Date of Award

August 2019

Degree Type


Degree Name

Doctor of Philosophy


Urban Education

First Advisor

DeAnn Huinker

Committee Members

Barbara Bales, Henry S. Kepner, Tracy Posnanski


developmentally appropriate instruction, early childhood mathematics education, early childhood teacher education, early mathematics learning trajectory, intentional instructional decision-making, mathematical knowledge for teaching


This qualitative, phenomenological study investigated how fifteen early childhood

preservice teachers’ (PSTs) mathematical knowledge needed for teaching and early mathematics

learning trajectory knowledge impacted the intentionality of instructional decision-making. The

central research question asked: In what ways do early mathematics learning trajectories inform

prospective early childhood teachers’ instructional decisions in ways that are likely to advance

student learning on the subitizing trajectory? The literature review revealed numerous studies

focused on the usefulness of learning trajectory knowledge on prospective elementary and

inservice teachers’ mathematical knowledge for teaching, lesson planning, instruction, and

assessment, but no studies were found regarding early childhood pre-service teachers’

understanding of an early mathematics learning trajectory to guide intentional instructional


A semi-structured interview protocol with stimulus texts was designed to elicit early

childhood PSTs’ understanding of subitizing, the subitizing trajectory, and the influence of each

on their instructional decision-making. Five themes emerged from the analysis of this data

offering insights into the intentionality of early childhood PSTs’ decision-making to advance

student learning: (1) demonstrates an understanding of subitizing, (2) recognizes and validates

the importance of subitizing for young children, (3) articulates learning trajectory progression

through dot arrangements, (4) demonstrates an awareness of the developmental nature of

children’s mathematical thinking, and (5) centers instructional decisions on children’s thinking.

Findings from this study suggest early childhood PSTs (a) demonstrated a keen interest in

understanding children’s thinking and were capable of crafting instructional opportunities that

aligned with the subitizing learning trajectory, (b) developed a complex and nuanced

understanding of the subitizing trajectory, and (c) engaged in a cycle of instructional decision-making

highlighting an intricate relationship between subject matter knowledge, pedagogical

content knowledge, and learning trajectory knowledge.