Four lessons learned from a BSME Internship

By Cory Saunders, 2016 Spring student at BSM

On Wednesday afternoons, my classmate Erin and I walked ten minutes to Derkovits School in Budapest, Hungary to host a math club for seventh graders. With the guidance of workshops led by Réka Szász and other collaborative resources, we created and led the activities for 4-8 students each week. In this reflection, I have compiled my observations into “lessons” I learned about my teaching.

Lesson One: Strategies for working through a language barrier.

The seventh graders in our group had a particularly strong grasp of English. I was impressed when I was explaining the rules of SET which involves several different adjectives and a concept of “same” and “different.” I was speaking at a normal pace and many of the students showed their understanding by playing correctly.

It was common for some students not to catch all of our explanations. They would explain to their classmates in Hungarian. I appreciated that this extra explaining was not seen as shameful or embarrassing, but rather as a natural and helpful gesture. Erin and I would always be open to explaining again. I noticed that we would rely on the students with the most confident grasp in English to guide the others. I think that this limited the interaction between the quieter students but I hope we provided ways for them to participate verbally or nonverbally.

I was also impressed with how well the students spoke English to us. I often forgot that they were English language learners. The students learn English at an early age and so they are fairly fluent by seventh grade. In that respect, it did not seem like there was much of a communication problem but I still outline some strategies that helped us.

Take an opportunity to practice Hungarian

Erin was much more comfortable with speaking Hungarian than I was. During name games, she would offer to speak in Hungarian so as to model her own language learning to the group. I was much more timid doing this, but I think my fear for looking silly or stupid may be what some students experience trying to speak English to native English speakers. It reminds students that we are much worse at Hungarian than they are at English and perhaps gives them confidence. With the mix of English and Hungarian during quick number games, we often spiraled into collective laughter at the confusion.

Not everything needs to be in English

Oftentimes, a student would show most of their understanding through hand gestures or partial English and we’d ask them to explain to their classmates. For some students, it is a lot of effort to think of a full, fleshed-out explanation in English. Therefore, Erin and I usually offered the option, “You can say it in Hungarian,” to help speed up the process. Sometimes it was less important for us to completely understand their explanation than for them to share their mathematics with each other.

Lesson Two: Mathematical games are great for differentiation.

Réka hosted a wonderful workshop on using mathematical games in the classroom. Often these games were in pairs. The game would be explained and often there would be a condition where one player would win at the end. Then we asked what the “winning strategy” was and who should go first to guarantee this condition. I love these games because as the student figures out the best way to win, they are using math to solve it, often without knowing it!

We played the two-player chip game where students are given 18 chips and students take turns taking 1 to 5 chips. The person who takes the last chip wins. Our students struggled with this and even I had a difficult time keeping track of who had gone first and who would end up being the winner. We had four pairs that day that were going at different paces. I noticed that for students who struggled, it helped to suggestively group the chips in groups of six and then let them discover why that format was useful. For students who had finished early, more questions could be asked, such as changing the initial number of chips, the number of chips that were allowed to be taken, or the winning condition.

In terms of a collaborative game, Erin and I also introduced the students to the Tower of Hanoi problem by using forints as the various-sized disks. For some students, figuring out the minimal number of moves is a wonderful challenge. Others who were struggling were given the minimal number of moves and then tried to see if they could achieve it. Students who finish quickly and want to learn more can easily experiment with four coins instead of three. Erin showed at the end how through recursion, we could actually generalize how many moves we would need in general. We’re not sure how much of that was understood by the students but giving students exposure to the interesting mathematics we’re learning can spark an interest for some students.

Competitive and collaborative

It’s also an interesting dynamic because although we are using the words “game” and “win,” the competitive environment leads to a collaborative environment where both players are trying to figure out the system. Often students of mathematics can be pitted against each other in terms of speed, skill, or creativity — and so the “loser” is actually a “loser.” The type of mathematical games we learned in the workshop are an opportunity for students to realize that “winning” is not really “winning,” but learning about the system is the true end goal.

Lesson Three: Manipulatives and role-playing guide understanding.

In connection to the first and second lessons, having tangible manipulatives is extremely helpful. We found this useful with the mathematical games (Lesson Two) but also later on when we started bringing logic puzzles to the group. For the various riddles involving weights, we would have chips represent the weights. At one point, I even acted as the scale and the students would test out their hypothesis by weighing the weights on the “scale” (my two hands). I just had to designate secretly which weight was the special one and then act accordingly. It also helped that Erin had made a decision tree for them on the chalkboard to organize their actions!

Sometimes preparing the manipulatives required extra time. Erin and I brought in a riddle related to data encryption which involved two people trying to communicate by sending a message through boxes with locks. I made the “box,” “messages,” “locks,” and “keys” for the students and they sent the box across the “ocean” (table). It was helpful with keeping track of which pieces were where. After they had figured out a solution, it was just a matter of refining, replaying, and recording their solution.

At other times, the role-playing was impromptu. Erin and I brought the flashlight bridge problem to the students. It turned out that the number of people in the puzzle matched the number of people we had, so we asked people to stand up and play out their proposed solution. We used a piece of chalk as the “flashlight” and I kept track of the time by holding up fingers on my hand. The students really enjoyed it and I like the idea of dispelling the idea that math only exists on pencil and paper while sitting still in a chair.

Lesson Four: Great planning leads to a great session.

Erin and I got together on Tuesday mornings for half an hour to plan our sessions. We greatly appreciated the suggestions from Réka through the activity log. We planned a warm-up which often was not math-intensive such as Zip, Zop, Zap or Buzz, Buzz. This broke the ice and let students get up and move around to get their energy going. Then we’d plan one or two major activities, such as a game or a set of riddles. We estimated about how much time it took, often overestimating to make sure we had enough time. Lastly, we had a filler activity or a few back-up extension activities. For us, this was the game SET, which students loved playing at the end. Often SET would be a reward for finishing an activity or an incentive. Since SET can be stopped at almost any point, requires little setup, and can be cleaned up easily, it was the perfect “filler” activity.

Along with planning the activities, Erin and I assigned each other to tasks such as “Pick up the colored pencils” or “Choose and print out riddles.” Great communication and fair division of labor made our sessions run smoothly.

Concluding thoughts

The Derkovits internship was a low-stress environment to interact with Hungarian students and share math. We loved to ask the students questions about their lives and classes. There was plenty of autonomy for us to share the activities we wanted but also plenty of support from Réka and our peers who were hosting clubs on other days. Most importantly, Erin and I looked forward to our time at Derkovits School every week. I’ll never forget the excitement of the students speaking rapidly in Hungarian about a puzzle we had presented, bouncing ideas off each other, and feeding off each other’s energy! I remember thinking, “This is exactly what I want my future classroom to look like” as the students were shouting a phrase to each other. I later found out that it meant “I’ve got it! I’ve got it!”

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Goodbye Fall 2016 Group!

Hope to see you again soon!

2016.09.29. Portréfotók és csoportkép a Budapest Semesters in Mathematics Education program tanárairól és diákjairól.2016.09.29. Portréfotók és csoportkép a Budapest Semesters in Mathematics Education program tanárairól és diákjairól.

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Community

At my home school, I hear the word community  multiple times throughout the day, and it is something that we, as a community, talk about constantly.  From my perspective, a community is a place where individuals feel comfortable being themselves while growing together alongside many other unique individuals. This growth may occur by walking through something with someone, by challenging one’s way of thinking, or even more simply, by being present in a time of need.

At my home school, I walk around campus and feel a part of something larger and more important. I feel comforted knowing that the next time I am going through a hard time, there is someone on campus there to support me and walk with me.  I also know that someone in the community is ready to challenge me to think differently about something or to become the individual I am called to be. For me, there is a sense of authenticity, support, and comfort within this community. Little did I realize that one of the hardest parts of studying abroad would be being away from this community that I call home.

Upon arriving in Budapest, I had a desire to find a community that would allow me to fully be myself during my time here. I feel like the community within BSM & BSME is still forming since there are a lot of individuals with different personalities between both programs, but I do see one slowly starting to take shape. I have also found a community within an international Christian fellowship group here in Budapest that challenges me to continue to share the light of Christ, but also welcomes me completely for who I am. This community has welcomed me with open arms and has reminded me of why a community is so greatly important.

One thing that I have noticed from the classroom observations I have done both in America and in Budapest is the need for a community within a classroom. There are multiple reasons for this need, but one important reason is that this community allows for students to feel comfortable asking questions and speaking up when they don’t understand something. The article that our practicum seminar class read today after I had written most of this post describes the community that should be developed in a math classroom as “a community that supports not only mathematical intellect, but also the growth of curiosity, creativity, passion, and the grit needed to persist through challenging problems.” I thought this was an excellent way of describing an environment for students to strive within the math classroom and then use skills learned from this community in their daily lives.

Last week in our practicum seminar class we talked about the importance of math talks – an opportunity for students to talk with each other about what they agree or disagree on in a solution to a problem. These math talks can help students understand the correct and different ways of thinking about a problem and develop a deeper understanding of the current math topic. In order for this to fully happen, there is a need for a classroom community. Students need to feel comfortable speaking up about something they agree or disagree on without feeling like they will be judged; students need to know it is okay to be in a vulnerable situation; students need to recognize that they are expected to help other students learn, not to compete against them; and lastly each and every student needs to feel and experience this classroom culture in order for this community to really form. Without such a community, I fear that some students would be too afraid to speak up when they disagree with the majority of the class.

In order for this community to form, it will take effort both from the teacher and from the students, but that effort will be so worth it in the long run. There is no how-to booklet on how to form such a community either, since each class will be different and form their classroom community in a different way.

I write this post because I have been reflecting on community a lot lately. It has been an important part of my life and I believe an important part of the classroom. I desire for my students to want to learn and because of that I desire for a community to form within each and every one of my future classrooms.

Now I also invite you to reflect on this by asking yourself: How have communities shaped who I am and what role do I see communities playing in my future?

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Spring 2016 Highlights

2016 Spring was a great semester with a tearful goodbye. Some photo memories.

Math Origami Workshop:

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Spherical Geometry workshop:

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Concept Building and Manipulatives class:

Megan made a Tower of Hanoi crochet for the Concept Building and Manipulatives Class, that she also used with grade 6 kids at her teaching internship:

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Practicum visit to the Pósa math camp:

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With Lajos Pósa:

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Discovery Learning with the Pósa Method class:

Visit to the Alternative School of Economics:

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Last class of the semester:

 

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Goodbye First BSME Group

We celebrated the end of the first BSME semester with a party at Réka’s. We ate palacsinta, talked in Russian, and played Dixit. We hope to see everyone again!

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I have been changed for good ♫♩

I heard that often times while studying abroad you change and grow a lot as a person. But before studying abroad myself, I didn’t quite understand the extent of this statement. I assumed it meant that I would collect new experiences and bring back a broadened world view. But as I sit on an airplane from Frankfurt to Montreal and think back to the Zoe who flew to Budapest 4 months ago, I can see that while I have had oodles of new experiences and seen far more of the world, I’m coming home with more than just a collection of memories. My time at BSME has changed me.

I think there is something about the way study abroad programs separate you entirely from your comfort zone in the US that makes you realize what is truly important to you. When I arrived in Budapest I didn’t have any routines established, As a result I found myself constantly making decisions about how I wanted to spend my time and trying to find those things that truly make me happy. As one example, my Budapest friends would probably find this hard to believe, but before Budapest I almost never sang with anyone or in front of anyone besides my family. Being here I have realized that music and singing are one of those things that I absolutely love and I am going to search for ways to continue once I’m home. In the other direction, I have made hard decisions such as realizing that even though I have done track for 9 years, it is something that I don’t love enough anymore to make it worth the required hours of training. I know it’s easy for me to fall into a routine, and I like things that are comfortable and familiar. Change is hard! But being here in Budapest I have realized how important it is to take the time to reflect on why you are doing the things you choose to spend your time on.

One thing that has come into focus as something I love is problem solving, and I have come to appreciate mathematics in a way I haven’t before. Before BSME, I had never been in an environment where friends solve math problems ALL THE TIME whether it is on paper tablecloths at a restaurant or while walking through the streets of Berlin. We were surrounded by math problems that had many different paths to the solution and instead of requiring high level mathematics, caused us to use previous concepts in a new way. This allowed us to not get bogged down by definitions and formulas and fully appreciate the problem solving side of mathematics. One of my favorite parts of the week became Tuesday mornings when before class my flat mate and I would go to our favorite tea shop to have “Posa Breakfast” where we worked on problems posed in the BSME course on The Posa Method. I have realized how much I love thinking about problems from multiple angles and the excitement of coming to a solution after taking the time to struggle through solving it.

Another change I see in myself is a confidence to know that even if I don’t totally know what will happen or what I am doing, if I just make my best decision, chances are it will all work out. There are many places where this lesson comes from: I’ll name a few. One is going to step aerobics class and not understanding the instructor speaking in Hungarian but still being able to follow along and figure out the steps. Another is when my friends and I tried to make pumpkin pie for Thanksgiving and couldn’t find canned pumpkin, or any pumpkin for that matter, so we cooked a squash. Then based on what we could find at the local grocery store we also had to make substitutions for Crisco, evaporated milk, and parchment paper, and after all that ended up with a delicious pie! Or just in general, when I had no idea what the cultural norms were so I gave it my best shot. I am a very indecisive person, and this often times comes from not knowing which option is best and wanting one option to be clearly better before proceeding. While I still have a long way to go with increasing my decisiveness, this term has shown me that it’s ok to just give a decision your best shot based on the information you have at the moment, stick with it, and see where it takes you.

When you study abroad, you have the rare opportunity to see the world from the perspective of another culture. No I’m not a Hungarian, but in Budapest I was not really a tourist either. After 4 months, I feel far more connected to the people and city than someone who only spent a few days there. When you study abroad you are seeing a country from a perspective that is hard to get without being there in person. It is very different to read about the Migrant Crisis on the news and to viscerally feel the pain and confusion of the migrants as they wait at the Keleti Station less than a 10 minute walk from your apartment. Through our BSME visits to schools and talking with students and teachers we were able to learn not only about math education but Hungary in general. Growing up in the US in history class we learn about the global political powerhouses. But what about the smaller countries? We never hear about what it was like to live in Hungary as it kept getting conquered and passed between regimes. While at BSME I had the unique chance to really focus on this often overlooked country’s history. I feel like now the world seems a lot smaller because I have personal connections to places outside of my home country.

Sean ended his last blog post with some song lyrics that have recently resonated with him, and I think I’ll continue his lead. The song that keeps popping into my head is from the musical Wicked and goes:

“Like a comet pulled from orbit
As it passes the sun
Like a stream that meets a boulder
Halfway through the wood

Who can say if I’ve been changed for the better?
But because I knew you
I have been changed for good”

Yes it’s a bit cheesy, but I know this experience at BSME has changed me, and I truly think it has changed me for the better. I was pulled from my normal life, and in doing so I met the most amazing people, learned a ton about math education, discovered a hidden gem of a city that I sadly don’t think I could have placed on a map 6 months ago, and learned a lot about myself. Thank you to everyone I have met in Budapest for making these four months amazing, wonderful, eye opening, educational, laughter filled and utterly magnificent. I am so, so grateful to have had this experience!

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At Pósa’s Math Camp

We spent a day at a Mathematics camp founded by Lajos Pósa. We observed whole class sessions, group activities, and a beautiful view of Budapest. We chatted with students in the break, and Nolan even joined them for a Bughouse Chess game.

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