During Practicum, participants will observe a wide range of Hungarian mathematics classrooms, and will also have the opportunity to teach a lesson themselves. Hence, they will obtain first-hand experience on how the methods learned in BSME are put into practice. Classrooms visited will range from ages 6-19, and will also include different profiles (e.g., mathematics immersion programs, alternative schools, students with disabilities). Participants will take part in pre- or post-lesson discussions with teachers and students.
Most of the classes observed will be in Hungarian, but translation will be provided. Practice teaching will take place in classes where students speak English.
In the seminar portion of the course, you will learn about education in Hungary, reflect on the classroom visits, and use micro-teaching to connect what you are learning at BSME with the educational goals in your home environment.
Credit transfer (to home institutions): Many American institutions have a global/world cultures requirement, in which students must study and reflect on a cultural experience that is outside of the United States. The Practicum course, which involves observations of Hungarian classrooms, interactions with Hungarian teachers and students, investigations of Hungarian society, and reflections on those experiences, would fit well in satisfying such a requirement. For more details, see the Practicum syllabus.
The aim of the course is to introduce the method of teaching mathematics to adolescents, developed by an eminent mathematician and educator Lajos Pósa. The main principle of Pósa’s method is that students discover mathematical concepts on their own through working on tasks that build on each other, all the while having the experience of thinking like mathematicians. The method was originally developed for gifted students in mathematics camps, but it has also been successfully implemented in a more general school setting.
Participants will play the role of students and solve problems from Pósa’s mathematics camps. (These problems will be interesting and challenging for the BSME participants, too!) Furthermore, participants will reflect on this learning experience, and will discuss the principles of Pósa’s method and ways of applying them to their own teaching.
Problem solving has had a long tradition in Hungarian mathematics classrooms, where students learn various problem-solving heuristics such has those identified by George Pólya. In this course, participants will engage with mathematical problems that are directly connected to the secondary school curriculum. Then they will reflect on this learning experience to uncover how to effectively implement problem solving in secondary classrooms.
Mathematical tasks introduced in this course foster a wide range mathematical thinking and reasoning skills: problem solving, problem posing, constructing definitions, conducting explorations, seeing the “big picture,” making connections within mathematics and to the world outside of mathematics, just to name a few. These tasks also call on the teacher to employ a variety of pedagogical techniques/approaches: manipulatives and technological aids, and different lesson formats (e.g., individual work, group work, whole class discussions).
Credit transfer (to home institutions): Many teacher education programs have a “connection to secondary mathematics” requirement, in which students must conduct an in-depth study of secondary mathematics with regard to both content and pedagogy. The PSM course, which investigates the problem-solving heuristics embedded in the tasks from the secondary school curriculum and explores how to implement problem solving in secondary classrooms, would fit well in satisfying such a requirement.
This course examines how concepts in various areas of mathematics (e.g., number theory, algebra, geometry) are developed throughout the K-12 curriculum. We identify specific concepts in a given area (e.g., functions in algebra, transformations/isometries in geometry), and study how they are developed as students play with fun mathematical games and hands-on manipulatives that also maintain the mathematical integrity and rigor of the ideas being explored. We also consider common student misunderstanding that may arise and discuss how the teacher may address them effectively.
Geometry is one of the oldest mathematical disciplines. Euclid’s Elements (c. 300 BC) is known to be the earliest comprehensive treatment of rigorous mathematical proof. Through geometry, secondary students learn about abstraction (how real figures translate to geometric problems) and the notion of mathematical proofs based on axioms and logical deduction; students also experience how everyday problems about length, area, and volume can lead to problems in geometry.
In this course, participants will be immersed in and learn about geometric thinking, the role of problem solving in geometry, wide range of geometric tools (including virtual tools like GeoGebra), and how ideas in geometry can be fostered in secondary students.
Credit Transfer (to home institutions): Many teacher education programs have a “Geometry for Teachers” requirement, in which students must conduct an in-depth study of geometry (at the secondary level) with regard to both content and pedagogy. The GPS course, which investigates the problem-solving heuristics embedded in the secondary school geometry curriculum and explores how to implement problem solving in geometry classrooms, would fit well in satisfying such a requirement.
Gamification, the use of game design elements in non-game contexts, has gained substantial attention in the past decade. Both game design elements and non-game contexts have a large variety and a great number of applications. This course will focus on the non-game context of education and present possible applications of game elements with special attention to teaching mathematics. After a brief historical and theoretical summary of gamification in education, we will study both micro-gamification and more complex gamified processes in practice. We will examine the history of game elements and playfulness in Hungarian mathematics education, and see how they can be applied in North American classrooms. We will engage with fun mathematical games and hands-on manipulatives that can be used with students of various age groups. You will have opportunities to experience and enjoy them, and to reflect on how they can be used to enhance the learning of middle school and high school students. We will analyze both the mathematical content to understand how different mathematical concepts are interwoven into these games and manipulatives, and also the game elements to understand how they can be used to increase students’ motivation, engagement, and learning.