This is interesting. I teach adults working toward high school equivalency, and I find that these same roadblocks come up for them. One thing that I'm realizing now (as we work on fractions) is that students don't all intuitively understand that if two things are equal, that means they can replace each other. For example, if 1 1/6 = 7/6, then I can choose which expression is most convenient when I am subtracting 5/6. This is a really important concept in algebra, so I'm working on ways to both make it explicit and give students a chance to practice choosing the form of a number that works best for their purposes.
That's a great example! I had never noticed that before but I bet I will start seeing it now. That's also something that's tricky to find good practice for, which is probably why it never sticks for some people.
This is interesting. I teach adults working toward high school equivalency, and I find that these same roadblocks come up for them. One thing that I'm realizing now (as we work on fractions) is that students don't all intuitively understand that if two things are equal, that means they can replace each other. For example, if 1 1/6 = 7/6, then I can choose which expression is most convenient when I am subtracting 5/6. This is a really important concept in algebra, so I'm working on ways to both make it explicit and give students a chance to practice choosing the form of a number that works best for their purposes.
That's a great example! I had never noticed that before but I bet I will start seeing it now. That's also something that's tricky to find good practice for, which is probably why it never sticks for some people.