Adopting the standard regrouping algorithm

[blondeviolin]

Abby understands the standard regrouping algorithm when adding 3-digit numbers. She solves problems presented vertically just fine. When the problem is presented horizontally, however, she always begins by adding hundreds, tens, and then ones as you would do mentally. She can do two-digit add/sub mentally just fine, but three-digit gets to be a bit much to hold in her head. So, she starts writing down, but as she regroups there's a lot of erasing or whatever going on. Do I let her to continue to solve this way, or should I start encouraging her to rewrite the problem vertically? Or do I let her continue to do what is working for her, albeit a bit non-traditional?

 

She does subtraction similarly, but annotates the problems a bit more like the traditional algorithm, just horizontally.

 

[letsplaymath]

Encourage her to think through math problems her way, as long as it is mathematically correct. If you try to replace a method that works for her with a method that seems artificial to her, you run the risk of *discouraging* her from thinking things through. (For example, see this article by Constance Kamii.)

 

But I would suggest one tweak in her method: Instead of erasing as she goes along, tell her to put a single line through the partial answer and then write her adjusted answer below (or above, whichever feels more natural) the first. That way, she can still read the earlier figure, in case she needs to refer back to it. In a multi-digit calculation, she might have several partial answers, each adjusted as she continues the work, until she gets to her final number --- but she will always be able to see each step.

[blondeviolin]

Encourage her to think through math problems her way, as long as it is mathematically correct. If you try to replace a method that works for her with a method that seems artificial to her, you run the risk of *discouraging* her from thinking things through. (For example, see this article by Constance Kamii.) But I would suggest one tweak in her method: Instead of erasing as she goes along, tell her to put a single line through the partial answer and then write her adjusted answer below (or above, whichever feels more natural) the first. That way, she can still read the earlier figure, in case she needs to refer back to it. In a multi-digit calculation, she might have several partial answers, each adjusted as she continues the work, until she gets to her final number --- but she will always be able to see each step.

 

Thanks! I also don't want to encourage one way and her not understand the math as well. I want it to be solid, you know? (Though, I did want her to know how to do the standard algorithm.)

 

Having her just cross out the partial answer is a good idea. Sometimes she gets distracted in a multi-step problem and forgets what she was doing. Maybe such adjusting will help with that...because I don't see the distraction going away any time soon. (She is just six!)