Final Exam

1) Secondary Schooling in the 21st Century involves greater focus on relevant tasks and challenging curriculum. Classes will be organized around different career paths that students will choose. This will allow content to be taught in relation to practical application in those career paths which students have indicated interest in. These classes will incorporate real life experiences with the community, such as internship opportunities and professional guest speakers in the classroom. Curriculum will be more rigorous, pressing students to think critically and give reasons for their answers. They will be given challenging tasks that focus more on the process of solving the task than on the solution itself. Schooling in the 21 Century will also be more inquiry based, in which the teacher is not the disseminator of information, but rather the coach in guiding students’ thinking and discussion. This involves more activities in which the students explore and discover important concepts, rather than them simply being told them.
2) I will provide students with challenging tasks (such as POWs) that will require them to explore possible solutions to a problem without being told exactly how to do it. This will foster problem solving skills and allow the student to discover the need for certain questions to be answered. Students will be given opportunities to collaborate with their peers in order to gain insight into these challenging tasks. I do not believe that I will be able to incorporate these types of problems everyday in the classroom, or even every week, as they can be very time consuming. I can see myself practically including these types of exploratory and collaborative tasks at the beginning of each new unit. I may use these types of problems to introduce some of the key concepts that will be studied in the unit. I hope that by using these types of problems, students will value the concepts being studied further in the unit, as they will see a context for those concepts and a need for their development through the exploration of the POW.
3) During my first two years of teaching I want to incorporate more career oriented contexts for the mathematical concepts I will be teaching. I think it would be awesome to have guest speakers come in and share how math is used in their specific careers (especially careers that do not seem to involve math). I would like students to research the careers that they are interested in and give some kind of presentation on how mathematics is involved in these careers. I hope that continually relating the mathematical concepts in class to the real world, whether through careers or just daily life, would help students see mathematics as more than just “a subject that had to learn in school.” In my first year of teaching, I think I will focus on discovering some of these career applications myself and incorporating them into my lessons. I may also have students do the research project on careers they are interested in. In my second year of teaching, I may try to involve more guest speakers, possibly some of my students’ parents.
4) Later in my career I will try to incorporate more types of exploratory problems when introducing any new concept. Students will be constantly involved in collaborating about these exploratory problems. Later in my career I will also try to involve my students on in some community experience in which they see the applications of mathematics in different careers – maybe a field trip to a business where employees can explain how they use mathematics in their company.
5) These plans for action could fall under many categories. The challenging exploratory tasks could fall under “Creating New Curriculum Paths” as it proposes a more rigorous and discovery focused curriculum. The relevance to careers would also fall under this category as it gives a new direction or context in which all curriculum is to be studied. These plans for action also fall under “Powerful Teaching” since they involve making the curriculum more meaningful for students. They provide greater relevance to the content being studied and greater understanding for the need of these concepts. Students will also be allowed to explore new concepts through challenging problems (such as POWs) will give them opportunities to be more active and inquisitive learners.