![[Table of Contents]](/icons/up.gif){kind=icon}
In our interviews, teachers in these reforming districts described themselves as being in line with the general directions of reform in mathematics and writing. Comparisons of their questionnaire responses to national studies and to a study done more that a decade earlier in Michigan support the claim that classroom practice in these districts has moved in reform directions. As found in earlier studies of policy influences on school curriculum, teachers seemed more inclined to add new content and objectives than to abandon topics that receive little emphasis on recent reforms.
Although instruction in these reform districts seems roughly consistent with state curriculum goals, similarities between some state goals and national goals mean that teachers may be attending to national trends rather than the state policy instruments, however coherent those state policies may be. We examine the match between reported practice and these general directions first in mathematics, then in language arts.
On our surveys, the teachers reported on the amount of time they devoted to various ways of organizing mathematics instruction and on the time devoted to various topics in mathematics. By looking at the responses to these survey items, we are able to check whether teachers' general reports about their views of state policies are reflected in their instructional practice. Does their sense about the significance of portfolio assessment, for example, correspond with the content they choose to teach?
We must, of course, be careful not to assume that correspondence between instructional practice and policy directions show a policy effect. Such a correspondence might be due to teachers' responses to information about national trends as reported in practitioner journals or at professional meetings, or might indicate that national policy directions were influenced by the practice or goals of classroom teachers like these. However, these reports on practice can be combined with teachers' responses in our interviews and in other parts of the survey about the influence of various factors to get some sense of the role played by policy instruments and other sources of influence and information.
To get a better sense of the particular guidance teachers might perceive in each state's components of systemic reform, we sketch the broad outlines of content emphases for each state and examine teachers' reports of their practice for each state, gaining an impression of the correspondence (or lack thereof) between policy and practice for teachers in these particular schools. We then examine differences among states, both in the reported practice and in the specific direction of curriculum policy in mathematics.
Because few studies of teacher's content selections were completed before the current wave of reform, inferences about change in practice must rest on anecdotal information and on studies that overlap with our focal grade states and grade levels. Working in Michigan, Porter and his colleagues (see references in Porter, 1989) conducted the most systematic studies of mathematics content taught in the upper elementary grades. They found that fourth grade teachers spent more than 80 percent of their time on skills, primarily whole number computation and arithmetic facts. They spent less than 10 percent of their time on problem solving. Moreover, Porter notes that the latter figure is an overestimate of time spent on what reforms advocate, because it included story problems where the operation to use was obvious from the instructional context, as well as situations where students had to figure out what mathematical operations were needed to solve a problem. These figures are consistent with anecdotal reports that school mathematics in the 1980's concentrated on speed and accuracy of computation with whole numbers and on computation with fractions, decimals and ratios.
Table 1 displays the percentage of instructional time teachers in California reported spending on each of ten major content areas in mathematics. It is evident from these data that teachers at both elementary and middle school spread their instructional time across a wide range of topic areas, rather than concentrating most effort on computation as did the teachers described by Porter. Problem solving, in particular, takes up around 15 percent of the instructional time overall. Communication about mathematics also receives substantial attention, especially in elementary school.
The differences between elementary and middle school curriculum follow patterns one would expect from both traditional and reform curriculum recommendations. The amount of time devoted to whole number computation declines, though more than 10 percent of the time continues to be devoted to the combination of arithmetic facts and whole number computation and estimation. Attention to fractions, decimals, ratio and proportion increases, as does time spent on algebra. The time spent on problem solving and communicating about mathematics declines dramatically, perhaps reflecting a tendency to retain the traditional mathematics curriculum more as teachers prepare students for secondary school.
The document lists several specific areas for student learning: whole numbers and numeration; fractions, decimals, ratio, and percent; measurement; geometric concepts; statistics and probability; algebraic concepts; problem solving and logical reasoning; and calculators and computers. As in California, the emphasis is on understanding and use, rather than on rote memorization and hand computation.
Like in our California schools, teachers in our Michigan sample schools reported spending some time in each of the topic areas, even indicating some attention to algebra and to statistics and probability at the elementary level. (See Table 2) Most striking, however, is that a substantial amount of time was devoted both to problem solving and to communicating about mathematics. Although almost 25 percent of the mathematics time was devoted to whole number computation, estimation, and number facts at the elementary level, this seems small in comparison to the majority of time on these topics reported by Porter, who drew on studies at the same grade levels and of Michigan schools.
The state's portfolio assessment system provided more specific guidance regarding mathematics content, especially for teachers in our focal grades--4 and 8. Students were to place exemplars of their work on problem solving in these portfolios. Thus a central message in both the Common Core and the portfolio assessment was that problem solving was an important part of mathematics.
The reports of teachers in our sample schools indicate that they devote substantial time to this area, particularly at the elementary level, where 25 percent of instructional time on mathematics was on problem solving. (See Table 3.) Other areas of mathematics also received attention, however, with substantial time spent on whole number computation and estimation at the elementary level and on algebra and fractions, decimals, ratio and proportion in middle school. Seventy five percent of the Vermont elementary sample reported they had increased the overall amount of time devoted to mathematics instruction in the past three years. (See Table 3.1.) The increase of time may reflect the time needed in implementing the portfolio assessment.
The similarities among schools at the same grade level and the difference between grade levels are much more striking. At the elementary school level, it is clear that in the schools we selected--chosen from districts with a reputation for reform problem solving and communication about mathematics are major areas of emphasis, taking up about 30 percent of the time on mathematics between them. Whole number computation, estimation, and number facts take up about the same amount of time, but seem to receive substantially less attention than in the earlier studies reported by Porter. This apparent shift fits with the emphasis on problem solving in all three states and in national mathematics teaching associations.
At the middle school level, the patterns of content emphasis also run parallel across the schools, but show a shift emphasis from the elementary level. Most striking is the increase from elementary to middle school in the time spent on algebra, from less than 5 percent to about 15 percent and the decrease of time spent on whole number computation by about a factor of 2. These are changes in the direction that would be expected from the progression of the curriculum. One might even have expected a greater reduction in time spent on whole number computation and estimation, especially given the reputation of these districts for reform.
In addition to asking about mathematics topic areas, we also asked teachers about emphasis on various possible student objectives. This question has parallels on both the NSFMQ and NELS surveys. For this report, we focus on those areas for which such comparisons to these national samples are possible. For middle school, Table 4 shows the means for NSFMQ 5th-8th grade teachers and the NELS and RUC secondary school teachers.5
Vermont and Michigan middle school teachers report that learning to explain ideas in mathematics effectively receives strong emphasis compared with their other objectives and relative to NSFMQ. (See Table 4.) This seems consistent with what these middle school teachers reported about the amount of time devoted to problem solving and to communicating about mathematics. (See Tables 2 and 3.) California teachers, however, report that they give relatively little emphasis to learning to explain ideas in mathematics effectively as well as saying that they give relatively high emphasis to learning algorithms. (Table 4.) This finding is also consistent with what California teachers report about the amount time they spend on communicating about mathematics. Table 1 indicates that the amount of time devoted to communicating about mathematics drops from 13 percent at the elementary level to 5 percent at the middle school level. Once again, this probably reflects teachers' tendency to retain the traditional mathematics curriculum more as teachers prepare students for secondary school. It is worth noting, however, that Vermont and Michigan middle school teachers in our sample schools also emphasize a more traditional mathematical middle school curriculum (Tables 2 and 3), but they maintain their emphasis on helping students learn to explain mathematical ideas. Finally, we note also that Michigan teachers give especially low emphasis to applications in science and business and industry.
We can also make parallel comparisons at the elementary school level, except that we only compare to the NSFMQ 1st-4th grade sample. (See Table 5.) The NSFMQ 1st-4th grade teachers give highest emphasis to problem solving, concepts, and applications to everyday life; they give least emphasis to applications in business and industry, applications in science, and algorithms. Our elementary sample in all three states adds learning to explain ideas in mathematics to this list of most emphasized objectives. Teachers in Michigan and California also place heavy emphasis on increasing student interest in mathematics. Vermont teachers report more emphasis on learning algorithms, and teachers in Michigan and California report lesser emphasis on computation than the national sample.
Use of technology in mathematics instruction is advocated by many reformers. In these reform districts, almost all teachers report using calculators, but use of computers in mathematics instruction is rare. About half the elementary teachers reported some use of computers. Only a quarter of the Vermont and California middle school teachers reported such use, while none of the Michigan middle school teachers used computers (Table 5.1).
We start with a brief sketch of each state's content emphases and then consider teachers' survey responses in light of these. We then examine reported practices between states and account for differences by considering the specific direction of states' reform policies.
The survey data reflect some of these aims. Writing instruction at the middle school level, for example, focuses most on the process of writing. California middle school teachers report spending over five hours per week on having students draft, revise, proofread, and edit their writing. Considerably less time (two hours per week) is devoted to spelling, handwriting, and grammar and punctuation.
Reading instruction at the elementary level also reflects the aims of reform. Teachers report that during reading instruction their students spend three and one-half hours per week on comprehension strategies and responding to what they read. The least amount of time is spent on word recognition skills (30 minutes) and phonics (19 minutes). While students participate in a wide range of activities during reading instruction, there is some evidence that teachers give more emphasis to activities consistent with the direction of reform. Reform documents suggest that students gain a better understanding of what it is they are supposed to learn when they "are asked open-ended questions and invited to explore many possible answers" (English-Language Arts Framework, 1987, 15). Teachers report that students spend the highest percentage of instructional time understanding concepts. Teachers also devote a high proportion of instructional time to such activities as questioning, analyzing, and applying. Considerably less time is devoted to memorizing and classification activities (Table 6).
One other area of response also reflects another reform recommendation. California emphasizes "a literature-based English language arts curriculum that engages students with the vitality of ideas and values greater than those of the marketplace or video arcade" (English-Language Arts Reforms, 1987, p. 7). Elementary teachers in our survey report that their reading instruction is literature-based. When asked what percentage of time in reading instruction is spent on different sorts of reading materials, such as reading or subject basals, literature trade books, workbooks/worksheets, or something else, teachers say that 80 percent of instructional time is spent using literature trade books.
The survey data suggest that Michigan teachers in our study emphasize reading content that matches the direction of reform in the state. Teachers had not increased the amount of time devoted to reading over the past three years. However, both elementary and secondary teachers in our study indicate that they spend most instructional time on comprehension strategies and encouraging students to respond to author's intentions. As Table 7 indicates, teachers report spending over three hours per week on comprehension strategies and having students respond to what they read and barely over one-half hour per week on basic skills, such as phonics and word recognition.
There is some question whether teachers integrate reading into other subject areas as recommended by the reform documents. Michigan teachers in our survey say that they integrate reading with instruction in other subject areas, but when asked what instructional materials they use during reading instruction, teachers report that subject basals receive no attention. (See Table 8.) Based on our teachers' reports, some components of the language arts reforms, notably integrating reading into other subject areas, has not taken hold, while other components, such as activities related to students constructing meaning from texts, have.
Vermont's writing assessment program preceded the publication of the Common Core but nonetheless reflects its aims. Vermont's portfolio-based approach to writing assesses student writing in five areas: purpose, organization, details, voice/tone, and usage/mechanics/grammar. The writing portfolio assesses both the stages of the writing process (prewriting, writing drafts, editing, etc.) and the mechanics of grammar and spelling.
This combination of emphases is reflected in the survey responses. Elementary teachers spend nearly two hours a week on spelling, grammar/punctuation and handwriting. They spend over three and one-half hours a week on various stages of the writing process. Teachers report their students spend the most time per week writing drafts (70 minutes) with spelling (73 minutes) and grammar/punctuation (57 minutes) also receiving a larger proportion of instructional time. (See Table 9) Middle school teachers report a similar emphasis on both mechanics and the writing process, with relatively more emphasis on grammar, prewriting and editing activities. Insofar as Vermont's writing reform reflects an emphasis on both the process of writing and mechanics, teachers' survey responses are consistent with the direction of reform.
The emphasis on cooperative learning groups in California is reflected in survey comparisons. As already noted in our examination of individual states, both Michigan and California's elementary teachers report instructional practices that encourage students to construct meaning from texts. As Table 10 shows, both state's teachers also report spending roughly the same amount of time per week on reading instruction.
The organization of instruction, however, differs considerably. Michigan teachers emphasize more whole group and individual activities during reading instruction than their California counterparts. California teachers spend over four and one-half hours per week with students engaged in small group reading activities, such as working in pairs or teams and small group discussions; Michigan students spend less than two and one-half hours per week in these kinds of activities. (See Table 11.)
Careful readers will note that the sum total of time teachers report they allocate to each reading activity (Table 11) is greater than the amount of time per week teachers report teaching reading (Table 10). This probably reflects teachers' perception that time allocated to one reading activity may also be time allocated to another. For example, teachers may have thought that time allocated to small group discussions and small group lessons should also be included when reporting the time allocated to students working in teams or pairs. Though this explanation may not account for all discrepancies, we think that the larger proportion of time California teachers report spending on small group reading activities reflects a real difference in instructional practices between Michigan and California teachers in our survey. This difference is consistent with the emphasis given to dissimilar aspects of the language arts reform policies in the two states.
California and Vermont middle school teachers of writing both fit the general pattern of moving in the general direction of reform efforts, while continuing to give some weight to more traditional topics. The curricular guidance from both states stresses process writing. California emphasizes "a writing program that includes attention to the various stages of writing process from--pre-writing to post-writing." Vermont's Common Core underscores that a student should "understand and employ a writing process" (p. 3). While teachers in these two states do spend a great deal of time on the components of process writing, they also emphasize components of the mechanics of writing, such as spelling, grammar, and punctuation. (See Table 12.) As with other information on content emphasis, teachers may be following state guidance in their emphasis on process writing, or they may be responding to messages from other sources, such as the various writing projects.
[Perceptions of Influences on and Control of Instruction]