Manipulating Money in Math: Effects of SES and Home Experience with Money

It is an aspired learning goal to move flexibly and bidirectionally between the real world and abstract, formal mathematical understandings (Freudenthal, 2005). Physical manipulatives can support the transition from informal or concrete to formal or abstract mathematical understanding (Carbonneau et al., 2013; Martin & Schwartz, 2005). The seminal studies of Carraher et al. (1985) with children who worked as vendors show that money provides an authentic context in which children can learn mathematics even without formal schooling. Additionally, in schools, money is suggested to make math more relevant and engaging (Attard, 2018) and, when taught as measurement, to support the development of financial numeracy skills (Savard et al., 2020).
Perceptual richness in manipulatives, however, can hinder mathematical problem solving (Carbonneau et al., 2013). In particular, the use of realistic money has been reported to both enhance conceptual understanding but also lead to more errors in fourth- and sixth- graders mathematical word problem-solving (McNeil et al., 2009). Furthermore, effective use of manipulatives depends on students’ ability to manage dual representation—focusing on both the object’s symbolic and physical properties (DeLoache, 2003; Uttal et al., 2009). Money is a unique case because, while it is a physical object, it also carries additional symbolic information that students must relate to the task at hand. However, there is limited empirical evidence on its effects as a cognitive and educational tool. Moreover, there is evidence that students’ high prior knowledge of manipulatives could hinder their problem-solving performance while using them, for example, due to the effect of functional fixedness(Petersen & McNeil, 2013). Functional fixedness could activate children’s real-life knowledge of money and affect their effectiveness in using this material in a novel context (Munoz-Rubke et al., 2018). Following these observations, we argue that students’ socio-economic background including their parental subjective financial well-being and their home experiences with money which shape children’s prior knowledge of money may influence their interaction with money as a manipulative and their mathematical problem-solving while manipulating this material. The purpose of our research project is to examine the impact of money as a manipulative in an era dominated by digital transactions, where children may have limited exposure to cash at home but could still benefit from using it in school. Second, we aim to identify SES-related factors that influence students' prior knowledge of money and consequently its’ effectiveness as manipulative material in the classroom. In this project, we investigate how the use of money as a manipulative material impacts 3rd graders’ mathematical money word problem-solving performance, and how these effects are influenced by parents’ highest educational and occupational status (HISEI), parents’ subjective financial well-being (SFW), and students’ home experiences with money (HEX). Our primary objective is to examine whether the use of money as a manipulative enhances students’ math problem-solving after a brief instructional and practice session. Our second objective is to explore if the effect of money affects students differently based on SES-related factors (i.e., HISEI and SFW in Study 1, and HISEI and HEX in Study 2).
By answering these questions we aim to inform instructional strategies that promote equity and enhance mathematical education for diverse students as well as international efforts to integrate financial literacy into mathematical education, promoting essential life skills (OECD, 2014).

We employed a within- and between-subjects design to examine students’ performance on money-related word problems. In both studies, we assessed students’ mathematical word problem-solving in a money-related context with and without money as manipulative material in a classroom-assessment setting following a brief instructional and practice session (45’). This instructional session aimed to introduce money as a manipulative that students can use to solve mathematical problems and to model its’ use in money word problem-solving. Study 1 (n = 68) examined the role of money as a manipulative alongside students’ socio-economic status (SES) and parental subjective financial well-being (SFW). Study 2 (n = 97) focused on SES and students’ home experience with money (HEX). For the analysis, we used a mixed linear model and controlled for students’ prior mathematics and language achievement.

Materials:
Assessment Tasks In Money Math Word Problem-Solving
The researchers developed the mathematical word problems based on the 3rd-grade curriculum in mathematics (MENFP, 2011). It included 9 items with real-world money problems. We developed two versions of these problems (in total 18 items) with similar computational procedures and difficulty levels but slight numerical and pictorial variations.
Standardized national achievement assessment (ÉpStan)
We used data from ÉpStan, the Luxembourgish national school monitoring program using achievement tests in key academic domains and parent questionnaires to operationalize students’ general mathematics and language skills as well as their socio-economic background based on an index of parents’ highest educational and occupational position.
Subjective Financial Well-being (SFW)
Parents completed the short form of the Financial Well-being Scale (CFPB, 2015), which assesses overall satisfaction with financial status (e.g., “I have money left over at the end of the month”).
Home Experience with Money (HEX)
Parents completed a 5-item survey developed by the researchers. This measure is designed to capture the extent to which parents engage their children in out-of-school activities related to money. Parents indicated how often each activity occurred since the beginning of that year (e.g., “…Playing games that involve processing of play-money with your child such as “store” game, monopoly etc.?”).
Across both studies, the use of money as manipulative material did not significantly affect students’ mathematical problem-solving performance. The effect of money was not influenced by SES, but SFW and HEX showed significant interactions with the effect of money: students with a higher SFW and greater HEX performed worse when using money during mathematical problem-solving. Furthermore, we observed a gender effect favoring boys in both Money and No Money conditions despite similar prior academic achievement and SES.
Our findings suggest that the effectiveness of money as a manipulative is influenced by individual factors related to the real-life exposure of students to money concepts and experiences. The unexpected finding of a main gender effect warrants further investigation to ensure effective instructional sessions for all students when using manipulatives. Overall, our results highlight that considering individual differences, related to what students experience and learn out of school is crucial when integrating contextually meaningful materials into mathematics education.