I had a discussion last week when reviewing slope that went like this:
Student: Wait, how can you tell if the slope is positive or negative just by looking?
Me: Well, if you imagine traveling on the line from left to right, if you’re moving up the slope is positive and moving down the slope is negative.
Me: (points) So, starting over here … (slides hand) … and traveling this way … this slope is moving up. Starting over here … (slides hand) … this slope is moving down.
Student: But I don’t understand where you start.
Me: You start on the left.
Student: I’m still confused.
Me: (delayed enlightenment) Wait … can you tell your right from your left?
Left-right confusion (LRC) affects a reasonably large chunk of the population (the lowest estimate I’ve heard is 15%) but is one of those things teachers might be blissfully unaware is a real thing. (Note that LRC is at something of a continuum and affects women more than men.)
My own mother (who was a math teacher) has this problem, and has to use her ring finger whenever she needs to tell her right from her left. She reports that thinking about the graph as “reading a book” lets her get the slope direction correct.