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Teaching Problem Solving and Creating An Inquiry Based Mathematics Classroom
A Professional Development Program

The following staff development program was prepared specifically for Roger's Elementary School in Stamford Connecticut. The program was designed and implemented as a response to student deficits in select mathematical abilities as evidenced by standardized tests.

Concern:
As indicated by the percentages of students reaching the standard on the latest Connecticut Mastery Test (CMT) in mathematics for 4th graders there is a consistent weakness in select areas of problem solving and estimating geometric measurements and numerical calculations.

Response:
The areas of concern in the CMT results are commonly associated with weaknesses in conceptual understanding, mathematical creativity, and confidence in students. This program will focus on improving curriculum and/or the classroom practice of teachers to address these factors. Strategies will be designed and implemented by teachers with the facilitation of Scott Beall in a three part staff development sequence. Drawing from ideas presented in the workshop as well as their own resources, each teacher will craft a focus according to their personal background, experience, comfort level, resources, personal teaching style and the unique needs of their particular students. Key factors that will be viewed in the workshop are listed below:

Teaching practice

  • The art questioning to stimulate higher order thinking and discussion
  • Teacher modeling of the problem solving process for students, validating the need for persistence, the norm of false starts and experimentation
  • Considering teachers' own perceptions of what it means to "do mathematics" (questioning, classifying, sorting, creating, modeling, experimenting, vs. performing memorized procedures)
  • Creating a classroom culture that is safe for risk taking

Curriculum

      • Availability and knowledge of specific problem solving strategies that students can resort to in non routine problem situations
      • Utilizing authentic activities/games that provide real practice in estimating
      • Experience with inductive, discovery based activities that require students to think about mathematics as opposed to performing memorized procedural tasks
      • Experience with non routine problems to be solved over time and presented in written formats and/or class presentations
      • Group work strategies to enhance student discussion and reflection on issues of problem solving
      • Fostering students' reflection on the problem solving process through discussion, journaling and written problem write-ups.

    An Opening note to workshop participants

    It seems that all too often, students' experience their greatest fear and difficulty in mathematics when they are faced with dreaded "story problems." Most of us as adults have experienced this as kids; it has even become a popular topic for comics strips and comedians, such as the Gary Larson comic playing on a hypothetical nightmare portraying a young child at the gates of Heaven, with God requiring one last task for entry: to correctly answer a distance-rate-time story problem in a limited amount of time. The ability of students to apply mathematical tools to solve problems in unique situations, to identify relevant and extraneous information and evaluate the reasonableness of answers is directly related to the strength of their number sense and conceptual understanding of mathematics. Conceptual understanding is empowering to students. With it, fear diminishes and confidence increases. In this workshop you will have the opportunity to collaborate with your fellow teachers, reflect on what happens in YOUR classroom and consider ideas presented in our work session to further expand how you teach for understanding in your classroom.

    FORMAT

    Part I: Opening workshop
    March 14, 3:30-5:30pm

1. Group discussion and reflection
Define areas of concern--

Where are we now?
Where do we need to go? (objectives/outcomes)

2. Presentation/discussion
How will we get there? (curriculum and instruction)
How will we know we are there? (assessment)

a) A process for teacher inquiry--Action Research(AR)
b) Factors and tools for creating an inquiry based classroom

i) The art of questioning
ii) Student generated discussion--The Debra Ball classroom and Shea numbers
iii) Teacher modeling of non-routine problem solving
iv) Problem solving cycles
v) Open ended Problems of the Week
vi) Student reflection on the problem solving process

3. Teacher work sessions
Teachers group in common areas of focus for individual AR plans to incorporate strategies into their classroom teaching for the subsequent 10 days.

Part II: Implementation in the classroom
March 15-March 23

Implementation of strategies as planned, making observations and journal notes as appropriate for sharing out and evaluating the AR plan.

Part III: Follow up workshop--sharing out and tuning
March 24, 3:30-5:30pm