Avoiding Math Problems

A common refrain on the homeschooling message boards I frequent is when a parent, usually a mother, comes asking about which math program she should switch her child to because the child just isn’t getting it.  It needs to be “self teaching” as the mother “never understood math either.”

What to do?

The best thing to do would be to avoid this situation in the first place.  A parent intent on homeschooling, who knows she has trouble with math, would do well to take an active role in teaching her young child from the start.  At the same time, it is important to learn as much about math education as possible.  Liping Ma’s Knowing and Teaching Elementary Mathematics and Parker and Baldridge’s Elementary Mathematics for Teachers are two excellent resources to start with.

Relearning elementary math this way, with an eye toward the conceptual big picture, will enable a homeschooling parent with weak math skills to approach algebra with confidence, but it will take a lot of preparation.  A few years before the child will be ready for algebra, a parent in this situation should find an excellent algebra book and work through all of the problems.  For those short on time, the ALEKS Algebra I course will jumpstart a better understanding of algebra, but no matter what, it is important that the homeschooling parent be able to do all of the problems her child will encounter in his math textbook.  This might mean doing all of the child’s homework problems the weekend before they are assigned.

Most importantly, algebra and beyond is not the time to check out of the process.  It is critical that math not be farmed out to a computer program or a series of DVD lectures.   If this type of program is chosen, the homeschooling parent should stay involved, watching the videos and doing many, if not all, of the problems alongside the child.  This way, the homeschooling parent remains able to help the child when he gets stuck.

But the one who really benefits from all of this work on the part of the homeschooling parent is the *second* child to progress through the homeschool.  Ask me how I know!

Assuming responsibility for homeschooling a child is a big deal.  If the goal is academic excellence, it is imperative that the homeschooling parent be willing to put in the work necessary to develop, in Liping Ma’s words, a “profound understanding” of the material she is teaching.  If she is unable or unwilling to do that, she needs to be willing to farm that aspect of her child’s education out to a real person, be it a tutor or a classroom teacher.  Our homeschooled children deserve nothing less.

Posted in Thoughts | 4 Comments

Exacerbating Asynchrony: Why Homeschooling 2E Kids Makes Sense

When I made the decision to homeschool my now 16-year-old son just prior to his second grade year, my main goal was to fix his academic problems, and the sooner the better.  I quickly came to see that, beyond remediating academic weaknesses, equally important was the opportunity homeschooling offered to develop his academic strengths.  What we created in the process was a child that, for a time, would in no way fit into any sort of traditional classroom—advanced, behind, on level—and I wouldn’t have had it any other way.

Though I didn’t know it when we first started homeschooling, my son is twice exceptional, and in his case this means that he is gifted and also has dyslexia.  But at the end of first grade, he presented as somewhat less than bright—slow to understand, slow to respond, just plain slow—with isolated flashes of brilliance.  He could barely read a handful of CVC words and was unable to count to ten reliably.

I worked with him during that summer between first and second grades and somehow got his math to the point where he placed into a second grade math book.  But the reading was coming along at a glacial pace, and I knew he needed long term, intensive help if he was ever to approach grade level.  So, in August, I withdrew him from school and embarked on a journey that lasted close to nine years.

My first clue that my son might actually be gifted was the speed with which he blew through the second grade math book.  He finished it in two months, though one reason he could was that I read everything aloud and scribed for him, accommodations he needed to be successful.  I would continue to provide these accommodations for math until he was halfway through Algebra I at the end of fifth grade.

As for reading, each day we did a phonics lesson, followed by reading practice.  And then we practiced some more after lunch.  And still more at bedtime.  My son’s stamina for reading was low and splitting it up into a several sessions seemed to work better.

And writing?  Well, that first year we didn’t do any.

I think my son peaked on asynchrony, at least in the academic realm, somewhere around the end of third grade.  At that point, he had finished the fifth grade math book but could barely write a coherent sentence, and he certainly couldn’t spell.  His reading had finally taken off; the dysfluent sounding out was a thing of the past, and, to everyone’s great joy, he started reading for pleasure.

His achievement test scores over the years echo these observations:  Prior to homeschooling, we had some testing done, and all the scores were similar and well below the 50th percentile.  At the end of third grade, the spread was close to 70 percentile points, with the math being at the 99th percentile.  From there, the gap began to close:  30 points at the end of fourth grade, 15 at the end of 5th, and so on, until finally, at the end of 9th grade, our last full year of homeschooling, the big three—reading, math, and language—were all at the 99th percentile.

Twice-exceptional kids, at least the ones with a learning disability as the second exceptionality, need intensive remediation to be sure, but they also need to be given the ability to fly with what is easy for them, even if they need to be extensively accommodated to do so.  Simultaneously remediating and accelerating  is likely to produce great asynchrony for a time, and that is exactly what you want!  But this process will not happen in a traditional school setting.  Traditional schools cannot facilitate the extreme acceleration 2E kids need in areas of strength and the extreme accommodations they may need to get there.  Traditional schools will also drop any efforts at remediation once the child approaches average—and in the schools around here, average apparently starts at the 16th percentile!  In addition, it is critically important to remediate weak areas until they are in line with a child’s innate ability—and, by definition, a 2E child’s innate ability will be at the 99th percentile.

Homeschooling my 2E son was the most difficult and most rewarding thing I have ever done.  It is truly not for the faint of heart.  But the results—a confident, competent, and knowledgeable young man—have been worth it.  For us, homeschooling not only made sense, it was the only option.

Posted in Twice-Exceptional | 9 Comments

Beyond Joy: Balancing Challenge and Inspiration

Let me first say that I don’t believe in the joy of learning.  I think it is a myth propagated by people who don’t remember their own educations very well, or perhaps were never were truly educated.  Just because I don’t believe in the “joy of learning” per se doesn’t mean that I never ascribe positive attributes to the act.  Learning can and should be interesting much of the time.  It should be challenging.  It should be satisfying.  Occasionally, it should be inspiring.  And it should be as tear-free as possible.  Given all of that, you’d think that I would have made peace with the traditional tools of learning: textbooks, workbooks, and their ilk.  But, alas, I have not.

It seems as though about a month or so into each school year, I begin to reevaluate my choices and plans for Son8’s program, and this year I’m doing it again.  I am not happy with the crank-it-out, textbooky, workbook-ridden quality of our days.  Specifically, I’m having issues with literature, history, and science.

So what produces delight in our lessons?  I found last year that with Son8, high level information delivered in the form of a story worked really well.  Michael Clay Thompson’s language arts materials were spot on in this regard and are continuing to be this year as well.  Ellen McHenry’s The Elements, while not a story exactly, did have a cartoon character called the “Atomic Chef” who tended to get into trouble while mixing chemicals, occasionally resulting in his death; apparently these scenarios were hilariously funny to an 8 year old sense of humor.  The elementary history curriculum Story of the World has been another winner as it attempts to present history as a story or series of stories about interesting characters and events.  What all of these resources have in common is that they present complex ideas without dumbing down information or language.

But these types of resources are few and far between.

And then there’s the added complexity that, at least on the input side, Son8 is working on a middle school level pretty much across the board.  Because there seems to be a sense that middle school is the time to “buckle down,” increase output expectations, and develop study skills, there is a huge focus in most middle school resources on these things.  Whimsy and wonder are sorely lacking.

So what to do?

I broke down and ordered, at great expense, Oak Meadow’s fifth grade history (US) and seventh grade science (earth) syllabuses.  The history looks to be a good supplement.  It’s a bit weak on the input side, though it does have lots of good suggestions for supplemental reading.  The science, sadly for the kids who use it on grade level and as a stand alone, is incredibly weak on the input side, sometimes to the point of being inaccurate.  So given my review so far, you might think that I’ve already boxed it all up and sent it back.  Not so.

On the output side, Oak Meadow is all about whimsey and wonder.  For example, in a lesson about various explorers visiting the Americas before 1492, the following assignment appears:

Compose a short story about what terrible monsters and other hazards might await anyone who tries to sail around the world.  Illustrate your story with colored pencil drawings.

Or how about this one from the same lesson:

Go outdoors on a clear night and look for the North Star.  After looking at the night sky, close your eyes and imagine what it looks like.  Were the start twinkling?  Was the moon shining?  How did the air feel?  How did you feel when you looked into this huge expanse?  Did you think about how quiet or how big the sky is or what might lie a million miles away in space?  Jot down a few key words that contain strong visual images or intense feelings and use these ideas to write a poem about the night sky.

Moving to the science syllabus, the assignments are a bit more sedate, though this should probably be expected as it is for kids two years older.  But even though the assignments are a bit more sophisticated, they have a similar character.  Here is one from the astronomy section:

Write and illustrate a story of the life cycle of a star.

And another:

Write an imaginative story or an actual account about your experience of an eclipse.  Make it interesting, informative, and exciting for your reader.

So instead of replacing the resources that we’ve been using, we will be adding assignments like the ones highlighted above.  In fact, we’ve already started.  This past week, instead of having Son8 write a short report on what he learned about various regions of the ocean, I had him write a story about something that might have happened among the inhabitants in a deep trench somewhere.  The result was a story about Fish the angler fish and Weird the tube worm.  Son8 enjoyed the assignment and was particularly proud of the illustration he produced.

So my long, rambling point is that it is possible to balance a need for higher level input with more creative or even childlike output.  And I will definitely be keeping Oak Meadow in mind for when we need to move to high school level input.  Since Oak Meadow switches to using actual textbooks for high school, my reservations about their homegrown texts will be eliminated and we will be left with what they do best: creative and varied assignments that allow kids to become emotionally invested in both the subject matter at hand and the work they do with it.

Posted in Gifted, Thoughts | 5 Comments

Spoon Feeding vs Independent Learning: A False Dichotomy

A persistent myth in the homeschooling community is that independent learning is what all homeschoolers should strive for, and if you do it any other way, you’re “spoon feeding” information.

I disagree.

Some homeschoolers seem to believe that, especially during the high school years, students should be handed their books and a list of assignments and told to go for it. This approach may be optimal for some students, but I’m pretty sure that for the vast majority it is not.

Generally, textbook authors assume that their books will be used as part of the traditional school model, which features the presence of a teacher to distill the important information and explain it in a way that is accessible to students.  The teacher is available to answer questions, act as a role model for problem solving, and lead discussions about interesting, difficult, or ambiguous points.  Furthermore, a good teacher will also demonstrate his or her passion for the subject at hand.  Only after this interaction takes place do students engage in the solitary part of learning:  studying, writing, solving problems, test taking.  In this model, learning is a social and solitary act by turns.

Contrast the traditional school model with the fully independent learner method of homeschooling.  The student sits alone with a textbook, perhaps taking notes, answering the questions at the end of the chapter, or completing a problem set.  Finally, the student takes a test to demonstrate his newly acquired knowledge.  There are variations to this basic model, but the essence is the same:  intellectual discourse is static, as it is taking place between the author of the book and the mind of the student.  The dynamic social element is lost.

Unfortunately, most, parents aren’t in the position to be one end of scintillating discussion on a myriad of topics.  So, what to do?  A video lecturer can sometimes convey passion about the subject matter through the screen.  A mentor in the community can help provide intellectual discourse about a particular topic.  But frequently these options aren’t feasible for whatever reason.

Even if parents are learning along with their children, they can act as a role model for problem solving, perhaps in some ways even better than a real teacher would.  When Son14 asks me a question these days, I don’t always know the answer off the top of my head anymore.  I must do what he should be doing: I go to the book and figure it out.  It’s good for my son to see this, that knowledge is acquired and not ever-present.

Instead of total independent learning, I try to balance independence–wrestling with ideas in isolation–with some sort of human discourse, albeit not always as intellectual as I would like.  I do this partially with videos and mentors (well, *a* mentor), but mostly what it takes is a lot of work on my end–reading ahead, watching video lectures, solving math problems and sometimes having difficulty doing so, and translating Latin passages.  I can’t wing it anymore, but in order to make homeschooling a better choice than traditional school, I must act as a both a leader and a partner in the journey.

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Favorite Resources: Elementary Algebra by Harold Jacobs

This post is the first of a series about favorite resources that we’ve used over the years.  In order to qualify as a “favorite,” we must have used the resource in its entirety.  Very few seem to retain a favored status all the way until the end.

Elementary Algebra by Harold Jacobs qualifies.  This first year algebra text starts out gently, gently enough, in fact, so that the first six or so chapters suffice as a prealgebra course.  The text remains gentle, yet rigorous, throughout.  Gentle enough so that a gifted fifth grader could thrive using it.  And most importantly, gentle enough so that a formerly math-phobic homeschooling mother was able to give her student a solid introduction to algebra using it.

While much is made of the cartoons and mathematical anecdotes that seem to be the book’s trademark, the genius of Harold Jacobs is embodied in his problem sets.  They are generally broken into groups, each one developing the concept being taught a little further.  By the time the student gets to the final problem in the last group, he has, in a sense, discovered for himself  the bridge between his previous knowledge and the new knowledge presented in the lesson.  Frequently, concepts from future lessons are foreshadowed as well.

I hesitated to use the word “discovered” in the preceding paragraph.  The word “discovery” when used to describe an approach to math education is usually said with a sneer when spoken by folks on one side of the “math wars.”  But there is a place for discovery in education, even math education.  In fact, if it is done right, a discovery approach can be extremely powerful.

Harold Jacobs provides a structured discovery approach in his algebra text.  He begins with a brief explanation of the topic at hand.  Then the student moves to the problem set, where the true instruction lies.  The problems start out by offering practice on what is already known, either from past arithmetic courses, previous lessons, or the explanation just read.  But then they move seamlessly to the heart of the concept, which may not have been explained directly.

The following is an example of this process.  In introducing addition and subtraction of algebraic fractions, Jacobs offers some fairly straightforward examples, none of which have a variable in the denominator.  Furthermore, none of his examples need to have the solution simplified.  However, the corresponding problem set leads the student to both points and clearly illustrates how algebraic fractions directly relate to the arithmetic fractions he has been working with for years.

And so we have structured discovery.  Structured in that the process in going from point A to point B is scaffolded on the front end: Jacobs provides carefully crafted problem sets.  And structured in that the results of the process can be checked:  Did the student manage to get the correct answers?  Of course, it is also a good idea to check to be sure that the student is using reasonable methods to solve the problems even if he is getting the right answers, but incorrect answers are a clear sign that more direct instruction needs to take place.

So there it is.  Elementary Algebra embodies the genius of Harold Jacobs.  Jacobs not only provides a solid foundation for further algebra study, in its pages he also transmits his passion for mathematics.   I can’t wait to use it again.

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Third Grade Plans

My 8 year old son will be doing mostly 5th grade level work, with some accommodation for his 8 year old motor skills.  We are mostly doing the next level of things that worked well last year.

Math: We will be continuing with Primary Mathematics 5A this fall.  We had good luck last spring with accelerating math to double speed by losing the workbook and only doing the problems in the textbook.  We supplement with the old Challenging Word Problems books that, unfortunately, are out of print (but I bought a whole set back when Son8 was in level 1).  Son8 seems to retain the material well, is able to apply the concepts flexibly, and seems to be much happier going at a faster pace with less repetition.  In fact, there is research backing the idea that gifted math students do better with this approach (see this link).

Literature: We enjoyed the Ruby level of Mosdos literature last year, with its wonderful stories and beautiful pictures, so it was a no-brainer to continue on with the Coral level.  In fact, in reviewing the Coral level, I discovered that it seems to be doing a much better job with presenting literary elements than the Ruby level, so I’m excited about starting.  Son8 will even be doing some of the writing assignments, though I did not get the workbook.   He will also be reading books he chooses from a pile of classic literature that I just happen to have lying around here somewhere.

Grammar, Writing, and Vocabulary: To say that we loved Michael Clay Thompson’s language arts materials last year would be a huge understatement.  While there seems to be a huge jump between the Island level that we used last year and the Town level this year, we will go slowly; my plan is spread this level over one and a half years, finishing in the middle of 4th grade.  The writing component will focus on paragraph writing, which can only be a good thing.

Spelling: I’m stewing about spelling, which is completely nuts because Son8 is really good at it.  Unfortunately, he isn’t good enough for us to just drop it.  We tried Spelling Power last year, which from my perspective was great because he only had to study the words he didn’t get right on the pretest.  The problem was that when he didn’t get a word right on the pretest, he would throw a fit.  So no more Spelling Power.  Megawords is a workbook program for grades 4 and up and deals with, well, big words.  It teaches spelling rules and he’ll only be tested on words that he has studied.

Latin: We will be finishing volume 1 of Lively Latin and supplementing with Minimus Secondus.  Lively Latin has been straightforward and gentle.  I love having the pronunciation CD.  And best of all, it has been a wonderful complement to our grammar and vocabulary studies.  Son8 enjoys it and is actually quite good at it.

History: Instead of doing a four year history cycle, we will be doing three this first time around, consolidating the time period 1650 to present into a single year.  We will do this by going quickly through events from World War I on.  I have a few reasons for this.  First, I’m just not wanting to do deeply into the darker side of human nature with someone whose age is not in the double digits yet.  Also, for the past few years we have been enjoying supplementing Story of the World with picture books.  The visual element has added much to our study of history, and frankly, there just aren’t that many resources available for that time period.  Another reason is that I plan to break out American history as a separate study after we’re done with world.  Again, most supplemental resources for 8 year olds focus on the American side of things.  All of this is to say that we will use Story of the World volume 3 for about two thirds of the year and follow it with the last half of K12‘s History 4 course, which will bring us up to the present.

Science: We had quite a bit of luck with K12’s science courses aimed at grades 1-3, but last year when we did level 4, I started becoming less and less impressed with it until, finally, halfway through the year, I gave up on it altogether.  I decided to make the switch to Science Explorer this year, rather than in 4th grade as originally planned because, frankly, I was afraid if I waited a year, I might only get a year out of the program.  When I used it with Son14 back when he was in 5th grade, he was constantly telling me how underchallenging it was.  This way, I’m pretty sure to get two–and maybe even a full three–years out of the program.  We will be doing the earth science books this year: Weather and Climate, Earth’s Waters, Astronomy, Inside Earth, and Earth’s Changing Surface.  Actually, we’ve already finished the weather and climate book, and it’s been a good kind of challenging.

For hands on work, I’ve decided to have Son8 do several Science in a Nutshell kits.  These kits normally drive me nuts because they are inquiry-based which is edu-speak for “there are no right answers.”  But I think Son8 could use the relaxed approach that I intend to take with these kits.  So while I hope it goes well, I’m not completely convinced, and have only ordered two of the eight I intend to use.  They are: Water Cycle, Oceans in Motion, Destination Moon, Planets and Stars, Our Changing Earth, Rock Origins, Soil Studies, and Fossil Formations.

So that’s it.  I’m hoping for a year that is challenging but not too challenging.  My biggest goal for Son8 this year is to increase his stamina for writing–I’d like for him to be able to write three paragraphs in a sitting and to not freak out if he is required to write more than he deems necessary for math.  I actually thing that the three paragraph thing is more likely to occur.  We’ll see.

Posted in Days, Gifted | 2 Comments

High School: Plans for Year One

My 14 year old son is officially entering high school this fall, though he did high school level coursework across the board last year as well.  Most of his courses this year will be at the 11th grade level and are designed with an eye towards entering community college full time in two years.

Algebra II: Son14 will continue to use Algebra and Trigonometry: Functions and Applications by Paul Foerster.  Because I am not fit to teach math beyond first year algebra, we will also continue using the Math Without Borders lectures on DVD.  Son14 completed chapters 1-5  last year and will complete chapters 6-12 this year at a relaxed pace.  He will not be doing the trigonometry portion of the text, as he will get a full dose of that next year in precalculus.

Latin I: Son14 will also be continuing with Latin I using Cambridge Latin.  He completed the first half  of Latin I last year in a semester and this next year will spread out the second half over a full year.  Foreign languages are particularly difficult for Son14 because of his dyslexia, though Latin seems better than the modern languages because of the emphasis on reading rather than conversation.

American Literature: This resource intensive course will have two distinct strands: the literature piece and the composition piece.  The backbone of the literature strand will be Prentice Hall’s The American Experience.  Son14 seems to do well with an anthology approach, so that is what we will do.  We will also be using Michael Clay Thompson’s Self-Evident Truths series to study the Declaration of Independence, the Gettysburg Address, and King’s I Have a Dream speech.  In addition, Son14 will be reading the following whole works:

For composition, we will be using the following resources:

American History: Son14 will be using The American Odyssey (from K12) as well as various supplemental resources.  He and I will watch the lecture series from the Teaching Company called A History of the United States and I will read A People’s History of the United States by Howard Zinn aloud.  In addition, he will be reading the following books:

Astronomy: Son14 requested to study cosmology this year, and as I was wanting to put off biology for a year, I agreed, with the caveat that he also study traditional astronomy.  He will be using The Cosmos: Astronomy in the New Millennium by Pasachoff and Filippenko combined with the Teaching Company lecture series Understanding the Universe.  Son14 will also be using the Virtual Astronomy Laboratories provided by Brooks/Cole.  In addition, he will read the following books:

Health: Last, and least, is health.  Son14 will be using Health: Making Life Choices, which is apparently the only book on the market that incorporates human sexuality into the main text.  He will also be obtaining first aid and CPR certification as well as cooking experience as part of the course.

So that’s it.  I want to emphasize reading, writing, note taking, and organization this year while going a little lighter on the math and foreign language.  I’m hoping for an interesting and productive year.

Posted in Days, Gifted, Twice-Exceptional | 7 Comments