When should I allow a calculator for Pre-Algebra?

[justasque]

Curious...folks who are anti-calculator-- are you anti graphing calculator too? My children are too young for that, and I don't let them use calculators. But I remember having to have a graphing calculator at some point--algebra 1 maybe? I only went through algebra 2 in high school.

 

Yes, at least until the student has a *ton* of graphing experience under their belt. As previous posters have noted, it is only through graphing - plugging in x's to get the corresponding y's, and trying to understand the patterns so you can predict the outcome - that you begin to really understand what each term in the function is doing to the y value as you move through various x values.  And that understanding, in turn, helps you to understand what is happening to the corresponding real-life values in the problem you're working.  If you can graph it by hand, you can start to see why the ball will fall short of the target, and what you would need to change to make it fall closer.  You can see why the ticket sales aren't going to make up the initial investment in renting the theater, and get a sense of how you need to tweak the prices to make it work.  You can see where the trains are likely to cross paths, and thus the best place to put a new station.  You can see where the function begins to be less accurate in estimating the young trafficking victim's age based on their femur length, and adjust your algorithm accordingly so you can better serve their needs.  If you understand the math, you are in a much better position to use it accurately, and also be aware of its limitations.  And the world needs many, many more people who can do this.

[daijobu]

Graphing by hand is also fun!  I enjoyed making those "flower petals" when drawing polar coordinates.  It's also neat to try to draw in 3 dimensions, especially using spherical and cylindrical coordinates.  The endeavor really exercises your brain into seeing in 3D.  I don't know why anyone would want to skip this, especially if they don't particularly enjoy manipulating numbers, here's a chance to create a little art.  

[LEK]

I allow a calculator only when the lesson involves a lot of long and tedious calculations that are not the point of the actual lesson. If there are only a couple of long and tedious calculations on the page that day then she does them by hand but if the point of the lesson is not the actual calculations and there are a lot then I allow a calculator for the answer but only once she has set up the question and done all possible steps to make it as simple as possible. We are using AoPS and I have only allowed a very basic calculator, it just does the 4 basic functions.