First, an apology for posting this so late in the month. I had not intended to take off the month of July, but we had a family member in the hospital for the first two weeks of the month, and life is only just getting back to normal. Blog posts should get back to normal as well over the next few weeks.
And now: The administrator addresses a common question about math books.
Why is Saxon Math no longer considered honors level anymore?
This has been an on-going question/struggle for many families registered with PHEA.
short answer is because we use the South Carolina state standards to
define what is required for a college prep level class. As those
standards change what counts as honors does too. The old Saxon math
books do not currently even meet the college prep level standard as they
do not cover a number of concepts now considered to be part of Algebra
One of our moms sent a link to an article explaining why the writer believed the older Saxon books to be better (http://drshormann.com/2012/02/08/differences-in-3rd-and-4th-edition-saxon-algebra-1/).
I finally had a chance to read the article. The writer makes some good
points. I do understand the Saxon approach and also that the new books
were not written by Saxon and follow more loosely the Saxon method. For
the home school family who values a certain type of training (such the
classical approach explained by Doug Wilson), they will pick texts that
teach to the method they wish to use. I understand the desire to follow a
certain educational approach and am glad when parents have researched
enough to know what they want to accomplish with their children’s
education. In many cases I think picking the older books is a wiser
approach as far as completing the education of the child. I don't think
the public schools work well so I don't think blindly following their
methods is a good choice for homeschoolers.
The main drawback to
using the older Saxon books is that the SAT and ACT choose their test
questions based on the common agreement of what the scope and sequence
is in Algebra 1 (or Algebra 2, or Geometry.) So as the scope and
sequence changes (as it has in the past few years), what is covered on
those tests changes with it. The scope and sequence is now different
from what is covered in the older books. I believe this is one of the
main reasons we have been watching the SAT math scores drop each year.
So it is fine if a family wants to use the older book due to the
methodology. They should realize, however, that in making that choice
they are missing some concepts that will be on those college tests. Most
of the families asking about Saxon math being honors are looking at the
student’s GPA with a careful eye as they compete for scholarship
money. To earn the scholarships, the student must have high test
scores. This creates a conflict for the families – give up the
methodology they want, or perhaps end up with a lower GPA and test
One possible answer would be to use several different
books for each subject (Algebra 1, Algebra 2, etc.) to make sure they
cover everything. They could still use Saxon as the main text book but
use at least one other that follows the state standards as far as scope
and sequence goes. By doing this, the family would not only have the
primary methodology they want, they would also easily qualify the
classes as honors since they did more depth and the class was more
rigorous by covering two or more books. This is certainly not what the
student will want to do; and many moms will not want to do this either,
but it is the only way I see that they can meet both goals.
Posted by The PHEA Digest at 10:06 AM /
Tuesday, June 24, 2014
While we are taking a shorter summer break that usual this year, we have spent the last few weeks enjoying not having to visit the school table first thing after breakfast. We have spent more time playing in the backyard and visiting the library. We've been to the pool and eaten popsicles. We have even done an art project or two. We are enjoying the comparatively leisurely days of summer.
What about you? Are you taking a summer break? How are you enjoying it?On behalf of all of us at the PHEA office, I'd like to say, "Well done Moms and Dads!" Being responsible for your child's education is a big undertaking. We hope you enjoy your summer break.
And to all our graduates this spring: Congratulations!
Posted by The PHEA Digest at 7:59 AM /
Monday, June 16, 2014
We use a very literature heavy curriculum and while I do pick up a lot of the readers we need at book sales or online, there are usually several titles each year that I borrow from the library. This helps save us some money.
We rely heavily on the library for leisure reading books for the kids. My eight year old is a voracious reader, so it is great to be able to borrow enough books to keep her busy for a week or two and then trade those in for new books. The same is true of picture books for our five year old. I think this is more for my sanity that for his sake - one can only read "Stop That Ball" so many times before a little madness sets in. We have a great time discovering new favorites and checking out old friends. And when we pick out a book that we don't enjoy it is easy enough to return it to the library.
We also use the library for research projects. It is often difficult to find enough information on the internet written at a level a third or fourth grade level. But the library has plenty of books on most topics written specifically for children. Often we do our initial research on the library website, looking up suitable books and reserving them online. Then we go to the library to pick up the books we have reserved and to consult the encyclopedias or magazines that we cannot check out.
In addition to books, our library also has a nice selection of movies and music. I like that we can pick up a few videos for the kids to supplement our own collection. They have episodes from popular children's shows - we particularly like the Magic School Bus. They also have a pretty good selection of older movies, BBC films and book adaptations - Pride and Prejudice, Swiss Family Robinson, the Railway Children. We get science movies from time to time to go along with our studies as well.
As for music, the library is a great way to expose your students to different types of music without purchasing a whole collection. Last summer, for example, we checked out a CD of the Boston Pops 4th of July music and had a marvelous time marching around the house to patriotic music. There are many other classical collections available by composer, by theme and by performer.
In addition to books, music and movies, the library has many other great resources. It is a great place to find all kind of activities. This summer our library has a reading programs for toddles to teens. Each child gets a medal for reading a certain number of books as well as other goodies. Most libraries also have story hours and crafts available at various times as well as book discussions and other activities for teens. Check with your librarian for a complete list, or check out the events page of the library's website.
If it has been a while since you have been to the library I encourage you to stop by your nearest branch and see what they have to offer!
Posted by The PHEA Digest at 12:33 PM /
Monday, June 9, 2014
Everyone loves a good story. In fact, narrative is so essential to our humanity that God reveals himself to the world in a story. Art and the humanities are full of narrative elements. Symphonies and string quartets develop themes and motives to create sonic stories which include rising tension, a climax, and a resolution. Even 30-second commercials present stories of despair-turned-to-joy and promise us the same happily-ever-after if we buy their products.
Mathematics too is like a story. That may seem a strange idea, yet it seems strange only because we don’t usually teach mathematics as if it were one of the humanities––which it is. We are happy to teach literature and history and theology through discussion and essay assignments, but suddenly change tactics for mathematics. But what if we taught mathematics in a more human (and perhaps humane) way? What if we taught math in narrative contexts? First, however, I should explain what I mean by saying that math is like a story.
One of the clearest examples of the narrative quality of mathematics can be found in the greatest geometry text to come out of the ancient world: Euclid’s Elements. The Elements is divided into 13 books, the first 6 of which form the basis for what is still taught in high school geometry.
Euclid begins The Elements by presenting definitions, postulates, a few constructions, and the side-angle-side theorem for the congruence of triangles––and with that foundation laid, a world is opened for discovery. I can’t help but compare this beginning to the opening of Genesis. God creates the world out of nothing in six days, and Euclid creates a world out of concepts in 4 propositions.
After this grand opening Euclid unfolds several themes: first the triangle, then parallel lines, and finally parallelograms. Euclid’s handling of these themes is much like the development in a mystery novel where little observations soon uncover a complex web of intrigue. The climax of Book I occurs in the second to last proposition, which we know as the Pythagorean Theorem. Here, theorems on parallelograms and triangles suddenly unite to prove a beautiful and surprising truth: that squares built on the two sides of a right triangle are equal to the square built on the hypotenuse. Taken out of context and put in plain language as I have just done, the proposition seems hardly surprising or beautiful. But this too The Elements shares with the mystery novel. Unless we have followed the story it is not shocking to find out that a cook murdered a millionaire. Likewise, Euclid’s propositions are not surprising to anyone who is merely given them; the story must be read through from the beginning.
But reading the story through from the beginning is not an opportunity frequently given to students. As beautiful and precise as The Elements is, it is no longer used to teach geometry. The reasons for this are twofold. First, it is inefficient to wade through 46 propositions in order to teach the Pythagorean Theorem. It is far easier to simply tell students that A2 + B2 = C2. Second, textbooks are usually organized to present material in the most expedient way, rather than the way in which concepts actually developed and were discovered.
In other words, most textbooks take a CliffNotes approach and tell you all you need to know about the narrative without allowing you to encounter the narrative itself. This may seem an efficient way to prepare for tests but it misses the story and gives the student the impression that mathematics, like Athena, sprang full-grown from the head of Zeus (or from the textbook writers, in this case). The hidden tragedy is that test answers are much sooner forgotten than stories.
As a result, we often teach mathematics as if it were merely a list of skills to learn and concepts to memorize, and consequently treat students as robots to be programed rather than as souls to be cultivated. Students usually have no idea why certain concepts and formulas were developed, and even less idea where they came from. Consequently, students grow bored and frustrated and decide that they hate math.
This is precisely what happened to me in high school. I grew annoyed and confused and decided that math was less important––and certainly less interesting––than literature. Literature had a narrative I could understand; mathematics was nothing but a list of abstractions. Thus, teaching mathematics without properly introducing the narrative and expecting students to remain interested is like telling the punchline without telling the joke and expecting to get a laugh.
For the textbook, it doesn’t matter that Viete’s algebra was too bound to geometry (he didn’t believe one could add a squared number to a cubed number because it doesn’t make sense to add an area to a volume). Nor does it matter that a few years later Descartes simultaneously merged algebra and geometry and, through greater abstraction, liberated algebra from the constraints of geometry. If narratives like these do not matter to the textbook writers, we should not find it surprising when mathematical concepts and rules matter little to our students. But to a student who understands and appreciates the story, concepts do matter, because Descartes’s revision of Viete becomes a triumph on the level with the French discovery of the Rosetta Stone.
Despite my dislike of textbooks, there are several things they do well. They relay information efficiently and home schooling would be more difficult without them. Teaching from primary texts is, after all, messy and inefficient (but then, so is raising children). If you introduce a primary text into your math curriculum, you’ll find that it won’t fit neatly anywhere. Book I of The Elements won’t fit into your geometry textbook in any one place, nor will Viete’s The Analytical Art fit neatly into Algebra 1 nor Descartes Geometry into Algebra 2. The concepts from these and other works fall into textbooks in distilled, abridged, and reorganized forms––like meat in Spam or bologna.
Yet there is good news! Although textbooks remain the only option for many, growing numbers of home schoolers and classical Christian schools are finding ways to put primary texts back into math curricula. A good place to begin is with the first book of Euclid’s Elements. Although, as I said, it won’t fit neatly into your curriculum, Book I makes a great supplement to any high school math curriculum. It presents the basics of high school geometry in a logically complete system with fewer than 50 propositions, which makes it relatively easy to use alongside a modern textbook.
You may find, however, that the narratives, even in Euclid, are subtle and difficult to discover. But the work is worth the reward. When perception dawns, you may feel, as I have felt, that for a silent moment you stand upon a mountain overlooking a sun-splashed valley. And when this happens, you are thinking no longer as a mere student, but as a mathematician.
Daniel Maycock is the founder of Polymath Classical Tutorials (www.polymathclassical.com) where he teaches Classical Mathematics and offers summer workshops in writing and mathematics. Daniel also works for Memoria Press Online Academy where he teaches Composition, Literature, and Material Logic.
Posted by The PHEA Digest at 2:00 PM /
Monday, June 2, 2014
I took a few minutes the other night to read “And Then What Happened, Paul Revere?” by Jean Fritz. When I started flipping through this forty-five page book written for elementary school students, I didn’t think I’d learn anything I didn’t know before, but I was wrong. I knew that Paul Revere was by trade a silversmith. What I did not know was that in his ever-present need to provide for his large family, Revere was also at various points in his life a bell ringer, engraver, dentist and maker of false teeth. During the Revolution, not only did he take part in the Boston Tea Party and go on his famous midnight ride, but he was also a messenger for the Committee of Safety, lieutenant colonel in the Massachusetts militia, and commander of the fort at Castle Island. He also printed paper money for Massachusetts, helped set up a powder mill, and learned how to make brass and iron cannon. After the war Revere went back to his silver work, but he also opened a hardware store, set up a foundry where he made a variety of items from pumps and cogs to stoves and church bells. He also learned how to roll sheet copper and made copper sheathing for ships and roofs. During his 83 years, Paul Revere did a remarkable number of things. It seemed that by sheer force of will he was able to make a new opportunities for himself at every turn.
And he was by no means the only man of his time that pursued a variety of careers. In the course of our study of Early American History this year, we have had the opportunity to read about men like Benjamin Franklin, Eli Whitney and Robert Fulton (though I should point out that Whitney and Fulton came after the Revolution, but they are good examples nonetheless). All of these men applied their keen minds to a variety of pursuits. They had a great ability to adapt to the great changes taking place in America and to make something out of the new opportunities presented.
After I read through the book about Paul Revere, I started thinking about how different the expectations for a modern career path are. For the most part we send our students off to college where they quickly select a major and then narrow their focus within that major to an even smaller field of expertise. For the most part, our students are not encouraged to diversify their studies during high school and college. We send them off to college and the work world trained to do one specific job.
I’m not saying this is necessarily a bad thing. If I ever have a brain tumor, I’d certainly like a surgeon who has made neurosurgery his specialty!
But for most of us, I think more diversity would be a good thing. During the recent recession we saw many young people either just emerging from college or only a few years out of college who were unable to find jobs in their field of study. They were often forced to take jobs requiring skills well below their level of training. Or in some cases they discovered that they had not specialized enough to be eligible for certain positions and that more schooling would be required to secure a job.
It has been a long time since the days of “company men” – men or, to a lesser degree, women who worked at the same company from college to retirement ; sometimes working for the same company for thirty or forty years. The average tenure these days is 4.4 years according to Forbes. This means that the average person could hold fifteen or more different jobs during his or her lifetime. It seems unlikely that each job will require the exact same skill set.
I wonder if we are going back to the days of Paul Revere, when the ability to diversify one’s business pursuits will be the key to steady employment?
As our children approach high school, and especially as we are guiding them into college and beyond, to keep this concept of diversity in mind. If we train our students to be adaptable and to look for ways to create their own opportunities – as Paul Revere did – we will help set them up for a more promising future in an increasingly uncertain business environment.
Posted by The PHEA Digest at 2:53 PM /
Monday, May 26, 2014
Q: What if my student is really sick and we can’t complete 180 days in a calendar year?
A: When a public school student is really sick, the school puts the student on home bound instruction. A teacher comes out a couple of times a week and works with the student and the workload is greatly reduced.
We are not the public schools and cannot do the same thing, but we can work within our law to care for our student and still meet the requirements. How this works depends of course on what is wrong with the student and if they have a chronic or progressive disease or if they have suffered an injury and need time to heal while still remaining within the law.
Sometimes, the family can work with the doctors to provide documentation and doctors’ orders as to what the student is allowed to do. We know a student who suffered a traumatic brain injury that required suspending school for a period of time. The family needed to figure out how to continue doing what the law required while mostly taking time off to recover. The doctor ordered no testing and several other specific things for the student. We provided some suggestions for how to fit school in around the recovery time.
Another student was in a car accident which required multiple surgeries during the recovery time. That family essentially home schooled year round in order to take off the needed time for each surgery and recovery.
By law homeschoolers are required to teach each of the five subject areas within the 180 day school calendar. But within those parameters we have a great amount of freedom to tailor our school to our student’s needs. There are no restrictions or guidelines as to when to teach those subjects or how often they have to be taught during the year.
For families with a sick child, this means that subjects that require a student to sit at a table and work like math or handwriting can wait until the student is physically able to do that work - as long as you do some of each subject during the year. You may spend many days or weeks focusing on subjects that can be read quietly while resting, and other days, when your student is feeling better working entirely on math or other more difficult subjects.
We encourage you to allow your student to heal and recover as much as possible. Meanwhile, there are some subjects which can be done more easily with a sick student. If the student is able to read in bed, subjects like Reading or Literature, Science and History can be covered on a regular basis.
We have known some students with brain or eye injuries who were not able to read for prolonged periods without getting severe headaches. In these cases reading material aloud might be a good solution. In fact many subjects can be done orally if a parent acts as a “scribe” for the student, including composition and math. Not only does this help accomplish the necessary school days, but it might help develop better listening and thinking skills in your student.
Of course the solution and the extent to which you are able to cover certain subjects will be different for each family depending on the circumstances. These are just a few suggestions to get you started thinking of ways to fit school in around a prolonged illness.
For families with very sick children one of the major concerns is that the student might fall behind. While we do encourage you to do what school work your student is able to accomplish, we would also encourage you not to worry about falling behind. One of the great freedoms of homeschooling is that there is no exact standard for where the student should be academically. You may need to lower your expectations for what the student will be able to accomplish during the school year. You may also find that after the student recovers you are able to pick up the pace again and make up for lost time.
The concern about falling behind is doubled for high school students because they are trying to earn credits in order to graduate. While the standard for a credit earned remains the same, 150 hours of study, your student may need to spread those hours over more time. For example, it may take two years to complete one credit in Algebra 1. If your student is severely ill, you may need to add a year or two to high school so that you can work together at a slower pace.
The bottom line is this: if your student is sick, take the time needed to recover. When possible do some school work; seek creative solutions for putting school into the day, but expect to work at a slower pace.
Posted by The PHEA Digest at 5:08 PM /
Monday, May 19, 2014
Most of us are finishing up the school year. Some of us (well, me) are counting down the days to go until we have finished our 180 days and can take a long (and much deserved!) break. We do get a number of questions throughout the year regarding the requirement to school for 180 days and exactly what that entails. Here are the answers to some of them.
Q: Do we have to do school for a certain number of hours each day? Unless you are registered with your school district, the answer is no. You are free to set the length of the school day. So a child in early elementary may very well only take an hour or two to complete each day’s assignments.
Q: How many days of school does my high schooler need to do to receive a credit in one subject? High school credits are based on the number of hours worked and subject matter completed, not the number of days completed. Each credit requires 150 hours of time spent on that subject (spread between lecture, research, study and other assignments). To complete on credit in 180 days, the student would need to spend 45 minutes on the subject each day. Keep in mind though that different students take longer to grasp the material. If a student takes twice as long to grasp Algebra 1, it is still only one credit.
Q: Do we have to cover each of the required subjects in order to call it a school day? The law requires you to teach certain subjects (Reading, Writing, Math, Science and Social Studies, and in 7th grade and above Literature and Composition). When and how you teach them are up to you. I teach most subjects each day – our curriculum is laid out that way and it seems to work pretty well for us. My mom used to switch off science and social studies so that we had a little more time for science experiments and map studies that we might have if she was trying to cover both subjects each day. So plan your days so they work best for your family, but make sure you document that you did teach each subject.
Q: Do we get any sick days? The law requires 180 days and we do have to complete them. If you have one child sick while everyone else is working and you later work in the missed work into the school days to ‘catch up, you can leave your lesson plans showing the work as you made it up. If everyone is out with the flu, you just have to put those days in elsewhere. Doing Math review once a week during the summer is a good idea to keep those math skills sharp. Add reading a novel to that day and it will also give you 10-12 ‘make-up’ days for any sick days you missed.
Q: What if my student is really sick and we can’t complete 180 days in a calendar year? It is possible to do home schooling with a student who is really sick. The details of how that works is complex and too long for this post. I will post a more detailed answer to that question later this week.
Q: 180 days, are you kidding me? How can I keep my kindergartener busy that long? Your child may be so eager to learn that you breeze through all the books and workbooks in half a year. If you have an eager learner, consider moving on to the next grade level even if you are in the middle of the year. The freedom to move at the child’s pace is one of the great things about homeschooling. If you don’t want to start on next year’s books, find other educational things to do with the rest of your time. Try some science experiments, or take some field trips. Even if you don’t use Sonlight, I highly recommend checking out their book lists for each year. Most of the books can be used apart from the curriculum, and many of the titles are available at the library. Their website has a list of readers, history books, science books and read-alouds for each grade level. Mix and match, pick and choose as needed!