Course Goals: Math 451, Explorations of Middle/Secondary School Mathematics
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Course Goals: Math 451, Explorations of Middle/Secondary School Mathematics |
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Focuses on the content of middle and secondary school mathematics and appropriate teaching methods. Instruction will be guided by the NCTM Principles and Standards for School Mathematics and the Wisconsin Model Academic Standards for Mathematics. Emphasis is on problem solving, critical thinking, communication, and issues of technology as they relate to number and operations, the development of algebraic and geometric reasoning, measurement, data analysis and probability in grades 5-12. Students will investigate and review the content of current mathematics text series, and will observe and interact with learners engaged in studying these topics. (Math 301 highly recommended) (F)
· all six NCTM Principles and all ten Standards, as well as the Wisconsin Model Academic Standards for Mathematics
· big ideas of the five content strands of mathematics (as defined by PSSM) and how these ideas relate to one another and to the process strands
· scope and sequence of middle and secondary level mathematics
· connections among mathematical concepts and between mathematics and real-world situations
· the variety and roles of various representations used in mathematics
· the historical development of selected topics in the middle/secondary mathematics curriculum
· the role of research in mathematics education
· solve routine and nonroutine problems within each of the content strands of middle and secondary mathematics and give clear, accessible explanations of the mathematics involved in their solutions.
· analyze the mathematics involved in specific problems and identify possible steps to take with students as well as predicting possible student responses
· evaluate others’ solutions to mathematical problems for correctness, validity, efficiency and potential for extension/development
· identify common mathematical errors/misconceptions and discuss how to prevent/remedy them
· carry out common and alternative mathematical algorithms and evaluate them for correctness, validity, efficiency and potential for extension/development
· explain the reasons for steps in commonly taught mathematical algorithms
· correctly and consistently use commonly accepted mathematical terminology and notation
· choose and use appropriate manipulatives/technology to solve problems and represent/explain mathematical concepts
· identify and take steps to fill gaps in own pedagogical content knowledge
· identify and describe the progression of concepts within and across content strands, and discuss how misconceptions within one concept can affect learning of other concepts.
· identify, research, and create a visual presentation regarding historical connections to topics within the middle/secondary mathematics curriculum
· choose and present engaging mathematics suitable for use with a math club or as enrichment for talented mathematics students at the middle or secondary level
· carry out and present a review of literature on an appropriate topic within middle/secondary mathematics education
· every student can learn mathematics; it is important to have clear goals and high expectations for all students
· representing mathematics concepts appropriately is a large part of mathematics teaching
· students can construct their own knowledge about mathematics, and always have previous mathematical knowledge
· it is necessary to develop a positive disposition toward mathematics in themselves and their students
· there is more than one valid way to approach most mathematics problems
· mathematics is logical—it can and should explained rather than memorized
· research is an important component of mathematics education at every level
Approved January, 2006
For more information please contact: dbenjamin@edgewood.edu