Change: Tick Tock and Too Many Words

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.   

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/