Middle School Students' Understanding of Average

Abstract

The purpose of this study was to investigate 6, 7 and 8th grade students’ understanding of average and how these understandings change with respect to the grade level. Participants of the study were 18 students, 6 from each grade level. Semi-structured interviews were conducted to collect the data. Five problems related to the concept of average were asked to the students during the interviews. Problems were developed with respect to the literature review. Data collected were analyzed using content analysis technique. Analysis showed that most of the students understood average as an arithmetic mean, students mostly preferred the arithmetic mean algorithm as a strategy and they didn’t recognize average as a representative value. Results of the study were discussed in terms of the statistics education at middle school level.

Keywords

• average,measures of central tendency,statistical thinking

6 -8. Sınıf Öğrencilerinin Ortalama Kavramına Yüklediği Anlamlar

Öz

Bu araştırmanın amacı ilköğretim 6, 7 ve 8. sınıf öğrencilerinin ortalama kavramına yükledikleri incelemektir. Araştırmaya Bolu ilinde bir ilköğretim okulundaki 6, 7 ve 8. sınıflardan 6 öğrenci olmak için toplam 18 öğrenci katlanmıştır. Öğrencilere, değerlendirmenin 5 tane problem sorulmuş, sorunlu 3 problem alan yazını taramaktadır sonra Türkçeye çevrilmiş, 2 tanesi mevcut yazarlar tarafından yazılmıştır. Öğrencilerin onu biriyle yarı- yapılandırılmış görüşmeler yapılmıştır. Veriler içerik analizi yöntemiyle analiz edilmiştir. Bulgular büyük çoğunluğunun ortalanması, aritmetik ortalamada algıladıklarını, ortalama ile ilgili problemlerde ilk seçtikleri stratejinin aritmetik ortalaması veriyi temsil etme uygundur. Araştırmanın bulguları, ilk jestimde istatistik eğitimi tartışılmıştır.

Anahtar Kelimeler

• Ortalama, merkezi eğilim ölçüleri, istatistiksel düşünce

Kaynakça

1. Cai, J. (2000). Understanding and Representing the Arithmetic Averaging Algorithm: An Analysis and Comparison of US and Chinese Students’ Responses, International Journal of Mathematical Education in
2. Science and Techonolgy, 31, 839-855. Jones, G., Thornton, A., Langrall, W., Mooney, S., Perry, B., & Putt, J. (2000). A Framework for Characterizing
3. Children’s Statistical Thinking. Mathematical Thinking and Learning, 2 (4), 269-307. Leavy, A.M. & Middleton, J.A. (2001, April). Middle Grade Students Understanding of the Statistical Concept of Distribution. American Educational Research Association Annual Conference in Seattle, Washington, USA.
4. Leavy, A.M. & O’Loughlin, N. (2006). Preservice Teachers Understanding of the Mean: Moving Beyond the Arithmetic Average, Journal of Mathematics Teacher Education, 9, 53-90.
5. Mevarech, Z. (1983). A deep structure model of students’ statistical misconceptions, Educational Studies in Mathematics, 14, 415-429.
6. Milli E itim BakanlL L, (1998). lkö retim Okulu Matematik Dersi Ö retim ProgramL, “6. 7., 8. sLnLflar”. Ankara.
7. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: VA.
8. Pollatsek, A., Lima, S. & Well, A.D. (1981). Concept or computation: Students’ understanding of the mean,

9. Educational Studies in Mathematics, 12, 191-204. Randall, G. (2006). An Exploration of Students’ Statistical Thinking. Teaching Statistics, 28(1), 17-21.
10. Mokros, J. & Russell, S. (1995). Children’s Concepts of Average and Representativeness, Journal for Research in Mathematics Education, 26, 20-39. imKek, H. ve YLldLrLm, A. (2006). Nitel Ara t rma Yöntemleri. Ankara: Seçkin YayLncLlLk.
11. Watson, M. & Moritz, J. (2000). The Longitudinal Development of Understanding of Average, Mathematical
12. Thinking and Learning, 2(1&2), 11-50. YLldLrLm, H. H. (2006). The Differential Item Functioning (DIF) Analysis of Mathematics Items in the International assessment Programs. YayLmlanmamLK Doktora Tezi, Orta Do u Teknik Üniversitesi, Ankara.