By: Rachel Barry

I believe that the most
important skill to be taught in any mathematics curricula is critical
thinking. A student should leave
my class knowing how to work through difficult problems, using a variety of
strategies to develop solutions to these given problems. If a student has left my class, without
learning various methods to process through challenging situations, then I feel
that I have failed them. Critical
thinking is crucial for students going out into the real world.

There are many approaches
to develop critical thinking skills.
This comes more naturally to some students than others, and for some
students the context is important to dig into those critical thinking
skills. In most cases, seeing a
problem from a different perspective helps students realize a bigger picture that
there may be more than one way to solve a problem. This is a hard concept for some students to grasp
because in math there is one correct answer, however, there may be more than
one way to

*get*to that answer.
In this blog post, I am
going to share with you a couple ways that I use error analysis to build
critical thinking skills.

About once a week, I use
error analysis in warm-ups for students to decipher what another student did
incorrectly. They have to look
through a student's work, circle or explain the error that the student made,
and then correct the work from where the error was made. This process helps students in two
ways. First, I am able to address
common mistakes that students make before they make the errors themselves. Secondly, this builds students
confidence because they are made aware that other students make mistakes as
well.

For the attached warm-up, I shared this with students as a note (instead of the .pdf that you see) in Notability. This allows students to manipulate the work, instead of write over it. You can learn more about this Notability feature in this earlier blog post.

Another great method to
get students to think outside of the norm is to ask students why an answer is
incorrect. In a standardized test
warm-up activity, I ask why an answer choice is incorrect. Students then have to work backwards
from the answer to figure out what error the student made. Then, they provide the correct
answer. The extra step on the
front end ideally prevents students from making that same mistake when they are
taking a standardized test.

Analyzing distracters in
standardized test questions also can address the common student errors of
misreading the question or circling the wrong answer choice. For example, let's take a look at the problem below.

Many times students solve
for “x” correctly in a problem.
The question, however, does not ask for the value of x, but instead it asks them to find the value of "2x". Distracter analysis can be used to address students reading the problem incorrectly.

If you have any additional ways to use error analysis to build students' critical thinking skills, please share in the comments section!

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