Language Thinking Lab by Tymur Levitin

A student reads a mathematics problem. They understand every word. They know the vocabulary. They know the grammar. They can even explain what the sentence means. And yet they still do not know what calculation to perform. This tells us something important. Understanding the language of a mathematical problem and extracting its mathematical structure are not the same operation. Before the learner can calculate, something else has to happen. The sentence has to become a model. A word problem is not solved directly from language. The learner first has to decide which relationships inside the language deserve to become mathematics. That intermediate step is easy to overlook because experienced problem solvers often perform it quickly. For a learner, especially one working through another language, it can be the hardest part of the entire problem. A Sentence Contains More Than the Equation Needs Consider a simple situation: Marie buys three identical notebooks and one pen. The pen costs €5...