Ask school officials to explain Union City’s success and they start with prekindergarten, which enrolls almost every 3- and 4-year-old. There’s abundant research showing the lifetime benefits of early education. Here, seeing is believing.

One December morning the lesson is making latkes, the potato pancakes that are a Hanukkah staple. Everything that transpires during these 90 minutes could be called a “teachable moment” — describing the smell of an onion (“Strong or light? Strong — duro. Will it smell differently when we cook it? We’ll have to find out.”); pronouncing the “p” in pepper and pimento; getting the hang of a food processor (“When I put all the ingredients in, what will happen?”).

Cognitive and noncognitive, thinking and feeling; here, this line vanishes. The good teacher is always on the lookout for both kinds of lessons, always aiming to reach both head and heart. “My goal is to do for these kids what I do with my own children,” the teacher, Susana Rojas, tells me. “It’s all about exposure to concepts — wide, narrow, long, short. I bring in breads from different countries. ‘Let’s do a pie chart showing which one you liked the best.’ I don’t ask them to memorize 1, 2, 3 — I could teach a monkey to count.”

From pre-K to high school, the make-or-break factor is what the Harvard education professor Richard Elmore calls the “instructional core” — the skills of the teacher, the engagement of the students and the rigor of the curriculum. To succeed, students must become thinkers, not just test-takers.

When Alina Bossbaly greets her third grade students, ethics are on her mind. “Room 210 is a pie — un pie — and each of us is a slice of that pie.” The pie offers a down-to-earth way of talking about a community where everyone has a place. Building character and getting students to think is her mission. From Day 1, her kids are writing in their journals, sifting out the meaning of stories and solving math problems. Every day, Ms. Bossbaly is figuring out what’s best for each child, rather than batch-processing them.