tag:blogger.com,1999:blog-81195343610629013892024-03-08T01:23:30.679-08:00Multisensory MathM. Zecher, M.A., CALThttp://www.blogger.com/profile/13975157757275314758noreply@blogger.comBlogger19125tag:blogger.com,1999:blog-8119534361062901389.post-60129769648725131152014-10-22T20:07:00.002-07:002014-10-22T20:07:19.799-07:00Multisensory Math at ASDEC As many of you have noticed, this blog has not had an entry for some time. I have another blog just for my multisensory math classes. It is where participants in my distance classes can interact, ask questions, comment on the class and generally interact with each other and with me. <br />
<br />
I will try to post more frequently in the near future. Lots of things have been going on in the world of Multisensory Math. I have given workshops in several states and am scheduled for several more presentations in the near future. I seem to be traversing the country right now. <br />
<br />
You can see two Multisensory Math Presentations at the NCTM Regional Conference in Richmond VA in November 2014. I will also be helping to moderate a panel discussion about differentiation and reaching all learners. Recent presentations have included full day seminars in Ohio and Seattle WA. I will be giving presentations at the LDA National Conference in Chicago in February and in VA later in the spring. Look for a new Multisensory Math website in the near future as well. I am working on various projects as quickly as I can. <br />
<br />
If you are accessing this blog as part of the ASDEC Multisensory Math Class, you are in the wrong place! You should be accessing: asdecmultisensorymathonline.blogspot.com. It is there that you will find postings related directly to the course. M. Zecher, M.A., CALThttp://www.blogger.com/profile/13975157757275314758noreply@blogger.com0tag:blogger.com,1999:blog-8119534361062901389.post-50969953575652883442014-04-18T06:58:00.001-07:002014-04-18T06:58:04.582-07:00Change: Tick Tock and Too Many WordsIn 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.<br />
<br />
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.<br />
<br />
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. <br />
<br />
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.<br />
<br />
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.<br />
<br />
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.<br />
<br />
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. M. Zecher, M.A., CALThttp://www.blogger.com/profile/13975157757275314758noreply@blogger.com0tag:blogger.com,1999:blog-8119534361062901389.post-51736728364502154642014-04-11T07:54:00.001-07:002014-04-11T07:54:07.989-07:00LinkagesA 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. <br />
<br />
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. <br />
<br />
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.<br />
<br />
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. <br />
<br />
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. <br />
<br />
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/<br />
<br />M. Zecher, M.A., CALThttp://www.blogger.com/profile/13975157757275314758noreply@blogger.com0tag:blogger.com,1999:blog-8119534361062901389.post-431651040028804602014-03-28T11:35:00.002-07:002014-03-28T11:35:22.171-07:00Thinking Vertically About Teaching Math<!--[if gte mso 9]><xml>
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<b><u>Thinking Vertically:</u></b> For remediation
with older students, one needs to think of skills introduced but not
mastered. Begin to think about concepts which bridge multiple operations
and levels. Two examples are "Regrouping" and "Place
Value." With older students who have been taught procedures without
concepts this is a terrific place to begin. </div>
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Start by using manipulatives to model whole number
operations with the place value mat you were given. Ask students to
"prove by construction" answers to basic problems without
regrouping. With severe students I would recommend the craft sticks
because as I have said, the student may need to physically bundle and <i>unbundle
</i>quantities. If the student needs only to reinforce the concept, base ten
blocks may be used. After regrouping is introduced, practiced and
mastered, you can move the student to fraction concepts.</div>
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Creation of fractions with your fraction circles is a first
step. Students may keep one circle uncut to remind them of how many
pieces it takes to make a "whole." Other fraction pieces may be
used to add and subtract like fractions. If the solution is an improper
fraction, the students quickly see that laying the whole circle on top
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The next step is helping them understand that we may
"regroup" from the one's place value to the fraction place value by
moving "one" to the fraction place value and representing it as the
required circle "cut" into the required size pieces. The whole
can never be in the fraction place value unless it has been "cut"
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fraction place value.</div>
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The student learns that we may get a "sum" which
is improper in any place value by the operation of addition. We then
"simplify" the quantity to its proper form. We may need to
create an improper quantity in ANY place value in order to subtract. This
is a fundamental concept for both whole number operations and fractions.</div>
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The older student feels validated in that he or she is
working at higher levels of math, but is also beginning to understand the
fundamental math concepts which form the foundations of higher level skills. </div>
M. Zecher, M.A., CALThttp://www.blogger.com/profile/13975157757275314758noreply@blogger.com0tag:blogger.com,1999:blog-8119534361062901389.post-46346245939723746942014-03-28T11:33:00.001-07:002014-03-28T11:33:43.448-07:00What Comes Before & What comes After <!--[if gte mso 9]><xml>
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<b style="mso-bidi-font-weight: normal;">What Comes Before
& What Comes After </b></div>
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In thinking about the math courses, I wanted to ask each of
you to consider thinking about one concept such as multiplication or
fractions. Begin to think about how that concept appears at various
levels of instruction. What would be the earliest exposure a student
might have? What vocabulary is essential for the child to comprehend the
concept? How could a child experience the concept, practice the concept
and demonstrate proficiency at an early level?</div>
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Then, I would like you to jump ahead several levels and
years. How is this concept applied at higher levels of math? How
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application? How does one expand this concept to extremely abstract
levels?</div>
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As a primary grade teacher, we need to understand how what
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vocabulary so that we may go back to fill in gaps for those who need remedial
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You might also choose a concept such as division or
multiplication. Try to spend a few moments considering the various levels
and applications</div>
M. Zecher, M.A., CALThttp://www.blogger.com/profile/13975157757275314758noreply@blogger.com0tag:blogger.com,1999:blog-8119534361062901389.post-86535856976815693632014-02-23T06:42:00.001-08:002014-02-23T06:42:08.917-08:00Gross Motor ActivitiesThose of us who work in multisensory education know the importance of using large motor muscles as part of daily instruction. Using large movement helps to reinforce directionality and sequence. It provides a direct path to the brain in a way that fine motor movements do not. Think of the muscle memory involved in navigating a dark bedroom at night. You know where everything is without the aid of eyesight. You have tactile memory and spatial awareness. <br />
<br />
Now consider mimicking the direction and sequence of multi-digit multiplication operations, or numeral formation. These activities allow students the opportunity to get up, flood the brain with oxygen and move. Consider Geometry Simon Says, or even the direction and spatial movements associated with transformations of function. <br />
<br />
Dr. Joyce Steeves believed that students needed the opportunity to get up during a lesson each day. It might mean tossing a weighted object during skip counting or forming numerals in the air, but they do need to get up and not just to offer samples of homework worked the night before. <br />
<br />
I observed a wonderful lesson in North Carolina in which the 4th grade teacher in an independent school, used dry erase pens to write problems for the students to solve on various desk surfaces around the room. They were given a single sheet of paper quartered for completion. They could move to the various desks to copy and solve, work collaboratively etc. They were given a fixed amount of time and had to pass the papers in before exiting for the next class. There was a seat time discussion of the problems before dismissal so there was an orderly transition to the next class, but the students were well regulated and engaged...up and actively involved in the math lesson. M. Zecher, M.A., CALThttp://www.blogger.com/profile/13975157757275314758noreply@blogger.com0tag:blogger.com,1999:blog-8119534361062901389.post-60588018304898624682014-02-21T06:29:00.001-08:002014-02-21T06:29:34.961-08:00It's the Language As I return from my latest two day workshop, I am continually
impressed with the need to address instructional language. When I
completed my teaching degrees, I received no instruction in identifying
and dealing with learning differences. It was assumed that if a child
were not in special education he or she would be able to learn in my
class. That was many years ago. Within the first three years of my
teaching, all teachers were required to take a special education class
or some in house training in special needs. That is when I first
received training in multisensory methods as part of a public school O-G
based program. <br />
<br />
Now teachers are expected to teach
inclusion classes and sometimes work with another teacher to support
special needs students in blended classrooms. There is lots of talk
about differentiation. What I find in the field is that teachers are
not always given sufficient professional development to feel confident
in addressing the myriad learning differences that can occur in the same
class. <br />
<br />
One of the simplest vehicles for addressing
the needs of all students is clear, precise, concept oriented language
with a rate of speech that does not race of some student's heads. A
well articulated lesson delivered at a moderate rate of speech is more
apt to reach a greater number of students. <br />
<br />
Yes, there
are times when a faster rate of speech, emotion and excitement should
infuse the classroom with urgency. These are moment which inspire
students and engage them in questioning and analysis. However, when a
new concept is being introduced or sequential directions are given, the
rate of speech should allow for processing speed deficits and be
delivered in such a way to meet the needs of all students. M. Zecher, M.A., CALThttp://www.blogger.com/profile/13975157757275314758noreply@blogger.com0tag:blogger.com,1999:blog-8119534361062901389.post-2997859144432256822014-02-16T11:27:00.002-08:002014-02-16T11:27:36.867-08:00Additional Resources and Intern Comments I receive many questions from educators about the use of
manipulatives in the classroom. This is one reason that a sample
professional development contract involving me often includes
demonstration lessons. In these sessions, I teach the students in front
of their teachers to show how manipulatives will be received by the
students and how best to use them. I have taught in both public and
private schools, large classes and small. In very large classes, I
limit the time spent and the number of activities with manipulatives to
make sure that students use them efficiently. I also know that the more
you use manipulatvies, the more students get used to them and learn the
behavior rules associated with them. They get acclimated so to speak.<br />
<br />
I would like to relate a discussion I had with an intern after the
Skype session yesterday. This particular intern is at the end of her
practicum. She has been using multisensory math methods in her
classroom for two years. Basically her reaction includes the following
observations:<br />
<ol>
<li>The use of manipulatives is time consuming and
can be messy, BUT after using them she feels that she has done much
less reteaching. In other words, the concepts are retained more
thoroughly. </li>
<li>She has already seen growth in her assessment
scores. She uses both the <i>CMAT</i> and the <i>Woodcock Johnson </i>because many of
her students are funded. She teaches in a school for students with
learning differences and must answer to local schools as she assures
them that IEP goals are being met. Her administration is thrilled with student progress and growth in skills as well as comments. </li>
<li>She also believes that it
is important to go back in the CRA instructional sequence and link the
abstract to the concrete. This is one thing we recommend in the class
when students with variable memory seem to have lost what they had
previously mastered. A return to the concrete can be a good way to
review and cement gains. </li>
<li>Difficulties she has encounter are in
using the complete lesson plan. It takes practice. However, she does
like thinking through Joyce Steeves' lesson plan because it reminds her
to get all the strands of math in over time. </li>
</ol>
She will get to practice much more this summer when she works in the ASDEC summer program. We will be working together. <br />
<br />
Additional resources mentioned in a Skype session with my MSM II class yesterday include:<br />
<u><b>Elementary and Middle School Mathematics: Teaching Developmentally,</b></u>
by John A Van de Walle, Karen Karp and Jennifer Bay-Williams. It is a
little pricey but can be rented or purchased for Kindle. I have the
eighth edition which runs $149 new but closer to $100 used. It rents
for as little as $46. The earlier editions range from $2 to $32 used in
paperback. <br />
<br />
<u><b>Number Talks: Helping Children Build Mental Math and Computation Strategies</b></u>
Grades K-5 by Sherry Parrish - This is available for rent and purchase,
paper back (used and new around $40-50) New, it comes with a DVD<br />
<br />
<u><b>The Math Dictionary for Kids</b></u>, by Theresa R. Fitzgerald, Billed as the #1 homework helper, it runs anywhere from $5 -$8, new and used. <br />
<br />
<b>Teaching Student-Centered Mathematics Developmentally Appropriate Instruction for Grades Pre-K-2, </b>again
by John A Van de Walle et al. It is from Pearson Publishing. Various
editions run $15-$50 on Amazon. It is a series and includes various
levels so teachers could purchase the one which is appropriate for the
level they teach. <br />
<br />
Don't
forget LearnZillion for video ideas regarding the Common Core State
Standards and Hippocampus.org for a free, open source algebra course
with videos acceptable for student use at home. Hippocampus has other
resources available as well and it is well worth a look. M. Zecher, M.A., CALThttp://www.blogger.com/profile/13975157757275314758noreply@blogger.com0tag:blogger.com,1999:blog-8119534361062901389.post-767271705189671322014-02-15T06:29:00.001-08:002014-02-15T06:29:33.764-08:00Evidence Fractions- Look at the work of the Rational Number Project. You can find a compilation of the work from the University of Minnesota, find lesson plans, download fraction manipulatives and read of the success the project has had in public schools. <br />
<br />
In the Multisensory Math Program at ASDEC we use a similar concept based approach. Students create fraction concept cards for the student notebook. They choose their manipulatives and assemble card stock graphic organizers which they keep for reference. The illustrate key vocabulary and concepts and all operations. Reaction from teachers using them has been extremely enthusiastic. "The children love them." <br />
<br />
There is evidence to support using circular models first and then transitioning to other models. Teachers need to solidify concepts before teaching children to simply "push numbers around." So many teachers tell me that they wish they had been taught this way. You do not need commercial manipulatives to teach fractions either. You can print fraction circles on cardstock. You can use simple construction paper squares. Folded paper can come later after students fully comprehend the concepts and remember: fract- is a Latin root that means to break into parts. I suggest that students need to cut or break something to really understand the linkage. <br />
<br />
In addition, students need to comprehend that the "fractions of one" is a place value concept. This should be fully understood before decimals are taught. Students will benefit from using manipulatives to add, subtract and simply fractions and mixed numbers. Then, students can move on to the abstract level of experience using only numbers. M. Zecher, M.A., CALThttp://www.blogger.com/profile/13975157757275314758noreply@blogger.com0tag:blogger.com,1999:blog-8119534361062901389.post-82808244028050887662014-02-14T18:08:00.001-08:002014-02-14T18:08:37.344-08:00I Hate Fractions!I think I have never met a student who claims to be proficient in fraction concepts and operations. More often than not, I am met with the title of this post. Why do you think that so many students feel inadequate when it comes to fractions. <br />
<br />
I met with a student today who loved long division but would not even talk about fractions. "Could I use a calculator?" she asked. My students do not generally use calculators in sessions. I assure success by using student friendly numbers to teach concepts. We use calculators to check answers, to teach concepts such as transformations of functions or in cases where it simply makes sense not to struggle with complex solutions to function applications. We need a more exact answer. <br />
<br />
So why is it that so many students do not feel confident with fractions? We all need to ask ourselves this question. What is it that we are doing right and what is it that we are not quite conveying? So much of higher math depends on an understanding of fractions. We need to consider what the research is telling us (circular models are better introduction) and there is a need to move from the concrete to the abstract for many students. They need to understand the concepts before they begin to push numbers around in operations they do not understand. In my workshops and courses, I keep hearing the following statement, "I wish I had been taught this way." Or, "I know how to tell them to get an answer. I just can't tell them why it works." M. Zecher, M.A., CALThttp://www.blogger.com/profile/13975157757275314758noreply@blogger.com0tag:blogger.com,1999:blog-8119534361062901389.post-77342106002443765602014-02-09T11:25:00.001-08:002014-02-09T11:25:04.522-08:00Foundation Concepts We all look at modern curricula, textbooks, scope and sequence documents etc. and feel a bit overwhelmed. The Common Core State Standards initiative is one solution. It doesn't tell anyone how to teach or insist on specific content. It merely gives us a common set of skills with which students should be proficient at developmentally appropriate levels, or grades. <br />
<br />
Even the Common Core can seem daunting if you dig too deeply at first. I would advise checking out the summary document on the website itself. You will find that the essential skills for each grade level are listed in focus documents that are incredibly simple to comprehend. <br />
<br />
The Common Core Standards for math evolved from the NCTM Focal Points. For years these focal points formed a terrific guide for what needed to be mastered. They are based on recent research in how the mind processes math. This research has, I believe, fundamentally changed the way we teach mathematics. <br />
<br />
We no longer believe that simply having procedural fluency is enough. Students today must understand what they are doing. I see this almost everyday in working with students at in algebra. some of my private clients attend schools which use ancient textbooks, heavy in language and complicated drills but little focus in the underlying concepts.<br />
<br />
When we look at the evidence and milestones that students must achieve, consider investing additional time in teaching numeracy, construction and deconstruction of quantity for quantities up to and including ten, and of course, place value. Place value and the concepts underlying multiplication, division and fractions are essential. They simply must be done thoroughly. As important though is the way these concepts are introduced and developed. They cannot be rushed or taught procedurally for some test. They must be firmly placed and soundly developed to a level beyond familiarity. <br />
<br />
<br />M. Zecher, M.A., CALThttp://www.blogger.com/profile/13975157757275314758noreply@blogger.com0tag:blogger.com,1999:blog-8119534361062901389.post-47738391581143365242014-01-28T13:48:00.002-08:002014-01-28T13:48:47.617-08:00Manipulatives: Must Be Efficient & Effective For What Is Being Taught<!--[if gte mso 9]><xml>
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<br />
I continually state that the use of manipulatives is to
teach concepts. Manipulatives are used to give the students a hands-on
experience, one that is memorable and helps them interact with different
representations. This is a core principle of UDL (Universal Design for
Learning).<br />
<br />
The goal of using manipulatives is to illustrate a concept and then get rid
of them. Students should seldom perform calculations with manipulatives
unless it is skill building and aids in memory. For example, using
manipulatives to illlustrate/see calculations of large quantities using
craft sticks and a place value mat is extremely useful...for a while. It
reinforces our place value system and allows them to physically experience
regrouping and renaming-a concept that is one of our "continuous
threads." Once the student begins to recognize the concept and has
formed a mental representation of the procedure involved, we would want to move
the student to the representation and abstract levels.<br />
<br />
Picturing groups of quantities can certainly explicate the meaning of
multiplication and division. They can help automatize select facts.
They can illustrate the concepts of multiplication and division easily.
They should lead to the use of specific fact families-and for LD students a
very few- which are practiced and applied to the automatic level.<br />
<br />
An inefficient use of manipulatives would be using counters to solve
successive problems beyond the child's fact base knowledge system. This
is where the general education teacher and the special educator may part ways
in using a book or set curriculum. The published curriculum assumes that
the child using the textbook has attained certain skill levels. The
special needs student may not have the skills required to use the worksheets
and practice pages associated with a specific concept.<br />
This is not to say that a special education student cannot be taught higher
level concepts. It only means that, as the What Works Clearinghouse
suggests, struggling students practice math facts daily and as I say, use <i>THOSE</i>
facts in their activities. The teacher may make up a worksheet...yes, in
your spare time of course...to fit the needs of the struggling student.
Using a computer program such as Math Type, or the equation editor in MS<br />
<br />
Word, the teacher can create a simple worksheet with fewer problems on a
page, ample white space, and a restricted set of number facts which can be
practiced to complex levels.<br />
Take for example, long division. The typical text book would ask that
the student work with a single digit divisor and two digit dividends until all
multiplication facts have been worked through the division algorithm.
Then, as the student approaches multi-digit dividends, the student is expected
to have mastered the times table facts. This would preclude the special
needs student from doing the activities. The special education teacher
can easily create a worksheet using one of the tools mentioned above. The
worksheet might use only one times table throughout but include problems with
varying levels of complexity. This would prevent a student from simply
using counters to solve problems by hand repeatedly practicing unrelated and
isolated facts independently of each other, and leading to frustration without
serving to build any mastery of any fact families. <br />
<br />
As always, look at what you are teaching. Decide what your goal
is. Are you teaching a concept or practicing applications?
Applications do involve complexity, but student should be moved from using know
facts to incorporating new ones in ways that build fluency and competence and
do not lead to frustration. <br />
M. Zecher, M.A., CALThttp://www.blogger.com/profile/13975157757275314758noreply@blogger.com0tag:blogger.com,1999:blog-8119534361062901389.post-1015603550154253862013-09-24T06:18:00.000-07:002013-09-24T06:18:00.769-07:00Modifying Materials for differentiationStudents who have special needs are in your classrooms or sitting at dining room tables trying to do homework or worksheets which pose problems. The font is too small. There are 30 problems on a page. There is no space on the worksheet to write calculations, or the space offered is far too small for normal sized digits forcing the student to write in miniscule script.<br />
<br />
Keep in mind that students need space. They do need to conserve paper, trees and the cost of printing; but we do have recycling these days. Some students are simply unable to recopy all problems, maintain alignment and accommodate their learning needs on prefabricated instructional materials.<br />
<br />
If you have special needs students in your class, consider making one document per unit which incorporates specific features to enhance learning. Create a word processing document with the equation editor or a program such as <i>MathType</i>. Use 18 point font or larger. Place fewer problems on a page and provide ample white/work space for computations. If you are working on a word problems or fractions, provide a space for drawing a representation of the problem. This is easy to do if you use the "insert table" function and create a template which confines the problem to one quadrant, the representation to another, the calculations to yet one other and a space to write the solution and perhaps a justification of the solution.<br />
<br />
In worksheets that practice long division, integer operations, equation solving, you can also use the "insert shape" function to add lines for alignment, a number line or a space to insert a times table for reference. Use the "insert text box" to offer students a place to write the number facts they will use.<br />
<br />
On the second day of the unit, open the file again and save it under a new name. This allows you to double click on the equation and change the numbers without changing the format of your document. You can do this several times to use as warmups or homework. Thus, you can even create different worksheets for the same class. Your gifted students receive greater challenges and your students who struggle get a real chance to learn concepts and procedures in a student friendly format. I am posting two examples for review. <br />
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<br />M. Zecher, M.A., CALThttp://www.blogger.com/profile/13975157757275314758noreply@blogger.com2tag:blogger.com,1999:blog-8119534361062901389.post-79716916361627711662012-07-13T19:15:00.003-07:002012-07-13T19:15:56.619-07:00July 14, 2012<br />
A new summer program. Once again we are working with a wonderful group of young people. Students with a variety of gaps in their mathematical tool kits have come to us for a short summer tune up. In the math section of the middle school program we are working with manipulatives, illustrating concepts and applying them vertically through several operations and at different levels. Based on an intake assessment, we have begun with place value concepts, regrouping in addition and subtraction of whole numbers, and basic fraction concepts. We began with base ten blocks and asked students to "prove by construction." They have modeled quantities into the hundreds of thousands using manipulaltive objects. They have transitioned to the representational level to draw fraction addition and subtraction problems as they regroup from the whole number place value to the fraction place. Parents report that their children are coming home excited about doing math without pencil and paper. They are understanding math concepts at an entirely new level and enjoying it more. Next week we begin earnest work on multiplication, division, exponents, squares and roots. We will be making conceptual linkages using Unifix cubes, string and beads. M. Zecher, M.A., CALThttp://www.blogger.com/profile/13975157757275314758noreply@blogger.com0tag:blogger.com,1999:blog-8119534361062901389.post-51275833679571893662010-07-21T05:14:00.000-07:002010-07-21T05:24:17.159-07:00Thoughts on the Summer ProgramToo little time. Too many conceptual gaps. Here we are three weeks into a summer program with students. The young people who appear each day exhibit a huge disparity of skill levels and yet most are woefully unprepared in predictably obvious areas: fractions, decimal operations, estimation, multi-digit multiplication and of course. . .long division. Most of the students have been taught multi-step procedures with few links to the underlying concepts. They demonstrate, individually and collectively, the research supporting an emphasis on numeracy education. They cannot visualize quantity, therefore they cannot apply that knowledge to a useful purpose. <br /><br />They love games which reinforce patterns. They cut their own fraction manipulatives. They illustrate multi-digit multiplication with place value objects and various representational pictures. They learn a few selected number facts and patterns which aid word retrieval. They apply all of the above to algebra. They simultaneously work on multiplication, division, fractions and solving equations. They perform mental math with decimal fractions as they apply language which supports visualization. "How many pieces the size of one fourth can I make if I start with three and one half?"<br /><br />We play with dice. We use pictures of pizza drawn on dry erase boards. They chant the perfect squares. They learn the many appearances and applications of the number one. They are a joy to teach.M. Zecher, M.A., CALThttp://www.blogger.com/profile/13975157757275314758noreply@blogger.com1tag:blogger.com,1999:blog-8119534361062901389.post-32301656703585457702010-05-12T20:32:00.000-07:002010-05-12T20:38:56.997-07:00The Algebra ReviewHigh Stakes testing is upon us. Here in Maryland, our students must pass the High School Standards exam in order to graduate from high school. The algebra test is not excessively difficult, but not excessively easy either. Student who learn differently need lots of practice in basic skills, concepts and applications. Each year at ASDEC we offer an intensive review. The class is always small and we are able to give students individual attention and support. <br /><br />This year we handed out our usual packets, lots of summary pages with essential information and review samples. We focused on chunking similar problems in sets rather than exposing the students to a mixed review. We offered visual dictionary pages in which key terms were not only defined but illustrated. We used concrete manipulatives to illustrate core concepts and mapped them onto real problems from the test. <br /><br />The result: students wrote on the evaluations that they would recommend the review to other students who struggled. One student wrote, "They really make you <span style="font-style: italic;">understand</span> what the math is all about." No higher compliment...except maybe that they all pass.M. Zecher, M.A., CALThttp://www.blogger.com/profile/13975157757275314758noreply@blogger.com0tag:blogger.com,1999:blog-8119534361062901389.post-71137679164666766822009-08-17T08:46:00.000-07:002009-08-17T09:00:41.525-07:00Here Comes the Very Fun Math LadyThe ASDEC Summer Program is an intense month long experience for students. There are usually three programs serving students of all ages. The program for elementary students is the subject of this entry. <br /><br />In this program students receive one-on-one multisensory language therapy every single day. It is diagnostic and prescriptive. The academic therapists make every effort to provide the most positive experience these children can have, but it is still language reading, writing and spelling work. Students also receive training in mathematics, oral language and keyboarding. Most students do not relish spending half a day during the summer in an academic camp, but by the end of the program students at ASDEC often say it was one of the best experiences they have had. <br /><br />Math training for younger students focuses on numeracy, place value and the concepts underlying basic operations. Students use manipulatives everyday because many of those who come display typical deficits in math. Even though some of the participants are gifted in math, they may not demonstrate this giftedness due to processing and procedural difficulties. Instruction is both classroom and individual. It is diagnostic and prescriptive. The individual academic therapists work with the math instructor to see that the program is individualized to maximize the student's potential and address individual needs. <br /><br />Our initial session began with an assessment which was followed by work with manipulatives and numeracy games. On the second day I entered the building to retrieve my teaching materials and cart so that I could return to begin class. As I moved toward the elevator I heard one child say, "There goes the very fun math lady." I knew it was going to be a good summer, and it was.M. Zecher, M.A., CALThttp://www.blogger.com/profile/13975157757275314758noreply@blogger.com0tag:blogger.com,1999:blog-8119534361062901389.post-45016876718226726482009-08-08T07:07:00.000-07:002009-08-08T07:18:47.831-07:00ManipulativesManipulatives are used to teach concepts. They offer hands-on practice which helps students form lasting kinesthetic memories. They aid in concept internalization and retention . <br /><br />Research now suggests that quantity representation may be a core deficit in math disability. However, many students who are not identified as having a math disability also fail to automatize math facts or truly understand procedures they are asked to perform. Some students truly need to experience the growth of quantity to understand place value. They may need to physically bundle and un-bundle quantities to form tens, hundreds, thousands and more. Certainly, many students fail to understand regrouping if they have not physically had to unbundle a quantity of objects for that purpose. <br /><br />Younger students may benefit from using craft sticks or even dry beans to create place value models. They may use sticks and dollar store hair bands to create tens, and bundles of tens to create thousands. My young students even create a bundle of ten hundreds to create one thousand. They marvel at the size and weight of it. This is a terrific precursor to commercial place value blocks. Any home school parent can afford $3 for a thousand sticks, and teachers or schools may create entire class sets of manipulatives at very little expense. <br /><br />Purchase a place value mat or make your own using the table function of your word processor. Blow it up at the local office supply store. Have your students construct and name quantities as they match the manipulatives to the numbers they write. Practice the language of naming quantites. Practice creating quantites from written numbers. Pair the language of math with the physica representations. Your students will thank you for the opportunity to build and you will be building more than a collection of sticks.M. Zecher, M.A., CALThttp://www.blogger.com/profile/13975157757275314758noreply@blogger.com1tag:blogger.com,1999:blog-8119534361062901389.post-78346891518899417092009-08-02T11:52:00.000-07:002009-08-02T11:54:38.155-07:00Multisensory Math<b>The multisensory approach is a unique way of "thinking" about teaching mathematics.<br /></b><br /><p><b>This approach is: </b><br /><b> research based,</b><br /><b> advocated by the NCTM, </b><br /><b> applicable to </b><i>any </i><b>curriculum or textbook series, and</b><br /><b> appropriate for </b><i>ALL</i><b> students, but necessary for some.</b><br /></p><p>This program applies Orton-Gillingham multisensory instructional strategies to mathematics. This approach fits easily with recommendations from current research and suggestions from the National Math Panel regarding instruction for struggling learners. Hands-on work with manipulative objects is recommended for all students at all ages. It enhances both concept integration and memory. This approach is especially important for LD students and those with conceptual gaps. It is however, an approach which is appropriate for all students. <br /></p><p>The emphasis of our site is on helping all students be successful in math, helping teachers find ways of supporting struggling students, and informing educators about about learning differences which can impact student performance in mathematics. <br /></p><p><img src="http://www.multisensorymath.com/mediac/400_0/media/DIR_12146/12178.jpg" alt="" width="150" align="left" border="0" height="108" />In essence, a multisensory approach uses concrete manipulatives to teach mathematical concepts. We then transition students through the representational (pictorial) level of instruction until they are able to deal only with numerals/numbers at the abstract level. Manipulatives are used by all students because research has shown that multisensory input is stronger than unisensory input for creating lasting associations and memories. In more simple terms that means that the more of the brain that is involved in the learning, the stronger the memory. <br /><br /></p><p>It is also true that when students are given explicit instruction in foundational skills and concepts, less time may be needed for procedural instruction, so there is not a substantial increase in instructional time. Students are able to apply their knowledge across applications and are better at problem solving. Some studies indicate that students who use manipulatives for concept instruction including at the algebraic level, equal and even surpass their peers in summative assessments and retain the material longer.<br /><br /></p><p>If you are interested in more information, a workshop or a course; visit the www.asdec.org website for a complete list of current events. You may also contact me directly at marilyn@multisensorymath.com. or mzecherCALT@gmail.com. For workshops or full multisensory math workshops, contact The Atlantic Seaboard Dyslexia Education Center in Rockville, Maryland. <a target="" href="http://www.asdec.org/">http://www.asdec.org</a> <br /></p><b>Feedback from both teachers and students utilizing this approach is extremely positive. It must also be noted though that not all manipulatives are appropriate for all topics and that teachers and schools do not need to spend enormous sums of money for commercially produced manipulatives. There are many simple and inexpensive items which may be successfully used for instruction. Most of all, multisensory math makes mathematics instruction fun!<br /><br /></b> <b><br /></b>M. Zecher, M.A., CALThttp://www.blogger.com/profile/13975157757275314758noreply@blogger.com0