Charlotte A. Otto, Susan A. Everett, & Gail R. Luera

Using a Functional Model to Develop a Mathematical Formula

The unifying theme of models was incorporated into a required Science Capstone course for pre-service elementary teachers based on national standards in science and mathematics. A model of a teeter-totter was selected for use as an example of a functional model for gathering data as well as a visual model of a mathematical equation for developing the mathematical relationship for a Class 1 lever, M1D1=M2D2. In this study, 20 student groups (n=72) collected data using the model in an inquiry-based activity. All groups developed the qualitative relationship, 13 groups developed a correct mathematical formula, 6 groups developed one-half of the relationship (X = mass x distance), and 1 group attempted to develop a procedural relationship. The pre-service elementary teachers used a variety of model types in the activity including visual/pictorial, functional/physical and mathematical-both graphs and formulas. The use of the teeter-totter model as a visual and functional model of a mathematical formula was a factor in developing the mathematical relationship.

Identifying Fourth Graders' Understanding of Rational Number Representations: A Mixed Methods Approach

Bryan Moseley & Yukari Okamoto

This study examined average-, high- and top-performing US fourth graders' rational number problem solving and their understanding of rational number representations. In phase one, all students completed a written test designed to tap their skills for multiplication, division and rational number word-problem solving. In phase two, a subset of students sorted cards that showed part-whole, ratio, quotient, measure, and operator perspectives of rational number representations. Each perspective was shown in numerical notational, word-problem, and visual formats. The results indicated that top-performing students scored significantly higher in problem solving and showed more effectively linked rational number representations than the other groups. The results imply that successful rational number problem solving is intertwined with representational knowledge for a wide range of rational numbers and that the bulk of US students do not possess effective skills for working with rational number representations.

Effects of State Tests on Classroom Test Items in Mathematics

Brian T. Boyd

Classroom tests from nine eighth-grade mathematics teachers were collected from the 2003-04 and 2005-06 school years. These years represent one school year prior to the eighth-grade Ohio Achievement Test (OAT) in mathematics being implemented and the year after the eighth-grade OAT in mathematics was implemented, respectively. In addition, teachers were interviewed to determine factors that influence classroom assessment practices. Classroom assessment data were compared between the two years, and interview data were examined, to investigate the impact that the new state test was having on classroom assessment practices. An average of 87% of teachers' classroom assessment items were at the lowest depth of knowledge level during both years. Teachers relied heavily on curriculum materials for their test items, and these items tended to only assess students ability to recall basic facts or perform straightforward procedures. The presence of a state test did not entice teachers to assess students at higher depth of knowledge levels.

Conceptual Representations of Flu and Microbial Illness Held by Students, Teachers, and Medical Professionals

M. Gail Jones & Melissa J. Rua

This study describes 5th, 8th, and 11th-grade students', teachers', and medical professionals' conceptions of flu and microbial illness. Participants constructed a concept map on “flu” and participated in a semi-structured interview. The results showed that these groups of students, teachers and medical professionals held and structured their conceptions about microbes differently. A progression toward more accurate and complete knowledge existed across the groups but this trajectory was not always a predictable, linear developmental path from novice to expert. Across the groups, participants were most knowledgeable about symptoms of microbial illness, treatments of symptoms, and routes of transmission for respiratory illnesses. This knowledge was tightly linked to participants' prior experiences with colds and flu. There were typically large gaps in participants' (children and teachers) understandings of vaccines, immune system responses, treatments (including the mechanisms of pain medications and the functions of antibiotics), and transmission of non-respiratory microbial illness. A common misconception held by students was the belief that antibiotics can cure viral infections.