Make an abacus: a fun summer math craft!

Other than loose rocks and seeds that prehistoric people used to count with, one of the most ancient math manipulatives is the abacus, or counting frame.  If your

This Chinese abacus predates our written number system.

kids have one, great! But just like growing their own garden can tempt kids to eat their vegetables, making math "toys" can encourage them to see math as something fun and exciting.  So why not have them make one?

There are many ways to make an abacus.  You can find a variety of abacus types and a variety of materials they can be made from.  However it's made, it's a great math manipulative your students can use over and over.

The type of abacus you make depends on what you want to use it for.  A simple 100-bead abacus is a great way to show place value.  The traditional Chinese or Japanese abacuses are a little more abtract.  These ancient counting frames are still base-ten models-- that is, they represent numbers whose digits represent multiples of 10 based on their position in the number-- but they use fewer beads per row because a separate section of each row contains higher-value beads.  Click here for a tutorial on how these traditional abaci (or abacuses) work.

A ten-bead per row, 100 bead abacus.

Math programs such as Right Start routinely use a 100-bead type of abacus to model place value.  This abacus typically has 100 beads, arranged in ten rows of ten beads each, often with five of one color and five of another to make the numbers easy to read.  The abacus is held so that the rows are vertical, and the row on the far right is the ones' place, with the next row to the left being tens, then hundreds, and so on.  When decimals are introduced, a dot can be placed along the frame to redefine the rows as hundredths, tenths, ones, etc.

One of many abacus apps.

Of course, you can find online abacus apps and use those, but it's so much more fun to have a real one you can actually put your hands on! Especially if you made it yourself.

To construct your own abacus, you will need beads, a frame, and rods of some kind to string the beads on. The beads themselves can be plastic pony beads, wooden beads, homemade clay beads,  even paper beads.  The frame can be made of wooden strips, popsicle (craft) sticks, or cardboard.  The beads can be strung onto wire, string, pipe cleaners ("chenille stems"), toothpicks, or bamboo skewers.  Even string can be used.  This clever video shows an abacus made entirely of paper and tape!

Two types of abaci among
 my favorite math "toys."

My favorite, portable, sturdy abacus is made of 50 pony beads, strung 10 at a time onto bamboo skewers, with the skewer ends hot-glued between pairs of popsicle sticks.  But if all you have is Froot Loops, tape, and plastic straws, the cereal can be strung on the straws and taped to a frame cut from the cereal box.   Be creative!   Other options, with more detailed instructions, are linked below.

traditional abacus design 

mini traditional design

base 10 (American) design

Color can add hands-on interaction to assignments

Not every assignment that your child is asked to do will be as "hands-on" as she might need. Some worksheets and study guides tend to be so non-engaging that they end up being more busy-work than instructional aids. However, there are specific modifications you can make to the assignments which can increase her whole-brain involvement without affecting the intent of the assignment (or the grading of it).  One of the easiest modifications is to add extra concept-bridging steps to the assignment through the use of color.

No, I am not talking about coloring pages here.  Handing a child a picture to color rarely engages his brain in any way that reinforces learning.  On the other hand, asking a child to add colors to a diagram, text or drawing in a way that requires analysis of the words or pictures will make a significant impact to his learning.

A net and its solid.

Add color.  Highlighters, markers, crayons, and colored pencils are indispensable when it comes to helping your child sink her brain into a pencil-and-paper assignment.   In a recent math lesson, one of my students was having trouble visualizing the net of a geometric solid.  He couldn't see how the faces of the 3D drawing matched the faces of the net diagram. Ideally, we could have cut out a series of nets, then folded and taped them together to build paper models of the solids-- and we did do one just to make sure he understood the concept-- but that's very time consuming and we had many different solids to figure out.  This was a case where "hands-on" had to be a little more creative, and color-coding became the hands-on bridge from looking at a simple assignment to actually being able to work with it and analyze it.

The net and solid, color-coded.

For this assignment, I had him color-code the faces of the solid figure and the corresponding faces on the net; he was then able to make the connection between the 2D and 3D figures.  Once he could see the way the faces related to each other, where they connected, and the shape of each one, he could more easily match the solids to their nets.






Another use of color can help students understand math processes. For example, some of my students have struggled with long division or multi-digit multiplication, getting lost with all the different numbers that have to interact with each other.  Here we see a number multiplied by 23.  The digits 2 and 3 are color coded to match their products as the number is multiplied out:

In this way, a student can see that 1353 is the complete product of 3 x 451, while 9020 is the complete product of 20 x 451.  Notice the "placeholder zero" is colored an almost invisible gray to reflect the "invisiblitity" of the ten's place zero that makes 23 = 20 + 3.    Division can be analyzed the same way, writing each digit of the quotient in a different color so that the student sees what is happening in the process:

Color coding is equally effective in studying spelling rules.  Students who cannot identify the individual phonograms in a word are stuck with memorizing the unique spelling of every word they encounter, which severely limits their ability to spell. What they need is a way to see the phonograms in a word as they study its spelling. While my favorite hands-on spelling instruction is done by manipulating movable letter tiles, or physically cutting up words into syllables and letter combinations, this is not always practical. Instead, students can be shown how to color code the various phonograms in their spelling words.

Color-coded phonograms.

In this assignment, for example, a student might have been told to simply copy his spelling list.  That's easily done without involving much of the brain, even if he has to "copy each word five times each." Instead, modifying the assignment to add in some color-coding will require the student to analyze and interact with the words in a more hands-on way, which can increase the likelihood of actually learning to spell the words.



For the example above, the student may the words himself, changing the color of his pencil for each phonogram.  He could also write them in regular pencil and then underline the letters in different colors.  Highlighting or using colored pencils to circle the phonograms in a pre-printed list could achieve the same purpose for students who have diffficulty with writing.

The directions for the above example could go something like this:
1. Separate each word into syllables.*
2. Write single-letter vowel sounds in black, single-letter consonant sounds in blue.
3. Write double letter (same letter) consonant sounds in red, two-letter consonant sounds in green, two-letter vowel sounds in purple.
4. Underlined silent e..
5. If a separate, single-letter consonant or vowel sound follows another one, give it a different color (e.g., the "c" in escape, or the "a" in creation).

(*Note: I was taught that syllables are officially divided in the middle of double consonants: bel-low.  However, for the sake of identifying phonograms, the sound of a double letter such as /l/ occurs once in the word, so we can treat "ll"  as a single phonogram spelled with two letters, just like ph or sh, which are never separated.)

Color-coded roots, suffixes and prefix.

Besides learning the spelling of words, adding color can help children learn the meaning of words.  Vocabulary study often emphasizes prefixes, suffixes, and roots from Greek or Latin.  Color-coding can be very helpful for this as well.  Simply highlighting prefixes in one color, and suffixes in another, can help a student focus on the base words and analyze the meanings of words.  Or in a list of words that share certain roots, highlighting each root in its own color can call attention to the shared meaning of the words.

This concept can be easily extended to have students color-code the roots to match the corresponding key words in their definitions:

As you can imagine, analyzing words this way gets the hands, eyes, and brain involved in a manner that simply copying the words over and over cannot do. Similarly, color can be used to analyze text.  People have used highlighting to mark important information for years.  Why not use a variety of highlighting colors more intentionally?  If your child's assignment involves reading for information, he may use color to match information in the text to individual questions, either before he writes his answers, or afterwards.  While it may seem redundant to mark up a text in this way, the process actually increases reading comprehension by engaging the brain in a more concrete way than simply writing an answer.  Some schools teach this technique of "justifying" a response, requiring students to mark the information in the text that supports their answer:

This worksheet becomes more effective when the student

 uses color to match textual information to the questions.

Adding the targeted use of color to an assignment is limited only by the imagination.  A science diagram can be color coded to indicate the function of various structures. A history article might have facts highlighted that correspond to opposing political views. Whatever the student is asked to learn, color can help add hands-on interaction to even the most black-and-white of worksheets.

Laura Kasbar - Converting Apraxia and Scripting to Conversational Speech...

There are several people/companies that I get very excited about who are working with the special education community.  Asperger Experts is one of them.  Geminii is another company; they produce a speech therapy video system to improve verbal communication for children with autism, Down Syndrome, traumatic brain injury, or apraxia of speech due to other issues.

This video features the originator of Geminii, Laura Kasbar, who developed the videos for her own on-spectrum children based on her background in foreign language learning. She explains the research behind its development, as well as the research that has been done actually using Geminii, and shares some success stories.  She doesn't promise miracles; some children have used it and their command of language becomes asymptomatic, while others (especially adults who have lived their lives without speaking) may gain only a few words-- although, as Kasbar remarks, just being able to say "yes" and "no" can have a profound impact on a person's life.  She does admit that its effectiveness is limited for people who have seizures, as the seizures seem to erase any new learning.  (I have heard of that issue before.)  The system is currently available as a monthly subscription at about $98/month, with scholarships available.  Using the subscription, parents are able to tailor a program to their child's specific needs and modify it as the child progesses.

As Ms Kasbar explains, the strength of the video system is that children with speech apraxia may need as many as 8,000 repetitions of a concept to learn it, and learn best in short, frequent sessions.  Using a targeted video for a few minutes, several times a day over several months allows more input to the child's brain than he might get from years of weekly, hour-long sessions with a speech therapist.  While I am not a speech therapist, and have never used this program, nor do I yet know anyone who has, the principles used in its development make it a program I would recommend to anyone whose child has speech problems.

Signs that your child might benefit from a change of educational venue

Back in the day, my parents and grandparents didn't have much of an option when it came to how their children were educated.  It was pretty much understood that we would be going to the neighborhood schools.  That's what everybody did-- unless you were rich, in which case you went to a private school, or handicapped, in which case you were bused to the special school.  Whatever school you attended, you were likely to be surrounded by teachers who had been teaching for years and years.  They had their routines down pat, and taught the same thing every year because it worked. Except when it didn't, in which case you were generally out of luck.

Now things are very different. There are so many options out there for educating your child that a parent can become very confused, not to mention locked in a guilt-trip of worrying if they have made the right choice, and constantly second-guessing themselves.  Our children only have one shot at childhood, and what if we mess it up?  What if we make the wrong decision, and our child's future is in ruins?

The good news-- or maybe the bad news-- is that no perfect method of schooling exists.  There are benefits and drawbacks to every one: home schooling, classroom learning, online, hybrid, public, private.  Only you can decide which is right for your family and your child.  And it may be that what is perfect for your child one year becomes less effective in the future.  While too much moving back and forth can be detrimental to your child's education, it's okay to take each year as it comes.  For example, my two children started out in public school, but various circumstances made us decide on home school after they finished first (younger) and second (older) grades.  This proved successful for the next six years, but when our older child was ready to enter high school, he elected to rejoin his former classmates, as did his younger sister.  With proper planning, they hit the ground running and made a smooth transition back into public school.  When I was a public school teacher, I had students enter the classroom for the first time in sixth grade, while others made the opposite transition, choosing to home school for the first time during the middle school years.

The "default," of course, is still the neighborhood school.  The advantages to this option include easy opportunities to make local friends, trained teachers and specialists, and relatively low cost.  It also allows your child to experience a variety of adult leaders with different personalities and strengths. Another benefit is that someone else carries the responsibility for lesson planning, grading and monitoring your child for the bulk of the school day.

If you have doubts that your neighborhood school is the best choice for your child, there may be local magnet schools, charter schools, or private schools that would suit her better.  If your child is thriving in a group setting, but the curriculum or school philosophy is a poor fit, you should investigate these first.  But how do you know if homeschooling might be the best alternative?

Signs that homeschooling might be helpful

• anxiety- mental or physical distress that appears highest on school days.
• falling behind- needing help to keep up with the academic concepts.
• lack of challenge- needing more depth or breadth to the academic work.
• lack of interest- no excitement for learning.
• missing basic/foundational skills- significant deficits in math facts, spelling, writing, reading. 
• overload- inability to complete assignments in time allowed.
• physical unfitness- spending all day on school work, with no time to play.
• lack of time- no time for family activities, hobbies, personal interests.

On the other hand, what if you have been home schooling for a while and you suspect it might be losing its effectiveness?  Here are some things to look for:

Signs that classroom learning might be helpful

• loneliness- if interaction with scouts, youth groups, sports, home school groups isn't enough.
• boredom- when your student needs activities and resources that you can't provide yourself.
• seeking stimulation- some children learn better when discussing things with peers.
• lack of confidence- sometimes seeing that peers also struggle with learning is reassuring. 
• desire to interact with peers- even siblings aren't enough sometimes.
• competitiveness- the child who is challenged by others' success may lag behind at home.

What signs have you seen that might suggest your child would benefit from a different mode of education?