I would like to thank Dr. Karen Karp, my advisor and dissertation chair. Dr. Karp has long been a most supportive and encouraging mentor to me. As a student in her class and especially as her doctoral student, Dr. Karp inspired me to think critically and she has always expected me to succeed. I have the deepest respect and admiration for Dr. Karp.My words can never fully express the level of gratitude I have for the innumerable instances of guiding, supporting and teaching I have received from Dr. Karp. I thank Dr.Karp for the role she has played in my academic career. The purpose of this study was to investigate the impact of two different policies for implementing new mathematics standards in two schools, for grades two through five, on student understanding of the equal sign. The study also examined teachers' knowledge of the equal sign. The research used a mixed methods design to explore differences in student understanding of the equal sign as a result of how standards were implemented in two adjoining states with two different decisions as to when the standards would be implemented. This dissertation shares research that may be of interest to teachers, administrators, teacher educators and other stakeholders.The main constructs under investigation were student understanding of the equal sign, teacher knowledge regarding the equal sign including how it is taught and assessed, and the impact of different implementation schedules for new mathematics standards on student performance on their knowledge of the meaning of the equal sign -a standard that was not previously explicit in either state.The study was conducted in two adjoining Midwestern states in three separate schools (fifth grade students from one of the states are housed in a middle school building vii for overcrowding reasons and are equivalent to fifth grade students in an elementary setting). Each school as per their state mandates, followed the timeline for new mathematics standards implementation with one school in the fourth year of implementation and the other two (same district) in their first year.The sample was 1,182 students in second, third, fourth and fifth grade and their forty-two classroom teachers. Students and teachers from the three schools were given the Mathematical Equivalence Knowledge Assessment (MEKA) as a measurement of teacher knowledge and student understanding of the equal sign. Data from teacher interviews and surveys were used to complement findings related to their students' understanding of the equal sign and their classroom practices related to this topic. A hierarchical linear model was used to detect differences between student scores on the MEKA in each school in the two states.To determine the impact of teacher knowledge of the equal sign on student understanding of the equal sign an unconditional hierarchical linear model and a follow up ANCOVA were conducted using the MEKA results from both teacher and student participants. The same model was also used to detect significant differences found between student sc...

A sequence of five activities, progressing from concrete to abstract, can help students develop deep understandings of the mean.

An interdisciplinary activity connects mathematics and art from The Barnes Foundation museum in Philadelphia.

The dietary guidelines illustrated on the USDA's Choose My Plate diagram can also provide healthy portions of data analysis, health education, and cultural responsiveness.

Within a single internet search, thousands of results occur when looking for a lesson or mathematics activity. However, the results are not all of good quality. We present a mathematics lesson planning protocol (MLP2) to help process the search results and offer experiences of teachers using the protocol.