I am debating on whether to buy a class set of basic scientific calculators or graphing calculators for my 7th math /8th math /Algebra 1 classroom. As a High School teacher would you prefer students be more efficient in their handwritten work or more accustomed to using a graphing calculator to simulate and display data to interpret. My instinct is that in the beginnings of Algebra, it is most necessary to know the specifics of what the calculator is doing before you begin to explore via calculator in Algebra 2, Geometry etc. I always feel like if I show them that a computer can do it for them they will never do or find value in doing it for themselves... Thoughts? Insight?

Honestly, you're better off getting Chromebooks. They're more than graphing calculators but there's so much you can do with Desmos and Google Sheets in the Math 7 and Math 8 curriculum that I can't imagine teaching without them. Assuming you're in a common core state, in Math 7 you'll have to "Design and use a simulation to generate frequencies for compound events." I used Google Sheets and taught my students how to use the random command to generate things like coin flips and rolling number cubes, and having them write =if functions to record results. Google Sheets also allows students to create box and whisker plots (Candlestick Charts) which students need to be able to compare/contrast in 7.SP.3 and 7.SP.4. In Math 8, students have to start understanding correlation and lines of best fit for scatter plots (8.SP.1, 8.SP.2, 8.SP.3) and Google Sheets allows you to input data, create a scatter plot, then automatically draw the line of best fit. You can even calculate slope or y-intercept for the data by using =slope or =intercept, then write linear equations for the scatter plot. Desmos also helps with graphing slope-intercept form, systems of equations, even linear equations, far better than a graphing calculator. Then in Algebra, you start hitting things like piece-wise functions, physical application problems of quadratic functions, which shine in Desmos. My students had a project where they had to use shifts of linear, quadratic, and exponential functions to create a "roller coaster" on Desmos by restricting the domain in a piece-wise function. They went further than Math 8 and calculated the correlation coefficient of a scatter plot and interpreted it. At an absolute minimum, get two-line calculators so that when they're calculating volume of three dimensional figures in Math 7 and Math 8, they won't be doing it by hand. Ditto with radicals for distance formula and the Pythagorean Theorem. The only thing I really want them knowing how to do by hand is their integer operations, which I've observed too many teachers spending far too much time on students who will never understand that -2 + 7 is not -9. The SBAC (with the exception of the Number System standards) and everywhere else in the real world provides a calculator to solve problems, I never bought into the argument that "They must know how to divide this 6 digit number by this 2 digit number by hand!"

My son used a graphing calculator in MS, but parents purchased the calculators, not the class teacher. I would recommend putting the requisite calculators on the "needed" list, with only a few available for students not able to provide the necessary calculators for themselves. You have a great big heart, but unless money is no object, families need to have the option of providing the necessary equipment for their students.

I disagree. They do need to know how to "...divide this 6 digit number by this two digit number by hand." They do need to know how to simplify and approximate radicals by hand. They need to know how to do all of it by hand. Only then should they use the shortcuts that a calculator can provide, using the calculator as a timesaver, not in place of knowing the math. Math up through high school calculus isn't "brain surgery" - it's teachable, and understandable by almost all kids, given that it's taught at a developmentally appropriate time, and given enough time to absorb the concepts, and practice. The problem is that we are - not by choice - rushing them through, and also teaching concepts before they are developmentally appropriate. They are not getting the time and practice they need to learn the fundamentals, which means they now seem to "need" the calculator as a crutch. The fundamentals are fun and interesting in and of themselves at the appropriate level. Facility at the fundamentals will help them be able to do, and enjoy, math at the more advanced levels.