Numerical Magnitude Knowledge
One of my research interests investigates students’ numerical knowledge and whether this can predict later learning. My research in this area uses number line tasks with a variety of types of numbers: positive and negative integers, fractions, and decimals; this work has found that all numbers are not created equal, and, in fact, an understanding of complex numbers, like fractions and negative integers, is more predictive of improvements in algebra than an understanding of positive integers (Booth, Newton, & Twiss-Garrity, 2014; Young & Booth, under review). Through this work I also uncovered that while students do not conceptualize negative numbers entirely in a unique way, their knowledge of negatives is not equivalent to that of positive integers (Young & Booth, 2015).
 Twiss-Garrity is my maiden name.
Improving mathematics knowledge
My second research interest examines ways to improve students’ mathematics knowledge. Currently I am investigating whether the Worked Example Principle can be applied to elementary mathematics. A key part of this project has been working with classroom teachers and content specialists. Including practitioners in the material design has ensured that they are representative of what students are doing in real-world classrooms– thus providing ecological validity. I recently wrote a paper for teachers that explains the benefits of self-explanation prompts, and gives instructions for implementation in their classrooms. I am currently designing studies that explore ways to improve teachers’ knowledge of, and use of, research-proven principles like worked-examples and self-explanation prompts.