Publication: Etkinlik temelli öğretim yaklaışımının orantısal akıl yürütmeye dayalı problem çözme başarısına etkisi
Abstract
ETKİNLİK TEMELLİ ÖĞRETİM YAKLAŞIMININ ORANTISAL AKIL YÜRÜTMEYE DAYALI PROBLEM ÇÖZME BAŞARISINA ETKİSİ Bu araştırmanın amacı etkinlik temelli öğretimin orantısal akıl yürütme gerektiren kelime problemlerin çözümünde ilköğretim öğrencilerinin problem çözme başarılarına etkisini araştırmaktır. Bu bağlamda öğrenci problem çözme başarılarının, problem çözme süreçlerini etkileyen faktörlere (bilişsel sitil, orantısal akıl yürütme becerisi seviyesi ve cinsiyet) göre farklılaşma durumları üzerine odaklanılmış, öğrencilerin orantı kelime problemlerini çözerken kullandıkları çözüm stratejileri araştırılmış ve bu stratejilerin problem türlerine göre farklılık gösterip göstermediği incelenmiştir. Araştırma, “öntest-sontest kontrol gruplu deneme modeli”nde gerçekleştirilmiş, amaç doğrultusunda belirlenen alt problemlere korelasyonel araştırma teknikleri kullanılarak cevap aranmıştır. Problem çözme stratejilerinin belirlenmesi amacı çerçevesinde ise alan yazında tanımlı stratejiler ışığı altında öğrenci kağıt-kalem testlerinden elde edilen veriler nitel analiz teknikleri ile incelenmiştir. Araştırmanın örneklemini bir ilköğretim okulunda 7. ve 8. sınıfa devam eden 134 (65 kız ve 69 erkek) öğrenci oluşturmuştur. Veri toplama aracı olarak, problem çözme başarı testleri (orantı, yüzde ve üçgenlerde benzerlik) kullanılmış ve testlerin her biri kavramsal ve problem çözme bölümleri olmak üzere ikişer bölümden oluşmuştur. Problem çözme başarı testlerinin kavramsal bölümlerinde matematik dersi öğretim programında yer alan her bir davranışa ait birer soru yer almıştır. Problem çözme bölümlerinde ise; orantı problemlerinde 11 (5 bilinmeyen değer, 3 nicel karşılaştırma ve 3 nitel karşılaştırma ve önsezi), yüzde ve üçgenlerde benzerlik problemlerinde 5’er problem olmak üzere toplam 21 problem yer almıştır. Testlerin geçerlik, güvenirlik ve madde analizleri gerçekleştirilmiştir. Veri toplama aracı olarak, ayrıca orantısal akıl yürütme becerileri testi (Miller ve Fey, 2000) ve bilişsel sitillerin (alan bağımlı ve alan bağımsız) belirlenmesi amacıyla “Saklı Şekilller Grup Testi” (GEFT) (Witkin, 1971) kullanılmıştır. Araştırmacı tarafından, ilgili alan yazın ışığında, etkinlik temelli öğretim materyalleri tasarlanmıştır. Deney gruplarına problem çözme öğretimi bu materyaller aracılığıyla, kontrol gruplarına geleneksel öğretim yöntemi ile öğretim gerçekleştirilmiştir. Uygulamalar okulu matematik öğretmeni tarafından gerçekleştirilmiştir. Öğretim etkinlikleri sonrasında, •7. sınıf deney grubu öğrencilerinin orantı [t(33)=- 29,117, p=0,00<0,05, Xöntest=15<Xsontest=31] ve yüzde [t(33)=-14,951, p=0,00<0,05, Xöntest=16<Xsontest=27] problemlerini çözme başarılarında anlamlı bir artışın olduğu görülmüştür. •8. sınıf deney grubu öğrencilerinin orantı [t(32)=-32,433, p=0,00<0,05, Xöntest=18<Xsontest=33] ve üçgenlerde benzerlik [t(32)=-11,848, p=0,00<0,05, Xöntest=17<Xsontest=28] problemlerini çözme başarılarında anlamlı bir artışın olduğu görülmüştür. •Sontest puanlarına göre, 7. sınıf deney grubu öğrencilerinin orantı [t(64)=8,511, p=0,00<0,05, Xkontrol=23<Xdeney=31] ve yüzde [t(64)=2,544, p=0,01<0,05, Xkontrol=22<Xdeney=27] problemlerini çözme başarılarının kontrol grubu öğrencilerinden daha yüksek olduğu görülmüştür. •Sontest puanlarına göre, 8. sınıf deney grubu öğrencilerinin orantı [t(66)=5,695, p=0,00<0,05, Xkontrol=28<Xdeney=33] ve üçgenlerde benzerlik [t(66)=4,838, p=0,00<0,05, Xkontrol=22<Xdeney=28] problemlerini çözme başarılarının kontrol grubu öğrencilerinden daha yüksek olduğu görülmüştür. •7. sınıf deney grubu öğrencilerinin orantı [t(33)=-10,328, p=0,00<0,05, Xöntest=7<Xsontest=13] ve yüzde [t(33)=-16,049, p=0,00<0,05, Xöntest=7<Xsontest=14] kavramsal başarılarında anlamlı bir artışın olduğu görülmüştür. •8. sınıf deney grubu öğrencilerinin orantı [t(32)=-17,345, p=0,00<0,05, Xöntest=8<Xsontest=15] ve üçgenlerde benzerlik [t(32)=-10,743, p=0,00<0,05, Xöntest=7<Xsontest=13] kavramsal başarılarında anlamlı bir artışın olduğu görülmüştür. •Sontest puanlarına göre, 7. sınıf deney grubu öğrencilerinin orantı [t(64)=3,757, p=0,00<0,05, Xkontrol=11<Xdeney=13] ve yüzde [t(64)=3,106, p=0,00<0,05, Xkontrol=11<Xdeney=14] kavramsal başarılarının kontrol grubu öğrencilerinden daha yüksek olduğu görülmüştür. •Sontest puanlarına göre, 8. sınıf deney grubu öğrencilerinin orantı [t(66)=6,766, p=0,00<0,05, Xkontrol=12<Xdeney=15] ve üçgenlerde benzerlik [t(66)=3,977, p=0,00<0,05, Xkontrol=11<Xdeney=13] kavramsal başarılarının kontrol grubu öğrencilerinden daha yüksek olduğu görülmüştür. •Orantı problemlerinin çözümünde, ilköğretim 7. sınıf öğrencilerinden OAYBS’si yüksek olanlar düşük olanlara göre; alan bağımsız erkekler ve kızlar kendi cinsiyetlerinde alan bağımlı öğrencilere göre daha başarılıdır. •Orantı problemlerinin çözümünde, ilköğretim 8. sınıf alan bağımsız öğrenciler, alan bağımlı öğrencilerden; OAYBS’si yüksek olanlar düşük olan öğrencilerden göre daha başarılıdırlar. •Orantı problemlerini çözme başarıları açısından; 7. ve 8. sınıf öğrencilerinin orantısal akıl yürtüme becerileri arttıkça daha başarılı oldukları, 8. sınıf alan bağımlı öğrencilerin alan bağımsız öğrencilere göre daha başarılı olduları ve 7. sınıf kız ve erkek öğrencileri kendi içlerindeki alt gruplarda alan bağımsız olanların alan bağımlı olanlara göre daha başarılı oldukları görülmüştür. •İlköğretim öğrencileri Bilinmeyen Değer orantı problemlerinde daha çok “İçler Dışlar Çarpımı” stratejisi kullanılırken, Nicel Karşılaştırma orantı problemlerinde daha çok “Birim Oran” stratejisi tercih etmişlerdir. •İlköğretim öğrencilerinin “Denklik Sınıfı” stratejisini, hem bilinmeyen değer hem de nicel karşılaştırma problemlerinin tamamının çözümünde uygun bir şekilde kullandıklarına dair sonuçlar elde edilmiştir. Tartışma bölümünde ise çalışmada elde edilen sonuçlar alan yazın ışığında tartışılmıştır. Problem Çözme, Orantı İlişkili Problem, Etkinlik Temelli Öğretim, Orantısal Akıl Yürütme, Bilişsel Tarz Sayfa Adedi: xviii+229
The Effect of Activity Based Teaching Approach over The Proportional Reasoning Related Problem Solving Achievement The purpose of this research is to explore the effect of activity based teaching approach over primary students’ problem solving achievements while solving word problems that is related proportional reasoning. In this context, the focus was over students’ problem solving achievements which differentiated according to factors (cognitive style, the level of proportional reasoning skills, and gender) that affects problem solving process, the strategies that were used by students during word problems about proportion and whether these strategies varied according to the types of problems or not was analyzed. The research was carried out according to ‘the experimentation model that requires pre-test and post-test with control group’ and the answers were searched by applying correlation research techniques to sub – problems which were determined according to purpose of the research. In the frame of determining problem solving strategies, under the light of strategies defined according to field literature, the data gathered from the students’ paper-pencil tests were analyzed by using qualitative analysis techniques. 134 students (65 girls and 69 boys) that were attending to a primary school were forming the sample of the research. In order to gather data techniques such as, problem solving achievement tests (proportion, percentage and similarities in triangles) were used and the tests were composed of two parts, one was conceptual and the other part was problem solving. In the conceptual parts of problem solving tests a question was used for each behavior in the program of teaching mathematics. In the problem solving parts, 21 problems were used that composed of 11 (5 missing value, 3 quantitative comparisons and 3 qualitative comparison and prediction) problems about proportion, 5 problems about percentages and 5 problems about the similarities in triangles. The validity, reliability and item analysis of the tests were carried out. In order to gather data an additional proportional reasoning skills test (Miller and Fey, 2000) and in order to determine the cognitive styles ‘Group Test of Embedded Figures’ (GEFT) (Witkin, 1971) were used. Activity based teaching materials were designed according to related field literature by the researcher. The problem solving instruction was given to experimental group by using these materials and traditional teaching methods were used during the instructional phase of the control group. The applications were carried out by the mathematics teacher of the school. After the instructional activities, •A meaningful increase was seen among 7th grade experimental group students achievement in solving problems about proportion [t(33)=- 29,117, p=0,00<0,05, Xpre-test=15<Xpost-test=31] and percentages [t(33)=-14,951, p=0,00<0,05, Xpretest=16<Xposttest=27]. •A meaningful increase was seen among 8th grade experimental group students achievement in solving problems about proportion [t(32)=-32,433, p=0,00<0,05, Xpretest=18<Xposttest=33] and similarities in triangles [t(32)=-11,848, p=0,00<0,05, Xpretest=17<Xposttest=28 ]. •According to post-test results the achievement of 7th grade experimental group students was higher than control group students while solving problems about proportion [t(64)=8,511, p=0,00<0,05, Xcontrol=23<Xexperimental=31] and about percentage [t(64)=2,544, p=0,01<0,05, Xcontrol=22<Xexperimental=27] •According to post-test results the achievement of 8th grade experimental group students was higher than control group students while solving problems about proportion [t(66)=5,695, p=0,00<0,05, Xcontrol=28<Xexperimental=33] and about similarities in triangles [t(66)=4,838, p=0,00<0,05, Xcontrol=22<Xexperimental=28] •A meaningful increase was seen in 7th grade experimental group students’ achievement about the concepts of proportion [t(33)=-10,328, p=0,00<0,05, Xpretest=7<Xposttest=13] and percentage [t(33)=-16,049, p=0,00<0,05, Xpretest=7<Xposttest=14 ]. •A meaningful increase was seen in 8th grade experimental group students’ achievement about the concepts of proportion [t(32)=-17,345, p=0,00<0,05, Xprentest=8<Xposttest=15] and similarities in triangles [t(32)=-10,743, p=0,00<0,05, Xpretest=7<Xposttest=13]. •According to post-test results 7th grade experimental group students conceptual achievements in proportion [t(64)=3,757, p=0,00<0,05, Xcontrol=11<Xexperimental=13] and percentage [t(64)=3,106, p=0,00<0,05, Xcontrol=11<Xexperimental=14] was higher than control group students. •According to post-test results 8th grade experimental group students conceptual achievements in proportion [t(66)=6,766, p=0,00<0,05, Xcontrol=12<Xexperimental=15] and similarities in triangles [t(66)=3,977, p=0,00<0,05, Xcontrol=11<Xexperimental=13] was higher than control group students. •In solving problems about proportion, among the 7th grade primary school students, the ones who had higher OAYBS were more successful than the ones who had lower OAYBS and; field independent boys and girls were more successful than field dependent students according to their own gender. •In solving problems about proportion, 8th grade field independent primary school students and students who had higher OAYBS were more successful than field dependent students and students who had lower OAYBS. •In terms of achievement in problem solving about proportion, 7th and 8th grade students became more successful as long as their skills about proportional reasoning were increased, 8th grade field dependent students were more successful than field independent students and in the sub groups of 7th grade boys and girls the field independent ones were more successful than field dependent ones. •While Primary school students were using “the cross-product algorithm” strategy in solving missing value problems about proportion, they choose “unit rate” strategy in solving quantitative comparison problems about proportion. •The results which showed that primary school students used “equal fraction strategy” properly for solving both missing value and quantitative comparison problems was obtained. In the discussion part the results obtained in the research was discussed in terms of field literature. Key Words: Problem Solving, Proportional Reasoning Related Problem, Activity Based Teaching, Proportional Reasoning, Cognitive Style. Number of Pages: xviii +229
The Effect of Activity Based Teaching Approach over The Proportional Reasoning Related Problem Solving Achievement The purpose of this research is to explore the effect of activity based teaching approach over primary students’ problem solving achievements while solving word problems that is related proportional reasoning. In this context, the focus was over students’ problem solving achievements which differentiated according to factors (cognitive style, the level of proportional reasoning skills, and gender) that affects problem solving process, the strategies that were used by students during word problems about proportion and whether these strategies varied according to the types of problems or not was analyzed. The research was carried out according to ‘the experimentation model that requires pre-test and post-test with control group’ and the answers were searched by applying correlation research techniques to sub – problems which were determined according to purpose of the research. In the frame of determining problem solving strategies, under the light of strategies defined according to field literature, the data gathered from the students’ paper-pencil tests were analyzed by using qualitative analysis techniques. 134 students (65 girls and 69 boys) that were attending to a primary school were forming the sample of the research. In order to gather data techniques such as, problem solving achievement tests (proportion, percentage and similarities in triangles) were used and the tests were composed of two parts, one was conceptual and the other part was problem solving. In the conceptual parts of problem solving tests a question was used for each behavior in the program of teaching mathematics. In the problem solving parts, 21 problems were used that composed of 11 (5 missing value, 3 quantitative comparisons and 3 qualitative comparison and prediction) problems about proportion, 5 problems about percentages and 5 problems about the similarities in triangles. The validity, reliability and item analysis of the tests were carried out. In order to gather data an additional proportional reasoning skills test (Miller and Fey, 2000) and in order to determine the cognitive styles ‘Group Test of Embedded Figures’ (GEFT) (Witkin, 1971) were used. Activity based teaching materials were designed according to related field literature by the researcher. The problem solving instruction was given to experimental group by using these materials and traditional teaching methods were used during the instructional phase of the control group. The applications were carried out by the mathematics teacher of the school. After the instructional activities, •A meaningful increase was seen among 7th grade experimental group students achievement in solving problems about proportion [t(33)=- 29,117, p=0,00<0,05, Xpre-test=15<Xpost-test=31] and percentages [t(33)=-14,951, p=0,00<0,05, Xpretest=16<Xposttest=27]. •A meaningful increase was seen among 8th grade experimental group students achievement in solving problems about proportion [t(32)=-32,433, p=0,00<0,05, Xpretest=18<Xposttest=33] and similarities in triangles [t(32)=-11,848, p=0,00<0,05, Xpretest=17<Xposttest=28 ]. •According to post-test results the achievement of 7th grade experimental group students was higher than control group students while solving problems about proportion [t(64)=8,511, p=0,00<0,05, Xcontrol=23<Xexperimental=31] and about percentage [t(64)=2,544, p=0,01<0,05, Xcontrol=22<Xexperimental=27] •According to post-test results the achievement of 8th grade experimental group students was higher than control group students while solving problems about proportion [t(66)=5,695, p=0,00<0,05, Xcontrol=28<Xexperimental=33] and about similarities in triangles [t(66)=4,838, p=0,00<0,05, Xcontrol=22<Xexperimental=28] •A meaningful increase was seen in 7th grade experimental group students’ achievement about the concepts of proportion [t(33)=-10,328, p=0,00<0,05, Xpretest=7<Xposttest=13] and percentage [t(33)=-16,049, p=0,00<0,05, Xpretest=7<Xposttest=14 ]. •A meaningful increase was seen in 8th grade experimental group students’ achievement about the concepts of proportion [t(32)=-17,345, p=0,00<0,05, Xprentest=8<Xposttest=15] and similarities in triangles [t(32)=-10,743, p=0,00<0,05, Xpretest=7<Xposttest=13]. •According to post-test results 7th grade experimental group students conceptual achievements in proportion [t(64)=3,757, p=0,00<0,05, Xcontrol=11<Xexperimental=13] and percentage [t(64)=3,106, p=0,00<0,05, Xcontrol=11<Xexperimental=14] was higher than control group students. •According to post-test results 8th grade experimental group students conceptual achievements in proportion [t(66)=6,766, p=0,00<0,05, Xcontrol=12<Xexperimental=15] and similarities in triangles [t(66)=3,977, p=0,00<0,05, Xcontrol=11<Xexperimental=13] was higher than control group students. •In solving problems about proportion, among the 7th grade primary school students, the ones who had higher OAYBS were more successful than the ones who had lower OAYBS and; field independent boys and girls were more successful than field dependent students according to their own gender. •In solving problems about proportion, 8th grade field independent primary school students and students who had higher OAYBS were more successful than field dependent students and students who had lower OAYBS. •In terms of achievement in problem solving about proportion, 7th and 8th grade students became more successful as long as their skills about proportional reasoning were increased, 8th grade field dependent students were more successful than field independent students and in the sub groups of 7th grade boys and girls the field independent ones were more successful than field dependent ones. •While Primary school students were using “the cross-product algorithm” strategy in solving missing value problems about proportion, they choose “unit rate” strategy in solving quantitative comparison problems about proportion. •The results which showed that primary school students used “equal fraction strategy” properly for solving both missing value and quantitative comparison problems was obtained. In the discussion part the results obtained in the research was discussed in terms of field literature. Key Words: Problem Solving, Proportional Reasoning Related Problem, Activity Based Teaching, Proportional Reasoning, Cognitive Style. Number of Pages: xviii +229