Creating
Mathematically Connected Communities 



2004 2005


A Brief Description of the MC ^{2} Carlsbad 2004 Summer Academy The first of the MC^{2} summer academies was held at the Carlsbad branch of New Mexico State University from June 14 ^{th} to July 2^{nd} of 2004. The "content knowledge" portion of the academy was led by Dr. Ted Stanford and Dr. Tony Wang of NMSU's Mathematics Department; while the "pedagogical knowledge" portion was led by Cathy Kinzer and Kalle Jorgensen of NMSU's Department of Curriculum and Instruction, with assistance from Dr. Karin Wiburg and Wanda Guzman, also from Curriculum and Instruction. For the first two weeks, participants (primarily middle school mathematics teachers from school districts in southeastern New Mexico) spent four hours a day honing their mathematics skills, as they worked individually and in groups to solve original math problems created especially for the academy by participating NMSU math professors. Through minilectures, oneonone instructor feedback, and peer review, teachers were assisted in deepening their content knowledge, using that knowledge to solve "realworld" mathematics problems, and communicating their findings in ways used by professional mathematicians. The afternoons of those first two weeks were spent looking more deeply into how to teach these math concepts to students. Teachers studied each of the statemandated mathematics content standards assigned to their grade level; compared them to what their textbooks cover and to what their students are actually learning; and considered which combinations of various teaching processes (such as memorization, problem solving, and communicating ideas) might be most appropriate for teaching each of the content standards. During the second week, participants were also introduced to a modified version of Lesson Study – a method of working with colleagues to develop and test more effective ways of teaching difficult concepts – and began preparing a threeday instructional unit which they then taught to local summer school students during the third week of the academy. Each teaching experience was followed by a period of reflection and refinement, as the lessons learned from each day's teaching were used to guide and sharpen the next day's instruction. The final two
days of the academy were spent finalizing projects, and synthesizing and
sharing what participants had learned. The academy ended with a celebratory
luncheon at a local restaurant. A Brief Description of the MC^{2} Las Cruces 2004 Summer Academy The Mathematically Connected Communities (MC ^{2}) project held a threeweek summer academy in Las Cruces, New Mexico, at New Mexico State University from June 28 th to July 16 ^{th} of 2004. The purpose of the MC ^{2} Academy was to strengthen teacher content knowledge and the knowledge of how to effectively teach the mathematics of the middle school. Dr.’s Ted Stanford, Bruce Olberding, and Tony Wang, of NMSU's Department of Mathematical Sciences, and Dr. Tom Gruszka, of Western New Mexico State University’s Department of Mathematical and Computer Sciences, served as facilitators for increasing mathematical content knowledge. These mathematicians created openended problems based on teacher requests and the teachers worked together in groups to solve the problems. The teachers communicated their ideas with their colleagues and the mathematicians in an ongoing “mathematical conversation”. This process reflects how teachers are now being asked to teach in their own classrooms. In the Academy teachers also discussed New Mexico’s Standards and Benchmarks for Mathematics, reviewed the kinds of items that students will encounter on their state assessments, and examined curricula that are aligned to New Mexico’s standards. Groups of teachers from the same grade level then designed a mathematics unit to teach to students. Students from the SEMAA program worked with Academy teachers for four days during the 3 rd week. Every day after the teaching the group of teachers would reflect on the successes and challenges of the day’s lesson and, based on this information, would discuss what needed to happen the next day. Teachers were guided in this process by Dr. Akihiko Takahashi, from DePaul University’s School of Education, an international leader in studentcentered learning, and by the staff of the MC ^{2} project, headed by Dr. Karin Wiburg of NMSU’s College of Education. The goal of the Academy was to begin the process of creating a professional learning community of mathematics educators, and this was certainly accomplished. Mathematicians, K12 teachers, and teacher professional developers all shared their knowledge of mathematics and how students learn mathematics. The process generated some frustration, as any true learning experience does, but the knowledge of mathematics and teaching gained by all participants was extraordinary. The ultimate beneficiaries of this learning will be the students in southern New Mexico classrooms. A Brief Description of the MC^{2} Ruidoso Spring 2005 Academy The third MC^{2} math academy was held at the REC IX headquarters in Ruidoso, New Mexico over the course of seven weekends from January through April of 2005. The "content knowledge" portion of the academy was led by Dr. Ted Stanford, Dr. Tony Wang, Dr. Bruce Olberding, and Dr. Linda Zimmerman of NMSU's Department of Mathematical Sciences; while the "pedagogical knowledge" portion was led by Kalle Jorgensen of NMSU's Department of Curriculum and Instruction, with assistance from Dr. Karen Trujillo, also from Curriculum and Instruction. This academy was similar to the ones held in Carlsbad and Las Cruces in the summer of 2004, but modified to a weekend format: instead of meeting on Monday through Friday for three consecutive weeks, meetings were held approximately every other weekend, on Friday evenings and all day Saturday, with homework assigned between sessions. Academy participants – primarily middle school mathematics teachers from school districts in southeast New Mexico – worked individually and in groups to solve challenging, openended math problems developed for the academy by participating NMSU math professors. Through minilectures, oneonone instructor feedback, and peer review, teachers were assisted in deepening their content knowledge, using that knowledge to solve "realworld" mathematics problems, and communicating their findings in ways used by professional mathematicians. Time was also spent each weekend looking more deeply into how to teach these math concepts to middleschool students. Teachers studied each of the statemandated mathematics content standards assigned to their grade level; compared them to what their textbooks cover and to what their students are actually learning; and considered which combinations of various teaching processes (such as reasoning, problem solving, and communicating ideas) might be most appropriate for teaching each of the content standards. Participants also engaged in Lesson Study – a method of working with colleagues to develop and test more effective ways of teaching difficult concepts. Teachers gathered into regional groups, and each group identified a topic their students typically have difficulty grasping. Each team then worked together to develop a lesson designed to help their students understand this topic, and taught the lesson to their own students, observing how students responded to each stage of the lesson. Each teaching experience was followed by a period of reflection and refinement, and the refined lesson was taught to a different group of students to see whether or not the revised lesson worked better than the original. During the last weekend of the academy, each group's findings were shared with the others. The goal
of the Academy was to continue the process of building a professional
learning community of mathematics educators, and this was certainly accomplished.
Mathematicians, K12 teachers, and teacher professional developers all
shared their knowledge of mathematics and how students learn mathematics.
The process generated some frustration, as any true learning experience
does, but the knowledge of mathematics and teaching gained by all participants
was extraordinary. The ultimate beneficiaries of this learning will be
the students in southern New Mexico classrooms.
A Brief Description of the MC^{2} Las Cruces 2005 Summer Academy The Mathematically Connected Communities (MC^{2}) project held a threeweek summer academy at New Mexico State University in Las Cruces, New Mexico, from June 6 to June 23 of 2005. The purpose of the MC^{2} Academy was to strengthen teacher content knowledge – particularly in the areas of geometry, data analysis, and probability – and the teaching skills which would allow them to teach these mathematical concepts to New Mexico's middle school students more effectively. A variety of professors from NMSU's Department of Mathematical Sciences served as facilitators for increasing mathematical content knowledge. These mathematicians created openended problems based on identified teacher needs and requests, and the teachers worked together in groups to solve the problems and explore the math embedded within the tasks. The teachers communicated their ideas with their colleagues and the mathematicians in an ongoing “mathematical conversation.” Faculty and staff from NMSU's College of Education helped academy participants focus on how this deeper knowledge of mathematical content can be translated into more effective teaching, aligned with state and national standards and with the new type of standardized testing students are now being given. Content knowledge and the skills needed to teach this content were woven together in a coordinated effort between the involved education and mathematics specialists. One highlight of the academy was the opportunity to collaboratively develop innovative, focused math lessons, and to try them out with local middleschool students. The goal of this academy, as with the previous ones, was to continue the process of building a professional learning community of mathematics educators. Mathematicians, K12 teachers, and teacher professional developers all shared their knowledge of mathematics and how students learn mathematics. The ultimate beneficiaries of this learning will be the students in southern New Mexico classrooms. 
