Combining Math Content and Math Methods Celine Dorner Patty Chastain Pacific Lutheran University
Background � Pacific Lutheran University � Separate courses � Lack of mathematical background in teacher candidates � Realization that content and methods overlap, yet left gaps � Our recent experiences with DMI
Vision and Goals � Recommendations from CBMS Vol. 11: The Mathematical Education of Teachers and Washington State novice teacher competencies � Focus on students’ thinking and understanding of Mathematics through the use of DMI cases � Teacher candidates experience the mathematics as learners, and communicate their understanding to classmates � See how students learn similar mathematics, and how they can facilitate student learning in the classroom through familiarity with research-based instructional strategies based on NCTM recommendations
Grant requests � Planning time for development of essentially new courses � Document cameras � Stipends for former teacher candidates who would serve as advisors during planning stages � Breea Mearig � Jeff Tompkins
Planning: First Steps � Summarize recommendations of PMET and State competencies in mathematics for elementary teachers � Celine’s chart of Standards, topics, big math ideas, children’s thinking -> readings/resources � Comparison of “old” syllabi to find gaps and overlaps between standards and what we had been doing � Consultation with former teacher candidates about both of our classes - what they liked and wished for
Planning: Content decisions � Divide math content � Math 123 includes: Number sense and operations, including Cognitively Guided Instruction; algebraic thinking and problem- solving; proof � Educ 406 includes: Review of CGI; geometry; measurement; data and statistics; probability
Planning: Divide pedagogy instruction � MATH 123: � MATH > pedagogy � No practicum � Includes non-education majors � Group presentation project based on “big” problems from Fostering Algebraic Thinking Toolkit (2001, Driscoll) � DMI focus on considering student work and planning further instructional tasks (based on CGI) � EDUC 406 � Math < PEDAGOGY � Required to include focus on assessment, lesson planning, equity pedagogy, etc. � 60 hr. practicum (with literacy methods) � Structured observation (communication patterns) � Assessment of learners’ problem-solving skills � Develop 2-week unit plan suitable for practicum class and teach a minimum of 2 math lessons
Planning: Book selection � Hoped for 1 book that included both mathematics and methods, plus DMI casebooks � Chose 2 texts from MAA list of recommended texts (http://www.maa.org/pmet/resources/textbooks.html) � Van de Walle (2005) Elementary and Middle School Mathematics: Teaching Developmentally , Pearson Allyn & Bacon � Bassarear (2005) Mathematics for Elementary School Teachers , Houghton-Mifflin, � DMI: Making Meaning for Operations and Measurement in 1, 2, and 3 Dimensions
Planning: Agreed on “usual” instructional sequence � Math content � Focus on student learning � Discussion and reading about instructional strategies Math Student Content Understanding Instructional Planning
A Closer Look: Math Student Content Understanding Planning math content Instructional Planning � Math content � Math problems to solve; sharing using document camera � Group investigations/guided inquiry based on “big ideas” � Occasional direct instruction in various math topics � Connections between numerical, geometrical, graphical, and algebraic representations � Multiplication transparency � Video
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A Closer Look: Math Student Content Understanding Planning student learning focus Instructional Planning � Development of student understanding � Cases and videos of children doing mathematics, developing their own strategies, and sharing their work � Example � Ramon and Tanya are making diagrams to explain 1/3 + 1/3. Explain the reasoning of Ramon and Tanya
Math Student A Closer Look: Content Understanding Planning instructional strategies Instructional Planning � DMI questions: What does child understand? Go next? Questions for child? � Cognitively Guided Instruction � ( http://www.coehs.uwosh.edu/Anishinabe/Curriculum/legend18.h tm � Van de Walle, Elementary and Middle School Mathematics: Teaching Developmentally (2004)
Reflections: Orchids � Teacher candidates � Communication - verbal and written, esp. document camera � Deeper understanding underlying the math that they know and will be teaching � Better understanding of how children develop understanding and sometimes struggle with math concepts they thought were simple
More Orchids � Teacher candidates � have enhanced vision of how math can be done and taught � more highly value children’s development of ideas and strategies � Increased partnerships between math dept. and education (“guest teaching”, teaming; inservice teacher education) � Increased incorporation of technology
Reflections: Concerns (Onions) � “Chunks” of mathematics content have been deleted � Set theory, Logic � **different bases were scheduled for deletion, but consultation with former students convinced us to keep it � Bumpy coordination of math and pedagogy � There is still a need for more math (especially probability) and more pedagogy - we need another semester! � Students and instructors felt the workload was heavy for the credit � Need for more multicultural perspective, inclusion of families
Revisions planned for 2006-7 � Different books (4 books too expensive!) � Recommendations? � Review revised novice teacher competencies � Increased use of technology - recommendations? � MATH 123 � Increased math content: set theory, counting strategies? � Increased history of math? � Increased use of K-8 curriculum � Include some preliminary lesson planning � EDUC 406 � Reconsideration of assignments � More time and instruction on some math topics (probability, geometry) � Balance of “doing” versus “discussing” specific math activities (e.g. M&M Statistics, AIMS Mini-Metric Olympics; Plains Indian Star Quilts) � More focus on multicultural perspective and including families in learning (beyond newsletters)
Personal Reflections � Celine: Value of partnership, learning more about pedagogy, CGI, deeper understanding of the math � Patty: Value of partnership, connections with teachers and math department, teacher candidates more confident
Selected references � Developing Mathematical Ideas Casebooks: Making Meaning for Operations and Measurement in 1,2, and 3 Dimensions (Schifter, Bastable, & Russell, 1999) available from Dale Seymour/Pearson Learning. Videos are available, too, separately or packaged with the facilitator’s guides and casebooks. � Children’s Mathematics: Cognitively Guided Instruction (with two multimedia CDs), Thomas P. Carpenter, Elizabeth Fennema, Megan Loef Franke, Linda Levi and Susan B. Empson. Published through Heinemann. To find this book, go to Heinemann site and search for Children’s Mathematics. � CGI videotapes and summative log book complement the above publication. To order, contact Cheryle Wampole at the Wisconsin Center for Education Research, 1025 W. Johnson Street, Room 242, Madison, WI 53706, TEL: (608) 265-9698 FAX: (608)263-6448. CGI Logs & Videotapes — Elizabeth Fennema, Thomas Carpenter, Linda Levi, Megan Loef Franke, Susan Empson. $100.00 single set. � Thinking Mathematically : Integrating Arithmetic & Algebra in Elementary School by Thomas P. Carpenter, et al (2003)
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