EDCI 425: Spring 2010
Teaching Mathematics in the Secondary School
Thursday 12:00pm to 1:45pm
PAO 1197
Instructor: Jerry Woodward
Office: MATH 241
Office Phone: (765) 494-9578
E-mail:
Office Hours: Thursday 11-12, 2-3 or by appointment
Course Description
This course is designed for students who are planning to be secondary mathematics teachers. The course content is organized using Principles and Standards for School Mathematics published by the National Council of Teachers of Mathematics (NCTM) in 2000. Principles and Standards proposes a vision for mathematics classrooms “where students of varied backgrounds and abilities work with expert teachers, learning important mathematical ideas with understanding, in environments that are equitable, challenging, supportive, and technologically equipped for the twenty-first century” (p. 3). In this course, we will focus on NCTM’s six overarching principles (i.e., equity, curriculum, teaching, learning, assessment, and technology); five process standards (i.e., problem solving, reasoning and proof, communication, connections, and representations), and five content standards (i.e., number and operations, algebra, geometry, measurement, and data analysis and probability).
Course Goals
1. To develop lesson plans promoting students’ development of conceptual and procedural understanding of mathematics.
2. To develop understanding of student learning and development in mathematics by engaging in tasks similar to those that might be given to students.
3. To develop understanding of curriculum in context through teaching and working on mathematical problems from variety texts.
4. To develop understanding of the scope and significance of secondary school mathematics through an examination of state and national standards and mathematics education research.
5. To develop professionally through the demonstration of professional attitudes and work habits as well as the identification of professional organizations and resources that are available locally and nationally.
rEQUIRED MEMBERSHIPS
Student membership to National Council of Teachers of Mathematics (NCTM):
Information regarding student e-membership and an online application can be found at: http://www.nctm.org/benefits-student.aspx. Establishing yourself within this organization is professionally beneficial and allows you to gain access to valuable resources. School administration likes their teachers to be connected to the professional organization in their content area. A student membership costs $39 for a year and will allow you online access to the Principles and Standards. Additionally, you will be given online access to The Mathematics Teacher (the journal for high school mathematics teachers). If you would like to purchase a paper copy of the Principles and Standards or any other of their resources, your membership gives you a 20% discount.
Student membership to Indiana Council of Teachers of Mathematics (ICTM):
Affiliation with the state chapter of NCTM (in our case, ICTM) can also provide rich learning and collaborative possibilities. To apply for student membership, go to http://www.indianamath.org/ and mail $6 along with your contact information to the address provided. In addition to your own learning, these memberships indicate to future potential employers that you take an active role in your professional development.
Course requirements
Participation (20 pts)
Active participation in class discussions and activities, demonstrations that course assignments have been thoroughly read, and thoroughly completed assignments are required.
FIELD EXPERIENCE: PARTICIPATION & REFLECTIONS
A total of 15 hours of field experience in a mathematics classroom is required during this course.
Field Experience Participation (50 pts):
10-15 hours of your field experience will fall into this category. These will be completed in a local secondary mathematics classroom to which you will be assigned based on your availability during the school day. You will make some observations of the teacher, assist with classroom activities, and then teach a minimum of one time. I strongly encourage you to teach and do as much as your teacher will allow, as it will facilitate your transition into student teaching. Your participation MUST be structured into one visit per week or one visit every other week until you have completed your hours. While you may stay as long as you like for each visit, one visit can count for a maximum of two hours of credit. Thus you must visit the school at least 5 times during the semester. Only by completing the Field Experience Verification Form will the participation requirement be fulfilled. Please begin the participation as soon as you are able to coordinate your visits with your assigned teacher. Be very appreciative of him/her for allowing you to come into their classroom!
Alternative Activities – You may get credit for up to 5 hours of participation with any combination of the alternate activities listed below. For each activity you need to provide documentation of participation.
1) Attend ICTM or NCTM Conference
2) Assist with a Purdue Mathematics Outreach Activity
3) TA/SI experience in mathematics courses at Purdue University
4) Classroom observations in other high schools
5) Assist with middle school or high school math teams/clubs such as MATHCOUNTS or Math Field Day at Purdue.
6) Propose your own activity related to math education (subject to instructor approval).
Reflections (50 pts):
A total of 5 journal reflections are required, responding to the Field Experience Response Prompts (distributed in class). A minimum of 2 pages (double-spaced) is expected for each reflection. These reflections should be based on your 10-15 hours of classroom observations and not on alternative activities. One reflection will be based on your classroom teaching experience.
GATE C ASSIGNMENTS
The Gate C assessments connected with this course are requirements to proceed to student teaching. Note that you can pass this course, but not satisfy the requirements for Gate C assignments. Resubmissions of unsatisfactory work are permitted and encouraged. Your Gate C assessment items are to be included as an artifact in your electronic portfolio (Taskstream).
1. Process Standards in the Teaching and Learning of Mathematics
Principles and Standards identifies five process standards (problem solving, reasoning and proof, communication, connections, and representation) for the teaching of mathematics. This assignment allows you to demonstrate your understanding of and ability to apply these processes. For each of the five process standards, include the following, in order:
· The brief Principles and Standards definition/description of the standard
· A scanned artifact (consider samples from mathematics coursework) that demonstrates your understanding of and/or ability to apply the standard
· A discussion (at least 1-page (double-spaced) that explains how the provided artifact demonstrates that you have engaged in the process standard (cite the definition/description of the standard from Principles and Standards)
Draft due 2/18, Peer Review due 2/25, Final due 3/4
30 points (4 points per standard)
2. 1-Day Lesson Plan Within a Unit
You will design a 1-Day lesson plan (using the provided lesson plan format) that is appropriate for implementation in secondary mathematics. Included with the detailed 1-Day plan, you will describe the teaching unit that your lesson would fit within and make a teaching plan describing in a paragraph the lesson/activity to be implemented on each day of the unit.
Draft due 3/11, Peer Review due 3/25, Final due 4/1
30 points
1. Technology to Enhance the Teaching and Learning of Mathematics (Lesson Plan) Identify a previously written lesson plan. (You may utilize a lesson plan from an online database or one of your own with the exception of those written for this course). Revise the lesson to include technologies that enhance the teaching and learning of mathematics. Submissions for this assignment include: (1) the original lesson, (2) the revised lesson, and (2) a detailed discussion of the incorporated technologies and how their utilization enhances students’ opportunities to learn mathematics. You may want to include information from the technology principle as described in Principles and Standards (and information from other readings) to make the case that technology enhanced the lesson.
Draft due 4/8, Peer Review due 4/15, Final due 4/22
30 points
OTHER ASSIGNMENTS
Mathematics and Me (10 pts)
Write 2-3 pages double-spaced in response to the following writing prompts:
1) Describe your ideal mathematics classroom, whether you've ever witnessed it or not. What would a typical day in your classroom look like to an observer coming to sit in on your class? Describe what the teacher does, how the students participate, what the lesson or activity looks like, what the environment of the room is like, etc.
2) Describe the influences throughout your life have helped you to realize your ideal mathematics classroom as described above?
3) What do you hope to learn through this class?
Textbook Analysis (15 pts)
Select a math topic (be specific – selecting “algebra” is too broad), look at three high school textbooks, and compare the way they introduce the topic. The goal is primarily to identify
differences in the way the topic is presented, so chose the textbook accordingly. You will write
a 3-5 page (double-spaced) paper providing: a) a brief description of how the mathematical topic is taught in each, b) a description of way in which the textbook provides opportunites for students to engage in each of the NCTM process standards (problem solving, reasoning and proof, communication, connections, and representation) and c) your analysis of the pros and cons of the way each textbook introduces the topic (e.g., what might students gain or lose in terms of understanding? What limitations or benefits can you see for how you would teach the topic in this way?)
NCTM Artifacts (5 pts)
Spend some time perusing the NCTM website. Find two interesting and potentially helpful “things” from two different categories (e.g., articles, web links, people, technology tips, activities), post the links on blackboard with a brief description to inform others of the artifacts, and be prepared to share your findings in class.
Launch, Explore Summary (10 pts)
In groups of 5-7, choose a lesson from Core Plus that relates to an assigned topic. Your group will be split so that some group members will lead the launch with your classmates, others will lead the exploration, and others will lead the summary. Your group will sign up for a date where you will be responsible for leading the class through the entire lesson.
Philosophy of the Teaching and Learning of Mathematics (10 pts)
Write a 1-2 page essay that outlines your philosophy (beliefs and assumptions) regarding how mathematics should be taught and how students best learn mathematics.
Course Reflection (10 pts)
Please put time and careful thought into this paper. It will help me to better understand the experiences of prospective teachers. Your responses will be graded on a completion basis only, so make sure you answer all questions, but you can express your opinions freely. I can only benefit from this if you share honestly.
Respond in a page or more (double-spaced) to the following prompt:
Consider the ideas about teaching and learning mathematics that you held at the beginning of this course (review your Mathematics and Me paper and early reflections) and compare to your current ideas (review your teaching philosophy and later reflections). Write an explanation as to why you think different aspects of your beliefs either changed in some way or did not change over the past 15 weeks.
Point distribution
Mathematics and Me / 10
NCTM Artifacts / 5
Textbook Analysis / 15
Launch, Explore, Summary / 10
Gate C I Draft / 5
Gate C I Peer Review / 5
Gate C I Final / 30
Gate C II Draft / 5
Gate C II Peer Review / 5
Gate C II Final / 30
Gate C III Draft / 5
Gate C III Peer Review / 5
Gate C III Final / 30
Philosophy of Teaching and Learning Mathematics / 10
Course Reflection Paper / 10
Journal Reflections for Field Experience / 50
15 Hrs Field Experience, Teaching, and Verification / 50
Class Participation / 20
TOTAL / 300
Grading scale (based on policy of +/- grading):
A+ / 97 - 100.0%A / 92 - 96.9%
A- / 90 - 91.9%
B+ / 87 - 89.9%
B / 82 - 86.9%
B- / 80 - 81.9%
C+ / 77 - 79.9%
C / 72 - 76.9%
C- / 70 - 71.9%
D+ / 67 - 69.9%
D / 62 - 66.9%
D- / 60 – 61.9%
F / < 60%
TASKSTREAM
Taskstream is a commercial electronic portfolio system for which you must purchase a license. A four-year license as well as a short-term license is available. You may purchase your license directly from Taskstream or from Purdue University. You will use Taskstream to submit your Gate C assessments. See section GATE C ASSESSMENT for more details. Taskstream can be found online at: http://www.taskstream.com. Go to the Taskstream website and log-in to confirm that you have access to Gate C. If you do not have access or would like a refresher training session, please contact Doc Vinh, e-Portfolio Coordinator, at or by calling 494-3416.
POLICIES
CAMPUS EMERGENCY
In the event of a major campus emergency, course requirements, deadlines and grading percentages are subject to changes that may be necessitated by a revised semester calendar or other circumstances. Here are ways to get information about changes in this course: or (765) 494-9578; or check the blackboard page for our course.
BEERING HALL EMERGENCY
Students are required to visit http://www.education.purdue.edu/ODFD/resources.html to review the response procedures for emergencies in Beering Hall. It is necessary that you review these directions within the first week of your Beering classes. If you have any questions see your instructor.
ADAPTIVE PROGRAMS
Students with disabilities must be registered with Adaptive Programs in the Office of the Dean of Students before classroom accommodations can be provided. If you are eligible for academic accommodations because you have a documented disability that will impact your work in this class, please schedule an appointment with me as soon as possible to discuss your needs.
ACADEMIC DISHONESTY
Purdue prohibits "dishonesty in connection with any University activity. Cheating, plagiarism, or knowingly furnishing false information to the University are examples of dishonesty." [Part 5, Section III-B-2-a, University Regulations] Furthermore, the University Senate has stipulated that "the commitment of acts of cheating, lying, and deceit in any of their diverse forms (such as the use of substitutes for taking examinations, the use of illegal cribs, plagiarism, and copying during examinations) is dishonest and must not be tolerated. Moreover, knowingly to aid and abet, directly or indirectly, other parties in committing dishonest acts is in itself dishonest." [University Senate Document 72-18, December 15, 1972]