My visit to Margaret Island, Budapest, Hungary reminded me about breathing and that everything is about context. Margaret Island is an Island in Budapest where the Hungarians and tourists alike enjoy the outdoors and nature. It is a simple train ride onto the island, but you feel transported to another time and space, where the worries of life are no more. I am still trying to figure out how the people walking by with American accents have dogs. People around me are walking, jogging, carrying babies, strolling, playing, and people watching.

A Hungarian bank holiday commemorating the 1956 Revolution is on Monday, October 25. University students further ignited the revolt; these college students sacrificed their education and their lives for democracy. University students are an essential factor when it comes to making societal changes. The students in 1956 risked their lives and their future livelihoods to build a democracy. I like to think about the Hungarians who decided that the way things were did not work. They stepped into the unknown fight the then current communists. I do not expect to give my life to make changes to our mathematics educational system, but I feel like the urgency around a revolt is needed to make changes in the way we teach mathematics. I believe that teaching any subject can be about building democracy. Teachers can work to ensure that every student has access to rigorous math teaching and learning. Mathematics learning can contribute to the democratic process.

From my experience Mathematics teaching is conducted in basically the same way in the places I have visited (Hungary, England, France, Benin, Brazil, and the United States) all over the world. In these western locations most recently in Budapest, Hungary, there are pockets of teachers, who are experimenting with a democratic, constructivist, problem-solving approach. I endeavor to describe this because, with the description, we have an opportunity to understand how this teaching, more difficult may create an atmosphere of learning for all students.

What does constructivist teaching look like, and why is a democratic process? When you give human beings opportunities to ask questions and engage with difficult topics (even in math), then this is how democracy is promoted. Asking questions and getting answers is why democracy is so difficult. I think learning math in a problem-solving way can only help us engage in what it means to be democratic.

In a previous post, I talked about approaching the teaching and learning of mathematics using a Polya connection to helping students understand and learn mathematics in their context. Using a problem-solving approach requires planning, patience, priorities, and perseverance,

Planning (by the teacher and the student) for a constructivist-focused lesson may require more planning time than of a direct instruction focused lesson. In a constructivist lesson, students need to prepare problems as assigned by the teacher in advance (you know the whole flipped classroom thing) and the teacher must develop a series of problem-based questions for engaging the students in the classroom. These problems cannot be trivial. The teacher must prepare in content and process of learning to succeed in using the constructivist approach. It might take 4 hours to prepare for a single one-hour problem-solving class.

The problem-solving approach requires patience. The Teacher may have to wait while students process their learning and their errors. Patience is a learned behavior, and I believe that integrating technology as part of the constructivist process may be of use to compliment the teacher-student student-student interactions.

Learning about prioritizing covering material or slowing down so that everyone understands the details of the math. Is it possible for the teacher to decide to reinforce understanding via cooperative learning, or should she just keep going just in case she is accused of not covering the material? There are standards (common core), end of the year examinations (in Hungary, typically, at the end of grade 8 and the end of grade 12). If the 8th grader scores poorly then students sorted and selected for the less competitive high schools. And if you do not score well on the end of high school examinations, then you wait a year, or you cannot move forward. There are high stakes examinations in both the US culture and the Hungarian culture. These high stakes exams and processes give students the idea that if something goes wrong, one’s life might be ruined. The ideas about using the problem-solving approach in the classroom cannot ignore the system that our teachers and students exist within. A friend told me that she used to say to her kids, “it is just high school.” Knowing high school is not the end of the world is the correct way of neutralizing the perceptions, but this works I a setting with love and support and a safety net. What if you don’t have a safety net, then high school, or an exam, might be the only avenue to a different life. The pressure to succeed in the system sometimes ignore real learning so that students can meet particular checkpoints. How can we help teachers and students better prioritize?

How can mathematics learning include time for patience and priorities, when the system lets us know that it is not about learning, but about meeting the next milestone in life and learning.

Finally, when I think about my teacher observations, I worry about how we can help new in-service teachers persevere. This morning, I witnessed a teacher allow her students to learn. Right at the beginning of class, when the teacher presented three challenging trigonometry problems, one student said: “we have not done problems like this before.” The teacher said, “that’s right, but we are going to do it together.” The teacher allowed the students to unpack the problems in various groupings, small groups, individually, and on the board alone. Not every student was writing working, but every student was engaged in the process on a continuum. Some students were in shock by the level of rigor, but this was not a direct instruction lesson. Different students took the lead to share their thinking with their classmates. I witnessed this teacher allow her students to learn, no matter how painful it was to watch. This observation is one class, and my call is for more classes to happen this way. I am overwhelmed by how daunting this is. Can I persevere?