I saw this article about a school adopting enVisions Math for elementary grades. It was a typical “Everyone’s happy in Happy-Land” type of story complete with the usual accolades for how the program is “balanced”:
According to K-12 Mathematics Coordinator, Gregory George, “enVisionmath2.0 is what we call a balanced program. It emphasizes conceptual understanding, procedural fluency, and applications and problem solving with equal intensity. We believe this approach to math instruction provides a complete learning experience for students that honors understanding of concepts and the ability to solve math problems efficiently and accuracy.
But then you have this story in the Baltimore Sun about the same program, saying this:
Some elementary school parents and students expressed concerns about the program to the school board earlier this year, however, saying its “abstract” nature made it difficult and time-consuming for parents to help their children with math homework, even with online support tools. Those who complained said the program had caused children who once enjoyed math to hate the subject.
So which story are you going to believe?
If this is the first time you’ve heard the words “conceptual understanding, procedural fluency, applications and problem solving” in one sentence then you’ll likely believe that this program does it all. Those of us who’ve been around the block a few times recognize those words as meaning the program obsesses over “understanding” and provides inefficient, picture-drawing and/or convoluted approaches to addition, subtraction, multiplication and division in lieu of the standard algorithms, which are delayed until 4th, 5th and 6th grades.
This delay is justified by saying that’s what Common Core requires, even though it does not. This belief and practice persists despite words to the contrary from Jason Zimba, one of the lead writers of the Common Core math standards who states in an article he wrote that “the Common Core requires the standard algorithm; additional algorithms aren’t named, and they aren’t required.”
But the real key word here is “equal intensity”. In programs similar in look, feel and practice like enVision Math, students are made to drill (yes, drill) these inefficient strategies and in so doing they attain a “rote understanding” of the underlying concepts–an understanding that could have been attained by teaching the standard algorithms. For more about “equal intensity” see this. But the prevailing group-think of educationists everywhere posits that teaching the standard algorithm “too early” eclipses the understanding with kids gravitating to the procedure. And they claim they have the evidence that this is so.
In real-life, kids tend to gravitate to the procedure no matter what. I have seen this even with students in accelerated classes who are highly motivated and quite bright. I teach for understanding like many teachers, despite statement made that traditional math teaching does not do this. Most students glom on to the procedure. Procedure and understanding work in tandem; sometimes understanding comes first, sometimes it comes later.
The parents who complain that the approach used in enVision Math (and other comparable programs) don’t teach math as they were taught are castigated by those who are part of the pervasive edu-group-think. Ironically, those doing the castigating are for the most part adults who have attained understanding after having been taught in the traditional manner. After seeing how enVision Math does it they exclaim “If only I had been taught math this way.” They climbed the math ladder like the parents they put down for their mistaken beliefs. They then kicked it away when they reached the next level, and now insist on bad practices and eschew the practices used by traditional teachers. Regarding the practices used by Kumon, Sylvan, Huntington and other tutoring/learning centers, they get very silent and say “Well, we just don’t know to what extent it’s the tutoring or the program used in the schools.”
Who ya gonna believe?