Hi, I'm writing because in the just released EngageNY 6th Grade Common Core Math Exam sample questions, there is a serious conceptual error in the explanation for what constitutes a correct answer to a question about equivalence of algebraic expressions with terms x,y,z on p. 87 of the 6th grade downloaded file. You can access the file from the chalkbeat website found at the end of the post, but I've attached a pdf of an excerpt. I'm not a math teacher, but I hope that the math teacher community can reach out to Pearson or NYS to address this.
On p. 87, you will see that credit is awarded if a student substitutes randomly selected values and decides that two algebraic expressions are generally equivalent based on the particular substitution. This rationale is erroneous as it only proves the intersection of the expressions at that particular value, and says nothing about other possible values of x,y,z. In other words, evaluating expressions for equivalence by substituting an arbitrary value doesn't consider the chance intersection of different expressions at a single point, and is therefore an invalid approach. For example, the substitution of the values 1,1,1 would lead a hapless confused student to the erroneous conclusion that three of the expressions are equivalent.
I'm not attacking CommonCore, but I think there is a real story about test writers seemingly not understanding the underlying content of the material they are testing, as well as the aggravating factor of the time crunch to publish these tests. I hope that Pearson's curricula doesn't teach this method to 6th graders as a strategy, but I given the demands for increasing alignment between teaching and assessment, I worry that they might. The most worrisome big picture concern for me is that in an attempt to increase students' understanding, the curricula may be shifting towards cramming more algorithms (here substitution, to be used only as a non-determinative check) and neglecting to fully teach their correct and incorrect application.