Learning from Learners: Robust Counterarguments in Fifth Graders' Talk about Reasoning and Proving by Vicki Zack

This week I read "Learning from Learners: Robust Counterarguments in Fifth Graders' Talk about Reasoning and Proving" by Vicki Zack. I was initially drawn to reading this article, given it's approximate grade level to the class I teach, hoping to make some connections or gain some insights. In this article, Zack uses her fifth grade class as a subject group for her research surrounding the "Chessboard Problem." Her students are well versed in problem solving, as it is at the "core of their mathematics curriculum." Zack has her students' follow a distinct process when discussing their strategies for problem solving; firstly, they keep track of the thinking in Math Logs, they then share their solutions to a partner, a group of 4 or 5 and finally, a group of half the class (thirteen students.)
Zack then moves on to speaking directly about the "Chessboard problem." The students go through three tasks:
     Task 1: Find all the squares (in a four by four grid given as a figure). Can you prove you have             found them all?
     Task 2: What if ... this was a 5 by 5 square? How many squares would you have? Extensions were      subsequently posed.  
     Task 3: What if this was a 10 by 10 square? What if this was a 60 by 60 square? How many                square would there be?
Zack provided the class with a Ted-Ross strategy that came up with the following answers:
" The answer for the 10 by 10 grid is 385 squares. So take the answer for the 10 by 10 square (385) and 10 x 6 = 60 so multiply 385 x 6 = 2310 and you have the answer for the 60 by 60. What would you say?"
There are five counterarguments that are found as trends when students are coming up with reasons why the Ted-Ross strategy does not work. I was quite confused in the article whether the counterarguments were presented for the students to use or whether their counterarguments were merely looked at to see if they fit the previous counterarguments found.
I like the idea of the students' looking at a possible solution and trying to diagnose why it may be wrong. I think this shows true understanding of the task and may lead to possible correct solutions. A quote that resonated with me was "The students who have generalised a rule after testing it, use what they know and trust it." I believe this is so powerful; the feeling of self-belief! I do not think that if the counterarguments were provided that this would be as beneficial or meaningful.
I am also left wondering if the final task of finding the 60 by 60 squares is one that is too lofty. I would love to have a better understanding of time frame surrounding this task and if there were any students who were stuck on the 10 by 10 square for extended periods of time. My last desire is that there were work samples shown, I think it would lead to a deeper understanding of the students' thinking and process.