TT advertises their product as not needing any parental assistance, e.g. from their FAQ page:
Q7. Can students work through the program completely on their own with no help from Mom or Dad?
A. Of course! That’s the whole idea behind the Teaching Textbook™.
However, the definition of the associative property as given for both addition and multiplication is wrong. The property described in the book / CD as the "associative property" is actually a combintation of the associative and the commutative properties. Please see my
post on Unity of Truth for more details and the correct definitions of the properties.
I find this sort of error to be troubling as I imagine many students and parents would not catch it, especially as the product is billed as self-teaching. TT's response to this concern was less than satisfactory. They wrote:
As for the properties, we have rigorous definitions of the commutative and associative properties in Pre-Alg. and other books. At the Math 7 stage, we feel it is more important for the student to acquire a general understanding of the underlying concepts rather than overwhelm them with technical definitions. That's why we didn't draw a precise distinction between these properties.
I find this surprising as many state standards consider the associative property to be an elementary-school level concept (for example second grade in California). Further, when I checked the
Algebra 1 book, I found that the same error is repeated, and in fact expanded on, there. I quote from Lesson 26, page 126:
You already know the rule that two numbers can be added in any order (the commutative property of addition). Well, it turns out that this rule can actually be extended to longer strings of numbers. ... So our new rule is that a string of numbers (however many) can be added in any order. The technical name for this rule is the associative property of addition.
This, unfortunately, is wrong. The associative property is not the commutative property "extended to longer strings of numbers." It is a completely separate and independent property. Nor is it the rule "that a string of numbers (however many) can be added in any order," although it is
one of the properties that makes that rule possible.
After the above quote, the book correctly lists the equation defining the associative property, but then goes on to say things like:
That means the expression 3 + x + 4 + 1 can be rearranged any way you want and its value won't change. So 3 + x + 4 + 1 and x + 3 + 4 + 1 and 1 + 4 + 3 + x are all equivalent.
This example concretely shows the confusion on this topic by moving the operands around. This is possible only with the commutative property. The associative property
does not allow rearranging of operands. Please see
here for more on the commutative and associative properties.
Though these problems have been disappointing, overall, I would still recommend this program.