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Reciprocal Thinking

Hidden Numbers

Introduction This interview is based on the game "Hidden Numbers". Courtney begins by choosing shorter decimals as larger but after a wrong guess, she looks for zeros after the decimal point. Confusing decimals with fractions, she wants to know how many parts a quantity will be divided into. Comments: Text in italics Interviewer: Text in red Courtney: Text other colour

Interviewer: In this game, you have two mystery numbers and try to guess which is larger.

Interviewer: See the decimal point in both numbers? Courtney: Yes, I guess I'd better look at the whole number part first... Almost all children know to compare the units first.

Courtney: So that's a three...

Courtney: and that's a three too...So I think the top number is bigger because it's shorter. Courtney chooses the top number, expecting that as there are fewer pieces, they must be larger.

Her choice was wrong Courtney: ohhhh...

Interviewer: Let's try again Courtney: OK...I'll just check the first numbers..

Courtney: So I think it will be the top number, but I'll just check this door... This time Courtney is more cautious.

Courtney is now comparing a 2-digit whole numbe with a 3-digit whole number. Courtney: Ummm... it's still probably the top number but I'll just check here..

Courtney: So there are 3 hundred and something pieces in the bottom number and they would be really small, so I'll choose the top number...

Courtney has been lucky Courtney: Great!!! Interviewer: Try another one? Courtney: Yes

Courtney: I'll open these whole number doors again to check...

Courtney: I think it's the top number again, but I'll have to check for zeros after the point.

Courtney: Umm..and open this door...

Courtney: This really is a tricky one...I still can't tell... I guess I'll need to open this door... Courtney is now comparing two 2-digit whole numbers.

Courtney: ...and this door...

Courtney: I still can't tell! This one is a hard one...I'll open this door next.

Courtney: Well 2 isn't very big so it's probably the top number again... Interviewer: Are you sure about that or do you need to open the last door? Courtney: I guess I still need to check it.

Courtney: They're the same!! That was a trick question!! Courtney sees both of these as 7 with something divided into 32 parts.