# Problem Design – Thwarting

Thwarting is the second of two problem types I’m borrowing from Ben Blum-Smith’s blog, who was referencing Cody Patterson. (Jamming was the first).

I really like Ben’s definition here:  posing a mathematical task in which mindless execution of the procedure is possible but likely to lead to a wrong answer.

Thwarting is a great tool for pushing students to attend to precision (MP.6), as well as a formative assessment tool to see how carefully they can apply a concept. However, I want to draw a distinction between thwarting for authentic assessment and trying to trick students. I’ve seen questions like these:

What is the value of the digit in the thousands place in 304,561?
A) 4
B) 5
C) 500
D) 4,000

This is trying to assess the difference between a digit and the value of that digit. However, the structure of the multiple choice question makes it a nit-picky trick — students who have a strong understanding of place value could be likely to pick 4 because they are not familiar with a vague definition.

There are 12 eggs in a basket. You take three out. How many do you have?

See if you can catch the trick in this one. It’s not assessing a valuable, authentic skill, it’s just trying to trick the reader with the structure of a subtraction question.

To be authentic and useful, thwarting needs to take a concept with a relatively simple, accessible procedure and put a twist on that concept so that following the procedure without attending to precision will result in an incorrect answer.

Some examples:

From Ben Blum-Smith’s blog:
What is the area of the parallelogram below?

A car is driving at 60 miles per hour for 30 minutes. How far does it go?

A teacher asked his students to answer questions 31 through 54 in a textbook. How many questions did he ask his students to answer?

What is the length of line segment AC?

Red M&Ms are in a ratio of 1 to 3 in a bag of M&Ms. If there are 60 M&Ms in the bag, how many  red M&Ms are there?

A box with an open top has the dimensions shown below. What is the surface area of the outside of the box?

Factor completely:

Thwarting is most valuable as a formative assessment tool — if a student struggles with these problems, it means they haven’t yet developed the necessary fluency and attention to precision necessary to use them flexibly at a higher level. However, due to their structure, thwarting runs the risk of false negative — students who are conceptually sound but rushed through the question, or just happened to fall for a trap they wouldn’t normally fall for. Depending on the question, thwarting may give much better class-level information than student level as individual variability is washed out.

Finally, while thwarting gives valuable data on our students progress, it may be most valuable as a tool to create lively student conversation. Many thwarting problems would also fall under splitting, and the likelihood of students believing strongly in an incorrect answer can be an incredibly opportunity for students to construct viable arguments and critique the reasoning of others (MP.3).