Sunday, August 16, 2009
Standards Sundays: Grade 5 mathematical reasoning
This is the last set of math standards for fifth grade. It took awhile to write about them. Mathematical reasoning has eleven separate sub-topics - the most out of all five sections.
So you would think it's the most important right? Well, yes and no. It is important. Personally, math more about reasoning and logic than it is about computation. Plugging and chugging is a relatively easy skill to pick up, when compared to, say:
- how to approach a problem (i.e. determining when and how to break a big problem apart into more manageable chunks, which methods to use, sequencing and prioritizing information, etc)
- estimate to see if answer is reasonable
- know when and why estimations are sometimes a better answer than the actual answer
- apply strategies to increasingly difficult problems
- explain mathematical reasoning using pictures, graphs, words, charts, tables, symbols, etc
- perform accurate calculations
- check validity of results (in other words: how do I know I'm right?)
- make generalizations and apply to other situations
Holy cow, I don't think I ever realized this section was so complex until I see this list before me. There are several other, read-between-the-lines, things that these standards address too. Looking at this now, I'm going to confirm that YES, mathematical reasoning is the most important section in the math standards.
However. Of course there is a however. When on earth does Saxon (the most commonly used math curriculum in my local school district) really address these? Uh...NEVER.
Ok, well, not never. But definitely not to my liking. Even when JL created his own curriculum, he focused WAY more on the other topics than on actual reasoning. Of course his students were supposed to justify their answers, but the problems he poised were very pat and conventional. There was definitely very little "make generalizations and apply to increasingly difficult problems."
Hm, I'm reading through the this sections standards again, twice since I started on this post. Some of them are very vague.....and others are a little redundant.....and none of them state any specific level of competency. I guess these only apply to the problems associated with the other topics, but still. Knowing how to "analyze relationships and patterns" spans a spectrum of understanding. Where should fifth graders stand on this spectrum?
Well, in the end, mathematical reasoning isn't important because it isn't really assessed during mandated tests. Don't tell me that multiple choice questions are a good assessor of mathematical reasoning. Seriously, I will throw a book at you if you do.