The Dialectic, sometimes referred to as the Logic Stage, develops analytical skills in students. This stage hits about middle school, or approx. twelve to fourteen years old. Each child is different, but you will notice a change in the way that your child thinks and approaches his schoolwork.
This is the age that children really start to ask questions and explore. Memorization takes a back door to reason. I call this the "lawyer stage" as my children all seem to turn into little lawyers at this age, reasoning me to death and questioning every little thing that I do! As frustrating as that may seem, I remind myself that all this reasoning applied to academics is a great thing.
You can encourage the logic stage in your children by providing them with the resources to answer their questions. Be willing to drive them to the library to find the right book, surf the Internet alongside them, and encourage them to keep asking questions.
And don't be afraid when they question the Truths that you have taught them. This is your opportunity to teach the whys of what you believe. Truth will hold up to scrutiny.
One thing that you can do during this stage is introduce literary analysis. When your child is assigned a book, do a search on the Internet with the book's title. Or check out such sites such as NovelGuide - Novel Resource Guide and Literary Analysis (see Literature Helps for Parent Teachers for more sites). Use the information that you find at these websites to help your child analyze their reading material.
In mathematics, your child will move from simple arithmetic to pre-algebra. From the memorization of math facts to analyzing math concepts. They are preparing for the higher mathematics of geometry, algebra, and calculus.
For more on teaching individual subjects in this stage see Classical Christian Homeschooling: The Dialectic Stage: Grades 7-9 .