I met with a parent and tutor this pm about the progress of a student.
This student is perfectly capable in math, has strong procedural knowledge
and has a long history of being successful in math.
The grade began to slip in the later years of middle school in large part
because of a lack of attention to detail. In other words, such a reliance on
mental math and on "getting it" easily in earlier years had not allowed this
student to develop strategies to use when the answer came out wrong.
Consider what is valued in algebra.
Balancing equations or solving for a variable,for example.
There can be many steps one has to go through before successfully finding the
One small error in arithmetic along the way, and your answer is not correct.
Your procedure might be impeccable,and yet, you not only don't get the correct
answer, but you did not leave enough clues along the way to discover what went
wrong. You feel lost, confused and quite possibly, inadequate for the task at hand.
In the end, you might walk away from the problem in frustration and think you are
not "good" at math, which would be a sort of "logical"
(given your level of frustration and confusion at this point) yet inaccurate
assessment of our algebra skills (you did the procedures correct, on you messed
up on one little, itsy, bitsy arithmetic detail.
SWEAT THE DETAILS.
If you make "silly" arithmetic mistakes in doing an exercise about a new
concept you are learning, you will initially get the wrong answer, but if you
left tracks in the sand (i.e.: you wrote down
your steps in a neat and systematic manner), you can double back and rectify.
SO: check each step.
It's really easy even for a Ph.D. in math to multiply 6*7 and get 56 if
(s)he is not being careful. These are just details, but alot of math IS details.
There are some important concepts, but there are lots of details.In order to learn
the concepts, you must
sweat the details.
Algebra has some interesting ideas and techniques, but if you are not careful and
don't use the tool of arithmetic reliably, you are not going to see what algebra
has to offer.
That would be a great shame!!!!