It will happen. Students will make mistakes when solving math inquiries. In the past, these errors were met with red ink and low grades, leaving generations of students feeling as if math was a bottomless pit they could never escape. Now, errors can serve as learning opportunities students can use to master mathematical concepts.Why error analysis?
Error analysis is the process of reviewing solutions to math inquiries, identifying mistakes, explaining why they were made, and making corrections. For example, if a student completes 20 problems focused on multiplying rational numbers, and two of the answers are incorrect, did the student make calculation errors or does the student have an issue understanding the proper algorithm? Would your response change if the student answers 15 out of 20 incorrectly?
While it is important for educators to understand the types of mistakes students make, there is a crucial element missing. Students also need to learn how to identify and correct mistakes. The most effective types of error analyses focus on 5 common mathematical errors: conceptual, operations, reading comprehension, procedural, and silly (EA CORPS).
Conceptual errors
Conceptual errors arise from the failure to recognize, understand, or connect math ideas and principles. Indicators of conceptual errors include errors based on definitions of math concepts or repeated procedural or calculation errors. A student who identifies a four-sided curved figure as a quadrilateral may not recognize that quadrilaterals are formed by four straight line segments. Conceptual errors are the hardest to address and require planning and consistent practice to overcome.
Operations errors
Operations errors - also called calculation errors - can be a major roadblock to students trying to master mathematics. Addition, subtraction, multiplication, and division are at the core of the subject, and mistakes here can cause major frustrations. Many times, operations errors are minor, and students can prevent them by checking their work and taking additional time when solving problems. Repeated operations errors may indicate issues with conceptual or procedural understanding.
Reading comprehension errors
Some would argue that math has become "reading comprehension with numbers." Indeed, mathematics is a language. Therefore, it should come as no surprise that reading comprehension is a major issue in error analysis. This type of error occurs when a student misreads or misunderstands the text. It can stem from a lack of focus, rushing, or the inability to analyze text. Students understand the basic concept and apply correct procedures. There are also no calculation errors. Review the example below:
There are 5 cars and 3 trucks in the parking lot. Write the ratio of trucks to cars in three different ways.
Jon's response: 5 to 3, 5 : 3, and 5 / 3
Jon's response shows that he understands the concepts of ratios and how to write them. Jon's mistake stems from failing to order the objects being compared based on the prompt. Students can avoid reading comprehension pitfalls by highlight key words, close reading, using context clues, and using graphic organizers.
Procedural errors
Procedural errors are mistakes in processes when solving math problems. Errors include incorrect operations, incorrect algorithms, and incorrect or missing steps. This type of error can manifest when students work with the order of operations, for example. Some students will perform multiplication before division and addition before subtraction despite the order of the operations (left to right). Procedural errors also arise when students learn "shortcuts" before understanding concepts. They rely on shortcuts and fail to develop the conceptual or procedural fluency needed to master concepts.
Silly errors
Silly errors are not really silly, but they are the easiest types of error to fix. Many silly error excuses are easy to identify:
"I ran out of time."
"I thought the answer was right."
"I changed my answer."
"I didn't pay attention."
There are two important ways students can combat silly errors: focus and confidence. Focusing on problems, one at a time, can alleviate problems caused by failing to pay attention. Practice builds confidence, which is needed when nervous guts tell students to change the answers, but clear minds know the first answer is correct.
Join the EA CORP!
Click here for student error analysis guide.
Join the conversation on Twitter using #eaCORP.
Further reading:
Simple Activities can Help Reveal Students' Issues with Math Concepts
Is Reading Comprehension the Real Problem with Math?
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