Unrealistic responses to realistic problems with missing information: what are important barriers?

Abstract

It is a well-documented finding that students tend to neglect their real-world knowledge when solving word problems, even when realistic assumptions are needed. Although studies have successfully shown the extent to which students tend to provide unrealistic responses, the question of where this tendency comes from has yet to be answered. We focused on two major steps needed to solve realistic word problems: noticing missing information and making realistic assumptions. We conducted two studies with fifth graders (Study 1, N ¼ 108; Study 2, N ¼ 60) in which we compared students' (un-)realistic responses to problems that differed in how obvious the missing information was. Study 1 fostered only students' ability to make assumptions. Study 2 fostered this ability plus the ability to notice missing information. The results indicate that, if the missing information is not obvious, students' failure to notice it seems to be what prevents them from arriving at a realistic solution.

Context matters: the importance of extra-mathematical knowledge in solving mathematical problems

“…Alternatively, when they do not know the rules of the board games (Siegler and Ramani, 2008), how to use a ruler (MacDonald and Lowrie, 2011), or how to use cell phones (McMullen et al, 2019;McMullen and Siegler, 2020), they can have difficulties learning number concepts or spontaneously focusing on mathematical relationships. Although this understanding is in line with many mathematical competence definitions that state that a person possesses proficiency in mathematical competence when able to use mathematics in everyday life (Haara et al, 2017;Niss and Højgaard, 2019;OECD, 2019;Toomela et al, 2020) and many researchers have directed our attention to how using mathematics outside the classroom is a valuable skill (Gainsburg, 2008;MacDonald and Lowrie, 2011;Reinke and Casto, 2020), in reality many students (Reusser and Stebler, 1997;Verschaffel and De Corte, 1997;Altay et al, 2017;Krawitz et al, 2018) and teachers (Lee, 2012) make superficial connections between mathematics and real life and tend to neglect the real-world knowledge when solving mathematical problems. Accordingly, in the current study we aim to pilot tasks assessing extra-mathematical knowledge and how it is related to mathspecific skills.…”

Pengembangan Alat Peraga M3 (Mean, Modus, Median) dengan Menerapkan Konsep Statistika untuk Siswa di Tingkat Menengah

“…Dengan demikian, pembelajaran seharusnya maksimal apabila terjadi antara pendidik dan peserta didik, antar peserta didik dan peserta didik, antar pesera didik dengan bahan dan media pembelajaran, bahkan peserta didik dengan dirinya sendiri, namun dalam hal mencapai tujuan-tujuan yang ditetapkan secara bersama-sama, khususnya hasil belajar yang optimal. Pembelajaran matematika merupakan suatu siklus pembelajaran yang dilakukan oleh pendidik kepada peserta didik untuk mengembangkan daya nalar imajinatif sehingga dapat menumbuhkan kemampuan nalar peserta didik, sebagai upaya untuk mengembangkan penguasaan pembelajaran matematika yang baik (Harel, 2008;Krawitz et al, 2018;Moore et al, 2019;Susanto, 2013).…”

The role of reading comprehension in mathematical modelling: improving the construction of a real-world model and interest in Germany and Taiwan

“…In order to successfully construct a real-world model, students also need to structure and simplify the information, which also includes making assumptions. Students seem to lack meta-knowledge about modelling, particular the knowledge that solving modelling problems often requires learners to make assumptions (Krawitz et al, 2018), and it was found to be a particular strength of students educated in Germany compared with students educated in other countries. This is presumably because German students have more experience working with modelling problems (Chang et al, 2020;Hankeln, 2020).…”