In Krakow, I participated in one of dr Miosława Sajka’s lessons in the teacher preparation program. Mira had the students actively participate in a variety of activities that they could try in their classrooms, including think-pair-share, as well as three activities that were new to me. In one activity, called dominoes, students had to determine the differences between two solutions and justify why one is correct and the other is not while working together as a team. At the end of the activity, students have a visual representation of different concepts learned throughout the unit. Then, one of Mira’s students led an activity from the book, “Building Thinking Classrooms,” by Peter Liljedahl (a book that has remained on my “to-read” list for quite a while!) In this activity, students were given a task to work on in groups of two or three. The teacher facilitated by answering students’ questions and pausing to address misconceptions. Students from different groups were also encouraged to seek help from one another, which is an aspect of group work I have not seen before. I think that teaching students how to ask each other for help before asking the teacher can be very empowering for them, so I look forward to trying this when I return to the classroom. The class debriefed the activity and discussed strategies they could use to engage reluctant students. All of the activities I observed that day required students to get up and move around the classroom!
On the second day of my visit, I was able to give two lectures on Building Number Sense and Universal Design for Learning during the university’s “Mathematics Education Day.” It was inspiring to see so many future teachers attend! I led some activities from Jo Boaler, Steve Wyborney, and Fawn Nguyen, and then explained the basic theoretical framework of Universal Design for Learning, along with some examples of what UDL might look like in the secondary math classroom.
On the third day of my visit, Mira and I visited a local primary school and observed one of her former students from the teacher preparation program. In Poland, primary school goes until grade 8, and students switch to different teachers for different subjects starting in grade 4. We observed a 4th grade class and then a little bit of an 8th grade class. I think this may have been the best math lesson I have seen since arriving in Europe. Students were engaged in creating rectangles of different areas in order to explore the relationship between area and perimeter. The teacher, Martha, did some direct instruction, but mostly the students were working with their partner while she circulated the room to check for understanding and provide extra help.
It was great to see so many students engaged and excited about learning math while being challenged to think deeply and explore the concepts on their own. I appreciate Martha also shared how she helps her older students organize the content; she does not require students to keep their own notebook, but she organizes the notes on the drive for them. The 8th grade students were enthusiastic about this method, and stated that they prefer it, and they do make use of the materials that the teacher posts for them. Martha also showed us some pictures of her taking her younger students on a trip to the grocery store where she gave them a budget. This activity is closely aligned with my project and I look forward to speaking with Martha again so that I can learn more about what materials she used and how she assessed the students after the activity. I am also reflecting on the effectiveness of a lot of note-taking in my own classroom and thinking about what methods I might want to use next year.