A Study on Sixth Grade Students’ Misconceptions and Errors in Spatial Measurement: Length, Area, and Volume

Abstract

The purpose of the present study was to portray students' misconceptions and errors while solving conceptually and procedurally oriented tasks involving length, area, and volume measurement. The data were collected from 445 sixth grade students attending public primary schools in Ankara, Türkiye via a test composed of 16 constructed-response format tasks. The findings revealed a wide range of misconceptions and errors such as Bbelieving that all rulers are 30 cm long,^Bconfusing area formula with perimeter formula,^Bbelieving a box has more than one surface area,B using the volume formula for surface area,^Bbelieving that ruler must be longer than the object measured,^etc. These misconceptions and errors could be considered as the evidences indicating the sixth graders' lack of comprehension of the fundamental concepts of spatial measurement and their relationships and the procedures and formulas used for measuring length, area, and volume. The possible causes of such misconceptions and overcoming ways were also discussed.

Teaching Area Measurement and Subgoals through Problem Solving

“…However, this procedure, and the numerical result, may seem disconnected from the spatial characteristic of area (Baturo & Nason, 1996;Tan Sisman & Aksu, 2016). Students' conceptual understanding of the numerical result of an area formula may be limited if students view multiplication as a linear, arithmetical procedure only (Baturo & Nason, 1996).…”

“…In 2010, only 38% of Year 9 students were able to demonstrate their understanding of the area formula for a rhombus . Middle school students in Turkey (Tan Sisman & Aksu, 2016) and the USA (Martin & Strutchens, 2000;Strutchens et al, 2003) also experience difficulty applying area formulae.…”

“…Perhaps the most frequently cited cause of students' difficulty using area formulae is that mathematics teachers tend to over-emphasise area formulae (Huang & Witz, 2011;Kidman & Cooper, 1997;Kordaki & Balomenou, 2006;Kordaki & Potari, 2002;Martin & Strutchens, 2000;Nitabach & Lehrer, 1996;Outhred & Mitchelmore, 1996;Tan Sisman & Aksu, 2016;Zacharos, 2006). This over-emphasis comes in the form of a pedagogical focus on procedural fluency and rote memorisation of area formulae, often at the expense of conceptual understanding and strategic competence (Zeromska, 2010).…”

“…(2) Students measure perimeter by counting the squares around the outside of a shape drawn onto a grid instead of linear units (Owens & Outhred, 2006;Tan Sisman & Aksu, 2016).…”

“…Second, area measurement has applications in other school disciplines, particularly in science and technology (Huang & Witz, 2011;Smith, Males, & Gonulates, 2016), as well as in vocational subjects. Finally, the reasoning that students develop while learning area measurement can be applied in the learning of other mathematical strands such as operations with numbers, volume, multiplication, fractions, probability, algebraic multiplication, enlargement, and calculus (Davydov, Gorbov, Mukulina, Savelyeva, & Tabachnikova, 1999;Dougherty & Zilliox, 2003;Fernández, De Bock, Verschaffel, & Van Dooren, 2014;Hirstein et al, 1978;Kordaki & Potari, 1998;Outhred & Mitchelmore, 2000;Sarama & Clements, 2009;Tan Sisman & Aksu, 2016).…”