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Boston College Lynch School of Education
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Teaching Elementary Mathematics and Technology Lillie R. Albert,
Ph.D. Office: Campion
217 Office Hours: 11:00 AM to
12:00 PM Monday 3:00 PM to 4:00 PM Tuesday and by appointment Course Description and Objectives This course is organized around two major themes: Creating a Community of Learners and Collaborative Learning as Radical Pedagogy. This course will provide information about how children learn mathematics and about conceptual activities for supporting a community of learners. In this course, you will have many opportunities to create and participate in technology, manipulatives, assessment, culturally relevant, and collaborative group activities. The major features of these activities: o Address content reflecting the NCTM Curriculum and Assessment Standards o Emphasize the interconnectedness of mathematical ideas, concepts, and real-world contexts o Use teaching and learning strategies based on the latest cognitive and constructivist research and technology o Present a close linkage between mathematics and physical models o Promote mathematical literacy by conceptually connecting language, literature, mathematics, and other disciplines Readings Required Texts Cathcart, W. G., Pothier, Y. M., Vance, J. H., & Bezuk, N. S. (2001). Learning mathematics in elementary and middle schools. Upper Saddle River, NJ: Merrill.
Optional Texts Burns, M. (1991). Math by all means: Multiplication, Grade 3. New York: Cuisenaire Company.
Middle School and Secondary Mathematics Methods Lillie R. Albert, Ph.
D. Office: 217 Campion
Hall Office Phone:
617-552-4272 Office Hours: 11:00 AM to
12 Noon Monday 4:30 PM to 6:00 PM
Wednesday and by appointment Course Description and Rationale This course emphasizes ways teachers can provide an inclusive mathematics curriculum with interdisciplinary and thematic approaches. The assessed curriculum influences what students are taught and what is valued about mathematics content. Great care must be taken to ensure that what is assessed is consistent with what is to be learned and valued in schools. This type of assessment stresses broad and flexible approaches. This course will include usage and discussions about current assessment techniques (performance-based tasks, performance events and portfolios). If we are to prepare teachers for the mathematics classrooms of today and of the future, then we must ensure that our students understand the underlying principles and theories of their educational field. It is assumed that with a strong foundation of educational theory that include practical applications, prospective and practicing teachers will make informed pedagogical decisions and develop ways of enacting their decisions within the classroom. It is within this context that you will examine how your beliefs and values affect how you teach mathematics. Required Readings Watrall, E. (2001). Dreamweaver4/Firework 4: Visual jumpstart. . San
Francisco, CA: Sybex. Huetinck,L (2000). Teaching mathematics for the 21st century: Methods and activities for grades 6-12. Upper Saddle River, NJ: Prentice-Hall. Krussel, L. (1998). Teaching the language of mathematics. The Mathematics Teacher, 91, 436-441. Ladson-Billings, G. (1997). It doesn't add up: African American students' achievement. Journal for Research in Mathematics Education, 28, 697-708. Long, V. M. & Benson, C. (1998). Re: Alignment. The Mathematics Teacher, 91, 504-508. National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics. National Council of Teachers of Mathematics. (1995). Assessment standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
ED 421.01 Theories of Instruction
Course Rationale and Description This course focuses on learning and instruction. Explicit implications and applications of learning theories are discussed and examples are drawn from educational situations and problems. This framework includes not just teachers of elementary and secondary schools, but also professionals working in higher education and contexts outside of formal schooling. To the extent possible, then, theoretical concepts in concrete terms with a variety of examples from primary schools to corporate learning communities will be illustrated. Along with this focus, this course embodies a theme of "creating collaborative learning environments." This course will integrate readings, lectures, presentations, and discussions. You are expected to evaluate and generate ideas regarding aims, methods, and challenges of a particular theory as it might be applied to various instructional situations or problems, whether it be in the classroom, a community center, the church, or in the court room. Therefore, this course will provide the opportunity to inquire into aspects of your own work, as well as examine writing and research sources about instructional theory, then working toward understanding the possibilities of a theory driven orientation toward educational work. Required Readings Albert, L. (2000). The call to teach: Spirituality and intellectual life. Conversations on Jesuit Higher Education. National Seminar on Jesuit Higher Education.
Teaching Mathematical Problem Solving in Grades 4-12 Lillie R. Albert,
Ph.D. Office: Campion,
217 Office Phone:
552-4272 Office Hours: 4:00 - 6:00
p.m. Monday and Wednesday (or by
appointment) Course Rationale and Description Recent reports supporting the necessity for reform of school mathematics (e.g., Massachusetts Department of Education Curriculum Frameworks, 1996; National Commission of Teaching and America's Future, 1996; National Council of Teachers of Mathematics, 2000, 1989, 1991) insist on the improvement of the preparation for new and practicing teachers. Working toward that goal, this course seeks to employ an active learning approach to improve our understanding of teacher preparation in mathematics education, specifically in the learning and teaching of mathematical problem solving. One of the biggest challenges facing mathematics teacher educators today is the question of how to guide teachers in crafting instruction that helps students understand mathematics. Our approach calls for teachers to reject the notion that students are passive recipients of knowledge in the form of facts and ideas to be used in rote procedures. Instead, we assume that teachers must accept that learning, like understanding, occurs through action, not simply with replication. This course examines the complex issues, trends, and research regarding alternative approaches for teaching mathematical problem solving. The major areas that will be examined are the nature of mathematical inquiry; models for collaborative grouping; methods and materials for cultivating problem solving, reasoning, and communication processes; methods of assessing mathematical problem solving; and the impact of Vygotskian Theory on the teaching and learning of mathematical problem solving.
Required Readings Albert, L. R. (2000). Outside in, inside out: Seventh-grade students' mathematical thought processes. Educational Studies in Mathematics 41, pp. 108-142. Albert, L., & Jones, D. (1997). Implementing the science teaching standards through complex instruction: A case study of two teacher-researchers. School Science and Mathematics 97, pp. 383-91. Bonk, C. & Kim, K. (1998). Extending sociocultural theory to adult learning. In M. C. Smith & Pourchot, T. Adult learning and development: Perspectives from educational psychology pp. 67-88. Mahwah, NJ: Lawrence Erlbaum. Cohen, E. (1994). Designing Groupwork: Strategies for the heterogeneous classroom. New York: Teachers College Press. Cohen, E., Lotan, R., Whitcomb, J., Balderrama, M., Cossey, R, & Swanson, P., (1993). Complex instruction: Higher-order thinking in heterogeneous classrooms. In S. Sharan (Ed.), Handbook of cooperative learning methods, pp. 82-96. Westport, CT: Greenwood Press. Davydov, V. V. (1995). The influence of L. S. Vygotsky on education theory, research, and practice. Educational Researcher, 24, pp. 12-21. Doolittle, P. E. (1997). Vygotsky's zone of proximal development as a theoretical foundation for cooperative learning. Journal of Excellence in College Teaching, 8, 83-103. Hedegaard, M. (1990). The zone of proximal development as basis for instruction. In L. Moll (Ed.), Vygotsky and education: Instructional implications and applications of sociohistorical psychology pp. 349-371. New York: Cambridge University Press. Krulik, S., & Rudnick, J. (1996). The new sourcebook for teaching reasoning and problem solving in junior and senior high school. Boston, MA: Allyn and Bacon. Lave, J. & Wenger, E. (1996). Practice, person, social world. In H. Daniels (Ed.), An introduction to Vygotsky pp. 143-150. New York: Routledge. Tharp, R. G., & Gallimore, R. (1988). The intrapsychological plane of teacher training: The internalization of higher order teaching skills. In Rousing minds to life: Teaching, learning, and schooling in social context, pp. 249-265. New York: Cambridge University Press. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University. Wertsch, James V. (1985). Vygotsky: The man and his theory. In Vygotsky and the social formation of mind, pp. 1-16. Cambridge, MA: Harvard University Press.
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