Innovation in Curriculum: Context in Mathematics Curricula

Abstract

The past few years have seen the emergence of five mathematics curricula developed with support by the National Science Foundation for the middle grades: Mathematics in Context (MIC) (National Center for Research in Mathematical Sciences Education and Freudenthal Institute 2001), Math Thematics (Billstein and Williamson 1999), Connected Mathematics (CMP) (Lappan et al. 1998), MathScape, a View of the World from a Mathematical Perspective (Education Development Center 1998), and Pathways to Algebra and Geometry (Institute for Research on Learning 1997). One striking similarity that characterizes these middle school curricula, as well as their reform counterparts at the elementary and secondary school levels, is the pervasive use of context. Using a definition suggested by Borasi (1986), context is “the situation in which [a] problem is embedded” (p. 129). Context is usually supplied by the text of the problem, but it can also be contained in pictures, diagrams, or tables. A quick review of any of the curricula mentioned above shows that context is plentiful and varied. This abundance of context is in marked contrast with traditional textbooks, in which context appears only in brief introductions or end-of-section story problems.

Personal Experiences And Beliefs In Probabilistic Reasoning: Implications For Research

“…Given how statistics is often taught through examples drawn from "real life" teachers need to exercise care in ensuring that this intended support apparatus is not counterproductive. This is particularly important in light of current curricula calls for pervasive use of contexts (Meyer, Dekker, and Querelle, 2001;Ministry of Education, 1992) and research showing the effects of contexts on student' ability to solve open ended tasks (Cooper and Dunne, 1997;Sullivan, Zevenbergen, and Mousley, 2002).…”

Does this Answer Make Sense? Primary School Students and Adults Judge the Reasonableness of Computational Results in Context-Based and Context-Free Mathematical Tasks

“…Unlike previous studies that reported consistently low performance across the different number domains (e.g., Alajmi & Reys, 2010), our participants performed better in natural than in decimal numbers in context-free items (Task 1), but not in context-based ones (Task 2) in which the average performance in decimals was relatively higher. This probably indicates that the presence of context can potentially allow solvers to overcome difficulties associated with the difficulty of specific mathematical concepts or topics, since it enables the consideration of the problem in the context of real life (Meyer et al, 2001;Sowder & Schappelle 1989). However, it is worth noting that the presence of context was more beneficial for adults than it was for students, who performed relatively better in context-free than in context-based items.…”

“…The degree to which solvers consider this aspect in their judgements highly depends on the richness of their real-life experiences as well as their ability to rely upon them to make appropriate judgements (Alajmi & Reys, 2010;Masingila et al, 1996). Although contextualised tasks are not necessarily more interesting or engaging for students than decontextualised ones (Beswick, 2011), nor always associated with increased performance (Can & Özdemir, 2020), the presence of context can potentially support connections with real life (Meyer et al, 2001;Sowder & Schappelle 1989), and thus enable reflections on the external reasonableness of their answers.…”

Stimulus Control for Making Math Verbal

“…are probably the two most asked questions in a math class (Schwartz, 2006). The lack of function (i.e., embedded reinforcement for solving real world application) of mathematical concepts has prevented students from acquiring and loving math (De Corte et al, 2000;Meyer et al, 2001). By building function to fluency training, students can learn 2+3 as finding the sum of two measures through various mathematical problems instead of learning 2+3=5 as a math fact.…”