Article: Exploring Growth Trajectories of Informal and Formal Mathematics Skills Among Prekindergarten Children Struggling With Mathematics, written by Jessica M. Namkung, Peng Peng, J. Marc Goodrich, and Victoria Molfese (appeared in Learning Disability Quarterly 2019, Vol 42(2), p. 80-91).
Overview of the Study
The importance of math skills as students enter PreKindergarten is undeniable for student success in later years. In this article, the authors compare growth trajectories of math skills for typically performing students (TYP) and for those who exhibit math difficulties (MD) in a sample of 281 PreKindergarten students. Students’ skills were measured at the end of PreKindergarten (when students were identified as TYP or MD), the end of Kindergarten, and the end of First Grade using the TEMA-3. The growths and accelerations for the periods were then measured and analyzed within the two subsets of students. The authors concluded their study with results and a discussion for implications.
Informal Skills
The skills studied were divided into 2 categories, formal and informal. Informal skills involve the skills that most PreK students acquire before entering school, and include skills developed from common environmental interactions, such as quantitative conversations with adults or siblings, telling time, hearing or using numbers for counting, or comparing sizes of objects. These skills are largely obtained without the use of conventional math instruction (such as the use of Arabic numerals or operation signs). Informal skills are not formally developed in a school setting and vary vastly due to individual experiences of the students.
Formal Skills
Formal skills, on the other hand, are the math skills primarily acquired by formal schooling. These skills include the understanding and use of the Arabic numeral system, operations, and written computations. As students learn proper symbols and numbers, they are able to apply them to the qualitative informal math skills they have already obtained. The integration of the two skills develops their formal math skills as they become more efficient and fluent with prior informal counting skills. For example, instead of adding by counting the number of concrete objects in two sets, formal math skills allow students to memorize and recall basic addition facts, creating a strong foundation for learning and understanding more difficult mathematical operations.
Findings
The authors uncovered some expected findings, such as the fact that students with MD displayed difficulties with both informal and formal math skills as compared to their TYP peers. However, the patterns of rate and acceleration differed. Surprisingly, students with MD displayed significantly faster growth and acceleration of informal math skills than their TYP peers. Over the course of the study, the students with MD were narrowing the gap in informal skills acquirement and steadily growing toward the same achievement level of the TYP peers. For formal skills, however, students with MD not only grew at a significantly slower rate, but they also accelerated at a slower rate. This indicates that regarding formal math skills, the gap between students with MD and their TYP peers is widening.
The authors explain that the environment plays a large role in the development of students’ informal math skills, but students are subjected to vastly different environments before entering school. The authors cite that many parents prefer to place emphasis on literacy activities (such as reading a book) over math activities (such as counting). Additionally, they report that PreKindergarten teachers tend to focus more on social development than literacy or math. The development of math skills, therefore, seems to be a lower priority in the two environmental settings in which informal math skills would be largely obtained. Though the students with MD in this study exhibited faster growth and acceleration of informal math skills than their TYP peers, their informal skills–which are the necessary building blocks for formal math skills–may not be developed in time to keep up with classroom instruction to which they are already exposed. This would explain why the growth and acceleration rates of formal math skills are slower for students with MD than the TYP peers.
Recommendations
So what can we draw from this research?
- Parents should provide mathematically stimulating environments before children enter PreK. Look for ways to incorporate math skills into everyday activities, such as counting, playing cards or number games, cooking, comparing quantities, and telling time.
- If your student shows difficulties in math by the time he or she enters Kindergarten, remediation should perhaps focus more on formal (and less on informal) skills. Students with MD show an ability to increase their informal skills over time, but the gap in formal skills continues to grow.
- Both informal and formal skills, even assessed as young as PreKindergarten, are strong determinants of students’ future success in math. It is imperative to include math activities in students’ environments as they develop these skills. While literacy and socialization are certainly also important aspects of educational development, math skills should also be nurtured during this time.