I am spending my snow day planning for a presentation on technology integrated K-6 math instruction. The focus of my session is on generating student inquiry and keeping technology completely transparent. I am keeping this presentation aligned to state standards and vision, and doing so makes me very uncomfortable. These standards/essential questions/competencies seem to all center around being able to generate a correct answer for a test. This elementary math curriculum framework can be found at the Pennsylvania Standards Aligned System Website. Here's a few phrases I don't particularly care for:
Taken from the 2nd Grade Mathematics list of Big Ideas and Essential Questions:
1. "How do we know when it is appropriate to estimate or when it is appropriate to use mental math for an exact answer?"
The person that included the phrase "mental math" is clueless in the area of mathematics. Estimation and approximation are (in my view) much more "mental" than development of an "exact" answer, yet they are projected here as completely non-cerebral tasks.
2. "Develop extended understanding of multiple models, and properties of addition and subtraction, leading to fluency with efficient, accurate and generalizable methods to add and subtract multi-digit whole numbers and develop quick recall of addition and related subtraction facts. Select and apply appropriate methods to estimate sums and differences or to calculate them mentally."
Again, here they reference calculation as being done "mentally" and estimation as something that's done as an alternative to thinking. I also don't like the use of the words "efficient" and "quick recall" as they imply that the student that adds two numbers in 10 seconds is somehow better than a student that adds two numbers in 10 minutes.
As we move towards common core standards and the like, is this the language that is to be used? If so, mathematics instruction will never be more than an instruction of process. A focus on efficiency over a focus on an understanding of mathematics keeps us at this procedural level. Maintaining that estimation is done non-mentally, now we're completely missing the boat. Right answers are not the most important part of learning mathematics. Isn't it time we start asking our students to experiment and create in their math classes, instead of simply generate the same right answer that 25 other classmates generated?