Opportunities to Learn Reasoning and Proof in Eighth-Grade Mathematics Textbook

Year 2019, , 601 - 618, 31.08.2019

Muhammed Fatih Dogan

https://doi.org/10.17679/inuefd.527243

Cited By: 4

Abstract

In this study,
reasoning and proof activities in the eighth-grade mathematics textbook were investigated.
The reasoning and proof activities of the entire textbook were evaluated
separately based on the different learning areas, sections of the book, and
purpose of the activities. According to the results, these activities
constituted 7.7% of all activities in the book. The proportion of the
reasoning and proof activities differed by learning area, with 11.8% of the
total activities in Numbers and Operations, 7.8% in Probability, 7.4% in
Geometry and Measurement, and 5.3% in Algebra. In the learning area of
Statistics, no such content was found. When the sections of the book were
evaluated, most of the proof-related activities were observed in the Warning
section (55%); followed by 38% in the Information and Activity sections and
29% in the Warming-up section. This ratio was only 2.9% in the Examples
section, and there was no proof related content found in the Exercises
section. In examining the purpose of proof activities, it was mostly used for
investigating claims/conjectures (49 tasks), and making claims/conjectures (20
tasks). There were only 8 activities for evaluating an argument, but none for
producing arguments. The results conclude that reasoning and proof were not
sufficiently evident in the textbook; therefore, the engagement of students with
such activities may be limited.

Keywords

Reasoning and Proof, Textbook Analysis, Curriculum

Sekizinci Sınıf Matematik Ders Kitabındaki Matematiksel Akıl Yürütme ve İspatı Öğrenme Olanakları

Abstract

Bu çalışmada 8. Sınıf matematik ders kitabında
matematiksel akıl yürütme ve ispat etkinliklerinin ne oranda ve nasıl yer
aldığı araştırılmıştır. Bunun için okullarda yaygın olarak okutulan bir ders
kitabının tüm içeriği incelenmiştir. Bu incelemede akıl yürütme ve ispat
etkinlikleri öğrenme alanlarına, kitabın bölümlerine ve etkinliklerin amacına
göre ayrı ayrı değerlendirilmiştir. Elde edilen sonuçlara göre bu etkinlikler
kitapta yer alan tüm etkinliklerin % 7,7’sini oluşturmaktadır. İspat ile
ilgili etkinliklerin öğrenme alanlarına göre oranlarının Sayılar ve İşlemlerde
% 11,8; Olasılıkta %7,8; Geometri ve Ölçmede % 7,4 ve Cebirde % 5,3 olduğu
tespit edilmiştir. Veri İşleme öğrenme alanında ise ispat ile ilgili bir
içerik bulunamamıştır. Kitabın bölümlerine göre değerlendirildiğinde ispat
etkinliklerinin en çok Uyarı kısmında (% 55) yer aldığı; Bilgi ve Etkinlik kısımlarında
% 38, Hazırlık Çalışması kısmında ise % 29 oranında ispata değinildiği
görülmüştür. Kitabın Örnekler kısmında ispat etkinliklerine % 2,9 oranında yer
verilirken Alıştırmalar kısmında ispatla ilgili herhangi bir kavrama
ulaşılamamıştır. İspat etkinlikleri amacına göre incelendiğinde ise çoğunlukla
varsayımları araştırma amacıyla (49 etkinlik) sunulabileceği görülmüş; kitapta
varsayımda bulunma amacıyla sunulabilecek 20 etkinlik; bir argümanı
değerlendirmeye yönelik de 8 etkinlik mevcut olduğu belirlenmiştir. Öte
yandan, kitapta argüman oluşturma amacına uygun herhangi bir etkinliğe
rastlanmamıştır. Bu araştırma ders kitabında akıl yürütme ve ispata yeterli
düzeyde yer verilmediğini; dolayısıyla öğrencilerin bu tür etkinliklerle
etkileşimlerinin sınırlı kalabileceğini göstermektedir.

Keywords

Akıl Yürütme Ve İspat, Ders Kitabı Analizi, Öğretim Programı

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