I'm lucky that my 5-year-old son comes to work with me each day. His preschool is housed in the high school where I teach 9th and 10th grade. In fact, his classroom is literally across the hall from my 6th period and just around the corner from the room where I teach the rest of the day.
Not long ago, I went in to visit him and his peers during my plan period. He and his little buddies were sitting around a table doing a math worksheet. Two frogs on lily pads plus five frogs on lily pads makes a total of seven. Three frogs jump off and you're left with four. Good stuff for pre-K. Sure, an occasional finger was employed in these basic mathematical operations, but for the most part this computation was quick, confident, and alarmingly accurate for a bunch of pre-K-ers.
I listened as the little folks' conversations about math escalated until those little five-year-olds were adding and subtracting frogs accurately up in to double digits, and I kid you not, I heard one boy talk to another about the "pattern" he saw that the numbers repeated, and yes, he used the word "pattern." He pointed out that if he added three to nine it made 12, and if he added three to NINEteen, it made 22, and if he added three to twenty-NINE if made 32. Good stuff...not every 5-year-old will get that, but it doesn't seem unreasonable that every 15-year-old should.
I work with 9th graders daily, assisting them with their science, math and English homework. These are mainstream, good kids enrolled in "college track" coursework. So often, when I assist them with their math, I see a common problem--the inability to do basic addition and subtraction computation, even of one- and two-digit numbers. I find it astonishing that in the near decade of education between pre-K and 9th grade that such fundamental skills do not get mastered. Where is the disconnect? Why do I have 9th graders who still use their fingers to add numbers under 20 and cannot confidently, immediately state that nine plus three is twelve without stating the answer with the inflection of a question? I've had kids who are combining like terms to find an unknown in Algebra I, such as 3x+7x= 40, and they either pull out a calculator to compute the sum of 3 and 7, use their fingers, or simply guess (eleven?). I hear from my math counterparts that kids actually do well with the overarching concepts of Algebra, but where they fail is in computational fluency. How does this get missed?
I think we need to make our students play Yahtzee from a young age. It should be required curriculum.
I'm not a math teacher and I'm not intending to criticize math teachers. And I'm sure that there are plenty of language arts concepts that other teachers cannot understand why kids haven't mastered ("Why don't they just capitalize the first letter of the sentence! This is AP Bio, for crying out loud!"). How is it, then, that these kinds of basic skills which are masterable by the youngest of our ranks are still the focus of so much energy by the time kids get to high school?