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.

What to do when your child is overwhelmed by school expectations

These are the objectives to be taught in
 our local district's 6th grade math class.
The teachers will have about 7 weeks to
teach the 9 objectives before the quarterly 
benchmark test.  Some of these are 
combinations of what were 2-3 
separate objectives in past years. 

If your child cries over homework, or says things like, "I'm stupid!"  and "I hate school," he is likely overwhelmed by the demands made on his brain every day.  But what is a parent to do?

The reality is, school is a lot harder than it used to be, even just a few years ago.  Less opportunity for physical activity, and more rigorous instruction, combine to frustrate the child whose body and mind are still developing.

Here are a few recommendations from parents and veteran teachers:

1. Emphasize learning over grades.  Celebrate with your child when she has accomplished something difficult.  But don't rely on graded papers or report cards to tell you that she is learning.  Ask her to teach you how to do the math she learned today.  Keep a list of books she has read, or words she can spell. Meanwhile, think of a test as simply a snapshot of what she knew at a certain point in time-- and what she still may need to work on-- not "how smart" she is.  Students whose feelings of self-worth are tied to the almighty A are the ones who crash and burn when the work becomes more challenging.  And if your child's grades are less than stellar, don't despair.  No college ever asked about an elementary or middle school GPA.  Just make sure she is learning.

2. Let your child do things he can do on his own.  This means making sure he has meaningful chores, and takes care of personal responsibilities, so he can develop a feeling of personal competence.  A kindergartner can set the table, pack his own lunch and choose his own clothes to wear.  Sometimes children learn "I can't" when too much is done for them.  After all, if Mom does everything for me, she must think I'm not capable.  On the other hand, a child who has confidence in his own abilities is more likely to persist when the homework gets tough.

3. Make sure she has the right foundation.  Any child who has not memorized her math facts by 5th or 6th grade will be struggling.   Sadly, it is not uncommon to see students still counting on their fingers in middle school.  If your child still struggles with reading grade-level material in 4th or 5th grade, or handwriting, or spelling, or other basic skills, she may need extra help.  One cannot assume that every child will build a good academic foundation in today's schools.  The schools, not to mention the teachers, have little control over the content they are required to teach-- they often feel as if they must present the lessons with all the grace and delicacy of a firehose.  Even when some children don't master an objective, the entire class is forced to go on to the next one.  So if the parents notice that their child still needs to memorize the times tables, it is up to the parents to ensure that this happens.  Whether this is addressed through school-based remediation, parent-guided drills, private tutors, or even online apps, will depend on what best fits the situation.

4. Break it down.  Find out how much your child already knows, and what he's stuck on. Your child may feel overwhelmed by having to spell "centrifuge," but have him try to spell it a syllable at a time and it gets easier.  Cen -tri -fuge.  Butterfly?  Two words.  Caught? Three sounds:  c  augh t.  Does he know that "augh" represents the /a/ sound?  Same with math.  If he's dividing decimals, what does he already know about division?  Maybe he just needs to know how to place the decimal.  Maybe he needs to review division itself.

5. Make it fun.  Change the names in her word problems to her favorite pets or superheroes. Use Legos or snacks to model the math.  Can you make a game out of his homework?  Perhaps you can repurpose an old gameboard for a new game where your child advances for each word spelled correctly, and throughout the game will land on spaces that have a small treat.  If she is working on learning multiplication facts, she can use a set of flash cards as the game's question cards in order to move around the board.  If she needs to work on skills, there are online math drills such as TimezAttack, and reading help at Starfall and other sites.  

6. Know when enough is enough.  If the homework session has gone on too long, your child is less able to concentrate.  He may need a play break-- jumping on the trampoline, running to the mailbox, walking the dog, or even a couple of quick chores can clear his brain to think better.  Sometimes switching subjects or homework assignments for a few minutes is all it takes.  Breaking a long assignment into smaller chunks can be very helpful.  If your child is on the verge of a meltdown at the prospect of 15 math problems he must complete, have him pick three to do before he gets a two-minute break to talk to you about his favorite topic.  Or do half of the math problems before doing half of the spelling, then math, then spelling again. And just as important, if you see that the assignment is truly too long or too difficult, work with the teacher to make adjustments.  For example, if your child struggles with reading and must do a major book report, ask if the child may have extra time, or if you may use an audiobook, or alternate reading one page with your child reading the next one, or if the child may type or dictate the report or simply write fewer sentences.  A child who has a 504 or IEP may already be getting these accommodations, but even without these, you may choose to have your child earn a lower grade rather than lose his sanity.

7. Communicate with his teacher.  Please, don't be the parent who calls or emails the teacher multiple times per week.  But do let her know when there is a problem.  You will likely know before the teacher will!   A simple, "Sorry, Johnny worked for two hours on his homework last night before I made him go to bed," can be helpful.  Get to know how the teacher communicates best: some respond more quickly to emails than phone calls, or vice versa; most keep class websites, or send newsletters, to let parents know of upcoming assignments and learning objectives.  If you can possibly make it to parent conferences, be there.  Keep an eye on any assignments handed back, and if you have an online grade reporting system (Powerschool), use any information available there.  Also find out if any after-school tutoring or homework help may be offered at your school.  When you do talk to the teacher, you can ask her about what her preferred communication options are.  Find out when her conference period is, or if there is a good time to call before or after school (sometimes before and after school are the teacher's busiest times).

8. Eliminate distractions.  Make sure your child has a designated place to do homework that allows him to be in top form.  Some children do best in a quiet room by themselves; a desk in a bedroom is ideal for this.  Others need supervision, perhaps at the kitchen table.  If other people in the house create too much noise, foam earplugs might be helpful.  A protein-based snack before starting, or while working, can help your child stay focused.  Keeping supplies on hand in a specific spot-- paper, pencils, eraser, sharpener, glue, scissors, crayons, etc.-- will ensure that your student doesn't waste valuable time looking for them.

8 1/2. Eliminate more distractions.  The use of recreational electronics-- computers, video games, tablets, etc-- may seem like great stress relievers and even rewards, but on school nights may do more harm than good.  I've seen more than one child whose ADHD symptoms were made much worse after playing video games-- whether because of game apnea (two boys I observed would unconsciously hold their breath while playing, and the oxygen deprivation would cause visible behavioral changes) or the buildup of adrenaline with no physical outlet.  Instead, it may work better for the child to earn tokens or tickets for (calm) completion of homework and chores which can be redeemed on the weekends for screen time.

9. Reduce extracurricular stress.  Many students these days are overextended in sports and after-school activities.   A music lesson, sport, club, or another pursuit that a child has actually expressed an interest in can build a child's confidence and even boost her brain function, but there can be too much of a good thing.  Many families find that limiting each child to a single activity, or one to two school nights per week, is a workable limit.   Too many activities can result in a lack of adequate sleep, which may hinder your child's performance at school.

10. Use your resources.  As mentioned before, your child's school may offer after-school help.   Many local libraries do, too.  There are sites such as khanacademy.org, learnzillion.com, or even Youtube where you can search for topics such as "dividing fractions" or "direct and indirect objects" and find a video lesson.  (Be careful on Youtube.  Some of it is inappropriate for children.)  Your child's teacher may even list specific helpful resources on his website.

These are a few of the most common suggestions from parents and teachers I have known.  I hope they help you, or at least spark some ideas of your own!  May you and your child be blessed.

Custom Homeschooling on a Shoestring

While homeschooling is a slight tangent from my usual topic, it's the time of year when some parents are seriously considering whether it might be a beneficial option for their children.

There are many reasons people might consider homeschooling, and many ways of accomplishing it. This post is for those of you who have decided that, while homeschool is the best option for your family's needs, your budget is limited.  You may have researched various homeschool packages from Sonlight, Timberdoodle, Alpha-Omega, Calvert, etc., and found the prices out of reach.  Perhaps you looked into the free online public school options such as K-12 or Connections Academy, but don't feel that these would suit your family's needs.  You're thinking DIY is the way to go.  So now you're wondering, "Where do we start?"

You don't need some high-dollar curriculum package (although those are nice!), or even the free online public school set-up, to give your child a great education.  What you really need is time to invest in your child.  First, there is the time to plan and find the materials you need, but most importantly is the time you actually spend with your child.  You will be the one to know if she has trouble with her multiplication facts, or if she needs more work on handwriting, or is so excited about geology that you could spend a whole year reading, writing and learning about rocks.

Here's a basic DIY tutorial:

1. Investigate the homeschooling requirements of your state (assuming U.S. readers here, but whatever laws apply).  They vary considerably.  For example, in Virginia you may be required to submit a course description at the beginning of every year and evidence of progress at the end of every year, whereas in Arizona you simply file an Intent to Homeschool once.  There may also be required subjects, standardized tests, or other boxes to check.  You can find this information online ("homeschool requirements in the state of ___") or by calling your state department of education. Another good source is the  Home School Legal Defense Association, which has the latest information for each state.

2. Map out what you want your child to learn.  Depending on your goals for and philosophy of homeschooling, you may have specific ideas of what you want your child to study.  Do you want her to fall in love with literature, develop an understanding of the world, learn a foreign language, excel in math and science, think critically, write well, express herself through the arts?  What about this specific school year-- what period(s) of history do you want to study, and how much geography?  What areas of science, and what works of literature?  Art? Music?

If that sounds intimidating, don't worry.  Common Core aside, there are no set rules about what a child must cover at any certain grade level.  There are topics and approaches that are more appropriate than others, of course, for each age and stage.

You might find age-appropriate ideas in What Your ___ Grader Needs to Know, or your local school's curriculum, or a classical homeschooling plan such as amblesideonline.org.  If you like the idea of unit studies,  Five in a Row is a popular program that builds a week's worth of academic learning around classic children's literature.  There is even a program based on the Little House series. Discovering what you like, and what you don't, will make it that much easier to create your own custom homeschool.

Consider what your child's individual needs are, and where his strengths/weaknesses and interests lie. For example, if your 4th grader is a struggling reader, you might want to offer many high-interest, low difficulty books to build up his fluency instead of texts that might cause frustration. If your child is obsessed with Pokémon, walruses, or vacuum cleaners, there are ways to incorporate these interests into math, science, and just about any other subject.  Bear in mind that the older the child is, the more important it is to include his input in this planning stage.

The idea of what and how much you might want to cover in a year is called the "scope" of your lesson plans.  Educators call the complete list of what you plan to teach, and the order you plan to teach it, the "scope and sequence."  Depending on your state laws, this may actually be a required document that you submit to the officials.  Obviously, if you are using a commercial curriculum for one or more subjects that is already planned out, your scope and sequence will be pre-determined and you don't have to mess with it.  However, if you're coming up with your own plan, most people find it helpful to write out some kind of parameters to keep in mind as they go through their year.  By no means is it set in stone; the beauty of homeschooling is its flexibility.

Linked below is a very basic scope and sequence for a fictional 4th grader.  It is based on a 3-term school year, so assuming a traditional 36-week school year, that would be about 12 weeks each.  You may prefer to break your year down into 9-week, 6-week, or semester (18-week) segments. Whatever works for you is great!  Please note that this example is only one way to write out the information; you might do it differently.  For instance, some of my entries are written in unnecessarily vague educational jargon just because it's late as I type this and I'm too tired to use real English.  And there are also more subjects listed than a real 4th grader would be likely to need.  It could also be that I'm missing one that you plan to include, such as vocabulary or geography.  But I think you can get the general idea.  In case you want to try it yourself, I'm including a printable template:
sample scope and sequence
scope and sequence template

3. Determine your resources.  If you want your child to learn history and geography, do you have anything now that you could use to teach that?  You may already have certain educational materials collected at home: maps and globes, books on history and science, fiction books, educational DVD's, games, equipment and supplies. When we began homeschooling, we already had large wall maps of the world and the U.S.A., and a generic Illustrated World History Encyclopedia from the Barnes and Noble bargain shelf.  The book was enough to introduce each historical topic that we studied, and we used the maps to locate each country or event site as we got to it.  You might have other items, or none at all.  But for each subject you teach, there may be more available resources than you realize.

These may be community offerings: people you know who are experts in a particular field, libraries, museums, historical sites, theater groups and symphonies, universities, extra-curricular clubs, parks and recreation classes, churches, or homeschool support groups.  Maybe the local parks and rec offers a children's art class, or the children's museum downtown has some great science exhibits.  And there is a wealth of online educational resources, and even educational apps.

But what about actual curriculum? There might be a math text or spelling program that you have heard of and are dying to try out.  Ask around!  Homeschooling friends are often happy to loan out reusable curriculum that their children have finished with.  If you join a co-op or homeschool support group, there are often opportunities to share items.  Used bookstores, Ebay, Facebook, Craigslist, Amazon and online forums are also places that can help you score a ganga deal.  Be sure to do your research and know what the cost of the new item would be before shelling out anything for the used version.

 What if you know what you want to teach, but don't know how to start?  There are all kinds of books and websites available to help you.  Ruth Beechick's You Can Teach Your Child Successfully has helped countless families on their homeschooling journey.  Teach Your Child to Read in 100 Easy Lessons is a classic that gives parents a sequential, simple method of teaching their child to read.  Another favorite of mine is Reading Reflex, which I have discussed before.  There are articles on websites (here's an example), and online programs such as starfall, readingbear, bookadventure, and readtheory for reading, and Khan Academy for math.  A good librarian can help you find what's available on the shelves, and Googling "free reading curriculum" or something similar will get you started online.

It's a good idea to make a list of available resources before you need them.  Here's an example of a resource list, and a template you might use to create your own:
sample homeschool resources
homeschool resources template

You might notice that the resource form has a space for an electronic scheduling system. I have used both Homeschool Tracker and Homeschool Planner over the years; while not absolutely necessary, these programs allow the parent to keep a neat and immediately updatable record of everything their child has done, which can be invaluable if they ever need a transcript or some other documentation of their work.

4.  Divide and conquer.  Once you have gathered your resources, use your scope and sequence to come up with a daily/weekly plan.  Think of the old riddle, "How do you eat an elephant?  A bite at a time!"  Your scope and sequence is the elephant; your daily plan is the bite at a time.  So for every subject, look at your resources and determine how each could be reasonably spread out over the designated time period.  For example, if you want your child to listen to fifteen Newberry award books plus a collection of short stories and a book of poetry over the year, you might plan to cover five novels, a short story and twenty poems per 12-week term.  The daily plan would then be determined by the amount of reading your child can comfortably listen to in a single sitting.  Depending on the length of the chapters, you might decide to read and discuss a chapter a day of the novel along with a poem, or a short story and a poem.  A long chapter might be split over two days, while a couple of short chapters might be read together.  (Incidentally, reading aloud to your child is an excellent way to develop her vocabulary and listening skills, but a follow-up discussion of what you are reading is critical so she doesn't begin to tune you out.)

For history, you might work on one historical event per week.  On Monday you could read about it in a history encyclopedia and locate the appropriate places on a map; the next day your child might watch a You-tube clip about it.  Wednesday might involve a hands-on project.  On Thursday you might find more information about the event on child-appropriate website, and Friday you might have your child draw a small representative symbol on a timeline at the appropriate date.  By the way, if your literary selections are related to the history being studied at the time, your child can experience a greater understanding of the people and events.  For example, you might select titles such as Johnny Tremaine or American Girl's Felicity while studying the American Revolution.  Adding in special activities such as museum visits,  listening to music of the period, cooking and craft activities, and dramatic play also increase engagement.

Your math resource(s) may be online or text-based.  If you are using something like Khan Academy, you won't have a certain number of pages to assign, so you would set a daily time limit or a certain number of activities instead.  A twenty- to thirty-minute session of math might be as much as your child can absorb in a sitting, but you can plan to do a lesson introducing a concept (such as two-digit addition) early in the day, and then provide time for independent practice later on.  A third, short session of fact drill (using flash cards or online games) might be scheduled during another part of the day.

Older students who are highly motivated, but prefer a less structured style, might work better given a weekly assignment list instead of a daily one.  We found a daily assignment list worked well for us; my kids felt a sense of accomplishment as they completed each item.  When they dumped me for public high school, they hit the ground running and never once had to be reminded to do their homework.

As you plan each day or week, notice that there are at least three different types of school activities.  There are the oral activities, such as read-aloud and discussion items; the guided practice where you are actively helping your child with hands-on or pencil-and-paper work; and there is the independent work in which your child is working on an assignment by himself.  Silent reading, math problems, handwriting practice, and computer-based activities would fit in this category.  I found that having an even balance of all three types of learning worked best for us.

What is a good amount of time to spend on school each day?  It depends on the age of the child, of course, but it is unlikely to be anywhere close to what is needed in the classroom.  So much time there is spent on crowd control (lining up, getting supplies, transitioning from one activity to the next) and administrative tasks (collecting and passing out papers, taking attendance, making announcements)-- besides the fact that teaching one-on-one is far more efficient than one-on-twenty-five-- that finding your child done by noon should be a normal occurrence at the elementary level.  By middle school, my kids were more likely to stretch things out until 4 or even 5pm, but that included a break in the day for band or music lessons, cooking their own breakfast and lunch, and a pretty heavy load of academics.

Here is a sample week that gives ideas for doable daily assignments in a number of subjects.  Bear in mind that you would probably not want to start out doing all of this at once!  And every family's/child's needs are different; you might prioritize, add or eliminate different subjects based on your own scope and sequence.

sample homeschool week
homeschool week templateht

And a sample daily schedule, showing how everything might work in detail:

sample day's schedule
homeschool day template

Note: if you have more than one child that needs to be scheduled, and also want to figure out how to get your stuff done, I heartily recommend Managers of their Homes as a way to keep everything organized.  I've seen it used on Amazon for less than $10, but it's well worth the $25 price brand new. Here is a MOTH- inspired schedule for a family including a 9, 5, and 1-year old:

sample schedule for multiple children
multiple children schedule template

5. Adjust as you go.  Remember, the most common mistake new homeschoolers make is trying to do too much.  Many veterans recommend starting out slowly-- just a few subjects the first week, then gradually adding more in until you find your balance.  And don't try to plan too far in advance.  By using your scope and sequence, you can focus on planning just the chunk you need.  When I was doing this, I rarely scheduled out more than six weeks ahead in any kind of detail.  And what I did write was in pencil, always subject to change.

I'll leave it at that for now.

Homemade Stress Balls

Jelly Beadz stress ball.

Next time your child is studying the concept of volume, or maybe air pressure, why not make a stress ball?  It's an easy and fun way to work with measurement, and the result is a great sensory tool for kids who need to fidget with something while they work.

The easiest and cheapest stress balls are made by simply filling a balloon with flour, cornstarch, or sand, and tying it off.  Depending on the size of the balloon, you might need about a cup of filling material.

It doesn't work to just pour the material straight into the balloon-- there's not enough pressure to make the latex stretch.  Instead, use a funnel to pour the material into an empty water bottle.  (If the neck of the funnel is very narrow,  try stirring the flour in the top of the funnel, and/or poking a pencil through the hole until it all goes through.) Then blow up the balloon to about 1/4 of its full size.  Hold the neck of the balloon shut at the base, leaving as much of the neck free as possible.  Twist the neck once or twice to hold it, then carefully stretch the open end of the balloon over the mouth of the bottle.  Hold the balloon on the bottle while you turn the bottle over, letting the flour (or sand) flow into the balloon.  (It may not "flow" quickly; you may need to keep tapping the bottle till it all gets in the balloon.) Once all the flour is in the balloon, separate the balloon from the bottle, gently let all the remaining air out of the balloon, and tie off the neck of the balloon.

A more expensive, but much cooler,  version of the stress ball is made from water-absorbing Jelly Beadz.  I found mine online, a 1 lb bag for $17.  You only need 1/2 teaspoon of beads to make a stress ball, though, so a smaller bag would work fine.  Here's how it works:

Materials:

• 1/2 teaspoon Jelly Beadz (dry)
• 1 round balloon, about 12"
• 1 cup water
• measuring cup and spoons
• empty water bottle
• funnel

Procedure:

1. Place 1/2 teaspoon of Jelly Beads in water bottle, using funnel.*
2. Pour 1 cup of water into water bottle.  

   

   Air-filled balloon
   attached to water bottle.

3. Blow up balloon to about 1/4 its full size.
4. Hold the neck of the balloon shut at the base, leaving as much of the neck free as possible.  Twist the neck once or twice to hold it, then carefully stretch the open end of the balloon over the mouth of the bottle.  
5. Hold the balloon on the bottle while you turn the bottle over, letting the water and beads flow into the balloon.  You may need to swish the water in the bottle to loosen the beads.  If any beads stick to the bottle, let a bit of water back into the bottle from the balloon and keep going back and forth until the bottle is empty.
   
   

   

   Pouring water into
   the air-filled balloon.

6. Once all the water and beads are in the balloon, separate the balloon from the bottle, gently let all the remaining air out of the balloon, and tie off the neck of the balloon.  

   

   Air removed,
   balloon is ready to tie off.

   
   
7. Set the balloon aside for 3-4 hours to allow the beads to absorb the water.  When it is all absorbed, you have a very squishy, soothing stress ball.  

   

   These balls are all filled with Jelly Beadz.  The one on the left
   is made with a clear balloon; the others are regular colored balloons.

   *Note: another option is to pour the dry beads into the balloon before you blow it up, but I hesitate to try that with kids lest they inhale the beads.

Now, try these questions with your student: if you're studying volume,  try measuring the volume of the stress ball.  It was originally filled with 1 cup of water, plus a few tiny beads-- what should the approximate volume be?  Does the volume change after the beads absorb the water?  Why or why not?  How would you measure that?  (What would happen if you poured one cup of water into a two-cup measuring cup, and then dropped in the stress ball?)  What is the metric equivalent?  And why can't you just pour the water directly into the balloon without blowing it up and sealing in onto the water bottle?