My second BSME visit was to a partner school. Every week the BSME students have a visit to one of several partner schools around Budapest. The list is very interesting, and includes many English language schools, elite specialized schools, a school for the blind, and many more.

I was part of a visiting team, invited to learn about BSME, and the program arranged a special visit for us to the Petrik Lajos Bilingual Vocational School of Chemistry, Environmental Protection and Information Technology. This school was founded in 1879, so like many Hungarian schools, has an aura of tradition surrounding it. Many of Hungary’s chemists are educated and trained here. We were hosted by Márti Barbarics, who besides teaching math, is working towards a doctorate in math education.

Márta is piloting a problem-based math curriculum that seeks to actively engage students. This is a curriculum that is based on the Pósa Method, a project that is led by Péter Juhász, another BSME instructor (more on that in a later post). Márta described the project as quite an innovation, as compared to the traditional curriculum.

This was a curious fact, in light of Hungary’s fame and tradition in using problem solving to nurture the mathematical interest and expertise of some of the world’s most famous mathematicians and scientists! In fact, many in the US math circle movement trace the origins of math circle back to Hungary (http://mathcircle.berkeley.edu/program) while others point to Bulgaria, Romania and Russia.

Much of the problem solving method that have had a huge impact on US math education in past decades (and problem solving was quite fashionable, for a time) is encapsulated in George Pólya’s 1945 book, How To Solve It (https://en.m.wikipedia.org/wiki/How_to_Solve_It).

Pólya (http://www-history.mcs.st-andrews.ac.uk/Biographies/Polya.html) ended up at Stanford University. You might be interested in the Stanford Mathematics Problem Book (https://books.google.com.ar/books/about/The_Stanford_Mathematics_Problem_Book.html), or in that the Stanford Math Circle (http://mathcircle.stanford.edu) was founded in 2005.

As another sidetrack, one of Pólya’s most famous talks is, “Let us teach guessing”, and you might be able to find the video online. The workshops at HCSSiM start off with this exploration, called “The Watermelon Problem”, and I’ve find that it is a wonderful way to get the conversation started. [I also found out this fall from a delightful math seminar talk at Bard College, delivered by Moshe Cohen of Vassar, that this problem appeared in print as, “Cutting the cheese”, by J.L. Woodbridge, as problem E554 in the 1943 American Math Monthly.]

Back to the visit to the Petrik Lajos School, Márta had prepared a logic lesson for her students, based on some of Raymond Smullyan’s Knights and Knaves problems (in What is the Name of This Book?) She met with us before the lesson and described her students and her concerns that they might be hesitant toward the lesson, as it differently from the typical lecture mode of delivery. She was ready to explain that logic problems really do appear on the standardized exams, which they might find motivating. Also, Petrik Lajos is a dual language school, so the class would be taught in English.

Márta was partially right! The students did ask those classic questions, like, “will this be on the test?” But soon they were captured by the beautiful problems, and quite engaged. Márta’s students seemed to enjoy discussing each problem, and how to resolve them.

That’s part of the point. Students get engrossed by these delightful problems, and become open to genuinely learning the mathematics underneath, and really internalize the content. When skillfully used, an experienced math instructor can select and sequence good problems into an effective and enjoyable math course.

The Hungarian tradition in mathematical problem solving is now in the process of being rolled out to a wider high school audience, complete with educational studies of efficacy.

I liked what I saw at Petrik Lajos, but was curious to visit more Hungarian math classrooms. In later posts, I’ll write about more experiences I had with BSME classrooms, and two other school visits I was able to arrange independently of BSME.

## Leave a Reply