This weekend I read the “The National Strategy to Improve Literacy and Numeracy among Children and Young People in Ireland 2011-2020”. Why did I do this? I looked for inputs to improve one of the module concepts we are currently working on in our DGMATHSC3 Team, where we seek to support students to master cognition in written problem-solving at age of 8 to 10. Both literacy and numeracy define in this tasks and ask for the student to transfer from one to another. But first of all they are more then “reading, writing and arithmetics!”:
“Traditionally we have thought about literacy as the skills of reading and writing; but today our understanding of literacy encompasses much more than that. Literacy includes the capacity to read, understand and critically appreciate various forms of communication including spoken language, printed text, broadcast media, and digital media. Throughout this document, when we refer to “literacy” we mean this broader understanding of the skill, including speaking and listening, as well as communication using not only traditional writing and print but also digital media.Literacy includes the ability to use and understand spoken language, print, writing and digital media
Numeracy is not limited to the ability to use numbers, to add, subtract, multiply and divide. Numeracy encompasses the ability to use mathematical understanding and skills to solve problems and meet the demands of day-to-day living in complex social settings. To have this ability, a young person needs to be able to think and communicate quantitatively, to make sense of data, to have a spatial awareness, to understand patterns and sequences, and to recognise situations where mathematical reasoning can be applied to solve problems”
How to support students recognise mathematical reasoning in a written problem?
First of all,and this is elementary to understand the difficulty, we are neither completely on a pure mathematics path nor on a completely language path. We need to handle both not separately, but in the interaction or transformation from on into the other: The switch from literacy to numeracy.
If we take a closer look to the usuel learning materials, e.g. Zahlenbook or Westermann, we experience problemsolving mostly at the end of linear progression in a domaine or subdomaine. The student will treat a problem which is complexe and rich in complexity. This problem will demonstrate if the student can master a given topic in „realword“ context.
However if we take a look at the research done in this domain (e.g. Gamo, Sander and Brissiaud 2010) or the works of Guy Brousseau and Raymond Duval, we see how difficult it is for the student to transform the mathematical thinking out of the contexte given by literacy, even if he masters the topic.
We should therefore concentrate on the cognition that takes the student to „transform litteracy into mathematical thinking, plan a path and solve this“, the higher order thinking. We would train the students first of all in the skills we find in the domaine of arithmetic resolution problems (cf. plan d’études): Analyse literacy and create a mental representation, plan a solution path by recognizing patterns, solve the operations and during the whole task evaluate the correctness of the solving.
We leave aside the complexity of the other domaines, until the student got enough time to train the domaine skills and could reinvest the learned cognition form the problem-solving module to solve these complexe and complexity problems.
However, we will have to encourage the transfer of the cognition in given contexts. Therefore we should train the student in the different types of problems (6 types according to Vergnaud), make appear money, distance and quantity problems and then mix those who are similar, support the novice student by combination items and do afterwords semi-guided and challenging items. Give the student at age 8 to 10, the most possible contextes, so that he could learn to apply the cognition, master it in these contexts and reuse it later on.