sidoli, N. (2007). Visualisation and proof: a brief survey of philosophical perspectives. ZDM Mathematics Education, 39, 73–78.
- Herch, R. (1993). Proving is convincing and explaining [Electronic Version]. Educational Studies in Mathematics, 24(4), 389-399.
- Ilhan, A., & Tutak, T. (2021). A scale development study ıntended for mathematics teacher candidates: mathematical visualization perception scale. International Electronic Journal of Mathematics Education, 16(1), em0623. https://doi.org/10.29333/iejme/9578.
- Joseph, J. U. (2020). Adopting mathematics as a desired insrtument for the reduction of corruption in Nigeria. International Journal for Educational and Vocational Studies, 2(10), 821–827.
- Kim M., Kim S., Lee J., Ahn D., & Lee, Y. (2006). Characteristics of medical students’ learning styles and their relationships to GPA. Korean J. Med. Educ. 18, 133–140.
- Kolloffel, B., Eysink, T. H., de Jong, T., & Wilhelm, P. (2009). The effects of representational format on learning combinatorics from an ınteractive computer simulation. Instructional Science, 37, 503-517.
- Konyalıoğlu, A. C. (2003). Üniversite düzeyinde vektör uzayları konusundaki kavramların anlaşılmasında görselleştirme yaklaşımının etkinliğinin ıncelenmesi[Investigation of the effectiveness of the visualization approach in understanding the concepts of vector spaces at university level].[Unpublished doctoral thesis].Ataturk University.
- Konyalıoğlu., A. C., Aksu. Z. & Şenel., E.Ö. (2012). The preference of visualization in teaching and learning absolute value. International Journal of Mathematical Education in Science and Technology, https://doi.org/10.1080/0020739X.2011,633627.
- Knuth, E. J. (2002). Secondary school mathematics teachers' conceptions of proof. Journal for Research in Mathematics Education, 33(5), 379-405. https://doi.org/10.2307/4149959.
- Martin, K. (2020, March). A Picture Is worth a thousand words. Medical Writing, 29(1) https://Www.Researchgate.Net/Publication/ 341293384.
- McCormick, B. H., DeFanti, T. A., & Brown, M. D. (1987). Visualization in scientific computing: Report of The NSF Advisory Panel on Graphics, Image Processing and Workstations. https://www.evl.uic.edu/documents/visc-1987.pdf.
- McCoy, E.(2019, February 21). How our braıns are hardwıred for vısual content. https://Killervisualstrategies.Com/Blog/How-Our-Brains-Are-Hardwired-For-Visual-Content.Html Erişim Tarihi: 08.12.2021.
- Mirza, A., Fitriawan, D., Zubaidah, R., & Nursangaji, A. (2022). Prospective mathematics teachers’ understanding of proof in mathematics for high school. Al-Jabar: Jurnal Pendidikan Matematika, 13(1), 1-11.
- Muchoko, C, Jupri, A., & Prabawanto, S. (2019). Algebraic visualization difficulties of students ın junior highschool. International Conference on Mathematics and Science Education. Journal of Physics: Conf. Series 1157 032108 IOP Publishing doi:10.1088/1742-6596/ 1157/ 3/032108.
- Nelsen, R. B. (2000).Proofs without words II: More Exercises in Visual Thinking. Mathematical Association of America.
- Özdemir, M.E., Duru, A., & Akgün, L. (2005). İki ve üç boyutlu düşünme: İki ve üç boyutlu geometriksel şekillerle bazı özdeşliklerin görselleştirilmesi[Two- and three-dimensional thinking: Visualizing some identities with two- and three-dimensional geometric shapes],Kastamonu Eğitim Dergisi[Kastamonu education magazine],13(2), 527.
- Ozgun-Koca, S. Asli. (1998).Students' use of representations in mathematics education. Paper presented at the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education https://files.eric.ed.gov/fulltext/ED425937.pdf. Erişim tarihi: 6.02.2022.
- Özer, M, N., & Şan, İ (2013). Görselleştirmenin özdeşlik konusu erişisine etkisi[The effect of vısualızatıon on reachıng the subject of ıdentıtıes].International Journal of Social science. 6(1), 1275-1294.DOI: 10.9761/Jasss_258.
- Polat, K. & Demircioğlu, H. (2021). Contextual analysis of proofs without words skills of pre-service secondary mathematics teachers: sum of integers from 1 to n case. Adiyaman Univesity Journal of Educational Sciences, 11(2), 93-106.
- Polster, B. (2004). Q.E.D. Beauty in mathematical proof. Walker Publishing Company.
- Satılmış, Ş., & Tunç. M. P. (2022). Middle school students' views on the use of visualization in problem solving. Karaelmas Journal of Educational Sciences, 10(2),118 - 129. https://dergipark.org.tr/tr/pub/kebd.
- Schoenfeld, A. H. (2020). Mathematical practices, in theory and practice. ZDM - Mathematics Education, 52(6), 1163–1175.
- Shin, M., & Bryant D. P. (2015). Fraction ınterventions for students struggling to learn mathematics : A Research Synthesis. Remedial and Special Education. DOI: 10.1177/0741932515572910.
- Sinclair, N., Cirillo, M., & de Villiers, M. (2017). The learning and teaching of geometry. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 457-488). National Council of Teachers of Mathematics.
- Suh, J., & Moyer, P. S. (2007). Developing students’ representational fluency using virtual and physical algebra balances. Journal of Computers In Mathematics and Science Teaching, 26, 155-173.
- Stylianou, D. A. (2002). On the ınteraction of visualization and analysis: The Negotiation of A Visual Representation in Expert Problem Solving. The Journal of Mathematical Behavior, 21(3), 303–317. https://doi.org/10.1016/S0732-3123(02)00131-1.
- Tekin, B. (2010).Ortaöğretim düzeyinde trigonometri kavramlarının öğrenilmesinde görselleştirme yaklaşımının etkililiğinin araştırılması[Investigation of the effectiveness of visualization approach on learning of concepts in trigonometry at the secondary level].[Published doctoral thesis(No:274662)].Atatürk University.
- Tekin, B., & Konyalıoğlu, A.C. (2010). Trigonometrik fonksiyonların toplam ve fark formüllerinin ortaöğretim düzeyinde görselleştirilmesi[Visualization of sum and difference formulas of trigonometric functions at secondary level].Bayburt Üniversitesi Eğitim Fakültesi Dergisi[Journal of Bayburt University Faculty of Education],5(1-2).
- Ugurel, İ., & Moralı, S. (2006). Karikatürler ve matematik öğretiminde kullanımı[Cartoons and their use in mathematics teaching].Milli Eğitim Dergisi[Journal of National Education]. 34(170), 1-10. Retrieved from https://dergipark.org.tr/tr/pub/milliegitim/issue/36942/422504.
- Uysal-Kog, O. & Baser, N. (2012). The role of visualization approach on students’ attitudes towards and achievements in mathematics. Elementary Education Online, 11(4), 945-957. Retrieved from http://ilkogretimonline.org.tr/index.php/io/article/view/1457/1313.
- Yalın, H.İ. (2001). Öğretim teknolojileri ve materyal geliştirme[Instructional technologies and material development].Nobel Yayıncılık[Nobel publishing].
- Yenioğlu, S., Sayar, K., & Güner Yıldız, N. (2022). Öğrenme güçlüğü olan öğrencilere alışveriş problemleri çözme becerisinin kazandırılması ve günlük yaşama genellenmesi. Ankara Üniversitesi Eğitim Bilimleri Fakültesi Özel Eğitim Dergisi, Erken Görünüm,1-24. https://doi.org/10.21565/ozelegitimdergisi.841368.
- Yıldırım, A., & Şimşek, H. (2021). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in the social sciences]. Seçkin Yayıncılık[Seçkin publishing].
- Winer, M. L., & Battista, M. T. (2022). Investigating students’ proof reasoning: analyzing students’ oral proof explanations and their written proofs in high school geometry. International Electronic Journal of Mathematics Education, 17(2), em0677. https://doi.org/10.29333/iejme/11713.
- Zopf R., Giabbiconi, C. M., Gruber T., & Müller, M. M. (2004). Attentional modulation of the human somatosensory evoked potential in a trial-by-trial spatial cueing and sustained spatial attention task measured with high density 128 channels eeg. Brain Res. Cogn. Brain Res. 20, 491–509. DOI: 10.1016/j.cogbrainres.2004.02.014.
| APA | Tekin B, KONYALIOGLU A (2023). VISUALIZATION OF ALGEBRARY IDENTIFICATIONS IN RXR=R2 (PLANE) AT SECONDARY LEVEL. , 410 - 432. 10.35826/ijoess.3254 |
| Chicago | Tekin Birol,KONYALIOGLU ALPER CIHAN VISUALIZATION OF ALGEBRARY IDENTIFICATIONS IN RXR=R2 (PLANE) AT SECONDARY LEVEL. (2023): 410 - 432. 10.35826/ijoess.3254 |
| MLA | Tekin Birol,KONYALIOGLU ALPER CIHAN VISUALIZATION OF ALGEBRARY IDENTIFICATIONS IN RXR=R2 (PLANE) AT SECONDARY LEVEL. , 2023, ss.410 - 432. 10.35826/ijoess.3254 |
| AMA | Tekin B,KONYALIOGLU A VISUALIZATION OF ALGEBRARY IDENTIFICATIONS IN RXR=R2 (PLANE) AT SECONDARY LEVEL. . 2023; 410 - 432. 10.35826/ijoess.3254 |
| Vancouver | Tekin B,KONYALIOGLU A VISUALIZATION OF ALGEBRARY IDENTIFICATIONS IN RXR=R2 (PLANE) AT SECONDARY LEVEL. . 2023; 410 - 432. 10.35826/ijoess.3254 |
| IEEE | Tekin B,KONYALIOGLU A "VISUALIZATION OF ALGEBRARY IDENTIFICATIONS IN RXR=R2 (PLANE) AT SECONDARY LEVEL." , ss.410 - 432, 2023. 10.35826/ijoess.3254 |
| ISNAD | Tekin, Birol - KONYALIOGLU, ALPER CIHAN. "VISUALIZATION OF ALGEBRARY IDENTIFICATIONS IN RXR=R2 (PLANE) AT SECONDARY LEVEL". (2023), 410-432. https://doi.org/10.35826/ijoess.3254 |
| APA | Tekin B, KONYALIOGLU A (2023). VISUALIZATION OF ALGEBRARY IDENTIFICATIONS IN RXR=R2 (PLANE) AT SECONDARY LEVEL. Uluslararası Avrasya Sosyal Bilimler Dergisi, 14(51), 410 - 432. 10.35826/ijoess.3254 |
| Chicago | Tekin Birol,KONYALIOGLU ALPER CIHAN VISUALIZATION OF ALGEBRARY IDENTIFICATIONS IN RXR=R2 (PLANE) AT SECONDARY LEVEL. Uluslararası Avrasya Sosyal Bilimler Dergisi 14, no.51 (2023): 410 - 432. 10.35826/ijoess.3254 |
| MLA | Tekin Birol,KONYALIOGLU ALPER CIHAN VISUALIZATION OF ALGEBRARY IDENTIFICATIONS IN RXR=R2 (PLANE) AT SECONDARY LEVEL. Uluslararası Avrasya Sosyal Bilimler Dergisi, vol.14, no.51, 2023, ss.410 - 432. 10.35826/ijoess.3254 |
| AMA | Tekin B,KONYALIOGLU A VISUALIZATION OF ALGEBRARY IDENTIFICATIONS IN RXR=R2 (PLANE) AT SECONDARY LEVEL. Uluslararası Avrasya Sosyal Bilimler Dergisi. 2023; 14(51): 410 - 432. 10.35826/ijoess.3254 |
| Vancouver | Tekin B,KONYALIOGLU A VISUALIZATION OF ALGEBRARY IDENTIFICATIONS IN RXR=R2 (PLANE) AT SECONDARY LEVEL. Uluslararası Avrasya Sosyal Bilimler Dergisi. 2023; 14(51): 410 - 432. 10.35826/ijoess.3254 |
| IEEE | Tekin B,KONYALIOGLU A "VISUALIZATION OF ALGEBRARY IDENTIFICATIONS IN RXR=R2 (PLANE) AT SECONDARY LEVEL." Uluslararası Avrasya Sosyal Bilimler Dergisi, 14, ss.410 - 432, 2023. 10.35826/ijoess.3254 |
| ISNAD | Tekin, Birol - KONYALIOGLU, ALPER CIHAN. "VISUALIZATION OF ALGEBRARY IDENTIFICATIONS IN RXR=R2 (PLANE) AT SECONDARY LEVEL". Uluslararası Avrasya Sosyal Bilimler Dergisi 14/51 (2023), 410-432. https://doi.org/10.35826/ijoess.3254 |
