Calculators help adults, speeding up tiresome divisions of real world money problems, for example.Calculators help explore high level mathematics by utilizing repetitive graphing techniques, for example.
The question is: For basic arithmetic, simple graphing, fundamental equation solving, and other low-level skills, does the use, or the use prior to mastery, of calculators make children less capable of learning higher levels of mathematics?
What do students think?
What do parents think?
What do math teachers think?
How early is too early for each concept?
How does this compare to other technological advancements, such as spell checkers or search engines?
How much of the basics in math should be required without a calculator?
Which students are most affected by this phenomenon?
How do we compare internationally with our use of calculators in schools?
I have long thought a reorganization of current resources may solve many of the problems with math education in the early years. Most of us will probably agree that if children do not learn math early, they are most likely not going to excel at math later; in reality, these kids will often struggle just to meet basic levels for testing these days.
Here is a possible plan:
Instead of having 5 teachers on a grade-level be the “know-it-all” for all subjects, which it may be being suggested they are not, perhaps you could have three generalists, one math specialist, and one math/science specialist. In the beginning, these teachers would simply be chosen from those available. As time goes on, however, administrators could hire specifically to fill the math specialist position for each grade level. A massive reorganization would be required, but it makes more sense to me.
This is just the beginning of the idea, but I thought I would throw it out there. This requires no additional money, training, etc., simply a reallocation of the available resources.
Feel free to respond.
[If you respond to a blog post three years late, would anybody read it?]
This is my first post on this new blog. I have a number of ideas to get up on the page, but need to find the time to get it going. This post stems from my doctoral research. I would love to hear what you think about my thoughts.
The current situation for Texas high school math education, generally speaking:
The most advanced students typically take Algebra 1 in 8th grade, Geometry in 9th, Algebra 2 in 10th, Pre-calculus in 11th, and Calculus in 12th.
The least advanced students take Algebra 1 twice-9th grade and 10th, Geometry in 10th and/or 11th, and finish with Mathematical Models and Applications in12th, resulting in a minimum diploma.
Obviously, there are a myriad of situations in between. At worst, though, the least productive high school math students are 3 years behind at graduation. Of course, the level of learning is probably well below as well.
I would like to propose a new system for my pretend high school:
The highest level, in general, would be called a University STEM track, which has Calculus or AP Statistics as the expected final course.
The second level, in general, would be called a University non-STEM track, which has Pre-calculus or AP Statistics as the expected final course.
The third level, in general, would be called a Junior College track, which has Pre-calculus or Algebra 2 as the expected final course.
The fourth level, in general, would be called a Vocational track, which has Algebra 2 or MMA as the expected final course.
The fifth level, in general, would be called a Liberal Arts/Fine Arts track, which has MMA as the expected final course.
These five tracks can all lead to postsecondary educational opportunities, and each more closely relates to the ability, desire, and future plans for individual students.
An Algebra 2 example of how curricula would match the graduation tracks, while not being overly burdensome on teachers follows:
The university tracks(1 and 2) are to be parallel Algebra 2 classes. They should have similar six weeks calendars. The STEM curriculum/course should be more rigorous and in all ways a more challenging math class. Teachers may need to modify pacing, depth, and style, but the curricula should be similar enough as to not be considered a whole different course.
The junior college track would be the present on-level Algebra 2 course and is the stepping stone between the two major level differences. If a child wanted to take a step down from the university track or up from the vocational or fine/liberal arts tracks. It is unlikely that a student will be following a liberal arts track and choose to move to the university STEM track and be successful. However, track switches are possible, and this is a good compromise.
The vocational and liberal arts tracks would, like the university tracks, be parallel course tracks. The major difference, however, would be the theme of the courses pointing to non-mathematical or job cluster math. These math courses would be taught relatively close to the watered down versions that are acceptable today and are considered minimal. Depth of abstract math understanding is not the goal in this class, though learning Algebra 2 methods and thinking is still imperative.
“Placement” tests before 6th grade and 8th grade would be implemented to determine appropriate tracking levels, along with teacher recommendation and input from parents, students, and counselors.
Choice would be the norm, with input being expected from teachers and counselors to best match students with a track.
Additionally, brief, non-comprehensive, parent/student reviews of placement would be conducted semi-annually. If no changes were expected, the process could be bypassed.
Comprehensive reviews would be conducted annually, involving all parties. If no changes were expected, the process could be bypassed.
This is not the final development of the ideas, but a good start towards making high school math education more student friendly.