PLENK2010 Why do I consider my booklets unique? I am not writing about the usual things things that math books write about. My books do not have pages of drill exercises. There are lots of writers who have made those books. The problem I have seen, and write about, is the lack of comprehension of reading and writing word problems.
Most of the students I have encountered can and do learn to manipulate the numbers, but they don't really understand Algebra because they don't quite understand that it is a language, no matter how often we say "number sentence". They don't understand the grammar of "English sentence" either. Neither do their teachers unfortunately.
I have looked at many math texts for different grades, and various number-crunching methods are demonstrated and called "problem-solving", but NEVER have I seen a text show the lay-out that I was taught to use by my Grade 9 teacher half a century go.
I have asked people of various ages about this way of writing word problems, and there does seem to be a definite cut-off point before which it was formally taught and after which it was expected to be taught by the teacher but never explicitly mentioned by anyone: an open secret that became a closed secret.
The commercial writer of texts did not show the method and their test forms did not leave enough room for the full writing out of a complete word-problem solution nor were sufficient marks allotted to them. Consequently, as they became de-valued, less student and teacher time was paid to the art and now almost no students bother to tackle word problems. But what is the study of mathematics for, but to solve problems?
Another factor contributing to this "knowledge gap" is the subject silo: in high school as in university, each subject has its own dedicated staff of specialist teachers, even if the entire department is represented by one person. When these teachers talk about a "problem student' the discussion generally runs to the "Ain't It Awful" category rather than to the "what knowledge gaps have you observed?" category. The math and science teachers assume that the English teacher has covered everything so that the student can comprehend the text books and write essays, and they, perhaps not willing to tread on the others' toes, forebear to note "English" errors on "long" assignments. Perhaps also, they are at a loss to know what the knowledge/skill gap might be. The teacher of English, not being a specialist in mathematics or science forbears to remark on whatever "bad" writing they see in the others' classrooms. Yet, they are all missing a fundamental nexus of the CORE subjects. Regardless of how we think about what we have discovered, we follow the writing conventions determined by the Scientific Method of Problem Solving laid down by Sir Francis Bacon when we come to share that discovery; the English essay, the scientific experiment note, and the mathematics word problem solution are all laid out following that basic plan.
When my fellow Grade 9 students complained "Another essay! I don't even know where to start!" I wondered at their despair. I never had any trouble. I didn't even think about it. We had two years of lessons in writing essays in Grade 12 and 13. In those days, the last two years of high school WERE college-prep. Now they teach the formal essay in Grade 9 and expect the student to remember the details the rest of his life. They place it in Grade 9, I suppose, because so many students fall out in Grade 10.
It was not until I began to teach Grade 8 mathematics, science and English all together to an Adult Basic Education class that I saw why I had no trouble with high school myself. My mother had prepared me for Algebra by helping me with Grade 8 problems. "Mom, we don't do that in school!" "Maybe not, but bear with me. Let the unknown be x..." When she explained something to me, she always started with the background orientation. Her mother, although never published, had been a constant reader and essayist and poet. Although we had no scientists per se in our family, we came from a long line of farmers, who had the habit of observation and experimentation. The teachers in their high local schools were well read and well-trained. So I "naturally" internalized the pattern of writing that made book-learning easy.
Not everyone is so lucky. Furthermore, I firmly believe that it is the teacher's duty to make explicit these often-unexpressed understandings that create the scholar's culture upon which our economy now seems to rest.