We daily encounter problems of a mathematical nature and with their solutions implying the interrelating of data to obtain the correct responses. This is also the case with those problems labelled verbal narratives. However, what capacities are most crucial to resolving this type of problem? Is what matters most the speed of processing or does it all begin with the interpretation of content? A new scientific study strengthens the assumption that resolving verbal mathematics problems does not only involve dominating the subject even while this factor is determinant.
The mathematics program and curricular targets in primary teaching, handed down by the Ministry of Education, indicate that the resolution of verbal problems requires the application of mathematical knowledge (facts, concepts and relationships, rules and procedures) and linguistic capacities (reading and interpreting texts). The document states that such capacities are transversal to teaching and provide a means facilitating the learning of mathematics. However, the resolution of verbal mathematics problems may be challenging to many students, especially those with learning difficulties in this subject or who are at risk of developing them.
One of the most recent meta-analyses of the predictors of verbal problem resolution, undertaken by Xin Lin, made recourse to a multivariate statistical technique (structural equations models) that attempts to clarify the contribution of the cognitive and mathematical capacities of these activities among primary school students. The research evaluated factors such as understanding of the language, memory, attention and non-verbal rationalising (cognitive resources) and the understanding of reading, vocabulary and the recalling and application of facts (mathematical capacities). They correspondingly analysed 98 empirical studies and established analytical subgroups for younger and older students (from pre-school to the 2nd year versus from the 3rd to the 5th year).
In the subgroup of younger students, the results highlighted the recollection of mathematic facts, which apply cognitive resources, such as planning, to solve more complex problems. In the older student subgroup, the findings demonstrate the importance of mathematical vocabulary.
The solution begins in the vocabulary
One of the most important factors for consideration arises from the progressive utilisation of technical terms in the exercises that students are set to resolve that, in turn, implies a displacement from simple and daily language. In the early years, they are faced with problems such as: “Maria has two oranges and Inês has three. How many oranges do they have in total?” In subsequent age groups, the vocabulary deployed is more complex leading to questions such as: “Every side of Figure X is the same. The length of one side of the figure is 3 cm. What is the perimeter of Figure X?” Therefore, it is natural that academic capacities may make different contributions in accordance with the mathematical vocabulary involved. Hence, for older students, the mastery of the vocabulary used is a determinant factor in their being able to find solutions.
This analytical work clarifies how resolving verbal problems requires the consolidation of the cognitive and academic capacities. The study also indicates how the relevance of these resources may differ with age as conveyed with the greater ease with which older students are able to make inferences. This thereby concludes that helping students to accumulate academic knowledge, as a facilitator of cognitive flexibility, also plays a fundamental role in the resolution of verbal problems.
Damião, H., Festas, I., Bivar, A., Grosso, C., Oliveira, F., & Timóteo, M. C. (2020). Programa e Metas Curriculares de Matemática — Ensino Básico. https://www.dge.mec.pt/sites/default/files/Basico/Metas/Matematica/programa_matematica_basico.pdf
Lin, X. (2020). Investigating the unique predictors of word-problem solving using meta-analytic structural equation modeling. Educational Psychology Review. https://doi.org/10.1007/s10648-020-09554-w
Powell, S. & Stevens, E. A. & Berry, K. (2019). Effects of a Word-Problem Intervention on Word-Problem Language Features for Third-Grade Students with Mathematics Difficulty. Learning Disabilities: A Multidisciplinary Journal. 24. 1-14. 10.18666/LDMJ-2019-V24-I2-9835.