## Section 2: Analytic and Personal Essay/Goals

**August 2014**

Goal Statement

I continue to be interested in the development of rational number understanding, but have changed the focus to how teachers understand and assess students’ work with rational numbers.

**Learning Trajectories and Learning Progressions_FINAL**

This analytical piece is inspired by a session that we attended at the 2014 PME conference in Vancouver, Canada. It is an exploration of the recent history of learning trajectories, learning progressions, and the hypothetical learning trajectory.

**May 2014**

**May 2014 Analytical Goals Portfolio II**

**February 2012**

**Goals 2012** *(excerpted)*

It is clear that my major concentration is mathematics education. I have decided not to complete a traditional secondary concentration, and am striving to compose a unique, complementary course of studies.

I am interested in exploring ways of knowing and learning that will shed new light on mathematics learning and teaching. For example, the mathematics used in daily life around the world is replete with clever and adaptive calculations and solving strategies. These techniques may not be recognizable to teachers of standard Western mathematics. That does not diminish their value. As a matter of fact, the new approaches should help shed light on the learning trajectories of all children and inform mathematics pedagogy at all levels. By examining other disciplines, such as Literacy studies, and exploring sociocultural lenses on learning processes, I hope to inform my own epistemological stance on mathematics learning. The end result should be a view of mathematics that is respectful and welcoming to all learners.

**Goals 2010** *(excerpted)*

As a researcher, my interest is in learning trajectories. Current texts and even state and national guiding documents lay out a sequence that I don’t believe reflects the natural learning sequence: much of the research I have read indicates that there are meaningful differences between the order most textbooks present content, and the order in which children develop an idea. As an academic researcher I would like to gather data on the developmental sequence within the mathematical strands, and elucidate the interconnectedness between the traditional strands. I envision that my work will lead to a developmental textbook series that will exploit students’ natural learning tendencies and build deeper comprehension. The critical goal is a fluent adult who is able to model a situation mathematically, or at the very least, one who knows that there is a mathematical principle shaping it.