My starting K son is amazing with math skills, he's already not counting on
his fingers. I'm excited to see how he keeps progressing! And those
abilities are already showing benefits in how he tackles other problems.
I think you are trying to say phonics, direct instruction and memorization work
in educating young children. It is difficult to find public elementary schools
that focus on this type of instruction.
This article explains one of the reasons why "New Math,"
"Investigations Math," and Common Core Math don't work. Proponents
of these programs call practice "drill and kill" and rail against it.
When these programs are used to teach math, the kids come away in awe of math,
but unable to do it. Math is a discipline. That means among other things it
takes practice to become good at it, not just "higher level thinking."
And with that practice comes automaticity and ability to think at a higher
level, because you don't have to hold all of the lower level theories and
calculations in your head while doing higher ones.The reality is, as
this article intimates, you can't have math ability without calculation
ability. Math is a discipline that requires practice, including memorization, to
become good at it. The math ed. departments in the colleges of education are
ruining math education, because they don't understand this. Student
understanding comes AFTER the proficiency is developed, not before.
To "Chuck E. Racer" it applies more than just to math. Look at spelling
and writing. There is now less emphasis on grammar and spelling because they
want to push the "higher concepts" into younger grades. What is going
to happen in 10 years when the kindergartners of today still can't spell
anything correct or write a complete sentence?
RedShirt, you are correct. Their philosophy is called Constructivism. They
believe the child must construct their "own" truth, because there really
isn't any "truth." It's just what you perceive it to be. It
is the same philosophy that gave us the "New Morality" of the 60's,
even though many who promote it in Utah will deny that.
I would like to respectfully point out that much of what Chuck E Racer has
written is false. Simply put, the theory of constructivism suggests that
learners construct knowledge out of their experiences. There is no arguing over
what is truth in public school mathematics. Proponents of the common core are
not suggesting students construct their own truth about mathematics. The common
core is helping students construct a real knowledge and understanding of the
mathematics. If Chuck’s approach to mathematics actually worked, I
wouldn’t have a job – I teach arithmetic and algebra to college
students who never learned it – and there is no shortage of them. Sure
– many of them memorized the procedures long enough to regurgitate the
information on a test to get a grade (and many of them weren’t able to do
that much), but even the “good” students didn’t really
understand why they were following specific procedures. Every time I work with a
student who is having trouble mastering a math skill, I can attribute the
student’s difficulty to not understanding the why behind the procedure.
I am currently doing research in math education, interviewing students who
consider themselves bad at math. Every one of them talked about how they were
most successful when they had a teacher who explained WHY to do certain steps,
and they struggled the most when the teacher only explained procedures to
memorize. Chuck’s statement of “Student understanding comes AFTER
the proficiency is developed, not before.” is misguided. Does a surgeon
gain proficiency in his skill before he understands what is happening in the
anatomy? Not likely. Learning math is no different from learning anything else.
When we truly understand a concept we gain proficiency in using it. There is
nothing wrong with skill and drill, but if we only rely on that method of
instruction we will continue to have a society that is math phobic and
numerically illiterate. (Consider the fruits of the traditional ways of teaching
math.) I encourage Chuck and others like him to properly educate themselves on
the common core. Start by reading the Core Standards for Mathematical Practice.
Google it. There is so much more evidence to support the theoretical foundation
of the common core, but time and space here limit me.
Chuck E. Racer - you obviously don't know much about the common core. There
are standards in each grade level that require students to know math facts from
memory. Like this one, for example, from the third grade: "By the end of
third grade know from memory all products of two one-digit numbers". Or this
one from first grade: "Add and subtract within 20, demonstrating fluency for
addition and subtraction within 10." Procedural fluency is one of the
pillars of Common Core Math.