Annual Report Overviews

The finding that many teachers reported implementing traditional as well as standards-based strategies could be interpreted in at least two ways. On the one hand, perhaps many teachers divide their mathematics lessons into segments such that one part involves investigative practice and another part involves traditional practice. In the classroom observations, a few teachers indeed divided their mathematics lessons into segments with both investigative and traditional instructional strategies. For example, one teacher demonstrated how to represent double-digit addition with ones and tens blocks, had her students play an addition game with those materials in small groups, and then passed out worksheets for them to practice computation. On the other hand, it is possible that teachers describe their instructional strategies in the terms of standards-based practice (e.g., encouraging children to communicate mathematically or to explain their reasoning) without understanding how those strategies can be carried out effectively to influence children’s mathematics competence.

Further examination of teachers’ reports of the activities that children do in their mathematics classes revealed a mixture of strategies (see Table 2). Most of the teachers indicated that children engage in hands-on mathematics activities often or always, and many teachers reported that children solve real-world problems with mathematics often or always in their classrooms. However, some specific classroom activities that distinguish standards-based mathematics from traditional strategies occur less frequently. For example, in less than one-fifth of the classrooms, students often or always worked on an investigation or project that lasted a week or more. In approximately one-fourth or less of the classrooms, students often or always worked on portfolios, models or simulations, or designed or implemented their own investigations. Similarly, in approximately one-fourth of the mathematics classrooms and in one-seventh of the special education classrooms did standards-based assessments in which students provide descriptions or justifications of solutions occur often or always. In contrast, the frequency of children’s work with computers and calculators that teachers reported varied.

Thus, teachers described their own teaching as a combination of standards-based mathematics instruction and traditional practice. However, the findings are inconsistent and probably do not reflect true standards-based instruction. Teachers reported that children were infrequently engaged in activities that characterize investigative mathematics in their classrooms and that children often practice computation and review worksheet assignments. It is possible that teachers employ strategies associated with investigative practice while children engage in traditional activities. For example, a child could be completing addition problems and get help from the teacher. During the interaction, the teacher may encourage the child to explain her reasoning and to communicate mathematically. In this way, teachers could report their own behavior and children’s activities in terms of both standards-based and traditional practice. In light of these inconsistencies, it is unclear from teachers’ self-reports the degree to which standards-based instruction occurs in the district. The following discussion of direct observations from a small random sample of mathematics classrooms in the district illustrates a discrepancy in teachers’ self-reports of their teaching practices and what actually takes place in the district’s mathematics classes.

Ten observations of mathematics classrooms and three observations of special education classrooms provide a snapshot of what teaching practices look like in the ACME project’s baseline year.

Most of the lessons observed in general education classrooms (7 out of 10) covered the basic mathematics content of computation and numeration and number theory. However, some of the lessons (4 out of 10) covered topics that traditionally receive little attention, such as probability and data collection and analysis. The intended purpose of many of the lessons (7 out of 10) was to involve children in higher level thinking through developing and reviewing mathematical concepts. However, some of the observations (4 out of 10) involved traditional lesson designs that focused on children’s memorizing facts, practicing computational algorithms, and drilling addition and subtraction for mastery. Therefore, the mathematics content of the observed lessons were more often traditional than standards-based, but the intended purpose of the lessons was more often standards-based than traditional.

Teachers’ groupings of the children for most of the class activities varied. In the observed lessons of mathematics classrooms, teachers usually organized the children as whole groups (8 out of 10) or as individuals (4 out of 10). Several teachers also had children work together in small groups or pairs (4 out of 10).

The instructional activities that teachers chose for the observed lessons suggest that before implementation of the project teachers used a combination of standards-based and traditional approaches. Table 3 presents frequencies of instructional activities that were observed in each classroom for a large portion of the lesson. In most of the observed lessons (8 out of 10), teachers led class discussions and involved children in exploration of mathematical topics. In about one-third of the observations, children were passive participants while teachers presented information. For more than half of the observations, children were involved in activities that had investigative qualities. For example, they worked with manipulatives, recorded and analyzed data, or played games to develop knowledge or skills. Traditional practices, such as children’s answering textbook or workbook problems, occurred in fewer of the classroom observations.