Teaching adults mathematics

[infornography]

I am an instructor in a small trade school in the Dallas area. I teach several technical certifications.

Most of these require knowledge based learning (ie the type of learning that can be done using just rote memorization). Largely, the students who can grasp cognitive learning will succeed faster than those who rely almost exclusively on memorization, but both learning styles CAN succeed right up until I get to CCNA. For those of you unfamiliar CCNA is a Cisco router related cert. The content is not what is important however, it is the delivery and expectations.

CCNA requires cognitive understanding of the material. There is quite frankly too much information to simply memorize it all and it requires no small amount of math.

I have noticed that some students will grasp these conceptual ideas rather quickly, but those who don't.... often never do. This is very frustrating because as their instructor I want to see all of my students succeed in every module, but for the life of me I cannot figure out a good way of teaching the cognitive learning required for basic binary math in the time required to those who are not used to congnitive learning.

I am wondering if there are any other teachers out there, even ones who teach children, who have run into this problem and have found a solution. They keep wanting to use the same formula for every situation, or at best the same three formulas for a small variety of situations, but situations can vary so dramatically that they really need to understand how to put the formulas together for themselves in order to adapt.

Any ideas?

 

[rjh01]

Can you apply a test to separate those that will be able to grasp it easily from those that will not? Maybe give a lesson or two and then a test. Fail the test and you are asked to leave the course. Maybe with a refund.

I am not a teacher.

 

[infornography]

Well there are two problems with that approach. The first is that we tend to have low enrollment rates as it is and that would lead to a loss in profits.

The second is that even if they fail the course, they still get quite a bit out of it.

I could easily tell you long before a class gets to CCNA who has a chance to succeed and who will definitely fail. However telling this to the students would decrease morale and decrease the effort they put forth, therefore also decreasing what they get out of the course.

I do wish that schools would use more of a cognitive method of learning for the subjects that work with it, such as Algebra and Geometry. To a lessor degree Chemistry, Biology, and English. Probably work some basic logic classes into early elementary school as well. Teaching students to think and ask questions would greatly facilitate their scholastic career.

 

[rjh01]

But here is the summary of what you say
- You only have a few students
- More students = more profit
- You know who will fail and who will pass.

Those that will pass will pass. Those that will fail you then sell them extra lessons (maybe to keep up or sell them something else).

 

[Banbury]

In my experience (with private Math lessons) it's not so much a lack in cognitive thinking, but simply a lack of the basics in Math that is the problem. Try starting with basic Math problems (maybe even school level) and show your pupils how to solve problems with formulas. Then work your way up.
I would even include some Math theory on how problem solving in Math has devolped and what the purpose of it is.

 

[infornography]

Hmm... Interesting approach. Subnetting is a major departure from advanced math however.

It is really basic simple operations done in binary. What gets hairy is that is applied mathematics. The students can do the math itself, they just have a hard time applying it, which is more of a cognitive function.

That does help shed some more light on the exact source of the problem though, thanks. Its kind of like if you had a student that was good at the actual math if given an equation to work out, but could not do word problems well at all.

 

[Banbury]

Well, problem solving is of course a cognitive function . And a function that's not very well taught at schools. I was taught in Math to memorize equations and to apply them to a certain type of problem. This leads to difficulties in carrying over acquired knowledge to other types of problems. I think that's what you're seeing with your students.
You could try to compare the same kind of Math problem first in decimal and than in binary numbers. This might help your students understand that there is actually no difference between those number systems.