Lucy and Ethyl were analyzing the linear relationship represented in is table below. Lucy said the unit rate of change was 2. Ethyl said it was -½. Convince Ethyl why she is incorrect and why Lucy is on the right track.
Error analysis activities have been shown to be very helpful for students to confront misunderstandings and clarify their thinking. In particular, they:
Promote higher level thinking.
According to Robert Marzano, error analysis is at the top of higher level thinking skills. It requires students to create, analyze, and even prove their claim.
Aid in conceptual understanding.
The tricky part of having students do traditional algorithms is they sometimes lose the conceptual reasoning behind the steps. When students can find errors in a process and explain it (that part is key), they are really showing a conceptual understanding of the skill or concept
Rather than warning our students about errors to avoid, we can use errors as catalysts for learning by approaching errors as problem-solving situations. For example, a group of students can examine an erroneous procedure and use reasoning with concepts they know to determine why the strategy that was used does not always produce a correct answer.
Ashlock, Error Patterns in Computation, p. 9
Math Practice 3: Construct viable arguments and critique the reasoning of others
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.