UCSB Department of Mathematics
Center for Mathematical Inquiry
Projects Involving K-12 Collaboration

        An emphasis on examination of student thinking guides all center projects and all grade level work is aligned with the California Content Standards. The K-8 materials used the Center's programs have been developed in partnership with Mathematics in the City at City College New York and the Freudenthal Institute in the Netherlands, a National Science Foundation funded project, and have a substantial research base. The center has funding for partial support of teacher participants and whenever possible seeks cost sharing arrangements with local districts.

  1. Summer Workshops.
          Two workshops were offered in summer 2006: one on Algebra for teachers in grades 4-9 and a second on Number and Operation for teachers in grades K-6. The goal is to provide teachers with strategies to help their students succeed with the Standards in grades K-7 and in Algebra 1. These workshops include substantial focus on understanding number and calculation. By developing the important representations for numbers (open number lines, arrays and area model, ratio tables, and combination charts), the big ideas and strategies for understanding arithmetic can be constructed by students in ways that enable them to generalize and understand variation so they develop lasting conceptual understanding. The workshops last one-week and stipends are available to teachers from participating districts.
          During the fall 2006, two versions of the summer workshops will be offered for teachers whose districts agree to release them from classes on three subsequent Tuesdays. These workshops have been set up specifically so teachers, along with the credential candidates working in their classrooms, can participate in Lesson Study Groups.
  2. Thursday Afternoon Working Groups.
          These working groups provide follow-up for the summer workshops and opportunities for vertical teaming. Participants are able to collaborate with teachers in their districts on: further study of number and algebra topics, sharing student work and collaborative planning, vertical teaming with an emphasis on Elementary-Junior High collaboration. Follow-up can include class visits by mentor teachers, UCSB faculty, and graduate students with backgrounds in K-8 mathematical development.
  3. Project DELTA.
          These full-day workshops (usually on a Saturday) will enable participants to study a single classroom topic in depth using a lesson study approach using videos developed by Math in the City for this purpose. DELTA stands for Digital Environments for Learning and Teaching Arithmetic/Algebra. The videos bring the context of K-8 classrooms to the fingertips of participants for inquiry and examination. At each workshop, a single lesson will be studied in depth during the morning, and then in the afternoon participants will consider "mini-lessons" that help build and solidify the concepts and skills developed in the lesson. Discussion will focus on student thinking, how understanding is developed, and how context and representation influences their development. Different grades, levels, and topics are studied throughout the year.
  4. Lesson Study Groups.
          This project is new for 2006-07 and was designed in collaboration with the Teacher Education Program at UCSB. Participants are credential candidates and cooperating teacher pairs who have participated in summer workshops and want to deepen their understanding of mathematical development by working in grade level teams on lesson study using classroom materials that focus on the big ideas developed in the summer workshops. During fall 2006, the lesson study topics will be: inventory and early place value (K-1), the open number line for addition/subtraction (2-3), the array the array model for multiplication (3-5), and the ratio table (5-6).
  5. Focus on a School Site.
          The center will collaborate with an entire school or grade bands at a school. A good way to get to know the project is for Center staff to run a workshop on the teaching and learning of a mathematical topic K-8. School leadership will determine the exact format and topics of the work. Possibilities include: study of big ideas and representations in mathematical development in K-8 or appropriate grade band, strategies for inquiry based development of mathematical concepts, strategies for developing computational fluency with understanding, vertical teaming, video case lesson study, examining student work and curriculum planning, class visits, or establishing math clubs for students.

For more information about the above projects, contact:
Bill Jacob, Professor of Mathematics, UCSB
Mathematics Dept., UCSB Santa Barbara, CA 93106

The UCSB Center for Mathematical Inquiry is supported by grants from the Educational Advancement Foundation