Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Kate Kline, Ed.D.

Second Advisor

Theresa Grant, Ph.D.

Third Advisor

Mari Levin, Ph.D.

Fourth Advisor

Andy Isaacs, D.A.


Basic facts, mathematics, multiplication, strategies, subitize, visual


The learning of basic facts, or the sums and products of numbers 0–10 and their related differences and quotients, has always been a high priority for elementary school teachers. While memorization of basic facts has been a hallmark of elementary school, current recommendations focus on a more nuanced development of fluency with these facts. Fluency is characterized by the ability to demonstrate flexibility, accuracy, efficiency, and appropriate strategy use. Despite recommendations to focus on strategy use, there is insufficient information on instructional approaches that are effective for developing strategies, particularly for multiplication facts. Using visual imagery with dot patterns has shown potential for encouraging numeracy and thus provided the basis for this study on multiplication facts.

The purpose of this study was to determine if visual imagery in the form of Quick Looks could promote the development and internalization of multiplication fact reasoning strategies, thus leading to greater fluency. The study was conducted during the 2021–2022 school year and involved three experimental third-grade classrooms from two different districts who received instruction using visual images. Corresponding control classrooms from the same districts received instruction from the district-adopted mathematics curriculum. Participating students (26 experimental, 25 control) were interviewed on their basic fact knowledge at five different times during the school year and writing assignments were also collected during the same time frame.

Using a mixed-methods design, experimental and control classrooms were compared with respect to student progress towards fact fluency, the types of strategies used by students, and overall multiplicative understanding. Analysis revealed that the experimental group made statistically greater gains with respect to all three of these components as compared to their control counterparts. On the final interview, the experimental students had a mean fluency score that was significantly higher than the control group and were also statistically more likely to apply a reasoning strategy than were their control counterparts. Furthermore, a statistically greater proportion of experimental students demonstrated the highest multiplicative understanding level on three of the four interviews analyzed along that dimension. And although both groups demonstrated a wide variety of strategies on the final interview, counting-based strategies remained prevalent among the control students while reasoning strategies were more commonly used by experimental students. Overall, it appears that image-based instruction may encourage greater progress towards multiplication fact fluency.

Access Setting

Dissertation-Open Access