Barry Garelick’s article yesterday in Education News tackled the issue of teaching kids the “habits of the mind” that make up algebraic thinking before that student has learned algebra. He said what happens instead is that particular thinking skills are taught without content to support it.
In essence you get math problems without math.
That sounds productive doesn’t it?
Garelick points out what purveyors of this approach are simply engaged in wishful thinking:
Giving students problems to solve for which they have little or no prior knowledge or mastery of algebraic skills is not likely to develop the habit of mind of algebraic thinking. But the purveyors of this practice believe that continually exposing children to unfamiliar and confusing problems will result in a problem-solving “schema” and that students are being trained to adapt in this way. In my opinion, it is the wrong assumption. A more accurate assumption is that after the necessary math is learned, one is equipped with the prerequisites to solve problems that may be unfamiliar but which rely on what has been learned and mastered. It would indeed be amazing if we could teach students algebraic thinking skills devoid of the content that allows such thinking to occur. I tend to believe, however, that a proper study of this will show what many have known since the time of Euclid: there is no such royal road.
We simply can’t put the cart before the horse so to speak. If we do we’ll continually have frustrated students on our hands.