Would the real gatekeeper please stand up?
Removing the First Gatekeeper: Why Counting Matters
They say that algebra is the gatekeeper to higher level mathematics. Others have described fractions as the doorman for the gatekeeper of algebra. (NMAP 2008) Barriers to success in these areas of mathematics lead to inequitable opportunities. Mathematics educators are mindful of these gatekeepers, and work to mitigate their impact.
Actually, though, the sentinel deciding who has the most opportunity shows up for his shift much sooner in a student’s mathematical career. Where is this gatekeeper stationed? He is at the very doorway to learning about numbers, blockading success as students learn counting. I think it is time we sent this unwelcome guardian packing.
Why Counting Matters
We know that the greatest predictor of later success in school is early skill in mathematics. (Duncan et al. 2007) When students begin their education behind their peers, they tend to remain behind throughout their educational careers. The longer a learning gap exists, the more firmly entrenched the issue is, and the wider the gap becomes. (Valerie and Burkan, 2002) We have had the research for over a decade, and yet early childhood mathematics continues to be overlooked and over simplified. Why?
One reason is that this counting gatekeeper is a little hard to see. It doesn’t have a fancy name that reminds people of problems about trains moving at different speeds in the same direction. It doesn’t stack numbers on top of each other in new and exciting ways. It’s rather ordinary. It seems to be, well, too simple.
This watchdog wears the disguise of simplicity quite well. It takes advantage of a teacher’s busy schedule and lack of planning time, waving 99 cent thematic counting pages and shouting “keep moving!” And so, we often do. After all, we just need to teach them to count. That’s easy, right? We forge ahead unaware of later confusions that arise when children don’t learn to count with understanding.
What does that confusion look like?
Ten-year-old students who continue to count every number in order to find totals such as 8 + 5. Or when asked to place 100 on a number line from 0 to 1000, they do the following, failing to see the full continuum and the relationships between the numbers.
Or worse, when we ask these same students for estimates before performing a computation, they give us wildly impossible answers. This lack of number sense becomes a stumbling block as the expectations for each grade level continue to place more demands on students. When a student doesn’t actually understand the purpose of counting or the meaning of quantity, computation and estimation is an exercise in nonsense .
The messages we get from our guiding documents provide cover behind which the sneaky counting gatekeeper can hide. The Common Core for State Standards fails to include prekindergarten. The counting and cardinality standards are only included for kindergarten, and yet research tells us that students are continuing to develop skill at counting until 8 years of age (Clements and Sarama 2009). Students need experiences with counting out objects well beyond “covering their kindergarten standards.” In fact, counting should remain throughout the elementary curriculum, and can shift from counting whole numbers to counting other kinds of numbers like fractions and decimals as students move up the grade levels.
We have been lulled into a comfortable belief that early mathematics is simple. It’s just counting. But we have been fooled. Counting is so much more than saying the words and sliding objects. Students need daily opportunities to count objects, to organize objects, to compare and combine collections, and to estimate. These opportunities need to extend beyond preschool and kindergarten well into second grade and beyond. Students need to be given a purpose for counting with requests such as, “Please get enough markers so that everyone in your group has 2.” Students need to be engaged in real world purposeful counting, helping them attach meaning to the strings of number words that they say.
What can we do?
We need to provide buckets of objects, ways to organize materials, visuals and concrete tools. We need to allow students and teachers the time to simply be curious as students hone their skill and conceptual understanding of this critical milestone. We need to continually push the boundaries of what it means to count. We count in ones. We count in groups. We count by tens and ones. We compare the count. We internalize the count. We expand the count.
We need to provide training and coaching around these ideas in mathematical literacy for early childhood educators. Supporting educators of early mathematics needs to become a priority. Once provided with support and training, educators need time to truly be curious, to observe students at work, to ask compelling questions, to chase down students’ interests, and to have a deep understanding of learning continuums in order to gently nudge students along those pathways of learning. Early programs in mathematics need to be grounded in research about early learners and include an emphasis on developing a lifelong love and appreciation of mathematics.
When this vision of powerful and supported early mathematics is a reality everywhere, we have successfully dismissed the counting gatekeeper. We have made it clear, and we calmly show it the door with this message: You are not needed nor welcome here. Please go. And while you are gathering up your cloak of unimportance and simplicity, feel free to warn your friends Fractions and Algebra. We are coming for them next.
Here are links to networks of educators who are making a difference.
Harvard University Center on the Developing Child
Erikson Institute Early Math Collaborative
References::
National Mathematics Advisory Panel. Foundations for Success: The Final Report of the National Mathematics Advisory Panel. U.S. Department of Education; Washington, DC: 2008. Retrieved from http://www.ed.gov/about/bdscomm/list/mathpanel/reprot/final-report.pdf.
Duncan, G.J, et. Al. (2007). School Readiness and Later Achievement. Developmental Psychology, Vol. 43, No. 6
Lee, Valerie & Burkam, David. (2002). Inequality at the Starting Gate: Social Background Differences in Achievement As Children Begin School.