Convention Convention is an application service for managing large or small academic conferences, annual meetings, and other types of events! Submission - Custom fields, multiple submission types, tracks, audio visual, multiple upload formats, automatic conversion to pdf. Review - Peer Review, Bulk reviewer assignment, bulk emails, ranking, z-score statistics, and multiple worksheets! Reports - Many standard and custom reports generated while you wait. Print programs with participant indexes, event grids, and more! Scheduling - Flexible and convenient grid scheduling within rooms and buildings. Conflict checking and advanced filtering. Communication - Bulk email tools to help your administrators send reminders and responses. Use form letters, a message center, and much more! Management - Search tools, duplicate people management, editing tools, submission transfers, many tools to manage a variety of conference management headaches! Click here for more information.
Association: Name: North American Chapter of the International Group for the Psychology of Mathematics Education URL: http://www.pmena.org
Citation: URL: http://www.allacademic.com/meta/p117586_index.html Direct Link: HTML Code:

Parks, Amy. "Exploring the Challenges of Learning to Teach Reform-oriented Mathematics Lessons" Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Delta Chelsea Hotel, Toronto, Ontario, Canada, Oct 21, 2004 <Not Available>. 2009-05-26 <http://www.allacademic.com/meta/p117586_index.html>

Parks, A. N. , 2004-10-21 "Exploring the Challenges of Learning to Teach Reform-oriented Mathematics Lessons" Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Delta Chelsea Hotel, Toronto, Ontario, Canada Online <.PDF>. 2009-05-26 from http://www.allacademic.com/meta/p117586_index.html

Publication Type: Conference Paper/Unpublished Manuscript Review Method: Peer Reviewed Abstract: Purpose Over the last decade, a number of publishers have put out mathematics curricula designed to support elementary teachers’ efforts to enact the NCTM standards in their classrooms. Teachers have been asked to promote reasoning and problem-solving, to rely on the conventions of mathematics to determine right answers and to allow students to explore their own conjectures (National Council of Teachers of Mathematics, 1991). However, these curricula have been only moderately successful in helping teachers change their practices (Ball & Cohen, 1996; Remillard, 2000; Manouchehri, 1998). Learning to use these curricula in meaningful ways is especially difficult for novice teachers. The purpose of this paper is to discuss some of the teaching choices made by two elementary pre-service teachers as they implemented a reform curriculum, and to explore the ways that those choices made it difficult for them to enact that curriculum in a way that was consistent with the NCTM standards. Theoretical Framework To better understand the practices of the pre-service teachers I supervised, I decided to use Stein, Grover & Henningsen’s (1996) framework for looking at the cognitive demand of a task as it progresses through various phases of implementation: as it is presented by the teacher, as it is implemented in the classroom, and as it is interpreted by students. However, for pre-service teachers, who are often required to do thorough written plans, I felt it was important to understand the ways in which tasks were changed during planning. As a result, I modified the framework presented by Stein and colleagues slightly. I analyzed changes in tasks as they moved from the curriculum intended by the publishers, to the curriculum planned by the pre-service teachers, to the curriculum actually enacted in the classroom by the pre-service teachers and their students. I also drew on Henningsen and Stein’s (1997) work to look at the factors involved when teachers maintain the cognitive demand of quality tasks, as well as the factors involved when they reduce the cognitive demand of tasks. I used their findings as a starting point to explore the factors that affected the changes the pre-service teachers made to their lessons. Henningsen and Stein’s factors included: ·Removal of the challenging aspects of the task ·Allocation of too much or too little time ·Emphasis on correct or complete answers, rather than understanding ·Selection of inappropriate tasks ·Problems with classroom management Methods I was the field instructor for four pre-service teachers participating in a year-long internship program. Throughout the Fall semester, the interns gradually took over instructional tasks in the classroom and began “lead teaching” in February. I observed all four interns regularly in a variety of subjects, held post-observation conferences and taught a weekly teacher education seminar at their placement school. For this investigation, I focused on two of the four interns: Anna, who taught first grade, and Stephanie, who taught second. I observed Anna and Stephanie each teach two math lessons. I audio taped these observations and the post-observation conferences that followed, collected copies of their plans and made copies of the Math Trailblazers lessons on which they based their plans. For the analysis of each lesson, I mapped out the activities as suggested by Trailblazers, as planned by the interns and as taught in the classroom. I then looked for changes that occurred between stages. I used the interns’ written lesson plans as the record of the planned curriculum and the transcript of the lesson as the record of the enacted curriculum. I looked at each change that was made to see if it was likely to have increased, maintained or decreased the cognitive demand of the original task. Then, working one lesson at a time, I examined the transcripts of the lessons for the factors Stein and colleagues identified as contributing to cognitive decline. Factors they presented seemed to show up in very specific ways in the interns’ teaching so I created a new list of factors that was more descriptive of the work done by these two interns. I then focused in on four factors that contributed significantly to cognitive decline in all observed lessons. Data I observed Stephanie teach one second-grade lesson on volume and one on arrays. The Trailblazers curriculum allocated an hour for both lessons; in her plans Stephanie allotted 20 minutes for the volume lesson and 30 minutes for the array lesson. In the classroom, the length of both lessons was reduced further. The volume lesson lasted just 10 minutes, while the arrays lesson was cut to 22 minutes. During planning of both lessons, Stephanie eliminated work with manipulatives that the curriculum suggested. In the interviews, she said she thought that the hands-on work was not necessary to support student learning. During teaching, she modified both lessons further by eliminating partner and small-group work, although she had scheduled these activities in her written plans. In first grade, I observed Anna teach one lesson on moving around the hundred’s chart and one on grouping by tens. In her lesson plans, Anna cut the time suggested by Trailblazers for each lesson in half. The grouping by tens lesson lasted the planned half hour, while the hundred’s chart lesson lasted 22 minutes. In her plans for both lessons, Anna increased the amount of modeling suggested by Trailblazers. In the hundred’s chart lesson, she eliminated all independent and group work. Instead, she planned to have the children follow her work on the overhead throughout the lesson. During the interview, she expressed a fear that the children would not have understood the lesson if they had been allowed to work independently. In the grouping by tens lesson, Anna’s plans revealed that she had intended to follow the Trailblazer suggestion to begin by allowing children to experiment with various ways of grouping and counting; however, in the classroom, she eliminated this step and modeled for children how to count by tens using a ten’s frame. She then asked them to count their objects in the same way at their seats. Conclusions Virtually all of the changes made by interns in both planning and teaching reduced the cognitive demand of the original tasks. With a few minor exceptions, each change reduced students’ opportunities to think and reason, to communicate about mathematics and to focus on meaning rather than procedures. While I used only these four lessons as the basis of my conclusions for this paper, what I found is consistent with my observations of math lessons taught by both pre-service teachers throughout the year. In all four lessons, I identified the following factors as contributing to cognitive decline: 1. Too little time 2. Determination by teacher of right and wrong answers 3. Elimination of discussion after independent work (or no independent work) 4. Extensive modeling The common factors that Henningsen and Stein listed as contributing to cognitive decline needed to be modified to appropriately describe the interns’ teaching. While too much time was a common factor cited by Henningsen and Stein, that was never the case for the interns. Like the experienced teachers, the interns reduced the cognitive demands of tasks by removing complexity and taking over for students. However, the interns did this by changing the format of math lessons. They increased the amount of time spent modeling and decreased the amount of time spent in independent work and discussion. The experienced teachers described by Henningsen & Stein seemed to follow a launch, work, discussion format even when they reduced the cognitive demand of their tasks. The way classroom management affected the cognitive demand of the interns’ lessons also seems to be different from what was described by Henningsen & Stein. They reported that in some lessons, problems with classroom management led to environments where students were engaged in absolutely no mathematical activity. This never happened in the lessons I observed; however, concerns about classroom management may have influenced the interns’ decisions about how much independent work or discussion to allow. Concerns about discipline may also have encouraged both interns to cut their lessons short. Using the Henningsen & Stein framework to closely analyze lessons helped me as a field supervisor to identify common factors that led to reduced cognitive demand across the mathematics teaching of all four interns I supervised. This work informed my practice as a teacher educator. By naming observable behaviors such as excessive modeling or elimination of discussion, I was able to give more specific feedback in post-observation conferences later in the year and to work with interns during planning sessions to help them preserve the cognitive demand of lessons presented in the written curriculum. This beginning investigation suggests that researchers need to do more to understand the ways that teachers new to standards-based teaching adapt reform curricula, with attention to how teacher educators might support novices in maintaining the cognitive demand of tasks presented in these curricula. References Ball, D.L. and Cohen, D.K. (1996) Reform by the book: What is or might be the role of curriculum materials in teacher learning and instructional reform? Educational Researcher, 25(9), pp. 6-8. Henningsen, M. & Stein, M.K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28, pp. 524-549. Math Trailblazers (1998). Foundations of Math Trailblazers in Math Trailblazers Teacher Implementation Guide. Kendall/Hunt Publishing Company. Manourchechri, A. (1998). Mathematics curriculum, reform and teachers: Understanding the connections. Journal of Educational Research, 92(1), pp. 27-41. National Council of Teachers of Mathematics (1991). Professional standards for teaching mathematics. Reston: Author. Remillard, J.T. (2000). Can curriculum materials support teachers’ learning? Two fourth-grade teachers use of a new mathematics text. Elementary School Journal, 100(4), pp. 331-350. Stein, M.K., Grover, B.W. & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), pp. 455-488.

Promoting Teacher Learning of Mathematics: The Use of "Teaching-Related Mathematics Tasks" in Teacher Education

Teaching all children mathematics: Preservice elementary teachers perceptions of teaching diverse learners

Mathematics Virtual Learning Village: Occassioning Student Teachers' Learning to Teach Mathematics

What Discussions Teach Us About Mathematical Understanding: Exploring and Assessing Students’ Mathematical Work in Classrooms

Preparing Preservice Teachers to Teach Students Who are at Risk for Mathematics Disabilities: Evidence-Based Practices for Early Mathematics Instruction