Algebra 1 Negative Numbers The Number System

Positive and Negative Integers

Say something smart in the comments, and then go hang out at Chris Robinson‘s place.

8 replies on “Positive and Negative Integers”

I would imagine they mistakenly took “positive” to mean “non-negative”, so thought the zero would work.

I’m gonna guess that the student might be thinking of negative numbers as “numbers with the little line in front of them” while lacking some of the understanding.

I suspect that this student has a misunderstanding about integers. He might not understand what positive and negative integers are and how they are added to get a negative result. Or he could just be lazy and this seemed like the easy way out.

I’m a professional mathematician and I still make this mistake: I read “positive” and interpret it as “non-negative”. I think I learned it incorrectly long ago. I catch it eventually but it still causes me to misread things.

I think this mistake is very common, and it is not a deep conceptual mistake; it is just a mistake about vocabulary.

I guess they wrote an equation instead of an expression and used 0 as a postive number. I have no interest in whether we call 0 positive or negative. Just ask for two different expressions next time and we will know whether the student was being clever or trying to avoid negative numbers or both.

The difference between an expression and an equation can really become an issue – “solving” expressions, equal signs suddenly disappearing, etc. Students sometimes think that the equal sign just means where you put the answer. It is important to get across the point that a collection of symbols has a value even if you don’t write an equal sign, and the equal sign simply means both sides have the same value.

0 was the best solution the student could come up with for “a positive and negative integer”. The fault lies entirely with the question writer.

The question asked was very straight forward. It asked for one positive and one negative integer. 0 is neither positive or negative. It’s an understandable mistake, but there is nothing wrong with the question.

The question absolutely does not ask for “one positive and one negative integer”. It asks for “a positive and negative integer”. That’s one integer. (How many cats do I have if I have “a black and white cat”? How many sundaes do I have if I have “a chocolate and raspberry sundae”?)

This class of error is very unfair to students – it forces them to choose whether they will answer a different question to the one asked or attempt the (frequently impossible) requested task. Younger students may not have even learned yet that the teacher is fallible and it’s ok to seek clarification.

Comments are closed.