Modern math competition

Saw this brief exchange and thought it would be a good time to write down some ideas for a new type of math event:

There is a STEM Expo later this year w/ community partners and a 4th - 8th gr competition. Ideas on how to make comp more mathy? #MTBoS

— Jana Sanchez (@jsanchezmath) December 18, 2015

It will be clear below that these are all other people's ideas, I've really just added ideas for how you might score this.

Fold and Cut

Everyone gets a pair of scissors and three pages with a straight-line figure (a shape that has a boundary made up of polygons) in the middle of the page. For each shape, players try to find the smallest number of straight cuts they need to cut out each shape.

One example of a shape to cut out

Another example: cut the house and the tree at once (hard!)

Scoring for each shape:
10 points for least cuts
5 points for second
1 point for all who cut out the shape successfully, regardless of how many cuts it took

Reference: Fold and Cut Theorem.

Estimation

Set up an estimation challenge (number of marbles in a jar, weight of a collection of books, height of a blown-up picture of your favorite mathematicians, etc). All players write down:

1. Their estimate of the amount
2. An explanation of their reasoning
3. A value that they think is too low
4. A value that they think is too high

Scoring:

Each estimators performance is based on the absolute size of their error (|estimate - actual|) multiplied by the size of their low-to-high range, divided by 2 if the actual value is within their range. The lower the resulting value, the better.

20 points for best performance

10 points for second

5 points for third

1 point for everyone who estimates

Reference: Estimation180 has tons of great prompts for estimation.

Which one Doesn't Belong

Really simple: show players four things, then they figure out reasons why each of the figures could be the one that doesn't belong.

This is just a small sample of the ideas for Which One Doesn't Belong

Scoring:
1 point for every different reason + 5 bonus points if there is a reason given for each of the 4 shapes

Reference: Which One Doesn't Belong has a huge collection of great ideas for shapes, numbers, graphs.

Notice and Wonder

Pick a 3 to 5 math pictures, gifs, or videos to show on a large screen. Players write down the things that they notice ("I notice that ...") and wonder ("I wonder [what, why, when, how many, ...]..?").

From SolveMyMaths

Scoring (similar to WODB):
1 point for every notice or wonder + 3 bonus points for having both a notice and a wonder.

Reference: SolveMyMaths and MathHombre both have really nice collections. Mathematical Etudes has some excellent videos that don't seem to be as widely known among Anglophones. I'm sure there are others

Helping with homework

who: a high-school student in a semi-public venue
what: stuck on a homework question

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A few weeks ago, J1, J2 and I witnessed a frustrating scene: someone stuck in a corner of a party trying to finish math homework and a parade of adults failing to break through the block. The three of us, briefly, tried to help as well. I'll describe what we observed, and then offer an idea I had when reflecting on the experience.

The Block

The problem was about graphing functions of one variable for a high school algebra class. As far as I could tell, the student felt moderately comfortable with this topic, but hadn't achieved mastery. However, the meta-problem was a perception that the teacher was asking for something very specific, that idiosyncratic definitions were being used, and that the student didn't have the information required to answer the question. To be concrete, the problem/meta-problems were something like:

Problem: Graph the function , show your data set
Meta-problem:

1. my teacher defines "data set" in a particular way
2. A "data set" for graphing a function is the set of characteristics of the function we investigate to understand what the graph looks like (for example, is it symmetric across an axis, does it have a max or a min, etc)
3. I don't have my teacher-supplied "data set" for these functions
4. Thus, I cannot do this work

Strategies that were tried

I basically saw two approaches. The first was for the helper to offer their own interpretation of the questions, including supplying their own definition of "data set." These approaches all failed, I think because the definitions did not match the student's required form of definition and because they were presented without confidence. The latter meant that the student expected these weren't the same "data set" as what their teacher would have supplied and the former confirmed that.  I wonder how it would have continued if the helper had said: "Oh yeah, I remember this. Let's talk about it and you can help me remember what the data sets are for these other functions."

The second approach was to focus on completing as much of the work as possible. For example, "so just graph the functions and do that part, even if you don't know how to include the data sets." Honestly, I don't know why this advice was rejected, but I've seen it before. There seems to be a common aversion to doing an intentionally incomplete job. I guess the message that the incomplete work sends is "I couldn't do everything," while the student would rather send the message "I chose not do bother with this assignment." In other words, non-compliance is better than inability.

Strategies to try in the future

As I said, I've encountered this myself in the past and expect to see it again in the future. Here are my ideas for strategies to try:

1. Say, "I can't help you with this question, but let's play a game related to this part of math." In this case, the game could have been asking each other questions about the functions, say yes/no, with the objective of getting the other person to answer incorrectly or say they don't know.
2. Bluff that I know what the teacher wants but need their help remembering. Along the way, work through the actual concepts together.
3. As a last resort, tell the kid to leave the work and come do something else together. Even a 5 minute break could be enough of an emotional release. Also, my objective sense is that no single piece of work is worth the unproductive battle.

In the first two, at least the student will get to have a conversation about the actual content of the homework and may even learn more than doing the assignment. There will will probably be some lingering confusion about definitions, so those will need to be addressed later.

What do you think?

I would love to hear ideas from other parents. What do you do in these cases?
Also, it would be great to hear from teachers, too. What do you think parents should do when this happens?