Edward A. Silver
I am finishing this editorial on Labor Day, a holiday in the United States that is viewed by many as a marker of the end of summer. In the past, most U.S. public schools resumed classes immediately after Labor Day, although in recent years it has become more typical for the school year to begin prior to Labor Day, at some time in August. So it is at this time that I find myself thinking about R and R-the
rest and relaxation that I wish I had gotten over the summer! I hope that the readers of JRME were more successful than the editor in making time for at least some rest, relaxation, and renewal during the summer months. The focus of this editorial, however, is on another version of R and R that is also on my mind at this time: revise and resubmit.
Research Advisory Committee, Standards Impact Research Group
The terrain for mathematics education research has shifted considerably since last year when NCTM Research Advisory Committee (RAC) reported on its activities in JRME (RAC, 2001). New federal legislation (i.e., the Elementary and Secondary Education Act [ESEA], 2001) includes the phrase "scientifically based research" repeatedly (see House of Representatives Bill HR 1614 IH). The National
Research Council (NRC) has released a report, Scientific Research in Education (NRC, 2002b), which provides guiding principles for scientific inquiry and
discusses design for conducting scientific research, in response to increasing controversy about what counts as "scientific" in educational research. The RAND Corporation has supported the work of a Mathematics Study Panel to propose a strategic research and development program in mathematics education.
Wim Van Dooren, Lieven Verschaffel, Patrick Onghena
The study reported here investigated the arithmetical and algebraic problem-solving strategies and skills of preservice primary school and secondary school teachers in Flanders, Belgium, both at the beginning and at the end of their teacher training. The
study then compared these aspects of the preservice teachers' own problem-solving behavior with the way in which they evaluated students' arithmetical and algebraic solutions to problems. Future secondary school teachers clearly preferred the use of
algebra, both in their own solutions and in their evaluations of students' work, even when an arithmetical solution seemed more evident. Some future primary school teachers tended to apply exclusively arithmetical methods, leading to numerous failures
on difficult word problems, whereas others were quite adaptive in their strategy choices. Taken as a whole, the evaluations of the preservice primary school teachers were more closely adapted to the nature of the task than those of their secondary school
counterparts.
Marilyn Carlson, Sally Jacobs, Edward Coe, Sean Larsen, Eric Hsu
The article develops the notion of covariational reasoning and proposes a framework for describing the mental actions involved in applying covariational reasoning when interpreting and representing dynamic function events. It also reports on an investigation
of high-performing 2nd-semester calculus students' ability to reason about covarying quantities in dynamic situations. The study revealed that these students were able to construct images of a function's dependent variable changing in tandem with the imagined change of the independent variable, and in some situations, were able to construct images of rate of change for contiguous intervals of a function's domain. However, students appeared to have difficulty forming images of continuously changing rate and could not accurately represent or interpret inflection points or increasing and decreasing rate for dynamic function situations. These findings suggest
that curriculum and instruction should place increased emphasis on moving students from a coordinated image of two variables changing in tandem to a coordinated image of the instantaneous rate of change with continuous changes in the independent variable for dynamic function situations.
Eric J. Knuth
Recent reform efforts call on secondary school mathematics teachers to provide all students with rich opportunities and experiences with proof throughout the secondary school mathematics curriculum-opportunities and experiences that reflect the nature
and role of proof in the discipline of mathematics. Teachers' success in responding to this call, however, depends largely on their own conceptions of proof. This study examined 16 in-service secondary school mathematics teachers' conceptions of proof. Data were gathered from a series of interviews and teachers' written responses to researcher-designed tasks focusing on proof. The results of this study suggest that teachers recognize the variety of roles that proof plays in mathematics; noticeably absent, however, was a view of proof as a tool for learning mathematics. The results also suggest that many of the teachers hold limited views of the nature of proof in
mathematics and demonstrated inadequate understandings of what constitutes proof.