At UCLA Lab School, counting means so much more than one, two, three. Professor Megan Franke’s course, EDUC 134: Early Childhood Mathematics Education, introduced me to the importance of counting and operation skills that form the mathematical foundations of early childhood learning. Throughout the course, I explored the creative strategies teachers use to engage children with counting collections. I observed how students exhibit diverse strategies: some arrange the collections linearly, while others classify items by visual attributes such as color, shape, or even type of animal. I witnessed their growing sense of grouping, pattern recognition, and spatial relations, which are crucial to students’ mathematical experiences.
Real-life application problems reinforce mathematical thinking by enabling students to draw direct connections between abstract concepts and their daily lives. The Young Child & Mathematics shares a story of Willa, who counts her piñata candy and decides to evenly distribute them with her friends, intuitively exploring division and fairness (Turrou et al., 2021, p.23). When math becomes tied to familiar objects and spontaneous decisions, children begin to trust their ability to apply quantitative thinking beyond the classroom, in their informal, daily spaces. As Professor Franke reminds us, “Mathematical work is connected, not a sequence of isolated skills that should be worked on in a linear manner” (Turrou et al., 2021, p.17)
A year has passed since I’ve taken this course, and I was given the opportunity to shadow a level-wide counting collections field trip with Intermediate students to UCLA. Students brought their iPads to take photos of large clusters of objects they noticed around campus. Searching for objects, landscapes, or buildings arranged in regular patterns motivated them to pay attention to their surroundings with intention and mathematical curiosity. As students arrived on campus, the buildings they once imagined belonging strictly to daunting college students soon transformed into their mathematical playground.
A student pointed excitedly at the brick-colored tiles beneath her feet, proud to have discovered something countable (Figure 1). Another student collected a handful of hay from a bush (Figure 2). Later, we explored Powell Library (Figure 3), where students were infatuated by the towering shelves and the seemingly endless number of books. Their eyes lit up as they noticed not only how many there were, but how each shelf displayed a rainbow of colors. They eagerly discussed which books to selectively count. One student suggested, “Let’s count only the red ones!” because it was his favorite color, while another argued that counting all the white books would be easier since they stood out among the colored books. What began as a simple photo-taking task became a rich dialogue regarding estimation, categories, and choosing efficient strategies to count.
After taking photos, students gathered back in their classroom to start their counting collections. One student carefully began counting the white bricks in front of UCLA’s Royce Hall by twos, focusing first on the bricks in a single column. After confirming that there were 28 white bricks per column, the group assumed the adjacent columns would follow the same pattern, and decided to add 28 four times.
In figure 5, students who chose to count the light bulbs on the street lamps drew on their operation skills, particularly multiplication and subtraction. They multiplied the number of rows by the number of bulbs in each row, then subtracted three to account for the first row, which consisted of 9 light bulbs while the remaining 3 rows had 8 each. They also documented each lamp separately, labeling one as “big” for the larger, closer bulbs and two others as “small” for the lamp farther away, then combined the three totals to find the overall number of light bulbs in the collection. Observing students’ diverse yet optimal approaches further illustrated that there is no one fixed formula for counting.
Watching the students explore the UCLA campus like a scavenger hunt reminded me that mathematics can empower children to view their world through a lens full of pattern and complexity. By taking ownership of what they wanted to count, their confidence grew as they realized they could uncover mathematics in any space they entered. The joy of counting did not emerge solely from searching for large quantities of objects; it came from the autonomy they felt while learning mathematics as they walked through the world.
References
Turrou, A. C., Johnson, N. C., & Franke, M. L. (2021). The Young Child & Mathematics. The
National Association for the Education of Young Children.
Gayeon Koh is a senior at UCLA majoring in Education & Social Transformation and minoring in Data Science Engineering. She is an aspiring educator with a strong passion for AI curriculum development and the teaching profession, particularly for youth. She joined as a CONNECT Research Intern under Dr. Christine Lee’s supervision in 2024.
Questions about this post can be directed to Dr. Christine Lee (clee@labschool.ucla.edu)