General Mathematics Methods
EEND-690

Provides an overview of the materials, content and methodology utilized by educators for teaching mathematics.  Candidates explore principles in class and utilize them to develop lesson plan approaches, activities and teaching aids.

College of Education Mission

The mission of the College of Education is to prepare competent and caring educators who understand students, serve the community and develop professionally to become ethical decision-makers and leaders.

Understanding Students

• Understand the use of questioning techniques to develop critical thinking and mathematical thought progressions
• Develop long and short-term assessment strategies, including formative and summative assessments, such as rubrics
• To provide a context for understanding current educational practices and understand National Council of Teachers of Mathematics (NCTM) standards for curriculum change for the 21st century, including the following NCTM goals for students:
  
  • Learn to value mathematics
  • Become confident in one's own ability
  • Become a problem solver
  • Learn to communicate mathematically
  • Learn to reason mathematically
• To interpret the psychological principles of learning and teaching necessary for mathematics in writing lesson plans and developing materials for the learning environment
• To explore the use of technology packages, manipulatives and other techniques for engaging students in the learning process

Serving the Community

• Develop skill in the participation and design of individual and group problem solving situations
• Understand the aspects for instructional reform, curricular trends, Illinois Learning Standards, Common Core State Standards, Content Standards and the National Council for Teachers of Mathematics Standards
• To identify factors impeding progress in mathematics education

Finding Our Professional Selves

• To develop and understanding of the four steps of problem solving (Polya, 19)
• Develop planning techniques using evidence-based best practices in mathematics instruction
• To describe the changing emphasis in mathematics curriculum, teaching methods, and assessment
• To utilize mathematics evaluation and assessment as a means to improve instruction and meet individual skill levels of students
• To reduce anxiety and develop openness necessary for teachers to implement new methods of helping students learn mathematics
• To develop an understanding of the importance of alignment in objective, assessment, and learning activities in lesson planning

Access to standards referenced in this section can be found HERE

By the conclusion of the course, each participant will be able to do the following:

1. identify the components of mathematics lesson plans and understands how to develop short and long range plans IPTS (D – 3A, 5K    P – 3B, 3I); INTASC 7
2. design and plan mathematics lessons for diverse students, including but not limited to ELLs and students with special needs IPTS (D – 1A,1D, 1E, 1F, 1G,1J, 1L,3C,3O, 3P, 5M); INTASC 1, 7
3. write lessons utilizing learning theory and research methods, including Piaget, Bruner, Gagne and other learning theorists IPTS (D – 1B, 1C, 1I); INTASC 7 
4. design and write lesson plans for individual and cooperative problem solving IPTS (D – 4A, 4C, 4D, 4E, 4G, 4I, 4J, 4K, 4L, 5I); INTASC 7, 8
5. design and write lesson plans for mathematics utilizing research-based best practices, such as technology and subject integration IPTS (D - 2L, 2N, 3E, 5D, 5N, 5S, 6G, 6I, P – 3L, 5F, 5L); INTASC 7, 8 
6. examine and utilize manipulatives identified to teach mathematical concepts IPTS (D - 5C, 5S, P – 5F); INTASC 8
7. identify student actions necessary for more effective mathematics learning, including readiness levels for skills IPTS (D - 2E, 2P, 5E); INTASC 2
8. evaluate mathematics texts and skill continuums utilizing NCTM standards IPTS (D - 2B, 2I); INTASC 8
9. examine the development of a mathematical concept from primary through junior high, utilizing needs for development, remediation, mastery, and enrichment IPTS (D - 2C); INTASC 2
10. identify a variety of assessment techniques in mathematics IPTS (D – 3N,7A, 7C, 7D, 7E, 7F, 7I, 7L P – 7B); INTASC 6
11. develop techniques necessary for evaluating more effective mathematics learning IPTS (D – 3Q, 9A ); INTASC 6,8
12. analyze formal mathematical research for use by classroom teacher IPTS (D – 3G, 5B); INTASC 8

Course Readings

You will need to read the material in van de Walle (2010) in order to apply it to the discussions, learning activities, and lesson plans.

Discussions

Candidates will participate in small group or whole class discussions at various points in the course. Posts are expected to conform to standard English conventions and be free of spelling and other errors. Evaluation criteria for discussion posts will be provided. Please note that you need to post your initial response by Friday of the week the discussion is due and respond to at least one other post by Sunday of the week the discussion is due.  Full points will not be earned if there is not an initial and response post.

• identify student actions necessary for more effective mathematics learning, including readiness levels for skills IPTS (D - 2E, 2P, 5E); INTASC 2
• evaluate mathematics texts and skill continuums utilizing NCTM standards IPTS (D - 2B, 2I); INTASC 8
• develop techniques necessary for evaluating more effective mathematics learning IPTS (D – 3Q, 9A ); INTASC 6,8

Learning Activities

Candidates will complete various activities (e.g., evaluation of student work, use of virtual manipulatives) designed to check for understanding of course concepts and to scaffold learning.

• design and plan mathematics lessons for diverse students, including but not limited to ELLs and students with special needs IPTS (D – 1A,1D, 1E, 1F, 1G,1J, 1L,3C,3O, 3P, 5M); INTASC 1, 7
• write lessons utilizing learning theory and research methods, including Piaget, Bruner, Gagne and other learning theorists IPTS (D – 1B, 1C, 1I); INTASC 7 
• design and write lesson plans for individual and cooperative problem solving IPTS (D – 4A, 4C, 4D, 4E, 4G, 4I, 4J, 4K, 4L, 5I); INTASC 7, 8
• design and write lesson plans for mathematics utilizing research-based best practices, such as technology and subject integration IPTS (D - 2L, 2N, 3E, 5D, 5N, 5S, 6G, 6I, P – 3L, 5F, 5L); INTASC 7, 8 
• examine and utilize manipulatives identified to teach mathematical concepts IPTS (D - 5C, 5S, P – 5F); INTASC 8
• identify student actions necessary for more effective mathematics learning, including readiness levels for skills IPTS (D - 2E, 2P, 5E); INTASC 2
• evaluate mathematics texts and skill continuums utilizing NCTM standards IPTS (D - 2B, 2I); INTASC 8
• examine the development of a mathematical concept from primary through junior high, utilizing needs for development, remediation, mastery, and enrichment IPTS (D - 2C); INTASC 2
• identify a variety of assessment techniques in mathematics IPTS (D – 3N,7A, 7C, 7D, 7E, 7F, 7I, 7L P – 7B); INTASC 6
• develop techniques necessary for evaluating more effective mathematics learning IPTS (D – 3Q, 9A ); INTASC 6,8
• analyze formal mathematical research for use by classroom teacher IPTS (D – 3G, 5B); INTASC 8

Lesson Plans

Candidates will develop four(4) lesson plans that follow the USF Universal Design for Learning (UDL) lesson plan format for different grade levels aligned with the NCTM Content and Process Standards, as well as the Common Core State Standards. Notation of accommodations and/or modifications for at least one student must be included for each of the four lessons.  Within these lesson plans, candidates will be required to use best practices in mathematics instruction as outlined in the Lesson Plans Checklist assignment. Detailed instructions and evaluation criteria are available in the Assignments area.

• identify the components of mathematics lesson plans and understands how to develop short and long range plans IPTS (D – 3A, 5K    P – 3B, 3I); INTASC 7
• design and plan mathematics lessons for diverse students, including but not limited to ELLs and students with special needs IPTS (D – 1A,1D, 1E, 1F, 1G,1J, 1L,3C,3O, 3P, 5M); INTASC 1, 7
• write lessons utilizing learning theory and research methods, including Piaget, Bruner, Gagne and other learning theorists IPTS (D – 1B, 1C, 1I); INTASC 7 
• design and write lesson plans for individual and cooperative problem solving IPTS (D – 4A, 4C, 4D, 4E, 4G, 4I, 4J, 4K, 4L, 5I); INTASC 7, 8
• design and write lesson plans for mathematics utilizing research-based best practices, such as technology and subject integration IPTS (D - 2L, 2N, 3E, 5D, 5N, 5S, 6G, 6I, P – 3L, 5F, 5L); INTASC 7, 8 
• identify student actions necessary for more effective mathematics learning, including readiness levels for skills IPTS (D - 2E, 2P, 5E); INTASC 2
• examine the development of a mathematical concept from primary through junior high, utilizing needs for development, remediation, mastery, and enrichment IPTS (D - 2C); INTASC 2
• identify a variety of assessment techniques in mathematics IPTS (D – 3N,7A, 7C, 7D, 7E, 7F, 7I, 7L P – 7B); INTASC 6
• develop techniques necessary for evaluating more effective mathematics learning IPTS (D – 3Q, 9A ); INTASC 6,8
• analyze formal mathematical research for use by classroom teacher IPTS (D – 3G, 5B); INTASC 8

Lesson Plans Checklist

Following the USF lesson plan format, candidates will design four grade specific math lesson plans.  One must be at the primary (K – 2) level, one at the intermediate (3 -4) level, and one at the upper intermediate/jr high/hs (5 - 9) level (you may choose the grade level for the remaining lesson).  The following elements must be an integral part of at least one lesson:

1. Two different manipulatives in two different lessons
2. A lesson specific rubric
3. A children’s literature book
4. Problem-solving
5. Cooperative learning
6. A lesson that includes the use of appropriate technology (website, Smartboard)
7. A lesson based on an article read in Teaching Children Mathematics Journal

• write lessons utilizing learning theory and research methods, including Piaget, Bruner, Gagne and other learning theorists IPTS (D – 1B, 1C, 1I); INTASC 7 
• design and write lesson plans for individual and cooperative problem solving IPTS (D – 4A, 4C, 4D, 4E, 4G, 4I, 4J, 4K, 4L, 5I); INTASC 7, 8
• design and write lesson plans for mathematics utilizing research-based best practices, such as technology and subject integration IPTS (D - 2L, 2N, 3E, 5D, 5N, 5S, 6G, 6I, P – 3L, 5F, 5L); INTASC 7, 8 
• examine and utilize manipulatives identified to teach mathematical concepts IPTS (D - 5C, 5S, P – 5F); INTASC 8
• identify student actions necessary for more effective mathematics learning, including readiness levels for skills IPTS (D - 2E, 2P, 5E); INTASC 2
• identify a variety of assessment techniques in mathematics IPTS (D – 3N,7A, 7C, 7D, 7E, 7F, 7I, 7L P – 7B); INTASC 6
• develop techniques necessary for evaluating more effective mathematics learning IPTS (D – 3Q, 9A ); INTASC 6,8
• analyze formal mathematical research for use by classroom teacher IPTS (D – 3G, 5B); INTASC 8

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