Nye, B., Hedges, L. V. and Konstantopoulos, S. (2000). The effects of small classes on academic achievement: The results of the Tennessee class size experiment. American Education Research Journal, 37(l), 123-151.

The results of most previous research on class size have been ambiguous, at best. Most such studies were small and many were non randomized. The question of class size effect has not gone away. The present study, conducted as a part of Project STAR, involved 79 elementary schools in 42 districts in Tennessee. Achievement in mathematics and reading in K 3 was utilized as the criterion variable. In such a massive study, fluctuating class size and attrition were substantial extraneous variables. Further, very small schools were excluded from the study. However, the data analysis was appropriate and the conclusions appeared valid.

The major conclusion was that class size does have a discernible effect on student achievement, a positive effect of sufficient magnitude to be considered a major criterion in administrative planning. The effect was noted across the four grade levels involved in the study. A further finding was that the degree of this effect depended in part on the amount of time the students had spent in smaller classrooms. In other words, students who moved from small classroom to small classroom when transitioning grade levels were prone to do better than those students who were in a small classroom for the first time. In the final discussion the investigators did point out that it is not yet clear how small classes lead to higher achievement. However, the effect seemed clear, and further research should lead to a better understanding of this phenomenon.

Kuth, E. J. (2002). Fostering mathematical curiosity. Mathematics Teacher, 95(2), 126-130.

Problem solving, both within and outside of the mathematics curriculum, has received a significant deal of attention and discussion in recent years. While the attention on problem solving is based on legitimate concerns, Kuth contends that problem posing, typically overlooked in curricular and teaching discussions, is an integral part of problem solving. Drawing on the work of Brown and Walter, the author suggests that a student does not fully understand a problem's solution until he or she can start to generate a new set of related problems that emerge for the initial problem or its solution(s). Kuth maintains that once students begin to engage in problem posing, they are more likely to be motivated to learn more about mathematics, a motivation defined as "mathematical curiosity." Once students develop mathematical curiosity, they begin to explore mathematics as a discipline, not just as a solution to problems posed in a textbook or by a teacher.

The author provides several examples to illustrate how mathematical curiosity can be developed in a math class. While the examples are reasonably sophisticated, they provide good illustrations relevant to the secondary level and/or advanced math classes at the middle level and are built around mathematical problems that most teachers would recognize. Problem posing may lead to important generalizations that students uncover in the process and a deeper understanding of the solution to the original problem. Students are encouraged engage in an open-ended form of mathematical thinking.

Lee, V. and Loeb, S. (2000). School size in Chicago elementary schools: Effects on teachers' attitudes and student achievement. American Education Research Journal, 37(l), 3-31.

Akin to the question of class size is that of school size. Educational literature for decades has been replete with testimonial data asserting that small schools are better than large ones, both for the students and for the teachers. The present study, found in the same journal issue as the Project STAR study on class size, was conducted on 5,000 teachers and 23,000 students in 264 K 8 Chicago schools. Small schools were defined as those enrolling less than 400 students. Three distinct relationships were studied: school size effect on teacher attitude, teacher attitude effect on student learning, and school size effect on student learning.

The conclusions from this study were that (1) small schools positively affect teacher attitude (e.g., collaboration, cooperation, commitment, individual and collective responsibility for student learning), (2) teacher attitudes positively affect student learning, and (3) small schools positively affect student learning. In other words, school size influences student achievement both directly and indirectly through its effects on teacher attitudes.

Bay-Williams, J. M. (2001). What is algebra in elementary school? Teaching Children Mathematics, 8(4), 196-200.

In recent years many middle level mathematics instructors have been engaged in discussions concerning the appropriate age for the introduction of formal algebra. However, this discussion expanded to the elementary level in 2000, when NCTM replaced the K-4 Patterns and Evaluation Standards with a K-12 Algebra Standard. According to the author, the new standard included patterns and functions, part of the original 1989 standard and some topics beyond what had been traditionally considered to be algebra topics at the elementary level. Specifically the standard established four main themes for students in grades K-12:

Bay-Williams provides illustrations of how the new standards can be implemented with examples from first, fourth, and fifth grade classrooms. In summarizing the examples, she postulates three themes for algebra in Pre-K through 5 classrooms:

The author concludes the article by providing several sources for more information, support, and examples.

Penuel, B., Yamall, L., and Simkins, M. (2000). Do technology investments pay off? The evidence is in. Leadership, 30(l), 18-19.

In spite of two decades of hype and billions of dollars spent on technology for the schools, there are still many doubts and some distrust on the part of educators. Perhaps the results of a five year evaluation of the "Challenge 2000 Multimedia Project" can be enlightening. Multimedia Project students were compared to a matched non technology group and assessed on three variables; communication, teamwork, and problem solving. In order to assess the two groups on these skills, the SRI evaluation group gave each set of students a project and then studied how they solved it. Working in teams, students were to develop a brochure that would inform school officials about the problems of homeless persons. The judges, who were blind to group membership, scored the resulting documents on how accurately they represented the key content of information that had been provided, how well they addressed the most likely concerns of their audience, and how well the resulting document integrated text and graphics into an attention arresting brochure.

What were the results? The Multimedia Project students outperformed the comparison group on all three dimensions. Further, when tested on the basic academic skills of the process, the Multimedia Project group's performance equaled the conventional students. How did this happen? In the words of the investigators, "In Project classrooms teachers were more likely to take the role of facilitator or coach. They spent less time lecturing. They asked a greater number of open-ended questions and let students discuss ideas. They encouraged students to solve problems independently. They helped students develop new knowledge and integrate it into their multimedia presentations." Of course, teachers could do most of these things without technology, but will they? Well planned technology use seems to free teachers to be more open and less centrist than is typical in traditional classroom situations.

Schoenfeld, A. H. (2002). Making mathematics work for all children: Issues of standards, testing, and equity. Educational Researcher, 31(1), 13-25.

The teaching of mathematics has been at the very least a topic of intense educational discussion since the Russians launched the first satellite in the 1950s. Failed reform efforts (1960s "New Math"), falling test scores, equity issues in performance, and calls for new reforms have kept the discussions, at times a controversy, alive for nearly half a century. The latest calls for reform in math education came in the 1980s and resulted in a long-term and intensive effort from the NCTM. Schoenfeld reviews the history of math education during the last 50 years and highlights the problems, challenges and societal changes that led to the NTCM revision of standards that started in 1989.

The article is built around the principles of the NCTM Standards: equity, coherent curricula, teacher professionalism, and effective use of assessment and technology. Unlike many articles promoting a change in curricula on a philosophical basis, Schoenfeld offers an in depth look at a study of results from the implementation of the NTCM Standards in a large urban district and offers a summary of results from several other studies that support the need for change. The Pittsburgh, Pennsylvania, schools, serving about 40,000 students, implemented a coherent, district-wide effort to implement a standards-based mathematics curriculum in the 1990s. The district used both New Standards Reference Examinations and traditional assessment information (ITBS) to track the potential changes resulting from the newly implemented curricula. Results considered the level of implementation, compared performance levels of students at the same grade level in pretest/posttest comparisons (program growth), and looked at disaggregated results. Three clear observations emerged from the results of the study:

Schoenfeld clearly offers a research base that reinforces the efforts of the NTCM and schools that have chosen to pursue the Standards based curriculum. In conclusion, the author discusses the issues and obstacles faced by schools and our country if we hope to sustain improvement in math instruction. These issues include: curriculum reform, teaching as a profession, assessment, and ability and mechanisms for evolution

A variety of references is offered for readers wishing to pursue additional information. The real lesson in this article is one that dedicated NCA CASI accredited schools are already familiar with: If one is to succeed in improving achievement, the plan must be based on data, focus on students, have a high level of commitment from all staff, provide adequate training for the staff, be implemented over a long enough period of time to be effective, and be evaluated through a well defined assessment package.

McBee, R. (2000). Why teachers integrate. The Educational Forum, 640, 254-260.

Interdisciplinary studies, the integration of two or more forms of content in one intact and continuous learning sequence, has been both encouraged and intermittently practiced for centuries. Yet, have we ever examined this practice from the standpoint of the improvement of student achievement? Investigator Robin Haskell McBee, Assistant Professor of Elementary/Early Childhood Education at Rowan University, has done precisely that. While admitting that there are formidable barriers to curriculum integration (e.g., lack of planning time, lack of experience with this type of instruction, lack of curriculum guides to use as exemplars, lack of known processes or strategies for developing both the curriculum and instructional processes), McBee surveyed elementary and secondary teachers considered to be expert curriculum integrators by their principals and district administrators. In addition, ten of the elementary teachers were extensively interviewed. Techniques and strategies for integrating content are varied, depending both on the individual teacher and the nature of the content; however, the results in the student learning seemed clear. Students demonstrated:

How do these results sound to you? It sounds to me as if disciplinary integration is a viable candidate for consideration in school improvement efforts. It might even develop more flexible and more knowledgeable teachers.

McColskey, W. and McMunn, N. (2000). Strategies for dealing with high-stakes state tests. Phi Delta Kappan, 115-120.

As the schools of the NCA CASI region move into the performance accreditation mode while trying to deal with No Child Left Behind legislation and state testing requirements, high stakes testing is a concern that has become increasingly persistent and worrisome for schools. "How can we meet NCA CASI expectations and still meet, and do well in, state testing?" This is not an idle or foolish question. There has already been a discernable narrowing of goal selection in school improvement plans, due at least in part to state pressure to excel in the most basic academic areas. Of course, if these areas emphasized by state testing do fit the needs that the school perceives, that is well and good; but there is no question that state pressures are tending to dictate school goals in the NCA CASI improvement process. Another danger, treated in the present article, is that schools often resort to short term (quick fix) solutions in order to show immediate improvement on high stake tests. Authors McColskey and McMunn have reviewed the quick fix approach and make a strong case for more fundamental long-term measures.

McColskey and McMunn do not take the stance that short-term solutions are inappropriate, per se, but that reasonable and meaningful short-term solutions should be combined with long-term approaches that will assure both a broader curriculum for students and excellence in achievement as well. Among typical short-term solutions, the following are mentioned.

There is no question that such strategies will likely produce some improvement in test scores. Contrast these with the authors' suggestions for long term improvement (the reviewers comments are in parentheses):