Idaho's Leader in Lifelong Learning and Healthy Lifestyles s1

EDCI 404 Geometry for Middle School Teachers Spring 2013 3 Credits Mondays and Wednesdays: 3:30 to 4:45 pm ED 418 Final Exam: Wednesday May 8, 3-5 pm Instructor: Anne Adams Office Location: ED 405C Phone: 208-885-5273 Email: [email protected] Office Hours: Monday, 12:30 to 2:30 pm and by appointment

Reasonable accommodations are available for students who have documented temporary or permanent disabilities. All accommodations must be approved through Disability Support Services located in the Idaho Commons Building, Room 306 in order to notify your instructor(s) as soon as possible regarding accommodation(s) needed for the course.

 885-6307  email at  website at

College Vision

Idaho's Leader in Lifelong Learning and Healthy Lifestyles.

We seek teaching, learning, and living that transforms, invigorates, and nurtures. We expand lasting knowledge centered in local and global communities.

College Mission

The University of Idaho’s College of Education is the state’s flagship and land-grant research college focused on the preparation of professionals for schools, the movement sciences, and workforce counselors and educators. From our commitment to develop leaders in these fields emerges our responsibility to enhance the scientific, social, economic, and cultural assets of the state and develop solutions for complex problems.

We deliver on our commitment through focused, interdisciplinary excellence in teaching, research, outreach, and engagement in a collaborative environment at our residential main campus and our regional centers. Consistent with the land-grant ideal, our outreach activities serve the state and at the same time strengthen our teaching, scholarly, and creative capacities.

Our teaching and learning include undergraduate, graduate and professional education offered through both resident instruction and extended delivery. Our scholarly and creative activities promote K-12 academic achievement, human development and wellness, global awareness, and progress in professional practice.

Conceptual Framework University of Idaho educators CARE. Together we develop as scholar practitioners who value and professionally apply and advance:

Cultural Proficiency; Assessment, Teaching, and Learning; Reflective Scholarship & Practice; and, Engagement in Community Building & Partnerships.

Course Description

This course is part of planned program of studies in the College of Education at the University of Idaho. It develops a foundational understanding of topics in geometry and measurement for middle school teachers. Topics include congruence, similarity, transformations, polygons, Pythagorean theorem, circles, area , volume, problem solving, and proof. Intended primarily for students in elementary education who plan to teach middle school mathematics.

Prerequisite(s)

Math 236 and admission to Teacher Education or permission of instructor.

Course Goals and Expectations

By the end of this course, students will be able to solve problems and justify relationships involving polygons, angles, similarity, congruence, transformations, area.

Course Objectives

Knowledge of Subject Matter: The teacher understands the central concepts, tools of inquiry, and structures of the discipline(s) he or she teaches and can create learning experiences that make these aspects of subject matter meaningful for students.

Students will: 1. Derive area formulas such as the formulas for areas of triangles and parallelograms, considering the different height–base cases (including the “very oblique” case where “the height is not directly over the base”). 2. Explain why the Pythagorean Theorem is valid in multiple ways. Apply the converse of the Pythagorean Theorem. 3. Informally explain and prove theorems about angles; solve problems about angle relationships. 4. Understand dilations, translations, rotations, and reflections, and combinations of these. 5. Understand congruence in terms of translations, rotations, and reflections; and similarity in terms of translations, rotations, reflections, and dilations; solve problems involving congruence and similarity in multiple ways. [Based on recommendations from: Conference Board of Mathematical Sciences (2012). The Mathematical Education of Teachers II. Providence, RI: American Mathematical Society.]

Signature Assignment – Midterm Exam; Final Exam 6. Students will understand the role of justification and proof in geometry as it relates to reasoning and problem solving. 7. Students will know how to frame mathematical questions and conjectures. 8. Students will know how to communicate concepts through the use of mathematical representations (e.g., symbolic, numeric, graphic, verbal, and concrete models). 9. Students will understand the appropriate use of technology in teaching and learning of mathematics (e.g., graphing calculators, dynamic geometry software, and statistical software) [From Idaho Teacher Preparation Standards for Mathematics teachers]

Signature Assignment – Midterm Exam; Final Exam

Teacher Preparation Standards

1. Knowledge of Subject Matter: The teacher understands the central concepts, tools of inquiry, and structures of the discipline(s) he or she teaches and can create learning experiences that make these aspects of subject matter meaningful for students.

Signature Assignment – Midterm Exam; Final Exam

2. Knowledge of Human Development and Learning: The teacher understands how children learn and develop, and can provide learning opportunities that support their intellectual, social and personal development.

3. Adapting Instruction for Individual Needs: The teacher understands how students differ in their approaches to learning and creates instructional opportunities that are adapted to diverse learners.

4. Multiple Instructional Strategies: The teacher understands and uses a variety of instructional strategies to encourage students’ development of critical thinking, problem solving, and performance skills.

5. Classroom Motivation and Management: The teacher uses an understanding of individual and group motivation and behavior to create a learning environment that encourages positive social interaction, active engagement in learning, and self-motivation.

6. Communication Skills: The teacher uses knowledge of effective verbal, nonverbal, and media communication techniques to foster active inquiry, collaboration, and supportive interaction in the classroom.

7. Instructional Planning Skills: The teacher plans instruction based upon knowledge of subject matter, students, and curriculum goals.

8. Assessment of Student Learning: The teacher understands and uses formal and informal assessment strategies to evaluate and ensure the continuous intellectual, social, and physical development of the learner.

9. Professional Commitment and Responsibility: The teacher is a reflective practitioner who continually evaluates the effects of his/her choices and actions on others (students, parents, and other professionals in the learning community) and who actively seeks out opportunities to grow professionally.

10. Partnerships: The teacher fosters relationships with school colleagues, parents, and agencies in the larger community to support students’ learning and well-being.

Teacher Education Dispositions

 Attends regularly.

 Meets timeline commitments.

 Dress/Appearance is appropriate and professional.

 Maintains appropriate relationships with peers.

 Scholar-practitioner demonstrates adequate content knowledge that is current.

 Engaged, full participation and takes initiative.

 Maintains confidentiality and is ethical.

 Maintains appropriate relationships with students.

 Committed to and facilitates student's learning in a safe climate.

 Maintains appropriate relationships with teachers, administration, parents, and community members

 Respects and advocates for diversity.

 Responds appropriately to feedback and is flexible.

 Written work communicates clearly and accurately, and is in standard English.

 Verbal communication is clear, accurate, appropriate to the situation, and conventions used are standard for speaking situations.

Required Readings and Learning Resources

Required readings are available on UI’s library e-reserve. Frequent readings will be assigned. To access e-reserve for EDCI 404, go to: URL: http://db.lib.uidaho.edu/ereserve/show_course.php? pointer=3728 and log in with: Username: reserve Password: Gob89q

Geometer’s Sketchpad will be used for many course activities. UI has made this program (for PC computers) available to registered students through computer services on VLab. To get started, go to http://support.uidaho.edu/services/labs/vlab/

Later, when you return to VLab, go to http://vlab.uidaho.edu, log in with your UI username and password, and open Geometer’s Sketchpad. Optional Readings and Learning Resources

Driscoll, M., DiMatteo, R. W., Nikula, J., & Egan, M. (2007). Fostering Geometric Thinking: A Guide for Teachers, Grades 5-10 (Pap/Dvdr T.). Heinemann. Sinclair, N., Pimm, D., & Skelin, M. (2012). Developing Essential Understanding of Geometry for Teaching Mathematics in Grades 6-8. (R. M. Zbiek & S. Editor, Eds.). National Council of Teachers of Mathematics. McCrone, S. M., King, J., Orihuela, Y., & Robinson, E. (2010). Focus in High School Mathematics: Reasoning and Sense Making in Geometry. National Council of Teachers of Mathematics. Sinclair, N., Skelin, M., & Pimm, D. (2012). Developing Essential Understanding of Geometry for Teaching Mathematics in Grades 9-12. (R. M. Zbiek & S. Editor, Eds.). National Council of Teachers of Mathematics. Common Core State Standards: Mathematics content standards: http://www.corestandards.org/Math

Common Core State Standards: Standards for Mathematical Practice: http://www.corestandards.org/Math/Practice

Learning Activities and Assignments

Learning activities will occur both in and out of class. Students are expected to complete all in-class and out-of-class assignments.

Tentative Schedule of Activities:

Please treat this schedule flexibly. It will likely be modified based on the learning needs of the class members.

Jan 9 Mar 4-6 What is Geometry? MID-TERM exam: Monday March 4 Quick Images Ch 4 Symmetry & Transformational Using language to describe designs Geometry Folding Paper: Constructions Sections 4.1 and 4.2 Reading for next time: Education Development Center, Inc. (2000). Perspective: What Is Geometry? In Connected Geometry: A Habits of Mind Approach to Geometry. Glencoe/McGraw-Hill. Jan 14-16 Mar 18-20 Ch 1 Necessary Conditions Ch 4 Symmetry & Transformational Ch 1 Triangle Recipes Geometry Sections 4.3 and 4.4 Congruence and Similarity Jan 21-23 Mar 25-27 Ch 1 More Triangle Recipes Ch 5 Coordinate Geometry Sections 5.1 and 5.2 Discussion Volume (Content)

Jan 28-30 Apr 1-3 Ch 2 Area of Triangles Ch 5 Coordinate Geometry Discussion 1 (Content) Sections 5.3 Discussion Volume (Pedagogy)

Feb 4-6 Apr 8-10 Ch 2 Sides, Angles, Interior Lines, Points Ch 6 3-D Geometry and Spatial Ch 2 Classification & Hierarchical Visualization Relationships Sections 6.1 Feb 11-13 Apr 15-17 Ch 3 Naming, Describing, and Constructing Ch 6 3-D Geometry and Spatial Polygons Visualization Ch 3 Perimeter and Area of Polygons Sections 6.2 [no class meeting on Feb. 13] Feb 18-20 Apr 22-24 Pythagorean Theorem Ch 6 3-D Geometry and Spatial Discussion 2 (Content) Visualization Review for Mid-term exam Sections 6.3 and 6.4

Feb 25-27 Apr 29-May 1 Dissections and Proof Classroom activity Discussion 2 (Pedagogy) Review for final exam

Complete all IN-CLASS assignments - Students will be required to do a variety of activities during each class period. At the end of each class, students will be asked to self-assess the points they deserve for their in-class work that week.

Rubric for IN CLASS Work:

Students are to self-assess their in-class work and communicate that score to the instructor. The following rubric will help students determine their scores.

10 - 9 points - Is fully involved in the in-class activity. Offers ideas and expands on others' ideas. Is an active learner, providing support and encouragement for others' ideas and insights. Is a productive group participant, knowing when to lead and when to follow. 8 - 6 points - Responds to other ideas briefly and succinctly. Listens to others and makes a contribution to the group learning activity.

5 - 2 points - Listens to others, but makes only a few comments. Contributes a little to the effectiveness of the group discussion and learning activities.

1 - 0 points - Is uninvolved in the discussion and/or is disruptive to the group and learning activities.

Rubric for HOMEWORK/Mathematical Problem Solving

10-9 points Generalization, abstraction, and/or extension All problems honestly attempted. Careful and complete representations were included that illustrate key relationships or features of the problem. All work is shown clearly and completely. Solutions are clearly communicated. Justifications/ proofs are included where appropriate: This will always work for all problems … [generalization]. You just … [abstraction] because … [justification] 8-6 points Comprehensive solution(s) with full justification All problems honestly attempted. Careful and complete representations were included that illustrate key relationships or features of the problem. All work is shown clearly and completely. Solutions are clearly communicated. Justifications/ proofs are included where appropriate: - Got it! The answer is … [solution] because … [justification] - Here’s another way to do this … [alternative method]. This works because … [justification]. 5-4 points Basic/partial solution(s) with partial justification/ More than half of problems completed - When I did … [description of procedure] I got … [result]. Is that correct? - Here are my solutions to parts a) and b). I can’t get c) Help! 3-1 points Basic/partial solution(s) with partial justification/ Less than half of problems completed - When I did … [description of procedure] I got … [result]. Is that correct? - Here are my solutions to parts a) and b). I can’t get c) Help! Field Work

No Field Work Required.

Grading Policy

Letter grades are not provided on individual assignments. Points are assigned based on rubrics, which are provided for most of the assignments. Points will be distributed in the following way:

Midterm Exam 25%

Final Exam 25%

Class Activities 25%

Homework 25% Letter grades are not provided on individual assignments. Points are assigned based on rubrics, which are provided for most of the assignments.

In order to track your progress at any point during the course, simply sum the number of points you have earned up to that time and divide it by the number of possible points. The percentage equivalent of that quotient provides an approximate indicator of your course grade at that moment. Grade Cut-Offs for converting points to letter grades A: 90 % and above B: 80 to 89 % C: 70 to 79 % D: 60 to 69 %

**Please note: Unexcused late work will not be accepted. For late work to be excused, students must immediately discuss reasons with the instructor, who will then make the determination. Excused late work should be submitted as soon as possible. Please do not just wait and bring it to the next class meeting.

Incompletes: University policy permits grades of Incomplete (I) “only when the student has been in attendance and has done passing work up to a time within three weeks of the close of the semester, or within one week of the close of the summer session. It may be assigned only upon agreement of the student and course instructor when extenuating circumstances make it impossible for the student to complete course requirements on time (Extenuating circumstances include serious illness, car accidents [a doctor’s note is required], death of a family member, etc. It does not include lateness due to procrastination, the student's desire to do extra work to raise his/her grade, allowing a student to retake the course, etc.).” This does not include being overwhelmed with assignments and so unable to meet deadlines. Please organize your time accordingly.

Academic Integrity

The University of Idaho has as one of its core values the ideal of academic honesty and integrity. University of Idaho students live and work in a collegiate community which emphasizes their responsibility for helping to determine and enforce appropriately high standards of academic conduct. The faculty of the University of Idaho expects all students to adhere to the highest standards of academic honesty, and to refrain from any action which infringes upon academic freedom of other members of the academic community. Please refer to the University of Idaho - Student Code of Conduct Article II-Academic Honesty.

University of Idaho Classroom Learning Civility Clause

In any environment in which people gather to learn, it is essential that all members feel as free and safe as possible in their participation. To this end, it is expected that everyone in this course will be treated with mutual respect and civility, with an understanding that all of us (students, instructors, professors, guests, and teaching assistants) will be respectful and civil to one another in discussion, in action, in teaching, and in learning. Should you feel our classroom interactions do not reflect an environment of civility and respect, you are encouraged to meet with your instructor during office hours to discuss your concern. Additional resources for expression of concern or requesting support include the Dean of Students office and staff (5-6757), the UI Counseling & Testing Center’s confidential services (5-6716), or the UI Office of Human Rights, Access, & Inclusion (5-4285).

University of Idaho (UI) Nondiscrimination Policy

It is UI policy to prohibit and eliminate discrimination on the basis of race, color, national origin, religion, sex, sexual orientation and gender identity/expression, age, disability, or status as a Vietnam-era veteran. This policy applies to all programs, services, and facilities, and includes, but is not limited to, applications, admissions, access to programs and services, and employment. Such discrimination is prohibited by titles VI and VII of the Civil Rights Act of 1964, title IX of the Educational Amendments of 1972, sections 503 and 504 of the Rehabilitation Act of 1973, the Vietnam Era Veterans' Readjustment Assistance Act of 1974, the Age Discrimination Act of 1975, the Age Discrimination in Employment Act Amendments of 1978, the Americans with Disabilities Act of 1990, the Civil Rights Act of 1991, other federal and state statutes and regulations, and university commitments (see Faculty Staff Handbook (FSH) 3060). Sexual harassment violates state and federal law and policies of the Board of Regents, and is expressly prohibited, as stated in FSH 3220. The University of Idaho also prohibits discrimination on the basis of sexual orientation, as stated in FSH 3215. The entire FSH can be accessed online at http://www.webs.uidaho.edu/fsh. Questions or concerns about the content and application of these laws, regulations or University policy may be directed to: the Office of Human Rights, Access & Inclusion (208-885-4285); Regional Office for Civil Rights, U.S. Department of Education in Seattle (206-220-7900); Equal Employment Opportunity Commission, Seattle District Office (206-220-6883); or Pacific Regional Office of Federal Contract Compliance Programs, U.S. Department of Labor in San Francisco (415-848- 6969). Complaints about discrimination or harassment should be brought to the attention of the Office of Human Rights, Access & Inclusion (885-4285). Retaliation for bringing forward a complaint is prohibited by FSH 3810.

Library Resources (On Campus Classes)

As a UI student, you not only have access to valuable print and electronic resources from the university's library, but you also have the ability to set up a personalized reference appointment with one of the librarians. If you have assignments or research questions and aren’t sure how to make the most of library resources, feel free to contact the College of Education liaison librarian with questions: Rami Attebury, 885-2503, [email protected]. As always, you may also stop by the reference desk anytime Monday to Thursday 9 to 9, Friday 9 to 5, and Sunday 1-9, 208-885-6584, or visit http://www.lib.uidaho.edu for email or IM assistance.