Yesterday I posted a link to a free online math assessment. If you followed the link and took the test, I invite you to post your impression in the comments section. I made 30 out of 36 and missed the problems I expected to. I didn't know a formula or two and I also made a calculation mistake.
I found the 10th grade level test challenging. This test truly reflects the material covered in advanced level math courses (as in honors, college prep level - not regular). I wondered if the programs many homeschool families use actually cover some of the material that is showing up on national math standards.
I spent some time today looking at the scope and sequence of several math programs I hear homeschoolers use (and indeed, I've used myself). I looked at the programs' own scope and sequence(s) and I also consulted other reviewers for broader perspective.
To be honest, my interest stems from comments I have heard from other homeschoolers through the years regarding the level of "difficulty" of two specific programs, Math-U-See and Teaching Textbooks at the high school level. Let me be clear: I am not saying these programs are inferior, only investigating comments and preconceptions I have heard from other homeschoolers that they might not include all the topics typically found in comparable courses. My interest was doubly peaked by the types of questions I found on both this online assessment and other achievement tests I've seen in recent years.
Further note: These are my comments and perspectives and do not represent an exhaustive comparison.
To begin with, I looked at the scope and sequence for Math U See (MUS) at the high school level. I have heard that MUS was criticized in the past for being somewhat light-weight because it didn't include some topics, such as matrices, in the advanced levels.
Steve Demme has responded to such comments Cathy Duffy made in her review of Math-U-See. (click here for his comments). I appreciate Mr. Demme's perspective on "difficulty" and student skill mastery. I also appreciate that MUS addressed these honest concerns by adding additional materials and resources to their program. I probably agree more with Ms. Duffy about the necessity of proofs and postulates, so I'm glad that these have been recently added to the Geometry program.
I also read the newest scope and sequence and find nothing to be concerned about so long as the student completes the entire sequence on MUS courses at the upper level. There are some topics that are written into the upper levels that are usually introduced in lower course levels in traditional programs.
In regards to Teaching Textbooks (TT), I looked in great detail at the scope and sequence of the newest editions of algebra and higher courses. I've heard TT criticized by other homeschoolers who questioned whether it was truly "college prep" material. I understand those comments in regard to the first edition of the books, which did seem to leave out some topics normally included in algebra and above. It appears to me that all of these concerns are laid to rest in the newest editions. If you have a child to who is math and science oriented and heading to college in one of those fields, I would definitely invest in the newest updated versions of these courses in Teaching Textbooks. Again, I also suggest that you continue the course sequence has far as possible in order to cover all the traditional topics.
Finally, I retain some concern about the level of difficulty in word problems for both of these programs, as well as Saxon Math and almost any other math curriculum on the market for homeschoolers. This is not to say that "difficult" equals superior. However, it is important for students to practice with a variety of problems that require them to incorporate knowledge from several disciplines. I think that parents would do well to be sure their student practices the way problems are worded on standardized tests - which is often different from any text book.
Both MUS and TT incorporate real life problems in their materials and this is a real plus. Next week I'll complete a review for a supplemental program sold by Math Mammoth that uses real-world situations to teach practical application of algebraic (and above) math principles. These types of problems are part of most college level math courses. Don't skip this type of work with your student! Insist on it!!
It is also prudent to begin early to use some logic resources, such as those by Critical Thinking Press. These materials make students think outside the box and look for patterns in a way that straight text problems rarely do. Speaking of sequences and patterns - these are probably the most critical for test taking. If a student quickly recognizes the pattern and the sequence they can solve a problem with minimal calculations and save time.
So back to the question: What is being left out? From what I can tell - nothing! Both of these math programs, developed to be innovative or to specifically meet the needs of homeschoolers have responded to criticism and added topics previously left out. So long as the student completes the entire sequence of courses, they should cover all the necessary topics for upper level math.
I do think that some math programs are "more difficult" than others for a variety of reasons. However, I do not think you will shortchange your student to use either of the two programs mentioned here. Your selection of a math program needs to take many factors into consideration, including your student's future college plans, how independently the student needs to work, and general aptitude for math concepts.
As for the first question from yesterday: What do we learn from these tests? Any such assessment gives you a benchmark for your students progress compared to others nationwide. You can also see if there are any areas of weakness that need to be addressed. Then you'll be able to address those areas through your curriculum or through other resources.