Regrouping/Borrowing/Carrying/Whatever

Regrouping/Borrowing/Carrying...hmmm...sounds confusing.
What areyou(we) talking about? It is not surprising that
students become confused.Some 'experts' would insist you
do not say borrowing and carrying and that using the term
regrouping makes things perfectly clear, however,
I have not witnessed this supposition!

During the last few weeks, students have been introduced
to this strategy for adding and subtracting and the same
students who had problems with mental arithmetic
strategies continue to have problems with this strategy.
No surprise there!

Another element that has added to the confusion for some
students is that you can write questions horizontally
and vertically.Some 'experts' frown on writing questions
vertically while the text I am using writes them both ways,
but reserves writing questions vertically for three-digit
subtracting with regrouping.

I can see that I will have a busy summer getting all of
this sorted out so that I can present ideas to students
in a logical, comprehendable and comprehensive manner.
How did a simple basic skill like adding and subtracting
become so complex and confusing?

What's next? Restructure, review and present skills in
problem-solving situations.

Lisa

Positives and Negatives

Now that I have been teaching mental arithmetic for a while I
have noticed differences between the acquistion of adding
and subtracting strategies. As you would predict, the addition
strategies were easier for students to learn and have success
with this method of calculation. The subtraction strategies
were difficult for some students to use. They became confused
about some of the strategies that we were learning, especially
the 'count on' and 'count back'. Perhaps this was due to the fact
that some students still did not have a complete understanding
of the arrangement of numbers on a number line and that
subtraction is 'going backwards'.

Another critical difference that I noticed, especially for the
subtracting strategies was that if the student did not have
their basic facts memorized they did not have success with
mental arithmetic. The 'counting on their fingers' and using
a hundreds chart to assist with mental arithmetic seemed to
add to their confusion. Consequently, I have withdraw
teaching these strategies.

One positive observation to consider is that students with
their facts memorized became very quick at using mental
arithmetic and I had to keep sharp to stay with them.
That was very pleasing to see. Sometimes I learn as
much as they do.

Moving forward now will require teaching the strategy of
'borrowing and carrying' so students will have success with
adding and subtracting two and three digit numbers. This is
not a mental arithmetic strategy, but it is a valid and workable
strategy for calculation.

Liza

Mental Arithmetic

Mathematics/Arithmetic - What's in a Name?

After doing some research and rethinking, I've changed the topic
name of this discussion to mental arithmetic. Even though the
curriculum document uses 'mental mathematics' as their term,
it is really 'mental arithmetic or mental calculations' that they
are describing.

Does the term matter? Yes, especially if you want to be accurate,
learn more about this process and seek Web resources.
Search results for 'mental arithmetic' produce fruitful and
interesting results as opposed to 'mental mathematics' which
was not helpful at all.

Here is a link to a website that includes some description
and teaching strategies for this topic http://www.themathpage.com/ .
I found Lesson Four, Mental Arithmetic, to be especially useful
and I have started using the strategies recommended with
my students. The explanation of 'add by endings' really
filled a missing link to the strategies that were presented at the
DaCosta Math Workshop I attended in the fall.

Who is DaCosta? David DaCosta is (was) a university math
professor that is employed by the Southern Alberta
Professional Development Consortium to provide inservicing
workshops on the 2007 Alberta Mathematics Curriculum
to Alberta Teachers to assist them in implementing the
new curriculum.

My journey continues, let me hear from you.
Liza