I don’t want to give the impression that Talking Math with Your Kids always goes well. It does not. There are bumps in the road for sure.
I was having breakfast with Griffin (8) and Tabitha (5) over Thanksgiving weekend.
Griffin: It’s exactly one month until Christmas.
Tabitha: I knew that!
Me: That’s right 30 days.
T: So it’s zero weeks.
Me: How many weeks?
T: Zero
Me: In 30 days?
T: Oh! I thought you said 3 days.
G: So how many weeks is it?
Me: What do you think?
G: Well…five sevens is…er…six fives is 30 so seven fives is 35…Five weeks and five days! Is that right?
Me: Tell me how you got that.
G: [long pause]
Me: [long pause]
G: [frustrated] Just tell me if it’s right!
Tears followed shortly afterwards. I suggested we move on and talk about something else. Griffin cursed Tabitha’s name for making him wonder how many weeks this was. Emotions ran high and I told him we needed to discuss it later.
An hour later…
G: [on the couch, addressing me as I came down the stairs] Is it four weeks and two days?
Me: Did you do two sevens are 14, then double? Or did you do five sevens are 35, so five weeks are five days too much?
G: I did the thing with 14.
The most important message I can send my kids is that they can make sense using what they know. Their minds and the world are the arbiters of right and wrong, not me. In not telling Griffin whether he was right the first time, I was reinforcing my insistence on this principle.
I knew what his mistake was and I knew that he would find it if he stopped to think. Five sevens are 35 because seven fives are 35. And 35 is 5 bigger than 30. But that means five weeks is five days too big, not five days too small. I knew he could figure that out himself. Further, I knew that if he could not, we could talk about it and that he would learn from this conversation.
I also know that it is important to compromise. In the second part of the conversation, I knew that he knew he was right. But I knew that prodding too hard on the emotional wound recently inflicted could quickly lead to trouble.
So I compromised. Rather than have him tell me what he did, I offered him choices. I essentially asked him whether he had started from scratch (finding four sevens), or adjusted his previous answer (five sevens are 35).
Overthinking my teaching 
It seems like that’s so much more common than I remember, the plea: “don’t make me think… just tell me.” I got it daily for four weeks in my kindertgaten practicum, (and every night at home with my 4 yr old) Math, English, Science, anything…
I know that in English, early primary students are encouraged to use “kid spelling”. We don’t fret spelling, because getting comfortable with spelling patterns and conventions is more important than a right answer. I can still assess comprehension if they spell “school” with a K, or “train” with a CH.
It seems that math doesn’t have that same room for imprecision. You really have to draw out their problem solving narrative, and that can be tricky after a recent failure. We (or at least I) never really had thought about math instruction relying so much on emotional relationships and trust.
Thanks for illustrating/modeling that!
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