Dr. Warren’s blogger articles on math.

Multiples and LCM Made Easy with Millipedes

Over the years, I have found that students struggle remembering how to find multiples as well as least common multiples.  Somehow the wording doesn’t cue them into the process that they must execute to solve the math problems.  As a result, I continually associate multiples with millipedes and use the alliteration, multiple millipedes to help them recall and even visualize the process.   

To make the process easier, I have created a new publication (a document and PowerPoint) – Multiples and LCM Made Easy with Millipedes.  This product includes a PowerPoint lesson, as well as a comprehensive document that includes embedded memory strategies, step by step instruction, practice problems, a coloring activity, and an interactive game so that students can receive the practice they need while having fun.  Now students can learn the concept once and continue to remember the process over time. 

Click Here to learn more.  


Dr. Erica Warren is the author, illustrator and publisher of multisensory educational materials at Good Sensory Learning and Dyslexia Materials.  She is also the director of Learning to Learn, in Ossining, NY.  To learn more about her products and services, you can go to www.goodsensorylearning.comwww.dyslexiamaterials.com & www.learningtolearn.biz  
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Early Literacy: Letter, Number and Shape Challenges

Occasionally, I get inquiries from other learning specialists in the field that have difficult cases. Recently, a director of a tutoring academy asked me a question about a new student, and I thought I would share our correspondence for this week’s blog post.  Names have been altered to preserve anonymity.

 ———————————————-

Dear Erica:

I have a question about a new case.  When I first contacted you about two years ago, it was because I had a little 5-year-old girl who was way behind.  Your guidance really helped me.  Anyway her first cousin has come to us.  The girl turned 4 in June, and she is having a number of issues.   She has no number recognition and no letter recognition, except the letter “A” – because her name is Alice.  She does recognize most of the basic shapes.  However, she can only trace, but not copy them.  I asked her to write her name, but all letters were illegible – but the letter A.  I’m not sure it was even her name. She knew all her colors, but blue, which she called “lellow.” I had her color fruit, and she colored both grapes and an apple blue. She had no rhyming ability, and no concept of compound words.   I gave her the two words to put together.  I don’t know where to begin.  Do you have any suggestions?

Dear Sue: 
I like to work off of student strengths, and it sounds like Alice can trace.  So, I would use this ability and have her trace things and color them by placing images into dry erase pockets.  Be sure to get a variety of dry erase markers too.  

Here are my suggested steps:
  1. First, you can place letters, numbers, and different colored shapes into the dry erase pockets and ask Alice to trace them while saying the name (and color – if applicable) 5 times.  In the beginning, stick to one category and limit the instruction to 5 concepts.  For example, focus on the first 5 letters of the alphabet.  You can do both upper and lower case letters at the same time, or focus on one at a time. 
  2. Second, blow up a balloon and write each of the 5 letters onto it with a permanent marker.  Be sure to make the letters as large as possible.
  3. Third, toss the balloon to Alice and see if she can name the first letter she sees while tracing it on the balloon.  Pass the balloon back and forth.  You can do the activity too, so she can learn vicariously through demonstration.  After she can do each of the letters successfully, teach her the letter sound.  Toss the balloon up in the air.  Say you see the letter “B” trace the letter and say the letter name 5 times.  Then say “B makes the ‘b’ sound like balloon.”  Do this for each letter and then let Alice give it a try.
  4. Fourth, when Alice is ready, make the game even more challenging – Each time she gets the balloon and sees a letter, she has to come up with a new word that starts with the same sound – “B makes the ‘b’ sound like banana…”  “B makes the ‘b’ sound like ball….”  
  5. Fifth, when the session is over, encourage Alice to take the balloon home and teach the games to her parents and siblings. 

You can follow the same sequence for numbers and shapes.

Use the App Touch and Write.  This is such a fun, multisensory, motivating approach that I’m sure she will enjoy!

As another activity, you could also teach Alice about syllables:  I like to use kinesthetic movements when teaching this concept, where you and the student bounce on ball chairs, learn a simple song about syllables and then feel the syllables.  Here is a video I did that illustrates the concept: https://www.youtube.com/watch?v=FRVqZw_FS-c
I would start to teach her rhyming and blending once she has learned all her letters, numbers and shapes.  If you find that she likes to play games, you can check out my reading games primary too.  
———————————————-
I hope you found this blog helpful, and that sharing our correspondence has offered you some ideas.


Dr. Erica Warren is the author, illustrator and publisher of multisensory educational materials at Good Sensory Learning and Dyslexia Materials.  She is also the director of Learning to Learn, in Ossining, NY.  To learn more about her products and services, you can go to www.goodsensorylearning.comwww.dyslexiamaterials.com & www.learningtolearn.biz  

Teaching Mental Math to All Elementary Students

Many people think that mental math is too difficult for elementary learners, but, in fact, youngsters have wonderful imaginations and capacities to visualize that can be utilized while doing mathematical calculations.  In addition, it teaches them how to use their brains in an efficient, mindful and active manner.  What’s more it develops working memory, executive functioning skills and attention abilities that can serve them for the rest of their lives.

How Can Mental Math Utilize and Develop Working Memory, Executive Functioning and Attention?
Working memory is the key mental process that enables one to hold, manipulate, organize and process both new and stored visual and auditory information.  When employing working memory, students also develop their executive functioning skills as well as their attention so that they can retrieve, integrate, and process the problem at hand.

Teaching Children the Power of Visualization Makes Mental Math Fun and Memorable
Another important component of an efficient and robust working memory is the capacity to visualize what one is learning.  Creating mental imagery that can be adjusted like an internal movie can make learning both fun and memorable.  If you are interested in helping students to develop this capacity, you can play activities and games that will help young learners to develop this skill.  To learn about why and how you can teach this, CLICK HERE.

What Types of Mental Math Can You Teach Children?

You can begin by teaching very simple mental math problems by encouraging your students to visualize objects that they can then count in their head.  I also love to use mental math to teach simple addition and subtraction.  Instead of rote memorization, I have a different approach.  Here are a few examples.
  1. Students can learn to add and subtract simple addition problems by visualizing dice.  I have them do art activities and play games with dice until they feel comfortable that they can picture them in their heads.  Then when they have to add numbers that integrate 1-6, they can visualize a die and count up for addition and countdown for subtraction.  
  2. I teach funny memory strategies that students can visualize for learning how to add identical digits like 2+2, 3+3, 4+4 and so forth.  For example, with the problem 9+9, I tell them that the two nines are in love, and they get married.  When this happens they become one (1), and two heads are better than one (8). 
  3. Once they can add the identical digits, the mental manipulation comes in.  If they know that 6+6=12, then they can compute 6+7.  All they have to do is 6+6=12 and 12+1=13. 
  4. I am also a strong believer in integrating color, games and multisensory methods.  To learn more about my Mathematic Math Manual idea CLICK HERE.
You would think that mental math is only for bright or gifted children, but I have found that it works brilliantly with children with learning disabilities and even those with low IQ scores.  In fact, it works quickly, and I find that my students have great fun with it.  I would love to hear your thoughts on this matter.  Do you, too, use mental math when instructing elementary students?

Dr. Erica Warren is the author, illustrator and publisher of multisensory educational materials at Good Sensory Learning and Dyslexia Materials. She is also the director of Learning to Learn, in Ossining, NY.  To learn more about her products and services, you can go to: www.goodsensorylearning.com, www.dyslexiamaterials.com www.learningtolearn.biz  

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Strategies that Strengthening Math Abilities for Struggling Elementary Students

There is often an easy solution to helping elementary students that struggle with math.  But first, we must understand that the root of math troubles often results from one or more of the following:

  1. lack of experience and practice working with numbers and symbols.
  2. drab or humdrum instruction.
  3. problems activating the needed areas of cognition to solve these problems.
  4. weaknesses in the cognitive areas of quantitive reasoning, spatial skills, visual processing sequencing, and working memory. 

What Happens to These Struggling Learners in Our Present Education System?


Young learners often lose interest and motivation quickly when they have problems learning concepts. What’s more, when their peers exhibit learning mastery and they do not, it can feel embarrassing and humiliating.  If left unaddressed, anxiety, a poor academic self-concept and even helplessness can result.

How Can We Protect Students from Negative Thoughts that Quickly Damage One’s Academic Self Concept?

  1. Choose names for lessons that bring excitement and anticipation to the learning process.
  2. Make lessons “magical.”  Like a magician, teach your students tricks in an animated way that helps them uncover the answer. To read more about this CLICK HERE.
  3. Bring fun and enticing activities to the table.  Integrate manipulatives, games and movement into lessons. 
  4. Go multisensory in your lessons and teach to the 12 Ways of Learning.
  5. Pay attention to popular fads.  When I saw my students obsessions with rainbow looms, I quickly integrated the color bands and geoboards into my lessons.  
  6. Ask your students for strategy and lesson ideas?  When learners get involved with the teaching process, they often get more excited about the topic or instruction.
  7. Provide scaffolding.  Continue to walk your students through the sequence of steps required to complete a problem, until they can do it independently.
  8. Offer memory strategies to help your students encode and retrieve new concepts.  You can also ask them to generate their own strategies. 
  9. Teach metacognitive skills by thinking through the process aloud. 
  10. Integrate mindfulness into your class and teach visualization strategies.
  11. Teach your students how to be active learners.

How To Activate the Needed Regions of the Brain and Strengthen Weak Areas of Cognition?


But what if the core difficulties are the result of weak areas of cognition or learning disabilities?  One of the best ways to assist is to act like a personal trainer for the brain and help students activate and strengthen foundational skills. 
I created Quantitative and Spatial Puzzles: Beginners for this population of learners.  Eight, engaging activities help students improve upon: 
  • quantitative reasoning
  • spatial skills
  • visual processing
  • sequencing
  • working memory
These engaging activities were designed for 1-5 grade students, but I often use them with my older students to help fortify these key cognitive abilities.   The activities also can be printed and placed into math centers, used or morning warm-ups and offered as fun activities for students that finish their class assignments early.
If you would like to learn more about my new publication, Quantitiative and Spatial Puzzles – Beginners, CLICK HERE or on any of the sample images.  I hope you found this blog helpful. Please share your thoughts and comments.

Dr. Erica Warren is the author, illustrator and publisher of multisensory educational materials at Good Sensory Learning and Dyslexia Materials.  She is also the director of Learning to Learn, in Ossining, NY.  To learn more about her products and services, you can go www.goodsensorylearning.com, www.dyslexiamaterials.com www.learningtolearn.biz  

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Using Simple Images to Teach Math Concepts

Utilizing imagery and visual memory can be very
helpful when learning mathematics. 
A single picture can help a student define and remember a concept, or it
can even help them to recall the steps required to compute a problem.  What’s more, it often brings the “fun
factor” into the learning environment as students can pull out their crayons,
colored pencils or magic markers to complete the activity.

I recently learned about the Palm Tree Method from
one of my students. I scoured the internet to find its origin, but came up
empty handed.  So, although I did
not come up with this idea, it is still one of my favorites for solving
proportions.  
If you would like to learn about other imagery activities
to help your students learn math concepts, you might like my blog entitled Mathemagic or my products Measurement Memory Strategies or Why We Should Learn about Angles.

Dr. Erica Warren is the author, illustrator and publisher of multisensory educational materials at Good Sensory Learning and Dyslexia Materials.  She is also the director of Learning to Learn, in Ossining, NY.  To learn more about her products and services, you can go www.goodsensorylearning.com, www.dyslexiamaterials.com www.learningtolearn.biz  

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Using a Geoboard to Help Students with Dysgraphia


Recently I discovered the geoboard and now I love to use this product to develop mathematical skills, visual spatial skills, visual reasoning and fine motor dexterity.  In fact it is great for my students that have dysgraphia.

What is a Geoboard?
A geoboard is a math manipulative that students can use to explore basic shapes and geometry such as perimeter, area and coordinate graphing.  It consists of a wood board with evenly spaced rows of nails or a plastic board with protruding pegs around which string or rubber bands are wrapped.

How Do I Use My Geoboards?
Due to the popularity of rubber band bracelets, one can get a huge variety of colorful rubber bands in many different sizes.  I have organized mine into sectioned plastic boxes so that my students have many options to choose from.  Here are a number of fun activities that I offer my students in my own private practice.

For my young learners I use the geoboard to:

  1. learn the formation of letters and numbers.  It is a wonderful tool to use when students struggle with letter, number or symbol reversals.
  2. instruct about the many shapes – triangles, squares, rectangles…
  3. develop spatial skills where students copy a design I create on another geoboard or from a picture of a design that I created on a geoboard.
For my older students I use the geoboard to:
  1. develop writing skills.   Players create images that they then described in writing so that another player can create the image by following the directions.
  2. teach and review coordinate graphing.
  3. teach and review the plotting of points on a coordinate plane.
  4. creating, line, frequency and bar graphs.

If you too are using a geoboard, I would love for you to comment below this blog.  Also please share if you are using the geoboard in other creative ways.

Click on the image below to purchase on Amazon:

Free Visualization Game: For Improved Reading, Writing, and Memory

Developing your student’s ability to visualize can provide them a “secret weapon” that can enhance learning capacity, improve memory and spark creativity.  In fact the research shows that visualization improves reading comprehension, creative writing abilities and the encoding and retrieval of math, history and science concepts.

Free Visualization Game:
I recently
finished a book that reviews the history and research behind visualization and
then provides teachers everything they need to assess and teach this complex
skill.  In celebration, I wanted to share
one of my favorite games, Picture This
and Draw
. The best part about this particular game is it not only develops the capacity to visualize, but works on verbal reasoning, expressive language, visual memory, fine motor integration, spatial skills, attention to details, and the ability to follow directions.  This game is one that I enjoy
playing with my own students.  In fact, I
played it this past week.  
Jenna and I went to opposite sides of the room with two pieces of paper and some colored markers. We each drew images on one piece of paper and then described our pictures in detail on the other piece of paper.  We hid our illustrations and then shared our descriptions with one another.  Our next task was to recreate the images by generating our own visualizations from the words and then drawing it on a blank piece of paper.  Once we finished, we compared the new drawings to the originals and analyzed the results.  
Jenna’s image is depicted to the right.  Please note that it is important to keep images very simple.  Below you will find a full description of the game.
Picture This and Draw:

Materials:
·     
Paper
·     
Colored
pencils or magic markers
Group Administration:
·         
Draw
a simple image, with no more than 3 – 6 very simple elements. 
·         
Have
one student or the teacher describe the image to the other students verbally or
in writing.  Use as many details as
possible. 
·         
Describe
the size, color, number, shape and the location of the objects on the
page. 
·         
Next,
have each student produce a drawing of his or her visualization based on the
description presented. 
·         
Make
sure each student can not see what the other students are drawing. 
·         
When
all the students have finished, share the drawings with the group and discuss
which student’s drawing is closest to the description. 
·         
Discuss
ways the presenter could have done a better job describing the image. 
·         
Review
each drawing and discuss what each student could do to improve his or her
visualizations. 
Individual Administration:
·          
You
can also play this game one-on-one.   
·          
Begin
by going to opposite sides of the room so that each player can not see each
other’s work (each player should have a set of colored pencils or magic markers
as well as two blank pieces of paper). 
·          
On
one page, both players should make very simple drawings with no more than 3 – 6
elements, as in Jenna’s image pictured above. 
·          
Then,
on the other page, each player should describe, in words, the image they drew
with as much detail as possible. 
·          
Next,
the players should share with each other the description of the image they
drew, while still concealing the drawing. 
·          
Each
player reads the other player’s description and completes a drawing based upon
it. 
·          
Finally,
the players compare their images and discuss in what ways improvements could be
made to the written descriptions, as well as the drawings.
If you would
like to learn more about the history of visualization and also access
assessment materials and many other fun activities and games that will teach
this needed skill, please come check out my new publication Mindful Visualization for Education as well as my two Teaching Visualization PowerPoints.


Dr. Erica Warren is the author, illustrator and publisher of multisensory educational materials at Good Sensory Learning and Dyslexia Materials.  She is also the director of Learning to Learn, in Ossining, NY.  To learn more about her products and services, you can go to www.goodsensorylearning.comwww.dyslexiamaterials.com, & www.learningtolearn.biz

Strategies for Teaching the Different Types of Angles and Lines

Using multisensory instruction always makes a lesson more
engaging and fun for students.  In fact,
one of my favorite learning modalities to integrate into instruction is
kinesthetics or movement.  For many
learners having to sit still is not conducive for learning, and other children
just need to get their bodies moving and their blood circulating form time to time to fully
focus on a lesson.

One of my favorite topics to teach are the different type of
angles and lines.  I like to cover these concepts
with a multisensory and interactive PowerPoint that I created, then I get the
students to use chants as well as their bodies to encode the information.  Just this week I created a free YouTube video,
where I share some fun activity ideas for lines and angles. 
If you like the video and would like to also acquire my multisensory
PowerPoint presentation, Click Here to learn more.

Dr. Erica Warren is the author, illustrator and publisher of multisensory educational materials at Good Sensory Learning and Dyslexia Materials.  She is also the director of Learning to Learn, in Ossining, NY.  To learn more about her products and services, you can go to www.goodsensorylearning.com, www.dyslexiamaterials.com, www.learningtolearn.biz  

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The Number Ladder: Turning Addition and Subtraction from Top to Bottom

I have never understood why the number-line extends horizontally from left to right.  Young learners often confuse their left from right and others have trouble remembering which way to travel when trying to solve simple addition and subtraction problems.  However, when viewing a vertical number-line, it makes conceptual sense that going up would equate with adding, while traveling down would result in subtraction.  Furthermore, when solving multi-digit problems, we teach students to line up numbers vertically.  Therefore wouldn’t it be best to commence instruction with the number-line extending up-and-down?

Turning the Number-line Into a Ladder
To make the learning process even easier, I like to change the number line into a ladder that travels up into the sky.  This way, when students are instructed to add, they climb up the ladder and when they subtract they descend down the ladder.  What’s more, when students eventually learn about integers, the number line can descend down “into the ground.”

Free Game that Teaches this Concept:  
I love to use a staircase to help students really understand the concept of adding and subtracting. If you would like a free game that is ideal for kinesthetic learners as well as a copy of my Number Ladder, Click here

I Also Offer Two Publications:

  • If you want to purchase an interactive PowerPoint that teaches adding and subtracting whole numbers as well as a PDF file with activities and games, Click here.  
  • If you would like to purchase an interactive PowerPoint as well as a PDF that teaches all about adding and subtracting integers and also offers two games click on the image to the right or Click here

Cheers, Erica

Dr. Erica Warren is the author, illustrator and publisher of multi-sensory educational materials at Good Sensory Learning and Dyslexia Materials.  She is also the director of Learning to Learn, in Ossining, NY.  
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Cognitive Exercises Solve Reading and Math Difficulties

Many young learners struggle with basic reading and math
because the cognitive skills required to do these tasks are weak.  Therefore, these children need to
strengthen these processing areas before they attempt to learn how to decode
words and execute basic computations. 
What are the
Core Areas of Cognition Required for Basic Reading and Math?

1.   Sequential
processing and memory
: The ability to scan, make sense of, and remember
information in a sequence or series.
2.   Auditory
processing and memory
: The ability to listen, make sense of, and
remember information that is heard.
3.   Visual
processing and memory
: The ability to scan, make sense of, and remember
visual information and symbols.
4.   Attention
to detail
: The ability to thoroughly and accurately perceive and
consider all the details and then determine the most important piece or pieces
of information.
5.   Speed of
processing
: The ability to perform
simple repetitive cognitive tasks quickly and fluently.
6.   Spatial skills: The ability to
mentally manipulate 2-dimensional and 3-dimensional figures.
7.   Tracking: The ability
to scan text from left to right.
 
Basic Exercises can Help to Remediate Weak Cognitive Areas

Each of the cognitive areas listed above can be strengthened.  However, what is most important is the
activities need to be focused and engaging enough to enchant young
learners.  From my work with
children over the past 15 years, I have recently created two publications that offer fun
activities and games that your primary students will be sure to love.  These activities can also be used with older students as a form of cognitive remediation.

Following
Directions Primary:

My newest publication, Following Directions Primary, offers
a comprehensive, 49 page, digital download that includes process of elimination and coloring activities.  It develops abilities with the use of cute animals and aliens as well as letters, numbers, shapes and arrows. As students
develop listening skills, they also enhance linguistic abilities and core
cognitive skills.  If you are interested in learning more about this publication
you can come to my product page.  You can even download free samples.
Reversing
Reversals Primary:

This past summer, I created Reversing Reversals Primary.  This two focuses on strengthening the
cognitive foundation needed for reading and math.  It also works on the cognitive areas that impact
students with dyslexia such as perception.  This publication, which is available as a digital download, offers 72 pages of activities and a game and teaches all of the cognitive skills with the use of colorful animal images.  If you are interested in learning more
about this publication you can come to my product page. You can even download a free samples.
By helping young learners to develop their core, cognitive
foundation before commencing with reading and math instruction, you can assure
that these students will have the abilities necessary to succeed. Furthermore, you can avoid learning difficulties and allow your young learners to progress with confidence.

Cheers, Erica

Dr. Erica Warren is the author, illustrator and publisher of multisensory educational materials at Good Sensory Learning and Dyslexia Materials.  She is also the director of Learning to Learn, in Ossining, NY.  To learn more about her products and services, you can go to www.goodsensorylearning.com
www.dyslexiamaterials.com & www.learningtolearn.biz  
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