Several years ago, I met two second grade teachers who boasted that their students could perform Addition with Renaming (e.g. 467 + 285) in ten different ways. They had just completed their sixth week of teaching the unit and possessed dozens of student work samples as proof. But their claim was only half true. Fifty percent of their students hadn’t mastered one method and struggled daily as their teachers and classmates introduced new solving strategies.
I assume that if the teachers had set out to teach the standard algorithm and one or two other ways of solving, then 90% of the class would’ve learned the topic following a week or two of practice. Those who mastered quickly could’ve worked with alternative algorithms and still wound up proficient in many strategies. Lost in the discussion was that the teachers used an extra month on a topic that shouldn’t have lasted more than five to ten instructional days.
I believe that teaching various solving strategies is a critical component of great elementary mathematics instruction. But - like any pedagogical technique - the practice can be overemphasized. Inundating students with various strategies often favors strong mathematicians at the expense of struggling learners, because it creates illogical practice habits and mismanages class time. Therefore, flexible thinking shouldn’t be the aim of the subject, but instead the inevitable outcome of good teaching and learning.
The most successful math teachers I’ve seen understand: If a strategy is worth teaching, then it’s also worth practicing, and too many methods can overwhelm students’ working memory, leading them to confusion. They also know that teaching a repertoire of methods can be the same as opting to not teach other topics. Weighing all of this, they encourage flexible thinking and praise creativity, while maintaining efficient pacing throughout lessons, chapters, and units. In doing so, they nurture the brain and subject’s elasticity, while optimizing each students’ mathematical potential.