Guiding Question:
- What is the level of engagement/participation in the math classroom? How are students motivated to participate?
- What are the trends and strategies in teaching and learning in mathematics?
- What techniques do teachers use to guide their students toward a "productive struggle" with math problems and ideas?
My TGC International Field Experience this summer took me to Lima, Peru. Through various presentations and cultural visits in and around Lima, I learned an extensive amount of culture, history, and Peru’s educational system. On the globe, the United States and Peru are relatively close. However, culturally both countries are significantly different in size, language, customs, and traditions.
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In Lima, Peru, I had the pleasure to work with Thalia Calderon, an English teacher at IE Stella Maris. Stella Maris is a school that has been around 50 years and was mostly built by the parents from funding. It is one of the largest schools in this area, serving more than 3000 students in two shifts ranging from 3 to 17 year olds. At Stella Maris technology is used whenever possible but it is very limited throughout the school. There are two technology labs, one for primary and another for secondary students. However, the primary technology lab has only 9 laptops with Internet connection, while the secondary technology lab has 12 laptops with Internet connection. There are 150 tablets that contain learning apps, but do not have Internet connection. The school does not have the capabilities at this time to have wireless connectivity. Several of the classrooms that were visited teachers relied on an LCD projector for their lessons.
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My partner teacher and I, with Thalia’s assistance, were able to visit a wide range of grade levels that included a variety of teaching and learning techniques, such as lectures, group work, student presentations of their projects, and discussions. Our time at Stella Maris included a visit to a Character Education class (4th primary and 4th secondary), Science (4th primary), pre-school, Math (4th primary and 1st secondary), and several English classes (1st, 2nd, 4th, 5th secondary).
Throughout our visit, the teachers constantly reminded students of the classroom rules and procedures when students were not following them, but overall there were no serious behavior issues that we witnessed and the students highly respected their teachers. We also noticed the importance of school cleanliness as at the end of each class volunteer students swept and cleaned up the classroom before the next group of students arrived. Students all came in wearing a clean uniform each day. One of the main differences and that made a big impact on me was that ALL the students came in with all of their school supplies each day. Teachers provided very minimal materials to students. Regardless of the activity, individual or group work, students had to provide the necessary materials, such as poster board, markers, rulers, etc. Having students bring their materials each day reduces loss of instructional time. In each class observed, teachers had the lesson objective posted and students knew the protocol of each activity and wasted no time in completing the task. Also, it seems that teachers in Peru instill in students the importance of taking highly organized notes with foldables, graphs, charts, and were all color coded. It was quite impressive to see at all levels the ability of Peruvian students’ note taking skills.
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In each of the classrooms observed, teachers asked for volunteers and in every case there were many students eager to share their responses, present to the class, or demonstrate their work on the whiteboard. It wasn’t clear to me what motivated students to participate, but they were. It did seem like the teachers were jotting down who participated so it could have been part of the students’ grade.
In the two mathematics classes observed, 4th primary and 1st secondary, the lesson techniques and strategies were quite different. In the 4th primary, the teacher began by reviewing three-dimensional shapes with students including the vocabulary, vertex, faces, and edges. As students responded to teacher questions, the teacher used those responses to either correct student thinking if mistakes were made or continued the discussion. The students used manipulates to create three-dimensional shapes. One advantage was that all students had the necessary materials to complete the task which was to build the given three-dimensional shapes, cube, pyramid, etc. However, a disadvantage, as a teacher, is that all the materials were slightly different. The students were using wooden sticks and play-doh to unite the wooden sticks. Some of the students’ clay was too soft and wouldn’t hold the wooden sticks in place or the wooden sticks were too small. Throughout the activity all the students were highly engaged and focused on completing the figures, including two students with autism. In the end, students were able to complete the figures and discuss the number of vertices, faces, and edges each figure had.
The 1st secondary classroom teacher used a different approach in her lesson. Teacher lectured students and students took beautiful notes. The lesson moved on to students working in pairs. They were completing a worksheet from the previous day that contained real-life math problems on two-step problems involving fractions and decimals. Students were required to demonstrate all of their work. As students completed the problems, teacher would lead a discussion on each of the problems.
Both teachers, due to different age levels and lesson topic, used very different techniques for their lessons. However, in both classrooms all students were engaged in the lesson and completed the task at hand.
Many people often dislike mathematics because it is not solely about getting the right answer, but knowing the process as well. Productive struggle develops strong habits of mind, such as perseverance and thinking flexibly, instead of simply obtaining the correct solution. While learning math, it is not expected at the outset of a problem that students will know how to solve it. However, the key is working through a problem, encouraging students to think while using prior knowledge, and not letting students get discouraged if their initial strategies don’t seem to work. Productive struggle promotes comprehension and mastery of a topic. It also provides students with a variety of options to solve a problem and lessens student dependency on spoon-fed answers.
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In both of the mathematics classes observed teachers allowed for some productive struggle. The 4th grade primary had to use the materials they brought to create prisms. They had to decide if to break the sticks or keep the length as well as decide on the amount of play-doh so that their structure wouldn’t be to heavy and disassemble. In the 1st secondary classroom, teacher used student work correct or incorrect and through questioning had the students discuss the approach the student used in the process of obtaining the solution and determine whether or not the solution was correct based on the context of the problem. Both teachers guided students individually in 4th primary and as a whole class in 1st secondary providing support and emphasis on students and their ideas.
As a mathematics teacher and during my time in Peru, I was interested to learn about the teaching strategies, techniques, and student participation that occur in the Peruvian classroom. However, due to teacher schedules, time was limited in my ability to observe further classrooms and/or speak individually with the teachers. However, with the limited findings I am pleased to learn that students are eager to participate, teachers use various techniques in their teaching and utilize productive struggle to maximize student learning.
My understanding of global education has dramatically changed because it was something I was completely unaware of and now it sits in the forefront of planning my math instruction. I would have to say, with confidence now, that global competencies that are important in my classroom and form part of my lesson planning. From the text, Cosmopolitan Patriots, this line had a big impact on me, “remember that you are citizens of the world” and we truly are. We may live in a specific location, however, we all belong to the same world and our actions affect it. That particular line reminded me of the webinar with Dr. William Gaudelli, when he asked, “who are you?” Indeed, we are defined by “nature”, institutional, discourse, and affinity, but in the end we are truly citizens of the world.