AskDrCallahan Blog

A common question is what course is next. This often comes from a parent who has done a variety of middle or high school math courses with a variety of vendors. The confusion becomes the treatment and the course names.Our general rule is to follow the path is as follows.

• Algebra
• Geometry
• Algebra II with Trig (often called precalculus)
• Calculus

A student who has had an algebra course (even if not the best) should be ready for geometry. The geometry course should incorporate a review of algebra to keep it fresh. (Jacob’s geometry does this well.) Except for those using Saxon (which does not have a separate geometry course) most vendors cover these topics first.

The big issue comes after that - with Algebra II with Trig - often called Precalculus. We have many students who have taken some form of algebra II or adavnced algebra. Parents ask us often - what have they covered and what do we need to do next. This is a tough question to answer - but here is our approach. We direct them to our website for online quizzes of the textbook we use for Algebra II with trig. We have links to quizes for chapter 1 to 8. If you have your student take these short quizzes you get a feel for what they are ready to do next.

What do you do before algebra? Is prealgebra required? We get these types of questions often - so here are some things to consider.

First - note that algebra is the abstraction (or generalization) of the basic arithmetic you have learned or taught in the k-6th grades. So instead of saying 2 apples + 3 apples = 5 apples as we might do in arithmetic, we  move to a more general 2x + 3x = 5x in algebra.

Second, you can decide to do prealgebra - or just jump straight into algebra. You can judge pretty well if a student is ready for algebra by the following criteria:

    * They need to know basic arithmetic.

    * They need to understand the idea of a equation - such as 2+3=5.

    * They need to understand the idea of a variable. For instance, in the statement 2 apples + ? apples = 5 apples — the question mark is a variable.  If they get this, they have the idea.

    * They should know something about graphing points on a number line and on a plane.  Furthermore, they should be able to read graphs and charts.

    * They need the ability to do abstract thinking. This one is a little harder to determine and comes with age. But if they understand variables, they likely are ready to think abstractly.

When we got to the “prealgebra” point with our daughter - we just plowed into algebra and took it slow. But if you feel you have conquered all of the above but do not want to plow into algebra just yet, you can choose a prealgebra curriculum  which provides or strengthens the above bullet points — or you can try this.

Take the next semester or year and explore math. Have fun with it. Have your student explore how math is used in their favorite hobby or passion. Use the web. library, and bookstore to find information about how math relates to their true love. Have them look for relationships in their hobbies. For instance, how is the length of a string related to tone in music? What is the relationship between distance a ball goes with a bat or golf club as opposed to where you held the bat or club? Whatever their hobby or interest - I can assure that you can find ways math applies. If not, let us know and we might be able to help you in the search!

We have just happened on “The Futures Channel.” This appears to be a great website for applied math and science. The site includes videos and applications of math/science in the real world. A good deal of content appears to be free - but only $35 per year to access the site otherwise.

A common question we get from homeschooling families is ”When do I start algebra?” Sometimes this question is more of an issue of “what do I do now?” when they have reached a point in 5th or 6th grade and do not know where to go. Many families are disappointed with the current math curriculum and cannot see how to get out the trap where one vendor has you on a path from 1st grade to 12th grade. The simple answer is you can start algebra as soon as they get the basics of arithmetic and can think in terms of abstract thought. The best approach to use is to do algebra from 1st grade by building it into everyday situations and normal thinking. Algebra is not a set of formal rules – it is a way of relating math to the real world. You can start that now – in the kitchen, in the workshop, and in the yard. See a great article about how to do this —- Algebra In the Early Years.

We have had several interactions with customers that have resulted in ongoing concerns about the preparation of homeschoolers as a population for college level math and science. For instance, a recent customer had used another homeschooling product for algebra 2. They then purchased our Algebra 2 with Trig and had plans to review the algebra 2 component then move quickly to trigonometry. However, they found the previous algebra 2 products had NOT prepared them for our algebra 2! We were shocked! We understand that their program may not have been as rigorous as ours, but they clearly had no preparation in previous algebra or geometry either.

 

Other customers have come to us after reviewing homeschooling options and expressed joy over finally finding something of caliber and dismay over what is being taught in the area of math to many of this nation’s homeschooling students. This concern is compounded by similar experiences where students having used other curriculum come to ours and cannot handle the pace. Some of our competitors have expressed similar concerns over the quality of homeschool math programs. Clearly, parents need to go into this decision with prayer. While we do not think math is the most important ingredient in education, we do believe that as homeschoolers we want to provide a higher standard - not a lower one. We do not claim to be the only product on the market that is providing a good math education. We are thrilled that others DO provide good programs also - and those we know, join us in our concerns!

“Why do we have to learn this stuff we never use.” That is the question every student asks about many subjects - but especially math. I know because I asked this question myself. In fact, while teaching university courses with lots of math I still find myself asking this question.Compare this to English - the subject I hope we all see a need for at some level. We all need to be able to read and write just to survive. But do we enjoy the grammar work - diagraming sentences and learning about sentence structure? I did not. But looking back I realize that some of it was needed so that I could communicate with others at some basic level. The point of the grammar was to understand how to read and write correctly - and eventually in school we started doing applications by using the grammar to read and write. The same thing is true of math and science. (I am using the term science globally which includes things like the science of economics etc.) The math courses we take are the grammar and the sciences are the application like reading and writing are to grammar. But, without the math, we can never hope to understand the sciences. Unfortunately, this is often missed in education. The point of math is to apply it - and courses in math should show application as much as possible. This is a great failure most high school geometry courses - which rarely show any application to the real world. So when choosing math textbooks and curriculum, look for applications. Applications not only makes a course more enjoyable, it actually teaches the real reason for math!