The blog post linked to above brings up a radical idea: avoid using counting words in math class until high school! Doing so would require more modeling and conversation about math before ever putting pencil to paper. This would ensure that students have a solid grasp on the logic behind various algorithms before attempting to reach the “end product” of correctly written problems and solutions.
Parenting Science has made similar suggestions for preschool classrooms. Because children develop a sense of quantity before they develop an understanding of counting words, preschool teachers might consider tailoring activities to their students’ natural progressions. Instead of making math time all about counting words, teachers could introduce activities dealing with concepts like comparison and estimation.
While these two articles differ theoretically, both contend that math is more than the correct use of counting words; instead, the reasoning behind the counting words is what counts, be it in preschool or in middle school.