Do
you have some students who rush through their math work, while others seem
frozen and unable to even get started? Do you have students who are chatterboxes
all day and then when you ask them to speak about mathematical concepts turn to
crickets? Do you struggle with students who aren’t engaged and don't see the
point of learning? Do you want to help your struggling students but aren’t sure
where to begin?
If you answered yes to any of these questions, using error analysis can help turn your math classroom around!
What is error analysis anyway?
Error analysis is a method used by teachers to identify the factual, procedural, or
conceptual mistakes commonly made by students in order to provide support where
needed. However, it takes on a slightly different meaning when teachers use it
as a way to teach mathematics. In this way, students are given a mathematical
scenario already solved by one or more fictitious students. The role of your
students is to determine which “student,” if any, is correct and identify the
errors made by others.
How do students benefit from this approach?
1- Slow Down and Speed Up!
When
students are asked to analyze the work of someone else, they can’t just get an
answer and move on. They must analyze and reason why an answer is or is not
correct. This helps students slow down while using higher-order thinking and
reasoning skills. Yes, you’ll still have early finishers, but my students spend
more time thinking than rushing when asked not just for an answer but to agree
or disagree with someone.
In
a similar way, using error analysis can have the opposite effect on some
students who might normally freeze up in math. Students who may have no clue
how to begin can use the example of someone else’s work as a starting point. They can see how
someone else solved the problem first and the steps they took.
This can provide
scaffolding for students who might otherwise feel overwhelmed. Agreeing or disagreeing also takes the pressure off of students who may be afraid to be
wrong because it isn’t their own work being analyzed.
2- Critical Thinking and Vocabulary Rich Dialogue
Many
students often know what they are thinking, or how they would approach a
problem, but have difficulty expressing their thoughts clearly and concisely.
Engaging in written or verbal dialogue can help students to process and really
understand the mathematical concepts they are working on. Students must think
critically to critique someone else’s work, and they must put themselves in
someone else’s place to try to make sense of their thinking.
My
students often disagree about whether or why a problem is correct or incorrect
at first. They acknowledge that one side is right, so they know they need to
both clearly present their own thinking and listen attentively to the critiques of others as each problem is dissected.
These
Agree or Disagree Problems will get
your students thinking critically and are the perfect starting point to get
your students talking on task. I’ve also included Math Discussion Stems and
Questions to jump-start and guide mathematical dialogue.
Grab these free math stems to get started on bringing math dialogue into your classroom!
3- Noticing the Why
While
I love a good math talk, this may be my favorite reason to use error analysis
to teach math. As students are deciding whether they agree or disagree with
someone, I pose a critical thinking thought question:
“What
would happen in real life if someone
made this mistake?”
While
some scenarios are frivolous and wouldn’t have severe consequences, others do.
If an employer makes an error in a paycheck, that can have real and lasting
consequences. If a team shows up late for a game because they calculated the
time wrong, they might lose a championship.
Students
quickly realize that accuracy is important and the impact of making
mathematical errors in the real world. I use this to reinforce why we work
together, check our work, and persist in making sure work is legible and
accurate. Suddenly, my students who couldn’t be bothered to do math are
interested and see value in learning what I’m trying so desperately to teach
them.
Knowing the “why” really does matter.
4- Targeted Support
This
is a bonus for teachers really.
When you use error analysis to teach math, you
get to know your students on a deeper level. My students LOVE using the agree and disagree cards to show their thinking. These simple manipulatives ensure that ALL students are participating, helping me get a grasp of each student's understanding.
When you watch and listen to
students as they reason through agreeing or disagreeing, you see beyond the
checkbox of whether a student meets a certain standard. When I walk around my classroom
and listen to my students’ arguments, I get a deeper sense of what they do
understand and the places they are getting stuck. I can target instruction for
small groups of students or review a concept with my entire class. I can choose
partners strategically and better plan for and support students who are
struggling as well as those ready for the next challenge.
Not convinced yet? Click HERE to try them out for FREE in your classroom!
Using
error analysis to teach math has helped my students in so many ways, and can
help your students, too. Bringing these types of activities into the classroom provides challenge, rigor, and critical thinking...all on standards that you already have to teach. What do you think? Do you Agree or
Disagree?
You might be interested in reading:
Looking for more printable and digital critical thinking math activities? Click HERE.
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