There’s a lot we can learn about teaching math skills from language arts teachers. For example, think about how we build writing fluency and grammar skills in language arts. Among other things, we certainly do these:
- Explicitly teach important skills and rules.
- Provide students with “mentor texts” and many examples of excellent prose to read and analyze; students who read a lot also write better.
- Ask students to review and correct examples which contain errors; this is often done in a “daily edit” format.
In math, most of our instruction traditionally focuses on the explicit teaching of math skills and rules, so we have that one down cold. Mathematical mentor texts are also used, though not as frequently, when we model solutions for students and share examples of worked problems.
We are not so good at teaching students to correct errors, and when we do teach it, we tend to focus on simple, careless mistakes in student work. This is inadequate. So, just as we give students practice in correcting writing by exercising their editing skills, we should give them opportunities to analyze and correct mathematical examples with errors. When students get comfortable looking for errors in mathematical work, they get better at noticing those errors more fluently and even automatically as they work.
One excellent place to find examples to use for this daily activity is Michael Perhan’s Math Mistakes blog. In it, the New York City math teacher collects student work and posts it periodically along with a blog post that discusses the errors in it. The posts are categorized by content area and by standard, so you should be able to easily find specific examples relevant to math skills or concepts you want to reinforce.
You can also create your own examples to use. As you collect and generate examples, be sure you are including all of the following types of errors:
- Careless errors. These are mistakes in copying or computation that result from a lack of precision.
- Computation errors. These are mistakes caused by a faulty algorithm, or from taking an inappropriate shortcut.
- Procedural errors. These are created when a student chooses the wrong process, such as subtracting instead of adding, dropping a remainder, or finding the volume of a figure instead of the surface area.
- Errors in reasoning. This comes from faulty logic and mistaken assumptions during the solution of a problem.
- Errors in interpreting a solution. Sometimes students can flawlessly produce a correct solution to a problem, but misinterpret what it means or how it applies. While this is a type of error in reasoning, I list it separately because it’s important that students know to look out for it.
What other strategies do you use to help your students learn to correct math mistakes? What other kinds of math skills errors do you ask them to look for? Share your thoughts in the comments.
Don’t miss the new 5 Principles of the Modern Mathematics Classroom, by Gerald Aungst.
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Gerald Aungst has more than 20 years experience as a professional educator, specializing in digital technology, mathematics, and gifted education. In his various roles as a classroom teacher, gifted support specialist, administrator, curriculum designer, and professional developer, he has worked to create a rich and vibrant learning culture. He is also passionate about improving learning opportunities for all students. Gerald is a founder of AllAboutExplorers.com and ConnectedTeachers.org.