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Mathematics Improvement through Problem Solving
MIPS Project Summary:
On April 15, 1998, the NSF funded the MIPS grant to Elizabeth City-Pasquotank County Schools under their Local Systemic Initiative. Elizabeth City-Pasquotank County Schools serves as the fiscal agent for a five (5) school system consortia that originally included Camden, Edenton-Chowan, Elizabeth City-Pasquotank, Gates and Hyde Counties. Since award, Edenton-Chowan has withdrawn from participation. They were replaced, with Project Officer and NSF approval, by Washington County Schools. With modifications including limited grant coverage only to those who teach mathematics, assurances about the inclusion of mathematical content, clarification on the process to select the elementary curricula(s), more information with regard to outside evaluation and the engagement of businesses and parents in the Project, the grant was approved for 54 months at a funding level of $1,144,200.
In all, MIPS will serve approximately 425 K-8 teachers of mathematics in the 5 districts over the full term of MIPS, including special education teachers and replacement teachers who are employed during the course of the project. There are four tiers of content/curriculum activity involved in MIPS: Teach-Stat, K-8; Connected Math Project, 6-8; Mathematics Development, K-5; and evaluation and adoption of one of the three elementary curricula, Investigations in Numbers, Data and Space, Everyday Mathematics or Trailblazers. All of the curricular elements we are pursuing or exploring are established national curriculums that were developed with NSF support and guidance. They align with National Standards and have student centered, problem/inquiry based learning as their bases. Teach-Stat is a critical core that supports inquiry based instructional change and curriculum integration. The Connected Mathematics Project is our middle school curriculum and it continues the process of relevant learning that is student centered and problem solving/inquiry based. The Mathematics Development is focused on working with a core of teacher leaders from each district around the issues of how children develop, form and use their mathematics understandings and knowledge to solve problems. This knowledge and information will inform the process for selecting the elementary curricula for each of the five districts.
We believe that we have made significant strides toward our goals and objectives. During the first nine months of the Project, we have involved 324 individual teachers from 7 school systems: Camden, Currituck, Edenton-Chowan, Elizabeth City-Pasquotank, Gates, Hyde and Washington. This includes 13,861 person hours devoted to MIPS: 8,555 to Teach-Stat; 1,256 to Advanced Teach-Stat; 1,986 to Mathematics Development; 1,162 to the Connected Mathematics Project; 851 to Administrator Training and 51 hours to video conferences from all districts. We identified 71 formal activities of which 64% were Teach-Stat related, 26% Connected Mathematics Project associated, 3% administrator training, and 7% devoted to Mathematics Development.
In our various offerings we have striven to model instruction that parrallels what we would like to see in our classrooms. We have actively engaged all participants in relevant, hands-on activities and problem solving. We provided each workshop participant with teacher editions and other materials to enhance their classroom instruction. We have made wide use of videos to model "best practices" for problem solving/inquiry based instruction. It is clear to us that quality curricula material is only one part of the equation for comprehensive systemic change and instructional imrovement. The other critical piece is the instruction itself. We know that embracing the concepts and practices of inquiry based learning is not easy for teachers, particularly in a high stakes testing environment such as we have here in North Carolina. We have emphasized this change throughout our professional development offerings and follow-up activities. Our Instructional Specialists and those mentor teachers who will soon be added to the effort will concentrate on inquiry based instruction through modeling and coaching.
Currently, we are in the process of setting up a MIPS resource center and instructional laboratory with the cooperation of Central Elementary School in Elizabeth City. This center will provide a resource center for trying out various curricula modules and lessons with students; a resource for evaluation; a library for reviewing and assessing materials; and it will serve as a MIPS teacher training center. We plan for the center to double as a GLOBE training center for teachers and students. This will further enhance our efforts to integrate instruction and give relevance to student learning.
Teach-Stat:
In the summer of 1997, we conducted 5 basic and 1 advanced Teach-Stat workshops. The workshops were 5 full days in length with 40 hours of instruction. A total of 7,032 person hours were devoted to these workshops. The workshops have been supplemented with 25 hours of follow-up during this academic year. So far, we have conducted 56.5 hours of follow-up activities. These follow-ups have included formal mini-workshops lasting 2 full days, to short-term (1 to 1 1/2 hour) "reunions" to share accomplishments and concerns. A major thrust has been to model lessons in "real-time" classrooms and to observe and coach teachers as they implement and focus on problem based/inquiry instruction. Ms. Gail Lane, the MIPS instructional Specialist has modeled 74 lessons in 18 schools in 5 systems. She has worked with 171 teachers in their planning, met with principals, done classroom observations and modeled lessons.
In our Teach-Stat workshops we modeled a problem/inquiry based instructional approach. We used the PCAI model of pose the question, collect the data, analyze the data, interpret the data, and then to report and defend findings graphically and verbally. Teachers, working in groups, were actively engaged in all phases of the investigative process. Within each workshop, time was devoted to the mathematical content as well as to the applications and vocabulary. Teachers learned about, explored, and used line graphs, scatter plots, box and whisker plots, stem and leaf plots, back to back stem and leaf plots, bar graphs, and line plots.
As a result of our Teach-Stat implementation, we are seeing a whole new genre of "hall art." We now see graphs and charts presenting a wide variety of data. We are seeing a much broader engagement of all students. Mr. Craig Laughton, Principal of Sunbury Elementary School in Gates County expressed, "At my school I have observed more risk-taking among classroom teachers, more creativity in preparing/planning lessons, and more variety in lessons. Teachers are using more real-life situations to increase the level of student understanding, and investigations are being done in other subject areas as well. As a result [of Teach-Stat] there is a higher student interest in mathematics. Several classroom teachers have now accepted new leadership roles and more are actively seeking financial assistance through grants in order to purchase more manipulatives for students." Students are provided with more opportunities to think critically, problem solve, and present and justify their findings.
Connected Math Project:
In the Summer of 1997, we conducted a full one-week Connected Mathematics Workshop on the 6th grade modules. We have followed that with 5 other one-day or half-day workshops on specific CMP modules, grades 6-8; Covering and Surrounding (6th), Data Around Us (7th), Stretching and Shrinking (7th), What Do You Expect? (8th), Data About Us (6th), Frogs, Fleas and Painted Cubes and Growing, Growing, Growing (8th), Looking for Pythagorus (8th), Accentuate the Negative (7th), Filling and Wrapping (7th) and Say It With Symbols (8th). Some of these workshops that we are participating in are workshops in Raleigh led by Dr. Susan Friel. The Raleigh workshops are for teachers from several districts across the State providing MIPS teachers the opportunity to network with a wider range of colleagues. In the summer of 1998 we will participate in and/or support 3 additional one-week CMP workshops. One week will be devoted for each grade level, 6-8.
A significant accomplishment has been the work by EC-Pasquotank, Dr. Friel and another teacher from a district also implementing CMP with regard to aligning CMP with the North Carolina Standard Course of Study. These alignments help overcome teacher and administrator resistance to changing curriculum and instructional approaches in our high stakes testing environment.
Mathematics Development:
MIPS provided 2 - one-week workshops entitled Mathematics Development during the summer of 1998; 39 teachers participated in addition to MIPS staff. A two-day follow-up was conducted in August, 1997. The workshop was developed by Dr.'s Friel and Bright (UNC-CH) and was led by Dr. Friel. It is our plan that selected teachers from within the group will take more leadership responsibility in our upcoming workshops and follow-up. This builds regional capacity and assures a resource for continued professional development for new and experienced teachers. These teachers, based on their teaching experience and knowledge gained from these workshops, will guide the processes in their schools and districts, for evaluating and adopting one of the various elementary curricula available under the MIPS Project.
In the workshop, teachers were administered a before and after Belief's Scale Survey with regard to belief's about children's understanding of numbers. Teachers learned and explored: number fluency, number sense, and number systems; developing operations; concepts and practices of Cognitively Guided Instruction, student interviews, place value, invented strategies; and the role of algorithms in solving mathematical problems.
The MIPS Project actively participates in the NSF Local Systemic evaluation initiative administered through Horizon Research, Inc. We have also utilized both formal and informal internal evaluation to inform our programs and the overall MIPS Project. It operates at several levels; formal evaluation of workshops and other significant offerings; formal daily feedback on workshop progress through reflective journals, and use of 3x5 cards to record positive and negatives for the day, knowledge charts, and authentic assessments; informal feedback from teachers and instructional specialists who interact daily with their teachers; and, feedback from district leaders. Our internal evaluation efforts have enabled us to adjust workshop schedules and activities and make adjustments in the follow-up activities and CMP modules offered.
Lessons Learned:
- It is every bit as much the problem/inquiry based instructional approach as it is the curriculum that really makes a difference for teachers and students.
- It takes more time and effort than ever imagined.
- Change is not easy, particularly in a high stakes testing environment where folks have developed comfort zones over the term of their teaching careers.
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