Exploring the Challenges of Designing A Program for Middle Grades - - PDF document

Exploring the Challenges of Designing A Program for Middle Grades Mathematics Licensure

Ron Benbow Mark Colgan Mathematics Dept. Mathematics Dept. Taylor University Taylor University Upland, IN 46989 Upland, IN 46989 rnbenbow@taylor.edu mrcolgan@taylor.edu

PMET Conference Kent State University June 3, 2006

• I. Introduction: Taylor University, math department, and math education program
• II. Creation of Middle School program

A.. PMET workshops

• B. Professional Standards

C.. TU middle school math program curricula

• III. Mathematics in the Junior High/Middle School (new) course (MAT 280)
• A. Overview and objectives
• B. Field Experience component
• C. Sample activites/assignments
• IV. Course Assessment Research results
• V. Lessons Learned: what went well and what we would do differently
• VI. Questions/Comments?

• I. Course Overview

MAT 280 MATHEMATICS IN THE JUNIOR HIGH/MIDDLE SCHOOL MWF – Spring 2006 3 Credit Hours Course Description: An integrated content-methods course for middle school and introductory high school preparation. This course is a study of the mathematics taught in the middle grades (grades 6-8 with extensions to grades 5 and 9) with special reference to teaching aids, laboratory methods, and pedagogy, including classroom use of manipulatives and technology. Corequisite: MAT 180 or permission of the instructor. Objectives: 1) To help prospective teachers develop an adult-level understanding and conceptual knowledge of the mathematics content taught in the middle grades, particularly algebra, rational numbers, geometry and measurement, and data analysis and probability. 2) To involve prospective teachers in mathematical activities that will equip them with the skills and resources needed to effectively teach mathematics to a wide range of diverse learners, including experiences with a variety of manipulative materials. 3) To give prospective teachers opportunities to experience working with middle-grades students so they can appreciate the joys and challenges of working with these students. 4) To provide opportunities to develop, analyze, reflect on, and teach mathematics lessons appropriate for middle-grades students. 5) To involve prospective teachers in reflection and discussion of current issues in mathematics education so they can further develop their philosophy of teaching mathematics, particularly as it relates to active learning, fun, technology, connections, communication, and teaching from a problem-solving perspective. TEMP Program: Prospective teachers will participate weekly in the TAYLOR- EASTBROOK MATHEMATICS PROJECT (TEMP), which gives Taylor students an

• pportunity to teach mathematics lessons at local schools. Students will work in teams to

develop an appropriate lesson each week (like team homework) and then teach the lesson in teams at a nearby school. Team lesson plans will be submitted in advance for assessment, and then a one-page, individual reflective report will be due following the teaching experience. More specific information will be provided early in the semester.

EACS TU Partnership: Prospective teachers will have the opportunity to participate in the East Allen County Schools TU Partnership, which involves Taylor students and faculty meeting twice with EACS 5th grade students, once in Ft. Wayne and once at Taylor. The purpose is to help these young students begin thinking about attending college and provide positive role models for them. Between visits, Taylor students are encouraged to communicate with their EASC students by e-mail. This experience will provide additional valuable insight into the thinking of young middle-grades students. You will be asked to write a short paper summarizing your experience with your EACS student. Text: Rubenstein, R., C. Beckmann, and D. Thompson. Teaching and Learning Middle Grades Mathematics. Key College Publishing, 2004. Grades:

• 1. 2 Exams

30% 90 - 100% A's & Requirements

• 2. Quizzes

15% 80 - 89% B's

• 3. Notebook & Papers

20% 70 - 79% C's

• 4. TEMP & EACS

25% 60 - 69% D's field experiences

• 5. Resources File Project

10% 3) Notebooks will be graded 3 times during the semester. They should be organized by sections of a loose-leaf notebook and should include class activities, notes, homework, reflections, and one Mathematics Teaching in the Middle School (MTMS) paper. 4) Students will receive credit for their participation each week in the TEMP field

• experience. Feedback from your schoolteacher, instructor observations, and the quality

and timeliness of TEMP reports will all contribute to the score for TEMP lessons. 5) Students will create a file of mathematics activities suitable for use with middle-grades

• students. The file should include activities sorted into the four categories of 1) algebra,

2) rational numbers and other number operations, 3) geometry and measurement, and 4) probability and statistics. Students should document how each activity involves the various NCTM process standards of problem solving, reasoning and proof, communication, connections, and representation. The file should include at least 5 quality activities for each of the four categories. You may work together in groups to find the activities, but each student should have his/her own file for future use.

• II. Sample Activities
• A. We studied the textbook's 7 cooperative learning strategies by having the students in the

course involved in an activity that fit each strategy:

• Think-Pair-Share
• Round Table
• Co-op
• Learning Stations
• Random Reporting
• Pairs Check
• Jigsaw

Various activities in the textbook linked a different cooperative learning strategy with a different concept in algebra. Students were able to experience each strategy while also learning effective ways to teach algebra.

• B. We also did a variety of activities to help students experience multiple representations of

concepts, particularly with rational numbers (candy bars, fraction strips or bars, pattern blocks, Cuisenaire Rods, tangrams, decimal squares, Base-10 blocks, etc.)

• C. We did activities to help students go beyond simple procedural knowledge to more conceptual

knowledge, so they could understand the concepts in a deeper way. This included activities where we discussed the rules for addition, subtraction, multiplication, and division of both fractions and decimals, and why the rules work. See the excellent textbook for more details: Rubenstein, R., C. Beckmann, and D. Thompson. Teaching and Learning Middle Grades

• Mathematics. Key College Publishing, 2004.

• III. MAT 280 Course Assessment—Spring 2006
• A. Please answer the following concerning the extent to which the 5 main objectives of the MAT

280 course were met. Please comment if you have particular thoughts or suggestions. Key: SD–strongly disagree D–disagree N–neutral A–agree SA –strongly agree

Was this objective met?

• 1. To help prospective teachers develop an adult-

level understanding and conceptual knowledge

• f the mathematics content taught in the middle

grades, particularly algebra, rational numbers, geometry and measurement, and data analysis and probability.

SD D N A SA

8 8 Comments:

This is the methods class I have been waiting for! It was very helpful to actually do the activities that the students would do. Yes, it was done very well. I am disappointed there aren't classes like this for the high school level.

• 2. To involve prospective teachers in mathematical

activities that will equip them with the skills and resources needed to effectively teach mathematics to a wide range of diverse learners, including experiences with a variety of manipulative materials.

SD D N A SA

1 5 10 Comments:

Showing how to use manipulatives effectively is great because mostly we just hear about them. All the sheets and manipulatives will be so helpful to have! I really liked that we used the manipulatives and did not just talk about them. I used and learned a lot about different mathematical teaching materials that I had never seen before (Fraction strips, tangrams, etc.) Our use of multiple manipulatives and activities introduced numerous methods of teaching various concepts.

• 3. To give prospective teachers opportunities to

experience working with middle-grades students so they can appreciate the joys and challenges of working with these students.

SD D N A SA

6 10 Comments:

I loved the field experience. Being able to teach has been a huge step for learning about teaching. The lab was frustrating to me at times because of the time it took and trying to do it in a group. However, I did learn some valuable lessons from it.

• 4. To provide opportunities to develop, analyze,

reflect on, and teach mathematics lessons appropriate for middle-grades students.

SD D N A SA

7 9 Comments:

TEMP reports were a great way to encourage reflection. We had so much discussion. So I was always analyzing and thinking. This was great! Yes, because I never really wrote a lesson until this class.

• 5. To involve prospective teachers in reflection and

discussion of current issues in mathematics education so they can further develop their philosophy of teaching mathematics, particularly as it relates to active learning, fun, technology, connections, communication, and teaching from a problem-solving perspective.

SD D N A SA

1 1 7 7 Comments:

This class has really got me thinking about my overall teaching philosophy a lot. We could have done more of this. Class discussions of lessons from previous weeks were helpful to see what the rest of the class was doing.

Sample Quotes from students (Spring 2006) on the course and field experience: We need more classes like this that specifically take each topic we will teach some day and show us ways to teach it. It is important to grow and mature, but I do not think it is possible without reflecting on the past. This class has really shown me a lot about who I am as a math teacher and as a person. The TEMP field experience was the … best part of the course. I really enjoyed the group activities. I am learning to more appreciate the non-traditional way of teaching math. Working in groups of three was another thing that I enjoyed about this

• experience. I would have felt very overwhelmed if I had needed to write lesson plans and teach

all by myself. Excellent idea to get us in the classrooms and teaching. It helps make what we learn in the classroom have a practical, weekly context. We always need more classroom experience! Extremely important. I learn so much about teaching through practice. Until this semester, I really didn’t realize how much technique and skill goes into teaching. There is so much more to it than just the math part of it. I realized how much better the class will be organized and how much more interesting the class period will be if you take the time to develop a good lesson. I was also able to use a lot of different teaching materials, which I had never seen before.

References/Resources: Middle School Mathematics

Rubenstein, R., C. Beckmann, D. Thompson. Teaching and Learning Middle Grades

• Mathematics. Key College Publishing, 2004.

Papick, Ira. Algebra Connections. Connecting Middle School and College Mathematics (NSF), Prentice Hall, 2005. Beem, John. Geometry Connections. Connecting Middle School and College Mathematics (NSF), Prentice Hall, 2005. Perkowski, Debra, and Michael Perkowski. Data Analysis and Probability Connections. Connecting Middle School and College Mathematics (NSF), Prentice Hall, 2005. Albert, Jim. Teaching Statistics Using Baseball. MAA Classroom Resource Materials, 2003. Key Curriculum Press. Tinkerplots www.keypress.com/tinkerplots Connected Mathematics. Prentice Hall www.math.msu.edu/cmp/Transp.html Middle Grades MathThematics. McDougal Littell. (The Stem Project) www.mlmath.com TIMSS videos; http://nces.ed.gov/timss/Video.asp (CM)2 Project. (Connecting Middle School and College Mathematics) www.teachmathmissouri.org Indiana Middle School Math content Standards. www.indianastandards.org/ Modeling Middle School Mathematics. www.mmmproject.org. NSF-funded initiatives: MMAP, MiC, MathScape, CMP, MathThematics Stigler, James W., James Hiebert. The Teaching Gap. New York; Free Press, 1999. The Mathematical Education of Teachers, Parts I, II. Conference Board of the Mathematical Sciences, AMS, MAA, 2000.