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?

Building Early Literacy Skills is not Rocket Science.

Every piece of advice I've ever seen about promoting early literacy in children can be summed up in three words: "Read, read, read!" That goes without saying.  In fact, nearly every baby shower gift I have given in the last twenty years has been accompanied by a copy of Pat the Bunny, or in a pinch, a board book.  Because you can read to babies, and I personally think you should.

However, some parents worry that they aren't doing enough. There are books and videos that promise to Teach Your Baby to Read.  Is that kind of targeted early instruction necessary?  I think not. Babies can learn to recognize sight words, to be sure, but that kind of reading limits the reader to only the words they have been taught.  Waiting until the child's brain is actually ready to use the "building blocks" of words-- the letters and combinations of letters-- is much more effective.  

But how, then, is a parent to make sure that a child is ready for the instruction when he goes to school?  Reading to babies, toddlers, and preschoolers definitely prepares them to enjoy and appreciate reading.  Babies learn that books contain words, that the words don't change, and the words may tell a story or share information. The books may even introduce letters and letter sounds, but the mystery of how those letters work is still something that most children will need to be taught later. So, beyond simply reading, what are some other things you can do with your baby or young child that will increase his chances of being a strong reader and writer in the future?

First, help your baby to communicate.  Through body language and sounds, we all send and receive information.  Every interaction you have with your child can increase her communication skills!  Use eye contact, smile, laugh; mimic her facial expressions.  Encourage her to mimic yours.  Many parents have found that teaching "baby signs" to their little ones not only reduces the frustration of terrible twos (when toddlers know what they want but lack the words to express themselves), but also builds brain connections that encourage verbal communication later on.  In fact, everything you do to facilitate communication with your child will build brain connections that will later be used in reading and writing. 

Talking to your baby will build his vocabulary.  A 2013 Stanford study found that babies who enjoyed the most verbal interaction with their parents had a significant advantage over less-talked-to peers. (1)  By age three the talked-to babies had heard an estimated thirty million more words, and understandably had a much larger vocabulary than the children of the less chatty parents. Of course the larger a child's vocabulary, the more words he can read and comprehend.  (And unlike words from the tv or computer audio, actual interaction with people promotes retention of the vocabulary-- simply put, the words mean more when they come from someone who loves you.)

As important as knowing what the words mean is learning to distinguish the individual sounds within the words.  I have mentioned in previous posts that word play is important to building the auditory processing skills that allow a child to read well.  Listening to (and later repeating) rhyming words in nursery rhymes, poems and songs, and alliteration in tongue-twisters, all help a child's brain sort sounds into meaningful units. He will learn to hear the differences between the sounds of cat vs bat, bat vs bit, and understand that the difference in a single sound can change one word to another word. This skill is critical to reading.

Besides sound discrimination, a little brain needs to develop visual discrimination in order to be able to tell the letters apart.  Shape-sorting, identifying pictures, and simply naming things he sees are all helpful activities.  Babies can "point to the dog" or "point to the cat." And babies are hard-wired to learn names for things.  It's not unusual for a toddler under the age of two to be able to identify the letters of the alphabet; this skill is no more difficult than identifying a simple drawing of a dog or a tiger. And while some educators prefer that children learn to associate a letter with its sound(s) before learning its name, I disagree.  Learning to distinguish a Q from an O, for example, is a lot easier if you can call each by its name rather than trying to explain "this round shape with a tail stands for the sound /k/ and this other one without a tail can sound like /oh/, /ah/, /uh/", etc.  So go ahead and read Dr Seuss' ABC, and sing the ABC song, to let your little guy learn his letters.  Just keep it fun!

Playing with three-dimensional letters can also help the child cement their forms in his mind. Letters can be formed out of play dough, or even cookie dough.  A simple alphabet puzzle allows the child to take the letters out and manipulate them, while still learning that they must be oriented in a certain way on the page (or puzzle board.)  This is an important skill as well; some experts in dyslexia say that the dyslexic brain's mental maneuvering of the letters can cause reading difficulty.  The letters on a page may seem to move around, orienting themselves in any direction.  According to the author of The Gift of Dyslexia, playing with 3-D versions of letters helps solidify the child's perception, so that the printed letters will stay still on the page. (2)  Kinesthetic learners are also helped by holding and moving the 3-D letters around.  They remember things they feel and move more than what they see, so giving their brain experience with "real" letters will help them transfer the knowledge to 2-D images of the letters-- aka "print"-- later on.

Fine motor skills and organization skills will also help build a foundation for good writing. That's why kindergarten used to include such activities as painting, sorting or stringing beads, and lacing cards, as well as coloring and drawing. Even babies can begin to work their fine motor skills by picking up Cheerios or other small finger foods and putting them in their mouths. Finger painting, swirling pudding around on a high chair tray-- these activities build the brain-muscle connections that will later make forming letters with a pencil much easier.  But of course writing is more than just a physical task; it also requires organizing thoughts into words and sentences.  The ground work for that can begin with babies, too.  Beyond the obvious "exercise" of having actual conversations at whatever level the little one is capable of,  organization can also be fostered through activities as simple as putting toys in a toy box and laundry in a hamper. Playing with a shape-sorting ball or ring stacker can further develop these skills.  (Although, to be honest, I've never seen a child actually use either of those toys for its intended purpose.)  In years to come, the child will be using those fine motor skills to form letters and words (or type them), and will be organizing his ideas into words.

Preparing your child for school success does not take extraordinary measures.  Especially in the early years, it's all about interacting with your child in positive ways: talking, playing, and reading with your little one will set the groundwork for future literacy instruction.  These are natural things that most parents do with their children anyway.  The little brain is absorbing language, sorting sounds and organizing things she sees.   And that's why, with effective instruction at the right time, most school-aged children can learn to read and write without a whole lot of trouble.  So relax!  Enjoy your baby and watch her grow.

1) https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3710871/

2) http://davis-method.narod.ru/Gift_of_Dyslexia.pdf

X-rated Math: So inappropriate for their cognitive stage it's obscene, and what you can do.

No, I'm not talking about math with explicit language or subject matter.  The subject of this post is math concepts that are presented in a way that does not match the student's cognitive abilities.   If you want to skip down to some practical ideas to help your student, scroll down till you see the pink elephant.   The next bit is just background explanation.

It is happening more and more these days, due to the reality that the people making curriculum decisions are not knowledgeable about the cognitive development of children.  They assume, incorrectly, that the brain is like a container that you can simply pour knowledge into, and the sooner you get started pouring, the more time you'll have to pour more stuff.  They don't realize that the brain develops in specific stages.  In some ways, the early brain is like a colander whose holes will gradually close;  in the beginning, there is plenty of room to fill it with all kinds of critical information, but if you try to put in certain things too early they will simply leak through the holes.

The best plan is to put in the big "rocks" first-- the big ideas about the world and physics and love and math that children learn through play.  Taking turns, falling down, sharing, and quantities.  As the holes begin to shrink, we put in smaller, but still concrete rocks: more detailed ideas like dealing with anger, letter sounds, operations with numbers, and measurement.  These smaller rocks fit tinto the spaces between the bigger rocks.  As the student matures, the "holes" in the brain get smaller and smaller, allowing ever finer, more abstract ideas to settle into the spaces between the bigger concepts. Finally, the holes are completely gone, and even concepts as fluid as sand and water-- calculus, philosophy-- will be retained.

At least, that's the Holt model, based on what I've been taught about cognitive development and what I have observed in my years of teaching infants through adults.   The trouble is, when curriculum does not follow this model, abstract concepts are presented too early and the students simply cannot grasp them.  Or they may be able to hang on to an idea long enough to pass a test, but nothing is retained.  The students' time and the teacher's time is wasted, to say nothing of the potential for the student to give up on the subject entirely.

Case in point:
After a lesson on finding the constant of proportionality, a sixth-grader was recently given a problem like the following to solve (edgenuity.com; granted, it was actually from the website's seventh-grade series, but we're all about advancement these days, so the 6th grader was expected to learn it.)  Just a side note, I am not convinced that giving 6th graders terms like "constant of proportionality" to use even makes sense; something about the abundance of syllables tends to make the brain shut down.

Jenna is developing an equation that will represent the same proportional relationship as the graph:

How will the ordered pair help her when she finds the equation?

a) The product of the coordinates will be a constant term in the equation.
b) The quotient of the coordinates will be a constant term in the equation.
c) The product of the coordinates will be a coefficient in the equation.
d) The quotient of the coordinates will be a coefficient in the equation.


Those of you who have 6th graders don't have to imagine the deer-in-the-headlights look that accompanies this problem.  You've seen it.

So here's the concern:  the 6th-grade brain, generally speaking, is just beginning to be able to think in abstract concepts.  The most basic level of abstraction happened in preschool, learning that numbers can represent quantities: 7 can stand for seven apples.  The next level was learning that symbols can represent operations: 7 - 3 means taking away three from the original seven.  But all of elementary-level math is based on concepts that are no further removed than reality than that-- multiplication of decimals and fractions, long division, early geometry-- all of these ideas can be conceptualized just two degrees away from reality.  The student does not have to think abstractly.  Around the age of twelve, a child's brain matures and will generally grasp that x can stand for a variable quantity, and he may begin to solve for x using simple procedures. But this particular problem asks the student to think through concepts that are not just three degrees removed from reality, but several degrees:

1st degree. The numbers represent actual quantities.
2nd degree. A "product" is a result of multiplication, a "quotient" is a result of division; "constant term" means a number without a variable in an expression, and "coefficient" refers to the number in a term that precedes a variable.  A fraction can be called a quotient because it is essentially division.
3rd degree. The ordered pair (4,6) means that every time x = 4, y = 6.
4th degree. The graph represents a relationship between the quantities.
5th degree. The relationship shown in the graph can be expressed as an equation.
6th degree. The ordered pair can be used to create the equation.

So, to answer the question, the student must think at least six degrees beyond the concrete level.

Here are the thought processes needed to solve this problem:

1. The equation will be in the form y = __ x.
The student needs to know that this means "what must I do to x to make it equal to y?"

2. The student needs to know that the coordinate pairs in the graph represent the related values for x and y.  When x is 4, y is 6.  When x is 0, y is 0.

3.  The question then is, what can you multiply x by to make it equal to y?  This requires a knowledge of fractions, as well as how to use multiplicative inverse to solve for x: if 6 = 4x;  6 = 4(6/4).  So, the equation for the graph is  y = 6/4 x.

4. The 6 and 4 from the coordinate pair are now recognized as the numerator and denominator in the fractional coefficient.  Fractions can be thought of as another way of writing a division problem; which means they are also quotients.  So, the answer to the original problem is d) The quotient of the coordinates will be a coefficient in the equation.

But remember, we are talking about a sixth-grader here.  If he has practiced the procedures enough to be able to find an equation for the graph from the ordered pair, he still may not be able to understand what it is that he has done.  If he understands what he has done, he may not be able to explain it.  And if he can explain the concepts behind the process, he still may be unable to wade through the terminology of products, quotients, coefficients, and constant terms in order to answer the question being asked.  Normal result?  Tears, screams of frustration, total meltdown.  And with enough repetition, unrelieved frustration produces defeat and apathy.

So, if your child were faced with a problem that was beyond her comprehension, how could you help her?  In an ideal world, you would be able to modify the curriculum to fit the student.  If you are homeschooling, by all means choose something that is student-friendly, such as Math-U-See, Mammoth Math, Singapore Math, Key to, Teaching Textbooks-- and every math curriculum worth its ink will offer a placement test so that you can select the appropriate level of its series; never buy a math curriculum simply because it is listed for a certain "grade level."  If your child is in a classroom, however, you aren't likely to have a say in the curriculum or the pace of instruction.  More often than not, even the teacher's hands are tied on those issues.

However, there are still a few ways to help.  In a homework session, for example, if she is already frustrated, crying, or in any way approaching meltdown, have her take a break.  No one thinks best when emotions are high.  She needs to go do something completely different-- walk the dog, play a musical instrument, do a chore, read a book.  Preferably, she will be doing something she enjoys and/or does well.  This is not the time to ask her to practice spelling if she is a poor speller!  But it's not necessarily the time to go play video games or eat a piece of cake, either-- that feels more like a reward for giving up than a temporary switch of brain focus.

When she is calm again, have her look at the problem and identify everything that she recognizes or understands-- whether it is a single word, or what a number represents, or what kind of answer the question is looking for.  For example, in the problem above, the student might know that in the coordinate pair, the first number is x and the second is y.

Next, look at what she doesn't understand.  Is it because of the "mathy" jargon used? Sometimes just knowing the vocabulary isn't enough if there is too much of it in the text.  Help your student translate anything in the problem or answer choices from math jargon into easily understood words.  In the example above, it might help to look at the answer choices first and rewrite the sentences:

If it makes more sense to the student, she should feel free to use symbols instead of words; "x" instead of "multiplication" and "÷" instead of division would be fine.


The final step is to identify what the student still needs to know to solve the problem.  The student may or may not be able to explain what it is that she doesn't understand!  Help her use whatever resources she has available to find answers.  This could be as simple as using the student's textbook to find examples of the given problem.  Or perhaps there is no textbook available, but the student has internet access.  Have her type in as many of the important terms from the problem as she thinks would be helpful.  For example, a quick internet search for "proportional relationship graph equation" brings up several helpful videos on Learnzillion, Khan Academy, and YouTube.  Have her choose the ones that seem most appropriate (some include grade level indicators), most understandable (with graphics), and/or easiest to digest (less than 5 minutes).  After watching a video, have the student decide whether her question was answered, or if she has learned anything helpful towards solving the equation.

If the student returns again and again to the point of frustration, please don't push.  Her brain may just not be ready yet.  Given a few more weeks, months, or in the case of very abstract concepts, a few more years, she can get the concepts.  Try to communicate the same sense of confidence you had when she was learning to ride a bike-- after the first few falls, you might say, "Let's try again tomorrow," but that certainly did not mean that riding a bike was too hard for her.  It just meant that she hadn't had enough practice to develop the skills yet.  It's the same with math.  Back off, stay focused, keep working, and she'll get there.

Meanwhile, make sure she's got the foundational skills of knowing her math facts and has good reading comprehension in other areas.  If she is weak in these areas, help her build them up and the rest will come as her brain matures.  And if she is developing gaps in her learning because the curriculum insists upon pouring in "sand and water" concepts before the holes in the colander are closed, please be ready to help her refill when her brain is ready to contain them.

When Reading Assignments are Above Reading Level

It is not uncommon these days for a student to be given assignments in which the text they are expected to comprehend surpasses their instructional reading level.

Some homework is too hard for kids to read.

Both of the sentences above say similar things-- but imagine trying to wade through the first one when you are still learning to read the second.  This is frustrating enough with a single sentence, but when students are asked to digest entire passages, or even books,  that are beyond their reading level, many simply shut down.  Unfortunately, because the content of standardized testing is designed to be more "rigorous" than in years past, teachers are pressured to increase the rigor of the daily assignments to reflect these tests.

For the record, there are three reading levels that are generally refered to in educational circles: independent, instructional, and frustrational.  All three are determined based on the actual written words that can be identified, the vocabulary used, as well as the sentence length and structure.  A child's independent reading level is the level at which he can comfortably read and understand the text on his own.  The instructional level is the level at which he can read with some assistance for a word here and there.  Frustrational level is defined as the level at which a reader has less than 90% accuracy in word identification or comprehension.

Of course, most experienced teachers will tell you that the best way to increase a child's reading comprehension is to get them excited about reading, so that they read more and more.  The more a child reads, the more fluent his reading becomes.  It gets easier.  Problem is, the last thing that will excite a child about reading is to feel "stupid" because he can't understand what he is reading! Reading fluency increases when students read books at their level of comfort, and even lower.

So what's a parent to do?

There are actually two problems to address:  the child needs strategies to successfully complete the given assignments that are above his reading level, and uthe child needs help for continued growth in reading.

In order to successfully complete an assignment that is above his reading level, some scaffolding must occur.  "Scaffolding," as the name suggests, is a way of supporting his efforts so that he can work as independently as possible.  This may involve any of the following:

When the low-performing student must answer a bunch of questions that follow a difficult reading passage, he may feel overwhelmed.  (This is especially true in the case of a timed test.) Don't make him slog through the whole article first.  The following procedure (taught locally as R-CURAJ) allows the student to read for the information he needs in the most efficient manner:

1) First, read the questions:  have the child identify the most important words in each question, and circle or highlight them.  Have the child think about what kind of answer he might be looking for.  Will the answer include a number, a place, a person's name? What important word(s) might be found in the answer?

2) Next, have him skim through the passage to look for these words; when he thinks he has found the answer, have him underline the sentence(s) that include the information he needs.

3) Finally, have him read both the question and the answer to see if it all makes sense.  Can he "justify" his answer from the information he has underlined?

Is this cheating, because he may not read the whole passage?  No.  The objective is to have the child gather information from the passage.  Skimming is a valid reading skill that people use to find information without reading a whole passage.

Difficult passages are not just on standardized tests.  Sometimes they are in the students' textbooks. In this case,  the student may have no questions to help her, but must read an assigned text and be tested on it later. In this case, an old technique called SQ3R can help the student get the most out of her reading, and remember the information.

1) Survey: Have her look over the article (or chapter) to get a good idea of what it is about: read the title, any bold words, first sentences in the paragraphs, look at any accompanying pictures or diagrams.
2) Question: The student comes up with questions about what he might learn in the article.
3) Read: The student reads the article looking for answers to his questions.
4) Recall: The student tries to answer his questions from what he remembers in the article, looking back to make sure each answer is correct.
5) Review: The student explains what he learned to someone else.

Sometimes a student must read a short story or novel and write a book report, pass a test, or in some other way show understanding.  If the reading level is too high, this can be a Herculean task. These ideas can keep a student from drowning in frustration:

1. Gather any necessary background information.  If the novel is set in East Berlin during the Cold War,  or ancient Egypt, your student may miss important details simply because she is unfamiliar with the history.  Even a contemporary story may be incomprehensible to the student if it contains details outside of her life experience.  A child raised in a southern suburb, for example, may need explanations when reading a story about a child who lives in a New York City high-rise apartment. Use pictures, maps, timelines, internet resources, and anything else you might have to help the reader connect with the story.   Even better, if there is a movie version of the story, by all means let the child watch it before reading the book!  It is incredibly helpful to have the plot, characters, and setting already fixed in his mind before he attempts to read the story himself.  The movie will be different enough from the book that there will still be things to discuss, but it will be a thousand times easier to comprehend as he reads.

2. Help with unfamiliar vocabulary and difficult sentence structure.  You can pre-read the book and write definitions in the margins-- lightly, in pencil, if it's a school or library book.  If you own the book, you can even highlight the key words of the complicated sentences.  Here, for example, is a scaffolded sentence from the book Heidi:

                         sat down                                                      bottom
Peter generally took his quarters for the day at the foot of a high cliff, which seemed to reach far up into the sky.

3. Help the reader keep track of characters as they appear in the story.  Each character should be accompanied by a brief description. As the student comes across new information about each character, he can add it to the list.

4. Summarize the important events of each chapter.  Summarization is an important skill.  The student should be able to identify the major events in each chapter.  If he has trouble coming up with a summary, ask him if there was anything the main character(s) did or experienced in the chapter that the character(s) learned from, or that might cause or help solve a problem.

5. And of course, if there is an audio version of the book, allow the student to listen to it as he reads.

While these scaffolding techniques will help a child who is struggling with material she must read that is beyond her level, that is NOT the kind of reading that will be most helpful to her progress. The most helpful reading will be comfortable, easy books that allow the mind to relax and absorb the words.  The more of these that the student can read, the faster she will gain reading skill.

Not every child likes to read; however, if she seems to avoid reading, there may be a problem.  The problem could be as simple as not having found a book she likes.  In that case, take her to the library and show her how to look up books about things that interest her.  Does she like art? horses? science? spiders?  There are books for that.  In third grade, my lure was dogs-- I read every dog book the library had.

On the other hand, the problem may be lack of skill in reading. In that case, one of the best ways to get a reluctant student reading is to start her on a series.  Read the first one together, and let the student read the next. The same author writing about the same character tends to use similar vocabulary and sentence structure, so the reading seems easier with each new volume.  Plus, the reader is already familiar with the background of the story, so she can pick up each book with confidence.   Junie B. Jones, Magic Tree House, American Girl, Nancy Drew, Hardy Boys-- these are all stepping-stones to better reading.  The series Diary of a Wimpy Kid and Captain Underpants have the added feature of cartoon-style illustrations on almost every page.

Some teachers swear by graphic novels for getting kids hooked on reading.  Like comic books, these novels are highly illustrated, which helps the reader follow the story.  Some, like the Magic School Bus and Max Axiom, are non-fiction science books.  There are also historical graphic novels and graphic versions of classic literature.  Do be aware, however, that not all graphic novels are appropriate for children... some are a little too graphic.

The problem for older struggling readers, of course, is finding books they can read comfortably that don't seem babyish.   Reading aloud to siblings, younger friends, or even pets can sometimes take the sting out of reading low-level books, but there is also a unique kind of literature written especially for the struggling older reader.  Hi-lo books, as they are called, are high-interest books written at a low reading level.  Even high school students can enjoy reading these books.

While scaffolding the difficult reading assignments and encouraging comfort-level reading is important, however, if a child is truly struggling to read at grade level, he needs specific help.  There may be gaps in his reading instruction, vision or hearing deficits, or sensory processing issues.  One student I knew had auditory processing problems that originated in infancy, affecting both her vocabulary acquisiton and spelling.  Using subtitles on tv shows allowed her to better process the words she was hearing, and teaching syllabication and phonics patterns improved her spelling as well as her reading.  Other students may be dealing with dyslexia or general learning disabilities.  If you suspect any of these, it is important to get help.

But, as I explained in the opening of this post, your child may be reading at grade-level and still be frustrated with the assignments he is being expected to complete.  If so, please know that you are not alone, and I hope some of these suggestions will be helpful.

Not all solutions are created equal.

Asking a child to solve math problems in a way which does not take into account his cognitive development is a recipe for frustration.

Math instruction these days aims to help students understand what is happening in a math problem, so that they can solve it in a number of different ways.  That's great.  Unfortunately, the rapid-fire pace at which these solutions may be presented, coupled with the natural limits of the younger students' cognitive development, can sometimes just cause the students to not understand any of them.

Take this 6th grade problem, for example:  Sixty percent of Mr. Hall's math students have pets.   The actual number of students in his math classes who have pets totals 45.  How many math students does he have in all?

One sixth grade class was recently presented with two methods for solving this type of problem: the "tape method" and the "proportion method."  Because of the short time frame in which they were expected to master both methods, some students were left completely befuddled.

Given that many 6th graders are only beginning to develop their abstract thinking skills,  it would stand to reason that the best method to solve the problem would begin with something more concrete. As I've mentioned in a previous blog post, the Singapore Math curriculum is very successful at getting students even younger than sixth grade to solve problems which would traditionally require algebra; they do so by visually representing the problem with diagrams.  The tape method mentioned above is classic Singapore.  But in the long run, does it really matter what method is taught?  Let's compare these two in particular.

Here's the proportion method:

1. Create two equivalent fractions based on the numbers and percentages given.  In this case, the number of students with pets is the numerator (45), and the total number of students (x) is the denominator.  Likewise, the percentage of students with pets (60%) is the numerator, and the total percentage of students (100%) is the denominator:

We know that these two fractions are equivalent because they are referring to the same groups in the same ratio-- i.e., students with pets: all students.



2. Connect opposite numerators and denominators diagonally:

3.  Now, multiply the diagonal numbers (45 x 100) and divide the result by the lone number (60).  The answer is the x, or in this case, the total number of students.

Of course, this is the same as the algebra algorithm which sets 60x equal to 45(100), and then solves for x by dividing 4500 by 60.  Will a typical 6th grader understand this?  No. Even a demonstration that multiplying the opposite parts of two equivalent fractions will produce equal numbers-- if 2/3 = 4/6, then 2 x 6 = 3 x 4 -- may not transfer in their minds to (2 x 6) ÷ 3 = 4.  In fact, I bet I even lost YOUR attention in that explanation!   When it comes to math concepts, the fewer words that are necessary to explain them, the easier young children will understand them.

Without the background in algebra and a cognitive level that allows them to analyze abstract concepts, they will likely not understand what's happening in the proportion method at all.

In an attempt to simplify the process for sixth grade consumption, one teacher offered this formula:

 Unfortunately, this formula may be even more confusing than the algebra it represents.  It depends on the students remembering clue words for the concepts, instead of understanding what is actually happening with the numbers in the problem.  Like telling a student to look for words like "in all," "difference," and "equally" to determine whether to add, subtract, multiply or divide, it provides a                                                                                                                  crutch without promoting actual                                                                                                                comprehension of the sentences.

My math sense is somewhat disturbed to see that "part" and "whole" are identified in only one of the fractions here-- when the whole reason the formula works is that the "percent" is part of the whole 100%-- the two fractions are equivalent.

Also, many students may not recognize that the word "what" represents a number.   They may not understand which  number the "is" or "of" goes with.  For example, the first and last questions here both contain the words "what number is."  In the first question, "is" goes with "what number."  In the last, "is" goes with the 3.  So the student has to analyze the meaning of the sentence just to use the "shortcut;" for some, this is beyond their skill level.  (Ask me how I know.)

And then there are problems that don't fit the mold at all.  Where are the "is" and "of" in this problem:

Sixty percent of Mr. Hall's math students have pets.   The actual number of students in his math classes who have pets totals 45.  How many math students does he have in all?

A mature brain can analyze the problem and restate the problem as "45 is 60% of what number?"  But again, this requires cognitive maturity beyond many 6th graders.  The problem with this method is that it is completely word-based-- the numbers represent only words, so the concrete-thinking student easily becomes lost, not knowing what the numbers actually mean.

Worse, the words are actually assigned a false meaning-- looking at the formula above, a student will conclude that "is" and "of" both represent numbers.  If you really want to translate "is" and "of" into math, "is" becomes equals and "of" most generally indicates multiplication -- in this case, multiplication by the decimal equivalent of the percent. So:

What number is 75% of 4?  translates into (pre-algebraic) math:   ____ = .75 x 4
3 is what percent of 4?  translates into math: 3 = ____ x 4
75% of what number is 3?  translates into math: .75 x ____ = 3
And, from the original example, 60% of what number is 45?  .60 x ___ = 45

This method of finding percentages of whole numbers could easily follow the mastery of multiplying and dividing fractions, and converting between fractions, decimals, and percents. It would make more sense, because a typical sixth grader has actual experience with the concept of "half of 100" and can understand that, if we translate "of" as multiplication,  1/2 x 100 is the same as .5 x 100 or 50% of 100. There is no formula to get confused about.  On the other hand, the proportion method (as presented) offers a formula that is easily misapplied by preteens because the concept is not fully explained, and it is not fully explained because the students are not cognitively ready to understand the abstraction.

Now, let's take a look at the more visual "tape method:"

Sixty percent of Mr. Hall's math students have pets.   The actual number of students in his math classes who have pets totals 45.  How many math students does he have in all?

1. Draw a long rectangle (like a tape) which represents 100% of the whole quantity-- in this case, all of Mr. Hall's students.  Divide it into 10 segments.  Each segment represents 10% of the whole.

---------All (100%) of Mr. Hall's math students---------

2. Shade in the percentage indicated in the problem.  In this case, the yellow indicates students who have pets, which is 60%, or six of the 10% segments:

---------All (100%) of Mr. Hall's math students---------

                                            ------the ones with pets------

3. Label the part.  The yellow also indicates the actual number of students who have pets, which is 45:

4. Now divide the part by the number of segments shaded to find the value of each segment:   

     45 ÷ 6 = 7.5

5. Finally, multiply the value of each segment by 10:   7.5 x 10 = 75.

This method is very visual, so it is more likely that a student who is still developing abstract conceptual skills will understand it.  They will SEE that the 45 and the 60% actually represent the same value-- an idea that can easily be lost in the previous method.  If a student prefers to work with manipulatives, the diagram is easily converted to a paper strip, math blocks, modeling clay or anything else you might have.

It also is easier to explain how this same representation can work for the other percentage questions. The key each time is to figure out the value of the10%:

Q: What is 60% of 75?

1. Draw a long rectangle (like a tape) and divide it into 10 segments.  Each segment represents 10% of the whole.
                                          ---------------------------75----------------------------

2. Shade in the percentage indicated in the problem.  In this case, 60%:

3. Now divide the part by the number of segments shaded to find the value of each segment:   

              75 ÷ 10 = 7.5

4. Finally, multiply the value of each segment by the number of shaded segments, or add up the shaded segments:   7.5 x 6 = 45.

Q: 45 is what percent of 75?

1. Draw a long rectangle (like a tape) and divide it into 10 segments.  Each segment represents 10% of the whole.

= 75

2. Divide the whole (75) by 10 to get the value of each segment:  75 ÷ 10 = 7.5

3. Determine how many segments it takes to get  45 (either by adding, or dividing 45 by 7.5)

4. Count the number of segments.  Each segment is 10%, so 6 segments = 60%.

While this method is not completely foolproof-- there will still be students who are initially confused as to how 100% can represent any "whole" quantity-- the visual component allows a student to see what is happening to the numbers as he works with them.  He is then much more likely to be able to transfer that understanding to algebra as he moves forward with math.  By introducing the former method too early, however, the student may simply learn that math is a series of incomprehensible tricks and formulas that must be memorized.