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 6-18, 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. At the end of each day is a reflection session where participants share observations and connect their experiences to the theories learned in other BSME courses.
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.
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.
In this course, participants will learn how to promote mathematical thinking in secondary classrooms and foster students’ problem solving skills. Participants will engage with mathematical tasks that are directly connected to the secondary school curriculum. They will reflect on this learning experience as future teachers—they will discuss the purpose and effectiveness of each task, as well as how to create similar experiences for their future students.
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).
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.
In this course, participants will explore how technology can be integrated into the classroom to enhance student learning. They will learn about applications such as GeoGebra (interactive geometry, algebra, statistics, and calculus software) and Desmos (next-generation graphing calculator), and investigate how to use them effectively in secondary mathematics classrooms.
Participants will play the role of students, as they engage in technology aided problem-solving. They will then learn how to create such learning environment for their future students. Discussion questions will include: When and how should technology be used? How can the focus on important mathematical ideas be maintained while using technology in the classroom? How can technology be used to enhance both collaborative and independent learning? How can technology be used to provide appropriate challenge for all students? (And many, many more!)