Word Problems: Levels of Difficulty in Mathematical Language
“The power of mathematics rests on its evasion of all unnecessary thought and on its wonderful saving of mental operations.”
The mathematical language used in word problems is a source of anxiety for most school children. As they grow, it is expected that their semantic level will increase and they will be able to develop a greater lexical competence and capacity for resolution. Word problems contain several levels of difficulty with regards to language and semantic categories. In general, their understanding depends on various factors, such as the child’s experiences, prior knowledge, and practice.
When students start working with word problems, they begin to acquire a greater vocabulary. This allows them to deduce relevant data and analyze common mathematical operations such as addition, subtraction, multiplication, and division, either in a simple or combined form.
At Smartick, we offer varying degrees of difficulty in the language used in the word problems that we present progressively depending on the level of each child.
We start with a basic level of mathematical language, in which simple statements with direct operations are included. These are easy-to-understand questions, in which the language tends to be clear and brief, but also allows children to calculate operations and develop concentration, analysis and selection skills.
As the child’s vocabulary and knowledge increase, we introduce semi-complex mathematical language levels. Children begin to solve more difficult statements that require their attention to work out the type of operations needed (mixed operations are often included), as well as working with a wider vocabulary and more advanced grammatical structures.
Later, extra information is added to the word problems (often considered “unnecessary”) that requires the child to discern between vital data required to solve the problem, and information that can be dispensed with. At this point, we’re talking about a complex level of mathematical language, whose objective is to stimulate the capacity of abstraction and reasoning. In the same way, more complex (or “convoluted”) structures are used to challenge their understanding and their ability to identify and organize ideas.
Although many of these problems can be written more clearly and simply, the goal is for the child to reach an even richer vocabulary and level of comprehension, as well as be able to analyze from the simplest to the most complex of problems. It is also important that the child reads the whole problem and avoids the urge to “jump to the question” or “respond to the first numbers they see” because a word can change the whole result. Thus, with Smartick, children also improve their reading comprehension through mathematics, which is fundamental to their performance in all subjects.
Don’t forget to take a look at the Mathematical Problems and Their Semantic Categories Post, to help develop your child’s mathematical language.
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