By Dr. Eugene Maier
Recently, while browsing J. W. A. Young's classic, "The Teaching of Mathematics in the Elementary and Secondary School," published in 1907, I came across the following statement: "[Examinations] as a test of the pupil's attainments by some outside authority and in accordance with some outside standard... may be regarded as necessary evils and their influence upon instruction as bad... In any system in which all or nearly all hinges upon the result of an examination of some outside authority, the examination is a fact, to which the teacher is compelled to bend his teaching, and no amount of theorizing will ever lead him to do otherwise. Fortunately, this extreme form of examination is by no means predominant in the United States."
I wondered what Young, Professor of the Pedagogy of Mathematics Education in the University of Chicago, would write today, when the "extreme form of examination" of which he speaks has indeed become predominant in the United States. Departments of education throughout the land have turned to statewide examinations as a means of assessing student achievement and, if certain political factions have their way, nationwide tests are imminent. Here in Oregon, "content standards" have been established and statewide assessment which aims to measure students' attainment of these standards has been inaugurated at grades 3, 5, 8, and 10. Further, students must meet the grade 10 state performance standards in order to receive a Certificate of Initial Mastery which, if all goes as planned, will be required for high school graduation by 2003.
Political issues may debilitate the whole process. While, on the one hand, the American public will decry a perceived erosion of standards, on the other hand, as long as society maintains that a high school diploma is necessary for every respectable adult endeavor, parents and other interest groups will insist that their daughters and sons graduate, whatever the circumstances. Already, scoring of the tests has been adjusted. After last year's assessment in which only 39% of tenth graders met the state's standard for writing and 31% met the math problem-solving standard, the scoring method has been changed so that under the new method, these percentages would have been 44% and 39%, respectively. The state school superintendent maintained that the new scoring method was not a lowering of standards but "a much more accurate indicator of student achievement" and a state school board member said, in a deft bit of logic, "I definitely don't see this as weakening standards. The same total number is being called for. It's just that how it's computed is different." Despite these protestations, I suspect the hue and cry over the low scores had something to do with it. And, I suspect, adjustments will continue until a societally respectable number of students meet the standards or, what is more likely, other ways than meeting state standards will be devised to certify the successful completion of a high school program.
Meanwhile, one wonders what the influence of all these examinations on instruction will be. Would Young, if alive today, still view it as "bad?" I suspect so. Even though the nature of the tests may have radically changed over the last century -- and one can't fault the state assessment for its effort to emphasize conceptual knowledge, problem-solving proficiencies and communication skills over rote learning -- Young's basic premise still holds: teachers feel compelled to bend their teaching to the test. One would hardly expect otherwise, when their competency as teachers is judged on their students' scores. Most teachers, faced with this situation, won't focus on the quality of their mathematics instruction, they will focus on getting good test scores.
Unfortunately, getting good test scores doesn't depend on good mathematics instruction. Good math instruction will result in good test scores -- that's certainly the case with the Oregon assessment -- but to suggest to someone that their class' scores will increase if they change their instruction doesn't get an enthusiastic response, especially when there is a simpler, more direct way to accomplish the objective: teach to the test. There are tried and true methods for doing this: gather sample test questions and questions from previous exams, find out about the scoring rubric -- Oregon has Official Scoring Guides -- and then spend time every week or, if necessary, every day, coaching your class on how to score well on the test. Class scores will go up, but that doesn't necessarily mean their understanding of mathematics is any greater. The statement that higher tests scores means more meaningful knowledge is axiomatic at best, one can argue endlessly whether it is true or not.
So is the influence of state assessments on instruction bad? It is in that it diverts the focus of the instruction from the development of the students' mathematical abilities to the development of their test-taking abilities. It's also bad in that it takes tremendous resources, both time and money, to support the whole process What little time and money teachers have these days for their own professional development is being gobbled up by the demands on teachers to acquaint themselves and prepare their students for the assessments.
When it comes to instructional matters, we know teachers tend to teach the way they were taught and their notion of what mathematics is about is fixed by their own school experiences. For many teachers, as for other adults, this consisted of being shown one mathematical procedure after another, practicing them as one went along with little regard for underlying concepts so that mathematics becomes a collection of procedures, tending to the arcane and carried out in prescribed fashion.
But teachers also want the best for their students. Given the financial resources and a risk-free setting, teachers would welcome an opportunity to experience mathematics in a different way. The Oregon Department of Education's Office of Assessment and Evaluation reports that about 1000 Oregon classroom teachers gather for six days at 16 or more sites -- earning $110 per day -- to score the state mathematics performance assessment. Instead, suppose each year 1000 teachers were provided stipends to participate in an all-expense-paid, six-day workshop where they could deepen their knowledge of mathematics and experience for themselves the engaging and effective ways of teaching and learning mathematics envisioned in the Oregon standards. Which would have the most positive influence on instruction? I vote for the latter. I think Young would, too.