Algebra Connections: A Professional Development Model That Links Middle School Preservice and Inservice Teachers Faci

1.  Algebra Connections: A Professional Development Model That Links Middle School Preservice and Inservice Teachers Facilitated by Linda Phillips and Dr. Linda Sheffield  This session details a professional development project of a university class of preservice teachers and the mathematics staff of an urban junior high school that focused on algebra instruction and rich learning tasks. This project influenced the training component of a large math and science initiative currently underway in Northern Kentucky. 

2. Dedicated to the memory of Tara Greene

3. Who is involved... Linda Phillips, educational consultant, Myrtle Beach, SC Dr. Linda Sheffield, Regent�s Professor at Northern Kentucky University in Highland Heights, KY 9 pre-service teachers from NKU 6 in-service teachers from Holmes Junior High School in the Covington, KY school district

4. The Dilemma... Pre-service middle grades mathematics students needed some �real� teachers to work with� Junior high school mathematics teachers needed new instructional ideas as well as encouragement for working with their urban students in a low-performing school...

5. The Solution... Professional development that spanned the fall semester Once a month at the junior high school After school for 1.5 hours with preservice and in-service teachers together University preservice class held in the junior high library on those days for an hour before the joint session. Preservice and inservice teachers received needed credit for their time. (& a small stipend for inservice teachers) Linda Sheffield and Linda Phillips co-facilitated the sessions.

6. Project Objectives Explore algebraic projects for 7th & 8th grades Examine where algebra fits in the curriculum Experiment with instructional and assessment strategies Engage in mathematics dialogue with preservice and inservice teachers

7. The Content of the Professional Development Sessions Rich Learning Tasks - Non-routine algebraic tasks that supported the district�s curriculum map and served as hands-on investigations for junior high students Discourse - Talking, writing, and reflecting about the mathematics, teaching challenges and student learning and misconceptions Assessment - Various types of assessment techniques Follow-up - Inservice and Preservice teachers co-teaching junior high classes

8. How was the content chosen? Used Principles and Standards as a guide Matched curriculum, assessment and instructional strategies to state and district Core Content and University-required New Teacher Standards Chose activities that encouraged cooperative work, reflection and a variety of methods of solution

9. The Structure All teachers did the selected rich learning task for that month during the workshop. Preservice teachers designed a lesson similar to the one modeled and used that with the junior high students along with their inservice teacher. Teacher Teams shared results and student samples at the next workshop. Additional readings and written reflections were required of preservice teachers and inservice teachers earning university credit Preservice teachers also participated in additional sessions on campus

10. Workshop Format Teams told about their teaching experience Showed student samples Modeling and practice of new student task Discussion of professional readings

11. The Tasks Toothpick (patterns, relations, functions) Balance Problems (mathematical models) Jumping Jacks from Connected Math series, grade 7 (variables, patterns) Mystery Graphs (analysis of change) Made use of physical and pictorial models, charts, graphs, tables and graphing calculators

12. Toothpick Problem Use the toothpicks to make four squares in a row as shown below. Without counting, figure out the number of toothpicks you used. How many toothpicks would it take to make 10 squares in a row like this? What about 100 squares in a row?

13. The real math begins after the original question has been answered. Question the answer; don�t just answer the question. Will this method always work? How many different ways might I solve this problem? Why can several different formulas be used to answer the same question? What if the squares were not connected? What if the squares were not in a row? What if we used a different shape such as a triangle or a hexagon?

14. The University Work The preservice teachers were asked to Develop, teach, and reflect on lesson plans based on the rich learning tasks presented in each session Read and apply information from a variety of references such as The Learning Gap; the Teaching Gap; Making Sense: Teaching and Learning Mathematics with Understanding; Knowing and Teaching Elementary Mathematics; and Fostering Algebraic Thinking: A Guide for Teachers, Grades 6-10 and discuss them in class and online.

15. Our Reflections This was an excellent way to blend professional development for preservice and inservice teachers. It was an effective means of getting inservice teachers to try new approaches. More accountability and perhaps more creative assessment was needed to ensure that students used an open approach to explore the tasks in full. Using a lesson study group approach, richer investigations and better dialogue might have occurred if we�d required teams to do the exact task modeled at the workshop.

16. What we learned about Collaboration If you want preservice and inservice teachers to collaborate, you have to be explicit about how to do that. Our inservice teachers let the preservice teachers �do the work� of teaching the lesson to the junior high students and reporting out during the next workshop session.

17. What we learned about  Assessment After the first task, when teachers were asked �how did you assess this with your students?� they answered by describing students� behavior, how they liked doing the task, and if they seemed to �get it.� We needed to be more explicit about creating a rubric to assess this task so that teachers would go beyond �on/off task� as the measure of effectiveness.

18. What we learned about Instructional Style Teachers valued speed and �right answers� to these tasks vs diverse and multi-approach solutions. Teachers �led� or �showed� students what to do rather than allowing their learning to unfold. Teachers were frustrated when students were unable to derive a formula at the end of the task but did not consider modeling one for their students.

19. What we learned aboutWriting If teachers are going to ask students to write, they need to have a written entry-- preferably one they did themselves!-- to share with students.This will give the students a model of what a strong writing sample looks like and sounds like. Teachers often shared thoughts online that they did not discuss in person.

20. Teacher Comments: A Surprise� or not?? During the second workshop, teachers were reflecting about the students� work. This is what we heard: kids were working too far ahead, they got it too quickly, it was over before it started, they didn�t do it the way I showed them, I was trying to get them to�, I showed them how to�, I told them to�, I created a way to�, this was a good 20 min activity to throw in extra, it�s a good Friday fun activity, the one working alone figured it out as fast as the group working together, this kept them busy until the end of the period

21. Progress requires long-term commitment. Following the last workshop, preservice and inservice teachers wrote some of the following comments: �Allowing the students to find their own methods can only enhance their learning while giving them confidence.� �Using concrete models helped them tremendously to really understand rather than learning a bunch of rules for solving it.� �This morning several of the students who used to be primarily behavioral problems told me that math was now their favorite subject because I made it fun.�

22. Progress continued with Improving Educator Quality Grant �Planting Seeds, Cultivating Clusters: Strengthening Middle Grades Mathematics and Science� Ten lead teachers in 25 middle schools PD with lead teachers and middle grades students on campus in summer and monthly during academic year Lead teachers conduct PD, lesson study groups with others in their clusters and follow up in their classrooms Preservice practicum students placed with lead teachers

23. For More Information Linda Phillips:LJPhillips@earthlink.net Linda Sheffield: Sheffield@nku.edu See http://www.nku.edu/~mathed http://www.nku.edu/~mathed/algcon.ppt http://www.nku.edu/~mathed/ieq2003.html