Writing in the Mathematics Classroom: Does It Have an Effect on Students’ Mathematical Reasoning?

In this action research study of my classroom of 5th grade mathematics, I investigate how to improve students’ written explanations to and reasoning of math problems. For this, I look at journal writing, dialogue, and collaborative grouping and its effects on students’ conceptual understanding of the mathematics. In particular, I look at its effects on students’ written explanations to various math problems throughout the semester. Throughout the study students worked on math problems in cooperative groups and then shared their solutions with classmates. Along with this I focus on the dialogue that occurred during these interactions and whether and how it moved students to a deeper level of conceptual understanding. Students also wrote responses about their learning in a weekly math journal. The purpose of this journal is two-fold. One is to have students write out their ideas. Second, is for me to provide the students with feedback on their responses. My research reveals that the integration of collaborative grouping, journaling, and active dialogue between students and teacher helps students develop a deeper understanding of mathematics concepts as well as an increase in their confidence as problem solvers. The use of journaling, dialogue, and collaborative grouping reveals themselves as promising learning tasks that can be integrated in a mathematics curriculum that seeks to cultivate students’ thinking and reasoning.

On Modular Design of Field Robotic Systems

Robots are needed to perform important field tasks such as hazardous material clean-up, nuclear site inspection, and space exploration. Unfortunately their use is not widespread due to their long development times and high costs. To make them practical, a modular design approach is proposed. Prefabricated modules are rapidly assembled to give a low-cost system for a specific task. This paper described the modular design problem for field robots and the application of a hierarchical selection process to solve this problem. Theoretical analysis and an example case study are presented. The theoretical analysis of the modular design problem revealed the large size of the search space. It showed the advantages of approaching the design on various levels. The hierarchical selection process applies physical rules to reduce the search space to a computationally feasible size and a genetic algorithm performs the final search in a greatly reduced space. This process is based on the observation that simple physically based rules can eliminate large sections of the design space to greatly simplify the search. The design process is applied to a duct inspection task. Five candidate robots were developed. Two of these robots are evaluated using detailed physical simulation. It is shown that the more obvious solution is not able to complete the task, while the non-obvious asymmetric design develop by the process is successful.

EXPERIMENTAL INVESTIGATION OF FOLDED PLATE GIRDERS AND SLAB JOINTS USED IN MODULAR CONSTRUCTION

The folded plate girder, a newly proposed bridge girder, is investigated through this thesis. The folded plate girder is cold bent out of a single sheet of steel. The cold bending eliminates the costly and inconsistent shop welds found in traditional girders. The folded plate girder is meant for application in short span bridges. The girder was subjected to an equivalent 75 year lifetime loading to investigate the fatigue performance. The rebar detail used in the closure region between adjacent slabs has been investigated in the past by the NCHRP 12-68 project. This thesis will proposes a hooked rebar detail as a cost effective alternative to the previously recommended headed rebar detail. The proposed hooked rebar detail looks to improve upon the headed bar detail by increasing the clear cover, and reducing the cost of fabrication and shipment of the rebar. Six specimens containing closure regions are subjected to both positive and negative moment loading in order to investigate their behavior and failure modes under ultimate load.