Mistakes in maths are a normal part of the learning process and they are usually used as learning opportunities. Some mistakes are given greater importance than others, due to the cause of the mistake being more important. Let’s look at the reasons for the main types of mistakes in maths: careless errors, calculation errors and misconceptions.

Careless errors usually arise due to a lapse in concentration or rushing through a question, thereby not paying the question enough attention. A student may have written the question incorrectly, transcribed an answer from a calculator incorrectly, input the wrong figures into a calculator, or forgotten a negative sign. Careless errors do not on their own signify a lack of understanding.

Calculation errors involve carrying out incorrect calculations such as incorrect addition, subtraction, multiplication, division or applying powers, leading to an incorrect final answer. With calculation errors, the correct method has been followed, and therefore this type of error does not on its own signify a lack of understanding.

With careless errors and calculation errors students can usually identify and correct their mistake.

Mistakes arising from misconceptions very much signify an issue with understanding the topic. The Education Endowment Foundation (EEF) defines misconceptions as “an understanding that leads to a systematic pattern of errors." With misconceptions, the student is carrying out an incorrect process based on an incorrect conceptual understanding. For example, a common misconception with place value and ordering decimals is that a longer decimal number is larger than a shorter decimal number. A student may identify 2.135 as being larger than 2.3. Unlike careless and calculation errors, it is difficult for students to identify mistakes arising from misconceptions because they believe their understanding is correct.

Careless errors and calculation errors can be avoided by slowing down, re-reading the question, highlighting key words and double-checking calculations.

Misconceptions need to be exposed in order to be addressed, and fortunately, experienced teachers tend to anticipate the misconceptions within each topic. Misconceptions can be exposed and addressed through discussing the topic, using open-ended questions, exploring more than one method for a particular process, and allowing students to explain their reasoning. When students explain their reasoning, their level of understanding is apparent, and any issues come to the fore front.

I will be addressing some key misconceptions each week. Click here to view the first one.

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