Abstract
While the value of ‘schematic representations’ in problem solving requires no further demonstration, the way in which students should be taught how to construct these representations invariably gives rise to various debates. This study, conducted on 146 grade 4 students in Luxembourg, analyzes the effect of two types of ‘schematic representation’ (diagrams vs. schematic drawings) on the solving of arithmetical problems. The results show that the presence of schematic representations has a clear positive effect on overall student performance and that a non negligible proportion of students manage to reuse the representations encountered in order to solve new problems. While showing an effect slightly in favor of diagrams as opposed to schematic drawings, our results do not really permit us to draw any conclusions about the form that these representations should take, in particular since a differential effect was observed depending on the type of problem.
Highlights
While mathematics and literacy may have been viewed as two separate domains, educational stakeholders, in the United States, have attempted to bring these two domains closer together over the past three decades through the use of children’s literature, especially in the form of story picture books (National Council of Teachers of Mathematics [NCTM], 1992, 2004, 2018)
Based on the thematic coding analysis, 11 perceived barriers were identified which could be broadly grouped under five themes, namely Time Constraint, Lack of Pedagogical Knowledge and Confidence, Resource Constraint, Doubts about Outcome Expectancy, and Inhibiting Social Norms (Table 2)
An exception is the Encouraged and inspired by teacher’s own perception that teaching mathematics through children’s literature is an interesting and innovative concept category where relatively more in-service teachers (24.2%) cited this enabler, as compared to their pre-service counterparts (15.3%). Another exception is related to the category, Encouraged and inspired by recommendations found in the textbook guides for teachers, which accounts for 7.7% of all coding occurrences on the enablers perceived by in-service teachers, but it was never cited by any of the preservice teachers
Summary
While mathematics and literacy may have been viewed as two separate domains, educational stakeholders, in the United States, have attempted to bring these two domains closer together over the past three decades through the use of children’s literature, especially in the form of story picture books (National Council of Teachers of Mathematics [NCTM], 1992, 2004, 2018). Students performed satisfactorily in international mathematics assessments, they continue to exhibit negative attitudes towards mathematics (Mullis et al, 2016, 2020), which has drawn the attention of policymakers in Taiwan To address such concerns, the MET is encouraging mathematics teachers in Taiwan to design mathematics teaching and learning that are appealing to and potentially generate a meaningful learning for students, which could be manifested using children’s literature (e.g., story picture books). Given that teachers’ beliefs about mathematics teaching and learning can shape their mathematics teaching practice (Polly et al, 2013), teachers’ beliefs cannot be overlooked and should be properly taken into consideration This is in line with what Pajares (1992), a pioneering figure in the research field of teachers’ beliefs, argued: “the beliefs teachers hold influence their perceptions and judgments, which, in turn, affect their behaviour in the classroom”
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