In the field of multisensory education there are some things that
remain the same. The use of concrete objects and tactile if not gross
motor strategies to anchor the student in the learning are fundamental.
These strategies address the conceptual component as well as the
attentional component of learning. This is one reason that the
multisensory strategies work well with language based learning
disabilities as well as related learning differences such as ADD/ADHD.
They do not interfere with traditional learners and in fact enhance the
learning for all students. They provide experiences which are memorable
through multiple learning channels.

Some things are
open to interpretation and adjustment. In the field of education, we
sometimes practice certain strategies which seem to become imbedded in
our practice without question. They become tradition and though
anecdotal evidence may suggest efficacy, in fact they are not as
efficient or as effective as sometimes newer ideas. Take for example
the "mad minute." Though this may work for and encourage some students,
the timed stressful activity is a detriment to those who have
processing or retrieval difficulties. It is not that children do not
need to practice math facts, it is just that some methods of practice
may not be the best for some children.

When I
formatted the new math manual, in fact as I worked on it over the years,
I jettisoned some strategies that were based on a verbal approach to
teaching facts. As I reviewed the research on how the brain processes
mathematics, it became clear to me that using too many words and
convoluted stories to teach basic facts might be less useful than other
visual and numeracy based strategies being suggested by researchers such
as Dehaene and Butterworth. Over the years, the mFRI studies continued
to suggest automatic recognition of small quantities and building
larger quantity awareness on the construction and deconstruction of
smaller quantities. Thus I jettisoned the traditional O-G based
strategies based on language.

As I have updated the
Multisensory Math Manual, the approach of this program has become
multifaceted. I am attempting to combine the best of what we have from
the traditional multisensory approach and the best of what we can learn
from the research in mathematics. Please review the addition and
subtraction chart in your manual. You will find no verbal strategies
which ask children to use working memory to traverse and link known
facts to others. Directionality is an issue for many alternative
learners. Back and forth addition and subtraction based on words is not
easy for many of our students. Instead, the student is encouraged to
create the mental imagery for the construction and deconstruction of
quantity based on numeracy patterns. With these he can continually draw
on that mental imagery to solve even more complex problems.

I
have demonstrated this in our Skype sessions with subtraction across
place value. The What Works Clearinghouse suggests that multiple
representations be used for concepts and strategies. This is one reason
I use craft sticks, Unifix cubes, base ten place value blocks, tally
marks, dice etc. All of these can be used to create mental imagery to
support computation. Repeated exposure to numeracy patterns can form
the basis of more complex calculations. Experience with these patterns
will support memory and extensions to larger more complex applications.

Many
new text book series are beginning to employ this idea of pattern
recognition and numeracy in developing number sense. Older strategies
such as go to the ten and counting on may still be used. They are based
on skills and visual imagery. The number line and concrete
manipulatives are only tools in helping students develop full numeracy
awareness. We use all the tools available to us but for those students
who have language based differences we need to be careful of using
strategies based on too many words or associations of patterns based on
words. We need to remember that quantity does not have a single color
or shape. Over reliance on a single manipulative or rigid verbal
strategy actually may limit a student. Multiple representations are key
and memorable patterns based on visual stimuli and concrete
constructions are only the beginning.

We must
ultimately move students on to the abstract level and gently encourage
memory and retrieval through successful repeated practice which does not
discourage or lead to despair. The NCTM is emphasizing perseverance in
problem solving. It is emphasizing the great glow that students get
when they accomplish something challenging. Student should be
challenged, especially our gifted one. This is important but we need to
ask ourselves what exactly those challenges should be. Some of our
gifted students are gifted in ways that are not tested by a ticking
clock or their ability to remember stories about how to get to a target
sum. They can be defeated before they get to the mathematical starting
gate which is applications. To this end, the multisensory programs
always emphasize teaching for success and mastery. Thus, we seek the
best tools and strategies available in an ever changing educational
landscape. The new NCTM publication, Principles to Actions, emphasizes
concept based instruction and seeks to summarize where we are today.
The executive summary is available on line.

## Friday, April 18, 2014

## Friday, April 11, 2014

### Linkages

A word we use in the language field is "linkage." This is the connection between things like the sound and symbol correspondence. In math it might mean the connection between the quantity, the numeral and the name.

Numeracy is such an essential component of all mathematics and it must be addressed if it is a deficit for any student. Quantity awareness allows a student to fluently calculate, to estimate and apply. It has a spatial component when thought of along a number line. This can be an important component which lends itself to gross motor activities for the learning disabled child or the alternative learner.

One aspect of numeracy that goes beyond subitizing is pattern recognition. Think of place value and recognizing of four and four hundred are related. Subitizing allows us to recognize quantity but pattern recognition allows us to apply it at higher levels.

The What Works Clearinghouse suggests that children need to see multiple representations of math concepts. Absolutely, I agree. Keep in mind though that children need to have those representations linked so that the broad concept makes sense. Think fractions, decimals and percent! If a child comprehends 1/2 and taking one half of a quantity, he should also be able to link that to multiplication by 0.5 and taking 50% of a quantity. The careful teacher makes sure to revisit previously taught concepts and connect the dots and not just teach each new topic as if it exists as a set of procedures unto itself.

I routinely encounter teachers who attend my workshops and say, "I wish I had been taught this way." I believe it is because I stress a concept based approach and as we would say in the field of dyslexia, an approach that is incremental, sequential, cumulative and thorough with practice to mastery. To too many people though that sounds like procedures. It is not. The concept in math is the central piece for understanding. Without, applications are hit and miss. Procedural knowledge may get a student through one high stakes test but may be lost over time and not lend itself to applications such as problem solving. Procedures do not lead to deep thinking about mathematics.

The NCTM has a new publication which is really worth a look. Check out Principles to Actions on the NCTM website: http://www.nctm.org/principlestoactions/

Numeracy is such an essential component of all mathematics and it must be addressed if it is a deficit for any student. Quantity awareness allows a student to fluently calculate, to estimate and apply. It has a spatial component when thought of along a number line. This can be an important component which lends itself to gross motor activities for the learning disabled child or the alternative learner.

One aspect of numeracy that goes beyond subitizing is pattern recognition. Think of place value and recognizing of four and four hundred are related. Subitizing allows us to recognize quantity but pattern recognition allows us to apply it at higher levels.

The What Works Clearinghouse suggests that children need to see multiple representations of math concepts. Absolutely, I agree. Keep in mind though that children need to have those representations linked so that the broad concept makes sense. Think fractions, decimals and percent! If a child comprehends 1/2 and taking one half of a quantity, he should also be able to link that to multiplication by 0.5 and taking 50% of a quantity. The careful teacher makes sure to revisit previously taught concepts and connect the dots and not just teach each new topic as if it exists as a set of procedures unto itself.

I routinely encounter teachers who attend my workshops and say, "I wish I had been taught this way." I believe it is because I stress a concept based approach and as we would say in the field of dyslexia, an approach that is incremental, sequential, cumulative and thorough with practice to mastery. To too many people though that sounds like procedures. It is not. The concept in math is the central piece for understanding. Without, applications are hit and miss. Procedural knowledge may get a student through one high stakes test but may be lost over time and not lend itself to applications such as problem solving. Procedures do not lead to deep thinking about mathematics.

The NCTM has a new publication which is really worth a look. Check out Principles to Actions on the NCTM website: http://www.nctm.org/principlestoactions/

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