When tested, students have shown that they can be more successful with word or verbal problems than they are with equivalent problems that are purely symbolic (Nathan & Koedinger, 2000a, 2000b). The Journal of Mathematical Behavior, 18(2), 149–167. Other research suggests that skill in algorithmic computation may not correspond to students' ability to conceptualize the relationship between numbers in word problems (Fuchs et al., 2006). https://doi.org/10.1016/S0732-3123(99)00026-7 Stern, E. Instead of thinking through the context of the word problem to understand it, many students simply seek a simple application of arithmetic needed to produce an answer, whether it makes sense or not.
Word problems are not just for applications of already-known mathematics. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. Reston, VA: National Council of Teachers of Mathematics.
In fact, the most powerful way to use word problems in the classroom is as a means to help students learn math. Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics.
Math teachers are often concerned about students' abilities to transfer classroom learning into the world beyond the classroom, but this "suspension of sense-making" shows that the reverse is also difficult – students struggle to apply their knowledge and understanding of the world back into a mathematics classroom.
Having been conditioned with years of arithmetic, almost always involving obvious operations and the expectation that each problem has a correct answer, students develop a "compulsion to calculate" (Stacey & Mac Gregor, 1999) that can interfere with the development of the algebraic thinking that is usually needed to solve word problems.
Most teachers believe or assume that students will have more difficulty solving a word problem than solving an algebraic equation that represents the same mathematics without the words.
Because of this, they believe in teaching word problems only after students master solving similar problems as equations. Pre-service teachers’ conceptions and beliefs about the role of real-world knowledge in mathematical modelling of school word problems. https://doi.org/10.1016/S0959-4752(97)00008-X Verschaffel, L., De Corte, E., & Lasure, S. Realistic considerations in mathematical modeling of school arithmetic word problems. https://doi.org/10.1016/0959-4752(94)90002-7 Verschaffel, L., Greer, B., & De Corte, E.
Traditional math textbooks reinforce this belief by placing word problems at the end of practice sets.
This belief or assumption has been shown to be false, at least under some conditions. Dav Verstehen von Textaufgaben aus phychologischer Sicht.
Mathematical modeling tends to be a more complex process involving identifying questions to answer about the real world, making assumptions, identifying variables, translating a phenomenon into a mathematical model, assessing the solution, and iterating on the process to refine and extend the model (COMAP & SIAM, 2016).
The process to solve a word problem isn't necessarily as complex, as the problem itself usually gives the reader the question to answer and the information necessary to answer it, and doesn’t require modeling's level of meaning-making and interpretation.