# Exploring American Mathematics Education: Insights from Three School Visits

Von Yanyao Zhang

Thanks to the DAAD project “Mobil sein in der internationalen Lehrerbildung,” I had the opportunity to complete a study abroad semester at Columbia University’s Teachers College in New York. During this period, I attended a course on “Teaching Mathematics in Secondary Schools,” which included a weekly seminar and three individual school visits. As a future mathematics teacher in Germany who grew up in China, I found the visits to be incredibly interesting, both culturally and professionally. Therefore, I will dedicate this blog post to sharing my experiences from the three school visits, highlighting both positive and negative aspects related to mathematics teaching.

#### New Explorations into Science, Technology & Math (Nest + m) in Lower East Side, New York City

In general, I like the fact that in American schools each subject has its own classroom, which can be decorated by teachers (See Figure 1). In the Geometry classroom in Nest + m for example, the teachers decorate the walls with numerous motivational and instructive posters, like “We work to understand mistakes because they allow real thinking to happen so we can learn!” and “How to get more useful help in math class”, thus providing practical guidance for students (Refer to Figure 2, 3). This deliberate decoration creates an environment that is incredibly encouraging, supportive, and motivating — an important aspect for a math class setting.

Figure 1: Geometry classroom in Nest + m

Figure 2: Posters in Geometry classroom in Nest + m

Figure 3: Poster “How to get more useful help in Math class”

I was also impressed by how structured and well-planned the lessons were. Each lesson I observed began with a clear agenda. The teachers displayed commendable flexibility while being mindful of time, ensuring students received the necessary time while also fostering productivity. I noticed several NCTM (National Council of Teachers of Mathematics) process standards[1] in action, and it seems to be a standard practice for students to work in pairs or groups, which has the additional benefit of improving their communication and problem-solving skills (see Figure 4). Many exercises were based on real-life or science-related scenarios, which helped students to make connections between subjects and solving problems.

Figure 4: Students solving problems in groups in Algebra class in Nest + m

Besides a very full schedule with many single periods without any breaks for students and teachers, which seems to be common in many public schools in the US, the only thing that I didn’t like so much in Nest + m was how some lessons overly focused on exams. Phrases like “This is very important because something very similar is going to be part of the test” are frequently used. Encouraging exploration and curiosity alongside exam readiness would be a better approach and would enhance the overall learning experience.

**Chaparral High School in Parker, Colorado**

During my visit to Colorado, I took the opportunity to visit Chaparral High School in Parker, near Denver, where my friend’s father works. To begin, I’d like to highlight Chaparral High School’s schedule (see Figure 5). I appreciated the balanced blend of double and single periods, along with two late start days each week and strategically planned periods such as advisement and homeroom. Without double periods, it’d be hard to plan a lesson with group work and really give students time to explore and work on their own.

Figure 5: Chaparral High School Bell Schedule

I was most impressed by an Algebra I lesson in this school. It involved collaborative teaching with several students having special needs. The lesson was well-structured, comprising an introductory problem, the main activities, and exercises. The highlight of this lesson was the main activity, which involved students working in groups of 3-4. Each group was provided with a marble, a PVC pipe, a tape measure, and eight books. Their task was to roll the marble through the PVC pipe from various heights, ranging from 1 to 8 books, measure the distance the marble traveled, and record the corresponding heights in centimeters (see Figure 6). Students seemed to be very involved during the measurement and there was generally a very good learning atmosphere (see Figure 7). The questions on the worksheet help students to develop a conceptual understanding of the topic with self-collected data. I particularly like the inclusion of question 14, which encourages students to think about the scientific way of working, and question 15, which prompts them to reflect on their group work experience (see Figure 6).

Figure 7: Students doing the main activity in the hall

Unfortunately, the teachers did not initiate a discussion about the students’ results in class; instead, they collected the worksheets with the intention of addressing them in the next lesson. I asked the teachers after the class why they chose to move on to other exercises instead of discussing the students’ results. They explained that students progress at varying paces, with some having already completed the task while others had not. When I further inquired why the faster students couldn’t assist their peers who were progressing more slowly, given that they were working in groups, I was told that the faster students typically use the extra time to work on their individual homework assignments. This missed chance to improve students’ abilities in mathematical communication was, in my opinion, very unfortunate.

**Columbia Secondary School in** **Morningside Heights, New York City**

In Columbia Secondary School I observed three Algebra, one Geometry, and one Calculus lessons from four different teachers, including one student teacher. Overall, the lessons I observed felt quite old-school with primary frontal teaching. Take, for instance, the Algebra lesson on “Work with Graphs of Functions”. The teachers, with patient and supportive manner, guided the students through a collective worksheet, serving as a review at the end of the unit in preparation for an upcoming test. While the worksheet itself wasn’t bad (see Figure 8), the decision to complete it collectively was for me not so understandable. Working through the entire sheet as a class seemed to hinder individual progress and communication among peers and to miss the chance for independent thinking.

Figure 8: Worksheets “Work with Graphs of Functions” in the Algebra lesson

Despite having the luxury of a co-op setting, where two teachers collaborate in one class, its potential wasn’t effectively utilized, at least during my observation. There was minimal differentiation and collaborative learning, instead teaching primarily relied on lectures and neglected active student involvement in problem-solving activities. I found this missed opportunity for dynamic, student-centered learning rather unfortunate.

**Conclusion**

In conclusion, I can say that the school visits have been invaluabe in expanding my understanding of diverse teaching approaches in action. The opportunity to observe various methods in different schools, discuss my observations with my professor at Teachers College, and reflect on my future approach to teaching Mathematics has been been a blend of both useful and fun learning experience!

Yanyao Zhang, Heidelberg University

[1] NCTM process standards include Problem Solving, Reasoning & Proof, Communication, Connections, and Representation. These align closely with the „Prozessbezogene Kompetenzen“ outlined in the Mathematik Bildungspläne Baden-Württemberg (Argumentieren und Beweisen, Probleme lösen, Modellieren, Mit symbolischen, formalen und technischen Elementen der Mathematik umgehen und Kommunizieren).

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Autor/in (2024, 23. Januar). Exploring American Mathematics Education: Insights from Three School Visits. *Fokus Lehrerbildung*. Abgerufen am 1. März 2024, von https://doi.org/10.58079/vns3