Numeracy skills
Mathematics provides a set of tools for describing, analyzing and predicting the behaviour of systems in different domains of the real word. This practical utility of mathematics has always provided one major justification for the important role of mathematics in the school curriculum. In particular, the inclusion of application problems – traditionally in the format of word problems – was, and is intended to develop in students the skills of knowing when and how to apply their mathematics effectively in various kinds of problem situations encountered in everyday life and at work.
The PISA studies define mathematical literacy as follows (OECD, 2003, p. 24): “Mathematical literacy is an individual’s capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgments and to use and engage with mathematics in ways that meet the needs of that individual’s life as a constructive, concerned and reflective citizen.” The components of this definition are further elaborated in the above-mentioned document, e.g., the term “world” refers to natural, social and cultural objects.
The PISA literacy approach (OECD, 1999) requires students “be involved in the full mathematical modeling cycle”, solving tasks that address even out-of-school settings.
Since the application of mathematical knowledge usually requires the use of textual elaboration (at least in the phase of posing the problem), word problems are unavoidable.
Classroom word problems were categorized in several investigations according to features that are both mathematical and of cognitive representation nature. As far as additive structures are concerned, the following types of simple word problems were identified:
– combine,
– compare,
– change and
– equalize problems.
Bernstein’s educational knowledge codes, distinguishing between common sense knowledge and school knowledge (also called everyday and esoteric knowledge, respectively).
According to Bernstein’s argument, children are very early in their school career discouraged from connecting common sense knowledge and school knowledge. Even today it can be revealed that school success depends to some extent on students’ willingness and capacity to disclose common sense knowledge as a source of information in mathematics problem solving.
The role of culture in mathematics achievement incorporates the role of language competence. To understand mathematical word problems one has to be capable semantically analyze the linguistic components of a task, and furthermore, to identify important and redundant parts. (eg. task with a tennis party for students who have never seen any tennis). Well-documented results prove that the linguistic features of a word problem influence to certain extent the solution process.
Two effective strategies to promote connections between students’ mental representations and learning objectives to meet can be:
– rewording the word problem, or
– personalizing it.
– Another – even more radical – possible change in improving classroom environment is the use of reciprocal teaching in mathematics. The heart of this method is deliberately altering the roles and responsibilities of the teachers and students in the classroom. This change requires changes also in tasks that define mathematical lessons.
(source: Csapó, B. & Szendrei, M. (Eds.) (2011). Framework for diagnostic assessment of mathematics. Budapest: Nemzeti Tankönyvkiadó.)
adultbasicskills 