The 3-year old daughter of fellow Minnesotan, fellow math teacher and friend Megan Schmidt made the following proclamation a couple weeks back.
It takes three things to make a sandwich #Tmwyk
— Megan Schmidt (@Veganmathbeagle) May 23, 2014
This simple claim has led to lots of fun conversation. Let’s call the daughter veganmathpup (since she is the daughter of Twitter’s @Veganmathbeagle), or VMP for short.
All discussions with VMP are filtered through her mom via Twitter. All discussions with my own children are my best recollections of the recent silliness.
Open faced sandwiches
Veganmathpup’s assertion boils down to this: A sandwich needs these things: (1) a slice of bread, (2) a filling, (3) another slice of bread. I wanted to know about open-faced sandwiches. Is an open-faced sandwich properly called a sandwich? VMP was silent on this matter. So I asked Tabitha.
Tabitha (7 years old): That counts as a half-sandwich…actually more than a half-sandwich.
So an open face sandwich is not actually a sandwich for Tabitha. This gave me a chance to introduce the term misnomer.
Cookies
A week or so later, VMP claimed that “2, 3, 4 or 5 cookies can make a sandwich”. This was a clear violation of the earlier rule here. Two cookies, no filling? How can this be a sandwich when “It takes three things to make a sandwich”?
So I asked about Oreos. Does VMP think of an Oreo as 1 cookie? 2 cookies? Most importantly, Is an Oreo a sandwich? Megan related the following conversation.
Megan: [Handing VMP an Oreo] VMP, I have a question. Is this a sandwich?
VMP (3 years old): [Examining carefully] Um, no. It’s not.
Me: Why isn’t this a sandwich?
VMP: It doesn’t have things, like a burger.
Me: [Handing her two Oreos stacked on top of one another] Is this a sandwich?
VMP: [Examining even closer this time] No. it doesn’t have stuff in it. It needs lots of stuff inside like a burger to be a sandwich. I want a burger. Let’s get one [face full of oreos]. We won’t tell Daddy.
So many follow up questions I was unable to ask here. Does a Double Stuf Oreo have enough stuff inside to count as a sandwich? What about a Mega Stuf Oreo?
A Mega Stuf Oreo contains approximately 3.1 times the Stuf of a regular Oreo.
Marshmallows
Then the plot thickened.
Marshmallows btwn 2 graham crackers = sandwich (cuz there’s a burger). Oreo: still not a sandwich. @Trianglemancsd #sandwichchat
— Megan Schmidt (@Veganmathbeagle) June 3, 2014
Megan went on to report that, even after opening the Oreo to demonstrate that there is a filling, VMP rejected the Oreo as a sandwich because the filling is white.
Allow me to summarize:
- Three things are required for a sandwich.
- Unless they are cookies, in which case you only need two.
- An Oreo is one cookie, so is not a sandwich.
- Even if you want to call the Oreo wafers cookies and the Stuf the filling an Oreo is still not a sandwich because the filling is white.
- The filling in a sandwich is properly referred to as a burger.
I saw a flaw in the logic, though.
Marshmallows are white.
I asked about this. Megan reported that their marshmallows are colored.
I HAVE BEEN FOILED BY A THREE YEAR OLD!
So what do we learn?
Children have ideas.
Children use their minds. They think about things.
We can contribute greatly to our children’s learning by probing those ideas.
Formulating precise definitions is an important part of doing mathematics. Sorting things into examples and non-examples is part of this process. It really doesn’t matter whether we are sorting shapes (square, not square) or food (sandwich, not sandwich). And when the child is three years old, it really doesn’t matter whether she is consistent in her sorting.
What matters is that she is thinking in this mathematical way.
Starting the conversation
You can do as I did. Tell your child that another child says it takes three things to make a sandwich. Ask your child whether she agrees. Then ask about open face sandwiches and about Oreos.
But the bigger picture is important here too. There is a useful habit to develop as a parent—ask follow up questions when your child makes proclamations.
Other conversations we have had in this vein include Spirals, Circles and Armholes.