Educating Locally. Learning Communally. Living Freely.

Math Books - A Follow-up


Tuesday, August 26, 2014

The blog post in the July Digest has created a great deal of both concern and confusion. In an attempt to clear up both, I am writing a follow-up blog post.

The primary area of concern seems to be how to tell which books are honors level books.  This goes back to the question of how text book manufacturers determine what is covered in any text book.  The content in any text book is driven by a couple of different factors.  One factor is what the colleges want covered in order for their incoming freshman to be prepared to succeed.  They see a need for more challenging curriculum and ask manufacturers to push for material to be covered sooner so the student can get farther in each discipline during their high school years.  Not only have some concepts that used to be covered in PreCalculus moved into Algebra 1, but it is now fairly commonplace for Algebra 1 to be taken in 8th grade rather than 9th grade.  This allows the high school student to take a Calculus level math class while still in high school making him better prepared for college.

Another factor that influences and is influenced by the content (also referred to as the scope and sequence) is what the college entrance exams cover.  Testing to determine college readiness is problematic in some cases however over the more than half century that the SAT and the ACT tests have been given, there are trends that can be identified.  The tests cover the material that the colleges want evaluated in their potential students.  This means when the text book manufacturers follow the requests of the colleges and add new material, this new material will show up on the college entrance exams.

The biggest driving factor though is the state legislatures.  They are tasked with running the education in their states.  Every state legislature does this by handing the responsibility to the State Department of Education.  They make the rules and regulations that govern the PUBLIC school students.  When they agree with the colleges that the curriculum needs to be more rigorous, the text book manufactures will follow the standards set by the states.  (The two most influential states in this regard are California and Texas.  They buy a LOT of text books!)

All third option home school associations are under the authority of the South Carolina Department of Education (SC DOE). The SC DOE chooses the standards that govern what material must be covered to call a class college prep or honors.   This applies specifically to the public school students (and is of course one of the many reasons families choose to home school).

PHEA has never dictated what curriculum people must use. We firmly believe that the parents have the right and responsibility to research and pick the best curriculum for their students. Also, we do not check all the different curriculums against the SC standards to see if they meet the college prep (CP) level. Generally, we take the information parents give us on what they covered and what level it is when it comes to CP.  So a parent may use any book, including the older Saxon Math books, and call it CP.   

The issue comes from the fact that many families want honors credit to help increase their students’ GPAs for scholarships. The PHEA staff has talked it over many times, and the only fair standard we see is to use the SC State Department of Education standards on what constitutes a CP class to then define an honors class (This is fair as homeschoolers are competing for SC DOE scholarship money, so their standards are the one we should use.). 

Many parents have called or emailed to ask us if we would tell them what math books count as honors.  The problem with listing books as honors is that the designation is deceptive.  If a book is honors , must the student cover the whole book? Every lesson? Every problem of every lesson?  If they do not do all the problems and lessons in the book, when does it stop being honors and become college prep? In the public school system, there are usually four to five text books that are approved for each class.  High School A may use Forester Algebra 1 as their honors book and Pearson Algebra 1 as their college prep book. High School B may choose the exact opposite. They are both correct, and their honors course can be designated as honors no matter which book they use. It is what they cover from the book that makes the class honors.

To determine honors level, essentially, the parents have to look through the state standard on the class they are planning to cover (say Algebra 1). There are very specifically defined concepts that must be covered for it to be considered a college prep class. The wording for what constitutes an honors class (from the State Department website) reads:  The requirements for honors courses are greater than for college prep courses. Textbooks and/or other course materials must be differentiated and more rigorous than those used in college prep courses. An honors course must have a published syllabus that verifies rigor that is sufficiently beyond the college prep or tech prep requirements. After comparing the text book to the college prep level requirements, you then determine if there is more in the book that will be enough to bump it up to honors level. It is not easy, but this is the process that must be done to determine what must be covered in order for the book/class to be considered honors level.

Because both the standards and the textbooks are updated periodically a book that might have qualified as honors before may no longer meet the honors level requirements. It may not even contain all the concepts that are now part of the updated standards.  When we first started our co-op, we did the research and the older Saxon math was at the honors level, based on the SC standards 20 years ago. Now the older books no longer contain all the content the current college prep standards contain. The book didn't change, but the standard did.

Last month’s blog dealt specifically with the older Saxon Math books.  I think it bears repeating that for the home school family who values a certain type of training (such the classical approach explained by Doug Wilson), they can and should pick texts that teach to the method they wish to use.  Just be aware that the students may not be as prepared for college level courses or for the college entrance exams. They may however have a more solid grounding in critical thinking skills and in rhetoric and debate.    As home school families we need to think through our goals for our children and then pursue their education with plans that will help them attain the goals. 

Martha Freitag

What Makes a Great Read-Aloud?


Wednesday, August 6, 2014

    My children and their grandfather recently started reading Winnie-the-Pooh together.  Listening to the three of them as they laugh together over the story got me thinking about what makes Winnie-the-Pooh such a great book to read aloud.  Here are some of the things I have come up with:
  1. Great writing.  Pooh may be a Bear of Very Little Brain, but these stories are not simplistic.  Take for example the chapter which opens with Pooh counting his honey pots.  Pooh is interrupted, and the story diverges into other adventures, but close to the end Pooh suddenly, and with almost no explanation, decides that he has sixteen honey pots.  Many stories (including nearly every adaptation or addtion to the Winnie-the-Pooh series by other authors) feel the need to remind children of previous details or explain a plot point so that the child doesn't miss the subtle meaning.  A.A. Milne takes it for granted that his readers will remember what happened at the beginning of the chapter and appreciate the subtle joke later on.  I also love the way certain words are capitalized for emphasis - not something that is always apparent when read out loud, but interesting for the reader.
  2. The book isn't written just with children in mind.  For me this is the thing that distinguishes great children's literature.  Great books offer something to every reader, no matter how old he or she is.  Winnie-the-Pooh is full of subtle jokes and references to things young children would not understand.  This is the third or fourth time I have read or heard this book, and I still notice things I haven't before.  Similarly my eight year-old, who thought she was too old for Pooh, is enjoying the book because she gets a lot more of the jokes than she did the last time we read it. 
  3. Easy to read.  I enjoy reading aloud, and hearing stories read aloud.  But some stories are more suited to be read to oneself than to read aloud.  It has to do with the way the sentences are formed and the cadence of the story.  We read a book a few years ago which was intended to be read aloud.  But the structure of the sentences was odd; often an adjective or preposition was not where I expected it to be.  Grammatically there was nothing wrong with the sentences, but they weren't written they way we generally speak.  Because of this, my reading came out rather stilted.  By contrast even when Pooh mispronounces a word, the structure of the sentences makes them easy to read out loud.
  4. The Characters.  We all enjoy books with an interesting plot, or a plot-twist that we didn't see coming, but I think, ultimately, it is the characters that make a story great.  I love the variety of personalities in Pooh, and they way they are displayed in the story.  Pooh is a Bear of Very Little Brain, and he is quite Humble about it, but at the same time, we are not constantly bombarded with this information and, without at all meaning to, Pooh can occasionally be Quite Clever.  The small details of the characters keep them from becoming flat or uninteresting.
    In all, I think there is a great richness about the book that makes it perfect for reading out loud.  And Winnie-the-Pooh is not the only great book for reading aloud.  We have found and enjoyed many others.  Some of our favorites include: The Chronicles of Naria by CS Lewis, The Railway Children by E. Nesbit, Johnny Tremain by Esther Forbes, Carry on Mr. Bowditch by Jean Lee Latham, and Twenty and Ten by Claire Hutchet Bishop. 

 Reading aloud has been a rich part of our family life.  If you have never read aloud with your family - or gave it up when your kids outgrew picture books, I encourage you to pick up one of these books and give it a try!  

    And please, if you have any favorite read-alouds, let us know!

Great Resources: Bob Books


Monday, July 28, 2014

  Both my kids are in elementary school, so the days of learning to read are not far behind us - actually in the case of the younger one they are still upon us.  For him reading is an agonizing process of sounding out each letter and then putting the sounds together into recognizable words.  We have finally gotten to the point where he recognizes certain words or letter combinations, and I think he is about to cross over from reading the sounds to reading the actual words - all he needs is more practice.
  And so, Bob Books have been an important part of his reading program these past few months.
  Bob Books are designed to be a stand-alone reading program which introduces young readers to each letter sound.  In the first set of books, the students learn the typical sound a letter makes (so the letter C has the hard K sound [cat] as opposed to the soft S sound [cell]) as well as all five short vowel sounds.  Each set has 10 to 12 little books with short sentences and simple pictures to help beginners read by context - the picture shows what is happening in the text.  Each book adds new letters and sounds.  The boxed sets build on each other introducing students to increasingly more complex sounds and words until students are able to read both short and long vowel words.  Each story is about 12 pages long, though the books get longer as the student progresses.  Both my kids and I like that the books are fairly humorous - it helps keep reading lessons from being tedious.

  The Bob Books ( has a lot of information about how to use the program along with supplemental materials.

  That said, I have never used the program on its own.  For both my kids I have used Bob books as supplemental reading material.  For both of my children I have chosen reading programs that are more tied to phonics lessons and workbooks.  I tend to be a "by the book" kind of person and I wasn't confident that I could teach my kids to read using the more organic approach offered by Bob Books.  

So why do I love Bob books?

  Because it is hard to find readers that only use short vowel words.  As big as the "Easy Reader" market is, there are very few books that focus on words for the very youngest readers - those with short vowels, and only a few sight words.  Bob Books are fairly inexpensive and fit the need for short vowel words.  The first set of 12 books uses only short vowels.  The books have been a great supplement to our regular reading program and have the added bonus of allowing kids the sense of accomplishment that comes with reading a whole book by themselves.

  I highly recommend Bob Books to anyone with beginning readers.

Please note: These great resources are not paid endorsements.  We just like to pass along the books and materials that we find helpful in the classroom.

Got a great resource of your own?  Let us know in the comments section.  We are always on the look out for interesting products!


Why is Saxon Math no longer considered honors level anymore?


Wednesday, July 23, 2014

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.

The 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 1.

One of our moms sent a link to an article explaining why the writer believed the older Saxon books to be better ( 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 scores.

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.

Welcome to Summer!


Tuesday, June 24, 2014

  The Summer Solstice has officially passed, and many of us have finished, or are finishing up the school year.  It is nice to put the books away for a while - or at least to pretend that they aren't still lurking in the corner of the dining room waiting for me to finish issuing grades and get started planning for next year...
  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!

Great Resources: The Library


Monday, June 16, 2014

  This being the age of the internet, with all the information we could ever need (and more!) at our fingertips, it seems a little odd that I should tout the library - home of books - as a great resource.  But the truth is, I have found the library to be an excellent place to supplement our homeschool. 
  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!


Guest Post - The Narrative in Number: Teaching the Story in Mathematics By Daniel Maycock


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 ( 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.