An Investigation of Pre-Service Elementary and Secondary Mathematics Teachers' Number Sense

Abstract

Öz: Bu çalışmanın amacı ilköğretim ve ortaöğretim matematik öğretmen adaylarının sahip olduğu sayı hissini incelemektir. Çalışmanın katılımcı grubunu 464 matematik öğretmen adayı oluşturmaktadır. Çalışmada öğretmen adaylarının sayı hissi kullanma performanslarını ölçmek için araştırmacılar tarafından geliştirilen çoktan seçmeli 31 sorudan oluşan bir Sayı Hissi Testi kullanılmıştır. Sayı Hissi Testi hem sayı hissi sorularını ve soruların olası çözümlerini içeren iki aşamalı bir testir. Testte yer alan sorulara verilen cevaplar hem doğruluk hem de kullanılan çözüm stratejisi (Sayı hissi stratejisi/Kural temelli strateji) açısından analiz edilmiş ve sayı hissi puanı hesaplanmıştır. Veri analizi sonucunda testten alınan sayı hissi puanları, matematik öğretmen adaylarının sayı hissi stratejilerini kullanmada başarılı olmadığını göstermektedir. Öğretmen adayları soruları çözerken sayı hissi stratejilerinden daha ziyade kural temelli stratejileri kullanmayı tercih etmiştir. Çalışmada ayrıca öğretmen adaylarının; Sayı Hissi Testi'ndeki başarıları ile sayı hissi kullanımları arasında pozitif bir ilişki bulunurken, sayı hissi kullanımları öğrenim görülen bölüme ve cinsiyete göre bir farklılık sergilememiştir.Anahtar Kelimeler: Sayı hissi, sayı hissi testi, sayı hissi stratejisi, kural temelli strateji, matematik öğretmen adayı DOI: 10.16949/turcomat.96275 Abstract:The aim of the study is to investigate primary and secondary pre-service mathematics teachers' number sense. A total of 464 mathematics teachers are participated in the study. To measure the number sense performances of the pre-service mathematics teachers with a Number Sense Test, including 31 multiple-choice questions, was developed by the researchers. Number Sense Test is a two-tailed test which includes the number sense questions and their possible solution strategies. Students' answers of Number Sense Test were analyzed to find the number sense points in terms of two aspects; one of them were correctness (True or False) and the second one was solving strategies (Number sense strategy or Rule based strategy) of pre-service teachers. According to the data analysis, mathematics teachers had low performance and they preferred to use rule based strategies rather than number sense strategies. Although there is a positive correlation between Number Sense Test performance and using number sense skills, there is no significant difference between male and female preservice teachers and their departments at using number sense.

Monitoring proficiency: Growth of number sense in primary school

“…It has been also concluded in several studies that students prefer rule‐ and operation‐based strategies rather than number sense skills when solving test items (Menon, 2004; Reys et al, 1999; Yang & Li, 2008; Zanzali & Ghazali, 2002). In this regard, it is emphasized that teacher tendencies to use rules when teaching mathematics present a hindrance before the improvement and usage of number sense skills (Gülbağcı Dede, 2015; Kilpatrick et al, 2001; Yang & Li, 2008). Concentrating on standard written computational algorithms in mathematics instruction is regarded as another approach that hinders the improvement of number sense skills as it prevents thinking skills such as reasoning and estimation from emerging (Burns, 1994; Hiebert, 1999; Kamii et al, 1993; Reys & Yang, 1998; Yang, 2005; Yang & Reys, 2002).…”

“…Studies on number sense have been performed with pre-school students (Aunio et al, 2004(Aunio et al, , 2006Howell & Kemp, 2010;Jordan et al, 2007Jordan et al, , 2010, primary school students from Grade 1 to Grade 4 (Çekirdekci et al, 2016;Mohamed & Johnny, 2010;Olkun et al, 2015;Zanzali & Ghazali, 2002), and elementary school students from Grade 5 to Grade 8 (Akkaya, 2016;Harç, 2010;İymen & Duatepe Paksu, 2015;Kayhan Altay, 2010;Kayhan Altay & Umay, 2013;Lin et al, 2016;Şengül & Gülbağcı Dede, 2013;Torbeyns & Verschaffel, 2016;Yapıcı, 2013), and preservice teachers (Gülbağcı Dede, 2015;Şengül, 2013;Şenol et al, 2015;Yaman,2015aYaman, , 2015b. Among these studies, there are limited number of research works about measuring number sense skills and test development, especially in primary schools.…”

“…Given the studies concluding that improvement of number sense skills increases mathematics achievements in years to come (Jordan et al, 2007; Mazzocco & Thompson, 2005; McGuire et al, 2012), lack of instruments that aim to identify number sense skills of primary school students raises concerns. Studies on number sense have been performed with pre‐school students (Aunio et al, 2004, 2006; Howell & Kemp, 2010; Jordan et al, 2007, 2010), primary school students from Grade 1 to Grade 4 (Çekirdekci et al, 2016; Mohamed & Johnny, 2010; Olkun et al, 2015; Yang & Li, 2008; Zanzali & Ghazali, 2002), and elementary school students from Grade 5 to Grade 8 (Akkaya, 2016; Harç, 2010; İymen & Duatepe Paksu, 2015; Kayhan Altay, 2010; Kayhan Altay & Umay, 2013; Lin et al, 2016; Şengül & Gülbağcı Dede, 2013; Torbeyns & Verschaffel, 2016; Yang et al, 2008; Yapıcı, 2013), and preservice teachers (Gülbağcı Dede, 2015; Şengül, 2013; Şenol et al, 2015; Yaman,2015a, 2015b). Among these studies, there are limited number of research works about measuring number sense skills and test development, especially in primary schools.…”

“…Despite different perspectives, there is a consensus on the necessity of improving number sense skills (Gülbağcı Dede, 2015). According to NCTM (1989), number sense skills cover (1) understanding the meaning of numbers, (2) establishing the relationship among numbers, (3) comprehending the relative magnitudes of numbers, (4) understanding the effects of operations on numbers, and (5) developing and using reference points in the cases that require measuring (p. 38).…”

Ortaokul Öğrenci̇leri̇ni̇n Yüzdeler Konusunda Sayi Duyularinin İncelenmesi̇

“…It may be stated that the number of studies on number sense in Turkey has recently increased (Çekirdekçi, Şengül, & Doğan, 2016;Gülbağcı Dede & Şengül, 2016;İymen & Duatepe Paksu, 2015;Yaman, 2015). Considering the studies on the field of number sense, while studies focusing on investigating the number sense of students, teachers and prospective teachers are frequently seen, studies investigating number sense skills especially in a certain subject in mathematics are less frequent.…”