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Course Overview
This course will help you think about teaching and learning mathematics in grades K-6. It will not provide a "recipe" for good elementary mathematics teaching. Rather, the course readings, outside assignments, class and field activities and discussions will provide opportunities for you to think about learning and teaching mathematics in ways that enable you to make good instructional decisions. It is necessary to give careful consideration to the content and methods of mathematics instruction that will help your students be successful in today's world. The discipline of mathematics is growing and changing. Over half of all mathematics has been invented since World War II (Davis & Hersh, 1981). It is impossible for any one person to know all there is to know or to be able to predict the specific mathematical content of problems that one might encounter, but it is important for people to be able to make sense of mathematical situations. Success in the 21st century will be available to students who possess more than a large number of facts and computational skills.
Teaching in North Carolina requires that you use the Standard Course of Study to guide your curriculum decisions. Please be aware that the new standard course of study will be implemented in 2004-2005 which means that there will be one set of math competencies for your internship and student teaching and a different set for your first year teaching. There are four math strands with problem solving permeating the entire curriculum: number sense, numeration, & numerical operations; spatial sense, measurement, & geometry; patterns, relationships, & functions; data, probability, & statistics. At the end of each school year in grades 3-6, students take an end-of-grade (EOG) test. In a single two semester credit course, it is impossible to adequately work with everything that you need to know to be an elementary math teacher and everything you will be responsible for regarding EOG tests and other K-2 assessments. Instead of doing a little of this and a little of that, we will focus heavily on one strand and think about how to use what we learn about that strand to continue learning about other strands. In MAT 2030 the focus content was from two strands, patterns, relationships, & functions and data, probability, & statistics; in CI/MAT 3030 the content focus was from the number sense, numeration, & numerical operations. The content focus for CI 4030 will be geometry.
Course Goals
Goals for the course span across several interrelated areas. You will probably notice that they are stated as areas you are "beginning to" learn about since these are areas that you will continue to work on during your internship and ones that teachers work on improving across their careers.
Developing a Stance Toward Mathematics Teaching: You will be supported in developing and articulating a principled stance toward teaching mathematics.
Building a Teaching Repertoire: You will begin to build your knowledge of and skill in the formulation of mathematical goals, identification of mathematical concepts and relationships, appraisal of curricular materials and instructional representations of mathematics, selection of tasks, determination of organizational arrangements and assessment of student understanding that are consistent with your stance. You will learn to make analysis and reflection a regular and ongoing part of your teaching activity.
Developing Knowledge of Curriculum and Planning: You will begin to construct knowledge of mathematics curriculum and how to select and organize content, skills, and strategies. This will include exploring geometry in the mathematics curriculum K-6. You also will plan and teach a sequence of three math lessons during your full-time internship.
Understanding Children as Learners: You will begin to learn how children's mathematical knowledge, skills, and dispositions develop over time. You will learn to adapt your planning to the learning needs of individuals and groups.
Establishing and Managing an Equitable Community of Learners: You will explore what it means to create a learning community that fosters learning for all students, taking into account their gender, race, ethnicity, socioeconomic status, language use, special needs, and personal qualities. You will examine ways in which particular classroom discourse patterns and particular tasks influence diverse learners.
Assessing Students' Mathematical Understanding: You will have opportunities to think about the assessment of individual and group learning in mathematics.
Course Themes and Central Questions
In the contexts of teaching and learning mathematics, we will explore three major themes to help us work toward the course goals.
MYSELF AS A LEARNER: How did/do I learn mathematics? How do my own past and present experiences compare with what I want for learners in my own classroom? What kind of learning in mathematics will I need to continue to pursue across my career?
SOCIAL CONSTRUCTIVISM: How do diverse students learn mathematics? What role does social interaction play in their learning? How do learners construct understanding? In what ways am I similar to or different from the learners I will teach (e.g., race, ethnicity, culture, socio-economic, ability linguistic, gender)? What implications do these comparisons have for my teaching and my students’ learning?
ALTERNATIVE IMAGES OF PRACTICE: What do classroom practices that draw on recent research and theories look like? How can I create the kind of classroom I envision? What goals, materials, discourse patterns, and tasks will facilitate learning in mathematics? How should I plan for the kind of instruction I envision?
Professional Opportunities
The National Council of Teachers of Mathematics (NCTM) [ http://www.nctm.org/ ] is the national mathematics education organization dedicated to improving the teaching and learning of mathematics. It is a recognized leader in efforts to ensure an excellent mathematics education for all students and an opportunity for every mathematics teacher to grow professionally. There are some special opportunities available to you as a student. You can become a student member for one year with all of the benefits of regular members for half price ($36). Another option is the NCTM starter kit for $14. If you choose the starter kit I have to mail the checks and everything is mailed back to me and I distribute to you. With either option, the journal you would be most interested in receiving is Teaching Children Mathematics. Neither of these offers are requirements for this course.
The North Carolina Council of Teachers of Mathematics [http://www.ncctm.org/ ] is the state mathematics education organization. The state organization is recognized nationally for its quality and active member participation. You can join this organization for a small amount of money as a student. The annual state math conference is held each fall. The state math conference is highly attended by classroom teachers because there are many grade-level specific workshops and sessions throughout the conference as well as exhibits of mathematics materials and resources. The pre-conference program and registration are available online. On March 20, NCCTM is having a conference for pre-service and first-year teachers in Karpen Hall on the campus of the University of North Carolina at Asheville. Seminars and workshops are tailored specifically for you! A flyer with more details will follow. Extra credit will be given to students who attend for the day and write a reflection.
ASU has an active PTMA (Prospective Teachers of Mathematics Association). They have monthly meetings with engaging programs and speakers. Elementary Education majors are welcomed and encouraged to attend their meetings. I will provide advance notice about each meeting. Most of you have attended some of these meetings in the past. I encourage you to do so again.
The Math and Science Education Center (http://www1.appstate.edu/dept/msec/index.html) is located on the 2nd floor in Walker Hall. Available for check out are many wonderful math and science materials and manipulatives. They also have many journals available and you can copy limited pages for free. This is a terrific resource. If you have not visited, it's worth the trip.
Course Requirements and Evaluation:
Texts:
| Participation, Reading, Labs, & Writing to Support Learning | 30 points |
| Individual & Group Math Assessment | |
| Part 1 | 10 points |
| Part 2 | 10 points |
| Part 3 | 10 points |
| Investigating & Creating Geometry Resources | 30 points |
| Geometry in Our World Project | 10 points |
| *Test 1 | 40 points |
| *Test 2 | 40 points |
| Planning/Teaching/Reflecting Lessons | 20 points |
| TOTAL POINTS | 200 points |
| *You must average at least a "C" on the 2 tests to pass the course. | |
Your participation in our class activities and discussions is important not only for your learning but also the learning of others. You are strongly encouraged to be prompt for each class. 2 tardies are equivalent to 1 unexcused absence. Unexcused absences will result in the lowering of your grade. Prior notification (262-2233) of a valid need to miss class is a minimum condition for excusing an absence. For every unexcused absence, you will have 3 percentage points deducted from your course grade average.
Grading Scale (given as a percentage of the total points):
A = 94-100
A- = 90-93
B+ = 87-89
B = 83-86
B- = 80-82
C+ = 78-79
C = 76-77
C- = 74-75
D = 69-73
Participation, Reading, Labs, & Writing to Support Learning. The learning that I aim for in this course (clarifying, testing, and justifying ideas) depends largely on your attendance and active participation. Prompt attendance is expected at all class and field experiences. You will read and/or complete reading responses as scheduled. Writing can help you to clarify and stretch your thinking about teaching. We will do a series of writing to support learning in this course. The class will involve much student participation. It is particularly important that you complete readings, writing, and other assignments on time, because class and group discussions will generally be based on them. Your participation in our class activities and discussions is important not only for your learning but also the learning of others. Throughout the semester I will collect your writing, reflections, and labs. Due dates for this do not appear on your course schedule or block calendar.
Individual and Group Math Assessments: It is important to learn to assess individuals as well as groups in your mathematics instruction. There are three parts to this assignment. A handout with details for this assignment will be provided. Part 1 is due February 19; part II is due March 16 and part III is due April 30 .
Investigating & Creating Geometry Resources: As mentioned earlier, there are four strands in the NC Standard Course of Study. Descriptions of the strands can be found at [http://www.dpi.state.nc.us/curriculum/]. As a teacher you are responsible for helping your students work towards the objectives identified in the NC Standard Course of Study. You need to be familiar with appropriate resources that support learning related to the objectives. This assignment is divided into two parts. In the first part you will examine teacher resources available on the NC DPI website related to the geometry strand. In the second part you will begin to develop a resource file related to the geometry strand. Extensive details for this assignment are provided in a separate handout. Part I is due February 5 , and Part II is due March 18.
Test 1 & 2: We will explore and develop our understanding about the NC geometry strand. We also will explore children's understanding about this strand. The test will include all course readings, activities, & discussions thus far. The test will provide an opportunity for you to demonstrate your understanding about the strand from a teacher’s perspective. Test #1, February 19; Test #2, March 25.
Geometry in Our World Project: Aspects of geometry abound in our daily lives. Architecture, visual arts, applied arts, engineering, road signs, sports, and nature are just a few examples. You will explore geometry in our world and then create some type of product to use in your classroom that highlights geometry in our world. The product may be a webpage, PowerPoint presentation, construction, I-Movie, or something else approved by the instructor. It is due on January 29.
Planning,
Teaching, Reflecting Lessons: During your internship you will plan,
teach, and reflect about sequence of three math lessons. These lessons
may relate to any of the four math strands. Consult with your teacher about
what may be appropriate for your classroom. Your collaborating teacher
must review and initial your lesson plans at least two days prior to your
teaching the lessons. You will teach and write a reflection about your
lessons sometime during your full-time internship. The lessons and reflections
are due April 30.
CI 4030
Course Schedule & Assignments
The readings are available online
by going to the ASU libraries (http://www.library.appstate.edu/),
click on "reserves" and then search by instructor.
Click here
for reading response questions.
| Date | Reading/Focus | Assignment Due |
|
Tuesday, January 13 |
Overview of course
The Geo Gazette |
|
| Thursday, January 15 | Introduce Geometry in Our World
Project
Introduce Investigating & Creating Geometry Resources |
|
| Tuesday, January 20 | Read online: Math by All Means, Introduction pp. 1-3; 143-146 and do Reading Reflection | |
| Thursday, January 22 | Read online: Young Children's Ideas about Geometric Shapes and do Reading Reflection | |
| Tuesday, January 27 | ||
| Thursday, January 29 | Geometry in Our World Project
due
Reading Reflections |
|
| Tuesday, February 3 |
Introduce Assessment, Part I |
Read online: The Tools of Classroom Talk and do Reading Reflection |
| Thursday, February 5 |
|
Investigating & Creating Geometry Resources Part 1 due |
| Tuesday, February 10 |
Read online: The van Hiele Levels of Geometric Thought pp 347-350 and do Reading Reflection |
|
| Thursday, February 12 | Read online: Symmetry the Trademark Way and do Reading Reflection | |
| Tuesday, February 17 | Symmetry
References
Interactive Math Dictionary |
|
| Thursday, February 19 | Test #1
Assessment, Part I due |
|
| Tuesday, February 24 |
Introduce Assessment, Part II |
|
|
Thursday, February 26 |
Read online: Making Connections: From Paper to Pop-up Books and do Reading Reflection | |
| Tuesday, March 2 | ||
| Friday, March 5 | Introduce Assessment, Part
III
|
Read online: A New Kind of Assessment and do Reading Reflection |
| Spring Break, March 8-12 | ||
| Tuesday, March 16 | Introduce Planning, Teaching, Reflecting Lessons | Read online: Why are Some Solids
Perfect? and do Reading Reflection
Assessment, Part II due
|
| Thursday, March 18 | Read online: The Art of Tessellation
and do Reading Reflection
Investigating & Creating Geometry Resources Part 2 due |
|
| Tuesday, March 23 | ||
| Thursday, March 25 | Test #2 | |
| Friday, April 30 | Assessment, Part III and Planning, Teaching, Reflecting Lessons due |