Yıl: 2021 Cilt: 40 Sayı: 1 Sayfa Aralığı: 45 - 59 Metin Dili: Türkçe DOI: 10.7822/omuefd.845782 İndeks Tarihi: 07-02-2023

Matematiksel Modeller ile Öğretimde Hata Temelli Aktiviteler

Öz:
Matematik dersinin en önemli amaçlarından biri problem çözme becerisi yüksek bireyler yetiştirebilmektir. Matematik öğretim programlarında bu durum sıkça vurgulanmaktadır. Günümüzde iyi bir problem çözücü yetiştirme çabasını destekleyen en önemli yöntemlerden biri modellemedir. Bu çalışmada matematiksel modellerin öğretiminde hata temelli aktivitelerin, ortaokul matematik öğretmeni adaylarının modellemeye ilişkin hataları belirleyebilmeleri amaçlanmıştır. Yarı deneysel desen kullanılarak yürütülen araştırmanın örneklemini bir devlet üniversitesinin ilköğretim matematik öğretmenliği son sınıfında öğrenim gören iki farklı şubeden 62 öğretmen adayı oluşturmaktadır. Rastgele olarak bu iki şubeden biri deney, diğeri ise kontrol grubu olarak belirlenmiştir. Deney grubunda matematiksel modellerin öğretimi hata temelli aktiviteler kullanılarak, kontrol grubunda ise öğretici merkezli olarak gerçekleştirilmiştir. Veriler toplam yedi sorudan oluşan bir bilgi testiyle toplanmıştır. Bu testteki her bir soru için doğru ya da hatalı iki çözüm yapılmıştır. İki farklı çözüm kâğıdı şeklinde sunulan bilgi testi hem deney hem de kontrol grubundaki öğretmen adaylarına ön ve son test olarak uygulanmıştır. Çalışmada ANCOVA analizi sonuçlarına göre deney grubu lehine gruplar arasında anlamlı bir farklılık belirlenmiştir. Buna göre matematiksel modellerin öğretiminde hata temelli aktivitelerin doğru modelleme yapma sürecinde pozitif bir etkiye sahip olduğu belirlenmiştir. Bu çalışma doğru ve hatalı modelleri öğretmen adaylarına sunarak gerçekleştirilecek modelleme öğretiminin öneminin altını çizmektedir. Bu modelleme öğretiminin bilgisayar teknolojisiyle desteklenmesi önerilmektedir.
Anahtar Kelime: Hata Hata temelli aktivite Matematiksel model Model Matematik öğretmeni adayı

Error-Based Activities in Mathematical Models Teaching

Öz:
A mathematics teacher who makes preparations to improve the mathematical competence of the students takes into account the importance of modeling competence (Han & Kim, 2020). Moreover, it is thought that teachers should be able to interpret a mathematical model as well as design a mathematical model. Bilgili, Özkaya, Çiltaş and Konyalıoğlu (2020) examined the middle school mathematics teachers' error approach in modeling in their study, and they found that most of the teachers had difficulty in distinguishing the correct or incorrect solution while evaluating the solution performed. They also found that teachers had difficulties in explaining the modeling of concepts on which they did not have sufficient knowledge. In the light of the information provided, it is important for teachers both to have mathematical models competencies (Akgün et al., 2013; Han & Kim, 2020) and to be able to interpret these models (Bilgili et al., 2020). It is thought that it is important for teachers to be canalized to different teaching methods to maximize their mathematical competencies and skills such as problem- solving and modeling before becoming a teacher. It is also thought that this teaching process being error-based may be effective in meeting expectations. Based on the above-mentioned issues, the answer to the following question was sought in this study: “Do error-based activities have an effect on teaching mathematical models?” Finally, as in most experimental studies, it was tried to obtain a model between the independent variable of error-based activity and the dependent variable of teaching mathematical models in this study. In this study, one of the 4th-grade branches in the faculty where the research was conducted was selected as the experimental group while the other branch was selected as the control group. Therefore, the experimental design of the research was determined as a “quasi-experimental design” with an unbalanced control group. An unbalanced control group design, which is among the pre-test and post- test control group designs, was used in this study, which was conducted to measure the effect of error- based teaching of mathematical models on prospective teachers' skills to identify errors related to models. The research group of the study consists of 62 prospective teachers studying in the 4th-grade of primary education mathematics teaching program at a state university. There are 32 prospective teachers in the experimental group and 30 prospective teachers in the control group. The data were collected using a knowledge test containing seven questions. This knowledge test has been included in the study of Bilgili et al (2020). The researchers prepared two solutions, one of which was correct and the other was incorrect, for each question in this test. These solutions prepared by using different models were presented to prospective teachers as two different solution sheets. The prospective teachers, who were not informed about whether the solutions were correct or incorrect, were asked to evaluate the solutions in both solution sheets. The knowledge test was applied as a pre-test to the prospective teachers in the experimental group and control group. Then, an error-based teaching method was used to teach mathematical models to the experimental group, while the instructor-centered teaching method was used to teach mathematical models in the control group. The study was conducted for three hours a week and lasted nine hours in total. Pre-tests were applied one week before the application, and post- tests were applied one week after the application. In the control group, the lessons were taught by giving correct models for the concepts. On the other hand, in the experimental group, the lessons were taught by giving examples of both incorrect and correct models. For each question in the knowledge test, solutions were created using a correct or incorrect model. Therefore, different evaluation criteria were determined and scored. Before proceeding with experimental procedures for the experimental group and control group, it was necessary to test whether there was a significant difference between the groups' mean scores obtained from the knowledge test. Therefore, the Shapiro-Wilk test was conducted, and it was observed that there was no significant difference between the knowledge test pre-test scores of the prospective teachers in the experimental group and control group; also, the data was found to have a normal distribution (p> .05). However, significant differences were observed between the groups in terms of their success grades, regardless of their pre-test scores. In other words, the method used had an effect on students' error approaches. Considering the eta-squared values, it is observed that being in different groups explains 44% of the difference in the knowledge test post-test scores, regardless of the pre-test scores. However, it was concluded that knowledge test mean pre-test scores were also an important predictor of post-test scores (F (1.59) = 11.933, p <.01). Considering eta-squared values, it is observed that the knowledge test mean pre-test scores alone explain 16.8% of the difference in the mean post-test scores.
Anahtar Kelime: Error Error based activity Mathematical model Model Mathematics prospective teacher

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
APA Bilgili S, Özkaya M, ÇILTAS A, KONYALIOGLU A (2021). Matematiksel Modeller ile Öğretimde Hata Temelli Aktiviteler. , 45 - 59. 10.7822/omuefd.845782
Chicago Bilgili Sibel,Özkaya Merve,ÇILTAS ALPER,KONYALIOGLU ALPER CIHAN Matematiksel Modeller ile Öğretimde Hata Temelli Aktiviteler. (2021): 45 - 59. 10.7822/omuefd.845782
MLA Bilgili Sibel,Özkaya Merve,ÇILTAS ALPER,KONYALIOGLU ALPER CIHAN Matematiksel Modeller ile Öğretimde Hata Temelli Aktiviteler. , 2021, ss.45 - 59. 10.7822/omuefd.845782
AMA Bilgili S,Özkaya M,ÇILTAS A,KONYALIOGLU A Matematiksel Modeller ile Öğretimde Hata Temelli Aktiviteler. . 2021; 45 - 59. 10.7822/omuefd.845782
Vancouver Bilgili S,Özkaya M,ÇILTAS A,KONYALIOGLU A Matematiksel Modeller ile Öğretimde Hata Temelli Aktiviteler. . 2021; 45 - 59. 10.7822/omuefd.845782
IEEE Bilgili S,Özkaya M,ÇILTAS A,KONYALIOGLU A "Matematiksel Modeller ile Öğretimde Hata Temelli Aktiviteler." , ss.45 - 59, 2021. 10.7822/omuefd.845782
ISNAD Bilgili, Sibel vd. "Matematiksel Modeller ile Öğretimde Hata Temelli Aktiviteler". (2021), 45-59. https://doi.org/10.7822/omuefd.845782
APA Bilgili S, Özkaya M, ÇILTAS A, KONYALIOGLU A (2021). Matematiksel Modeller ile Öğretimde Hata Temelli Aktiviteler. Ondokuz Mayıs Üniversitesi Eğitim Fakültesi Dergisi, 40(1), 45 - 59. 10.7822/omuefd.845782
Chicago Bilgili Sibel,Özkaya Merve,ÇILTAS ALPER,KONYALIOGLU ALPER CIHAN Matematiksel Modeller ile Öğretimde Hata Temelli Aktiviteler. Ondokuz Mayıs Üniversitesi Eğitim Fakültesi Dergisi 40, no.1 (2021): 45 - 59. 10.7822/omuefd.845782
MLA Bilgili Sibel,Özkaya Merve,ÇILTAS ALPER,KONYALIOGLU ALPER CIHAN Matematiksel Modeller ile Öğretimde Hata Temelli Aktiviteler. Ondokuz Mayıs Üniversitesi Eğitim Fakültesi Dergisi, vol.40, no.1, 2021, ss.45 - 59. 10.7822/omuefd.845782
AMA Bilgili S,Özkaya M,ÇILTAS A,KONYALIOGLU A Matematiksel Modeller ile Öğretimde Hata Temelli Aktiviteler. Ondokuz Mayıs Üniversitesi Eğitim Fakültesi Dergisi. 2021; 40(1): 45 - 59. 10.7822/omuefd.845782
Vancouver Bilgili S,Özkaya M,ÇILTAS A,KONYALIOGLU A Matematiksel Modeller ile Öğretimde Hata Temelli Aktiviteler. Ondokuz Mayıs Üniversitesi Eğitim Fakültesi Dergisi. 2021; 40(1): 45 - 59. 10.7822/omuefd.845782
IEEE Bilgili S,Özkaya M,ÇILTAS A,KONYALIOGLU A "Matematiksel Modeller ile Öğretimde Hata Temelli Aktiviteler." Ondokuz Mayıs Üniversitesi Eğitim Fakültesi Dergisi, 40, ss.45 - 59, 2021. 10.7822/omuefd.845782
ISNAD Bilgili, Sibel vd. "Matematiksel Modeller ile Öğretimde Hata Temelli Aktiviteler". Ondokuz Mayıs Üniversitesi Eğitim Fakültesi Dergisi 40/1 (2021), 45-59. https://doi.org/10.7822/omuefd.845782