Solving NYC’s math problem
Math is a problem — one that a relentless onslaught of testing has not solved. Some assume kids are the ones failing, but it’s time to acknowledge that it’s our tests and the curriculum they determine are what’s failing. They have failed to lead to good teaching; they have failed to provoke students’ interest in or even curiosity about math. Instead, they’ve led to poor teaching, created barriers to equity, and led to the wide proliferation of math anxiety. (Just ask the adults you know how they feel about mathematics.)
One recent June morning at the Bank Street College of Education, however, a group of New York City high school kids from across the New York Performance Standards Consortium public schools — schools that use performance assessments rather than most Regents exams to graduate students — demonstrated to a stunned and delighted audience that they know how to solve the problem. The students reflect the ethnic and racial demographics of the city’s public high school population as a whole.
Introduced by Jonathan Katz, director of mathematics for the Consortium, students starred in a morning of mathematics problem-solving with each patiently challenging the participating adults in their small group to “dig in,” explore different approaches to solving the problem they were presented with, use inquiry and perseverance and gain some insight into the beauty and compelling process of thinking mathematically.
The adults, including representatives from the state Department of Education, Board of Regents, the city’s Department of Education, colleges across the metropolitan area, and others interested in learning more about math education were impressed and delighted to be led by the students into a deeper appreciation of mathematics. Students walked them through their own thinking process, read key entries from their math journals, and supported the adults in their group as they too hoped to gain that precious aha moment of understanding and the confidence that comes with meeting a math challenge.
The work of Katz and his team offers an answer to the decades-long problem of math and a way to advocate for change. They hope we can break old habits of teaching to the lowest level of mathematics as enshrined in typical standardized tests, an approach based wholly on procedure: Follow this formula, even if meaningless to you, and you will pass.
If taught correctly, every student can begin to think mathematically. A rich, non-routine math problem — problems that don’t have an obvious or immediate strategy — will challenge students to explore, raise interesting questions, and learn skills in a meaningful context that can then be applied to new problems.
A panel of six distinguished mathematicians and math educators who had participated that morning agreed. Kari Kokka, of the University of Pittsburgh, said students demonstrated a “much deeper understanding” of what they had learned than is usual and that we need to find ways to see this in more math classrooms. Mara Markinson, of Queens College, praised the students for their persistence over time and noted that the problem itself fueled the desire and curiosity to then learn the procedure. Tanya Maloney, of Montclair State College, observed students’ ability to be engaged, go beyond just the procedural, and “think about their own thinking.”
As one student explained: “Working on this problem took me to my limits . . . it’s an amazing problem because it keeps on surprising you . . . . I learned not to judge a book by its cover, since I thought “this is easy” and it ended up giving me a headache, but it was definitely worth it. I see math differently now because math is not only about numbers, it’s about the relationships and all mathematical topics are related to one another. It’s something that you will understand and feel when you work on a problem like this.”
Persistence, engagement, curiosity, questioning.
Why can’t all students share in this experience? Why do so many in students who go through the public school experience wind up with math anxiety and dismiss mathematics with the excuse of “not being a math person”? Why have we continued to limits the many opportunities for teaching the wonder and beauty of mathematics?
We need our elected officials, at the state level and the federal level, to finally acknowledge the failure of the past twenty years of excessive testing and permit mathematics education to flourish in new ways. The state and the nation have nothing to lose, considering the sad condition of mathematics instruction across our schools and the way in which math has been a hindrance to student achievement rather than a means for discovery and learning.