Promoting Cross-Notation Rational Number Knowledge

• In Event: Connecting Fractions and Decimals

Abstract

Rational number knowledge is a core component of mathematical development well into secondary school. An important, but under examined, aspect of rational number knowledge is the ability to fluently switch between fraction and decimal representations, herein referred to as cross-notation knowledge (Authors, submitted). The ability to flexibly use fraction and decimals in novel contexts appears to be an important feature of adaptive expertise with rational numbers (McMullen et al., 2020) Game-based learning environments have been shown to be promising means to support skills and knowledge related to the development of mathematical skills, including features of knowledge related to adaptive expertise (Brezovszky et al., 2019).

Thus, the main aim of the study was to test the effectiveness of a sequential integration of two educational games, Number Trace and NanoRoboMath, to promote cross-notation knowledge. Number Trace is based on number line estimation, implemented as a walkable platform in a forest in which the player controls a dog that tries to find the location of the bones on the number line determined by a given magnitude of a rational number (Figure 4.1). In NanoRoboMath the player moves a nanorobot along the number line using the four basic arithmetic operations (Figure 4.1). Both games require students to convert between symbolic notations fractions and decimals, in relation to their size and operations with them, as well connect symbolic notations of rational numbers with non-symbolic representations. The need to make connections between different symbolic and non-symbolic representations is expected to promote students' cross-notation knowledge with rational numbers.

A total of 14 7th grade classrooms (mean=13.2 years, SD=0.32 years) from 8 schools with 204 students (102 female, 102 male) participated in the study. The schools were from varying SES areas from a city in southern Finland. Eight classrooms were assigned to experimental group (116 students) and six classrooms to control group (88 students). Permission to take part in the study was received from the guardians of the students, principals, and teachers. At the start of each testing students were informed of their right to stop taking part in the study at any point. The ethical guidelines of the University of Turku and the Finnish national board on research integrity (TENK) were followed. After a pre-test, experimental group teachers had their students play the Number Trace game for three 45 minute sessions and the NanoRoboMath game for five 45 minute sessions, followed by a post-test. Control group teachers continued with business-as-usual instruction. Measures of cross-notation knowledge included mentally converting from/to fractions to/from decimals and the use of multiple notations (e.g. ½ + 0.5 = 1) in solutions on the arithmetic sentence production task (McMullen et al., 2020).

The game-based learning environment was successful in promoting cross-notation knowledge. Students who played the games outperformed students in the control condition on both measures of cross-notation knowledge (conversion ηp2 = .09; multiple notation solutions ηp2 = .04), even after taking into account pre-test scores (Figure 4.2).

Authors

• Jake McMullen, Turun yliopisto (UTU)
  Presenting Author

• Antti Koskinen, Tampere University
  Non-Presenting Author

• Tomi Kärki, University of Turku
  Non-Presenting Author

• Saku Määttä, University of Turku
  Non-Presenting Author

• Antero Lindstedt, Tampere University
  Non-Presenting Author

• Hilma Halme, University of Turku
  Non-Presenting Author

• Erno Lehtinen, University of Turku
  Non-Presenting Author

• Minna M Hannula-Sormunen, University of Turku
  Non-Presenting Author

• Kristian Kiili, Tampere University
  Non-Presenting Author