Course Outline, Fall 2007
EDU 492 Mathematics (Secondary School) 8/21 – 10/11 TR 4:50 – 7:30 p.m. EN D122
Instructors: Dr. Martin Hartog hartogm1@southernct.edu EN D127 (203) 392-5595
Dr. Kath Rondinone rondinonek1@southernct.edu EN D140 (203) 392-5591
Required Reading:
http://standards.nctm.org/
http://standards.nctm.org/Previous/ProfStds/index.htm
Supplemental Readings - NCTM Journals (most are available in the Math Department Library):
Mathematics Teacher (MT)
Teaching Children Mathematics (Arithmetic Teacher) (TCM & AT)
Mathematics Teaching in the Middle Schools (MTMS)
Journal for Research in Mathematics Education (JRME)
Dossey, et al, Mathematics Methods and Modeling for Today’s Mathematics Classroom
Tomlinson, C. A. (1999). The Differentiated Classroom: Responding to the Needs of All Learners, Alexandria, VA: Association for Supervision and Curriculum Development
Course Description:
Methods of teaching mathematics grades 7-12. Classroom management, learning styles, tasks, assessment, and incorporating technology. For teaching certification only. 3 credits.
Course Outcomes: Students will be able to:
Topics: This outline is developed to reflect the major themes recommended by the National Council of Teachers of Mathematics (NCTM), the National Council for Accreditation of Teacher Education (NCATE), as well as the Beginning Educator Support Training (BEST) portfolio requirements of the State of Connecticut.
DATE TOPIC
Worthwhile Mathematical Tasks:
Aug. 21 Overview of the Syllabus, NCTM Principles and Standards, Lesson Planning/Unit Planning
Aug. 23 Task Selection: Motivation, Initiation, Activities, and Closure/A Problem-Solving Approach to Mathematics
Creating a Classroom Environment:
Aug. 28 CAPT
Aug. 30 Learning Styles/Cooperative Learning
Sept. 4 Classroom Management/Discipline /Administrative, Parent, and Community Relationships/ Curriculum Library
Mathematics Curriculum
Sept. 6 Geometry
Sept. 11 Algebra
Sept. 13 Micro Lesson I Presentations
Sept. 18 Micro Lesson I Presentations
Discourse:
Sept. 20 Questioning
Sept. 25 Classroom Discussion: Teacher's Role/Student's Role
Assessment in the Mathematics Class:
Sept. 27 Assessment Standards / Traditional Assessment. Test Making and Grading
Oct. 2 Alternative Assessment. Portfolios, Writing in the Classroom, Journals, and Open-Ended Questions/ Rubric Making
Oct. 4 Lesson II Videotape
Oct. 9 Lesson II Videotape
Oct. 11 BEST/Connecticut Competencies
Key Assignments: The date of the assignment reflects the date on which the assignment is due. Note that the assignments are not in chronological order.
DATE ASSIGNMENT
Observation Reports
Sept. 6 Report 1
Sept. 20 Report 2
Oct. 2 Report 3
Lessons
Sept. 4 CAPT Lesson Plan Performance Task
Sept. 13 Micro Lesson I Presentations
Sept. 18 Micro Lesson I Presentations
Oct. 4 Lesson II Videos
Oct. 9 Lesson II Videos
Unit Plan
Sept. 13 Overview of the Unit Plan
Oct. 11 Complete First Draft Including Daily Lesson Plans and Assessments
Dec. Final Unit Plan
Article Critiques
Aug. 28 Problem Solving Article
Sept. 4 Cooperative Learning Article
Oct. 2 Alternative Assessment Article
Grading: Final grades will be determined based on the following percentages.
1. Presentation and Lesson Plan of Lesson I (15%)
2. Presentation and Lesson Plan of Lesson II (15%)
3. Unit Plan (30%)
Units must be composed of two weeks of lessons. This means if you teach in a school using a block schedule, the unit should have at least four lessons and an assessment lesson. If you teach in a school using 45-minute periods, the unit should consist of seven lessons plus one review and an assessment.
4. Observation Reports (15%)
5. Additional Assignments:
a. Article Critiques (7.5%).
b. CAPT Problem Lesson Plan (7.5%).
c. Daily assignments and presentations presented in class (10%).
EDU 492
Unit Plan Evaluation Summary
Name ________________________
Criteria Points
Possible: Received:
Overview of the Unit Plan 15 _____
Classroom Description
Discipline Policy
Homework Policy
Prerequisite Knowledge
Unit Goals
Methodology
Teaching Aids
Assessment
Daily Plans
Lesson Objectives 10 _____
Mathematical Tasks
Initiation/Motivation 10 __ __
Task Selection/Activities 20 _____
Closure 5 _____
Opportunity for Discourse 10 _____
Environmental Considerations 10 _____
Analysis of Learning 10 _____
Analysis of Teaching 10 _____
Total Score 100 _____
Grade _____
Unit Plan Letter Grades are assigned as follows:
90 - 100 A-, A, A+
80 - 89 B-, B, B+
70 - 79 C-, C, C+
60 - 69 D-, D, D+
Below 60 F
General Scoring Rubric for each section in the Unit Plan
Top Level (9-10)
Second Level (7-8)
Third Level (5-6)
Fourth Level (< 5)
Guidelines for Writing Critiques on Research Article
Article should address research on, or the application of, mathematics teaching methodology.
The critique should contain:
1. Title, author, date, and journal.
2. No more than 2 type-written pages, double-spaced using 12-point to 10-point font.
3. A description of the mathematics or teaching methodology presented in the article. Include results of the research conducted and/or effects of the methodology utilized.
4. Describe how the ideas proposed in the article do or do not reflect the guidelines set by the NCTM’s Principles and Standards or the Professional Standards for Teaching for effective mathematics teaching.
5. Your personal reflections on the article.
Assessment of the critique:
Score |
Criteria |
A |
The critique contains all its essential parts, a clear and complete description of the chapter, thoughtful reactions by the student, and does not exceed the 2-page maximum. Work is considered exceptional. |
B |
The critique contains all its essential parts, satisfying the conditions stated for the critique. |
C |
The critique contains all its essential parts, however, most of the parts are unclear or do not satisfy the conditions for the critique, or does not contain all of the essential parts, but the parts presented are clear and thoughtful. |
D |
The critique contains all its essential parts, however, all of the parts are unclear or do not satisfy the conditions for the critique, or the critique does not contains all its essential parts, but most of the parts are adequately presented. |
F |
The critique does not contains all its essential parts, most of the parts presented are inadequate. |
I. School Visitation Assignment
The purpose of the school visitation assignment is to familiarize student teachers with the schools in which they will be doing their student teaching and to have all students observe the practice of many of the methods being discussed in the methods course. The observations should be returned for evaluation in three reports. Each report will cover the observation of a minimum of five classes. For these five classes, at least two different teachers should be observed. The report should focus on the specific topics identified for observation as listed below for each teacher observed. However, the reports are not limited to those topics alone. If something very interesting is observed during a particular class, students should feel free to report their reactions to those situations.
Each report should include:
1.Teacher’s name and grade level(s) of the classes.
2.Subject(s) covered in the classes.
3.Date(s) of observations.
4.A discussion of the topics of observation as outlined for the reports below.
5.Insights that you make about the teaching and learning process as a result of your observations. The report should not be only a list of observations, but also a reflection upon what you observe.
For this report and subsequent reports, if you didn’t observe items mentioned to report on, ask your cooperating teacher about how they would respond under other circumstances. For example, if you didn’t observe any discipline problems, ask how the teacher handles discipline.
Report 1.
Students should observe the first few days of the academic year as indicated in the letter you received. You should obtain copies of the textbooks you will be using when you student teach, make a seating chart for the classes, and become acquainted with the names of the students. In addition, observations should focus on classroom management and discipline strategies used by the observed teachers, and a description of the learning environment created by the observed teachers. The cooperating teacher can help arrange for the visitation of other teachers as needed. Specific things to look for include:
-How are classes organized?
-What seating arrangements are utilized?
-How is attendance taken?
-What is the teacher's discipline policy and the principle method of maintaining discipline?
-What response did the teacher make to any particular student disruptions?
-How does the teacher handle homework?
-How does the teacher maintain his/her grade book?
-What expectations are made of the students?
-How does the teacher handle the first day of school?
-How does the teacher differentiate between different levels of classes?
Report 2.
During these observations the student should focus on task selection, motivation/initiation methods, teaching style, and closure techniques utilized by the observed teachers. Specific things to look for include:
-What techniques did the teacher use for the initiation of the lesson?
-What techniques did the teacher use to close the class?
-Did the teacher supplement lessons with resources other than the textbook? If so what?
-How did the lessons develop mathematical facts, skills, concepts and principles?
-How did the teacher make the transition from previously learned material to the present objectives of the lesson?
-How did the teacher address the diverse needs of different learners in the classroom?
-What assessment techniques were used to evaluate whether lesson objectives were met?
-What methods did the teacher use to make learning mathematics a sense-making experience?
-Did the teacher use methods that prepare the students for the CAPT test?
Report 3.
During these observations the student should focus on discussion, questioning, and manipulative/technology techniques used by the observed teachers. One of the observations should be in the Learning Resource Center/Computer Laboratory of the school, if available at this time. This may be helpful in planning Micro Lesson II. Specific things to look for include:
-What teaching aids were used?
-What technology was available to be utilized in the lesson?
-Was the technology utilized in the lesson? If so, how?
-What manipulatives were available to be utilized in the lesson?
-Were the manipulatives utilized in the lesson? If so, how?
-What types of questions were utilized? (e.g. open-ended vs. closed-ended questions; fact vs. higher-order cognitive questions, etc.)
-Did the teacher use techniques to encourage student participation in discussions? (e.g. wait time, asking the student to elaborate their responses, asking for student questions, etc.)
-Describe how the learning environment fosters the opportunity for students to explore sound mathematics, communicate their ideas, and take intellectual risks.
II. Lesson Plans.
Lesson plans should follow the format provided in the files in the MySCSU Courses section on-line. Each individual plan is part of a unit plan. Once the unit plan overview is established, each individual lesson must be planned.
A daily lesson plan should contain the following essential elements identified in the PLANS FOR LESSON form:
Mathematics Objectivesare behavioral objectives for the students tohave accomplished by the end of the lesson. For each objective the level of learning to be obtained should be identified. Levels of learning include concepts, facts, principles, and procedures.
Mathematical Task(s)are the projects, problems, constructions, applications, exercises, etc. that frame and focus the learning in the lesson to achieve the desired objectives. The teaching method taken must be consistent with the level of learning identified for the objective. Aspects of the task that should be part of the lesson plan are given below.
1. Materials needed should include any special materials for the lesson, such as rulers, compasses, calculators, overhead projector.
2. Initiation/Motivation is sometimes called the anticipatory set. This is the exercise that you will complete or have the students complete to recognize the need for learning the objective(s) of the day or to connect the topic to other topics you have already seen. This can be accomplished by using exercises that review previously learned topics that connect to the new topic or by posing new problems that lead into the lesson of that day.
3. Instructional Task or Activity will be the most extensive part of the lesson plan. It will include the teaching procedures you will use, tasks students will engage in, and examples/problems that you will use in class.
4. Closure is a review of the material learned that day. This should be used as an overview to help the students put the class in perspective.
Opportunity for Discourse is the way in which you will engage students in discourse as part of the lesson. In what ways will you orchestrate discussions? How will you promote student involvement in discussions? What tools will you use to enhance discourse? What key questions will you ask during the lesson to guide the discussions?
Environment Considerations are the ways in which you modify the learning environment for the particular lesson. What classroom arrangements and teaching strategies will you use? How much time will you allot to each part of the lesson? Will students work independently, in groups, or as a whole class? How will you encourage all students to participate in the lesson? How does the lesson address the learning needs of all students?
Analysis of Learningis the way in which you will assess the lesson. What formal and informal methods of assessment will you use during the lesson? This can include exercises from the textbook, questioning, journal writing, essay writing, homework, quizzes, presentations, and projects.
Analysis of Teaching (Completed for the videotaped lesson. May be completed for the unit plan if the lessons are done during student teaching) is the reflection thatshould be completed after the lesson. This should be your self-evaluation of what worked and what did not work. It should include what adjustments, if any, you made during the lesson, what you would do differently if the lesson was repeated, what worked really well, and how you would modify the lesson to make it more effective.
Notes on Unit Planning III:
The development of a good unit plan is essential to the teaching process. In developing a unit plan, the teacher visualizes the unit in advance. He/she needs to consider the characteristics of the students in the class, the abilities of the students, the objectives that need to be mastered, and the methodology that will allow the students to best master these objectives.
During the unit planning process, the teacher should consider prerequisite knowledge of the students, applications of concepts in the unit, methodology, and assessment of the objectives. The unit plan will help the teacher organize his/her thoughts ahead of time. In doing this, the lessons in the unit become part of a whole and a focal point of what will be accomplished during a class period.
A teacher who has carefully prepared a unit plan will find that the lessons will flow more easily, and many problems will have been averted. Anticipating student questions, organizing teacher questions and/or examples, and closing the lesson, are essential elements for a successful unit.
Overview of the Unit Plan
Unit plans demand attention to broader goals than those usually sought in a single lesson. The format of a unit is less important than the thought that goes into planning a unit. However, your unit plans should have certain common characteristics. They should include the following:
Class Description:What are the characteristics of the class, the ability level of the students, the number of students? Are there any special needs students? What is the discipline policy? What is the homework policy? (Note: Inclue discipline or homework policies for the class. You can attach it as an appendix if it is already prepared for your class.)
Prerequisite Knowledge: What are the concepts that the students walking into the class need to know in order to master the new topics covered in the unit plan?
Goals and Objectives: What are the goals and objectives of this unit? Goals are the general statements regarding what students will learn that are stated in the introduction to the unit plan. Objectives are specific statements that are written in the form of behavioral objectives that describe what the student will be able to do at the end of each lesson.
Initiation/Motivation: What techniques can be used to get the students interested in the ideas of the unit? How can the material be related to the students' interests? Are the problems in the text real-life applications for these students or should other problems be found?
Methodology: What methods can be used to present the material? Will the students work individually or cooperatively? Do the ideas lend themselves to the discovery approach? What teaching strategies are consistent with the kinds of outcomes expected? What can be done to provide for a high level of student involvement? What kind of student activities and assignments are appropriate?
Teaching Aids: Are the materials available that are needed to follow through on the methodology planned? Are there appropriate films, models, technology and manipulatives that can be obtained? Are there community resources that could be used? What worksheets need to be prepared?
Assessment: What forms of assessment will you use to determine whether or not students have met the behavioral objectives of the unit? Included in these forms of assessment could be tests, quizzes, projects, writing assignments, homework, etc.
Individual Lesson Plans: Are the separate lesson plans that make up the unit well designed and written? The unit should cover a 2-week period, including the time for assessment.