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Teaching for understanding or learning by memorizing?

Here is a news story about, "Reinventing Math Class", although it focuses on 3rd through 5th grades I believe it is relevant to adult education.  Are you an instructor that teaches for understanding or that teaches concepts by showing procedures only?  Like many of you, I struggle with teaching just what the learner needs to pass the GED Exam, make an educational gain, or move up a math level; but I also want my learners to remember what I am teaching them, too.  Teaching for understanding can take a bit more time instructionally because learners need that time to explore, develop, and reflect on what is really going on with the math they are learning.  They may even need to be untaught bad habits they learned when they were in school, which takes even more time. Time is something adult educators do not always have an abundance of with learners since some have spotty attendance or dedication to their education.  So what do we do?

I know what I do, but I would like to hear about what you do in your programs, too.

Here is the link to the news story:

Brooke Istas


S Jones's picture
One hundred

In my experience,there's a significant group of students who don't have enough of the concepts to pass the courses they need.   Taking the same class three times uses up an awful lot of time, too... 

We're working up an 8-session 1-credit module to build concepts to prepare for our Pre-Algebra course. Right now it's for students who've tested into that class but either are repeating or know they've got gaps; the first thing we do is an assessment of their mathematical reasoning. We had a student tell us that the value of the 2 in 425 was "four" -- and when asked "and how did you get that answer?"   "Well, two times two is four..."   he knows enough facts & procedures to land in pre-algebra but his performance on many of the other questions reinforced that he doesn't think of meaning. 

Then there's the fellow who struggled madly with some very basic fraction operations... andwas then discussing with another student that since he was taking one module a semester, and there were five modules in the course, "it will take me a quarter of a decade to finish!"  

It's worth figuring out whether this young man has some strengths in reasoning that we haven't tapped... 

I'm also playing with (okay, right now avoiding by checking email) the idea of developing apps that would target concepts...