Tentative Syllabus ED 3440

Course:	ED 3440 3 credits	Mathematics Methods in the Secondary School Fall 2010
Department:	Professional Education
Program(s):	Mathematics Education Major, B.S. (Teacher Licensure)
Meeting:	3:30-6:30 PM Mon	HS 231
Extras:	20 hours practicum	This will require at least 2 full days at a public school site.
Instructor:	Dr. Glen Richgels	HS 360 Office: 218-755-2824 Email: grichgels@bemidjistate.edu www: http://faculty.bemidjistate.edu/grichgels/
Office Hours:	7- 8 M-F 11-12 M-F
Course Description:	MATHEMATICS METHODS IN THE SECONDARY SCHOOL (3 credits) NCTM Standards, lesson planning, Minnesota Frameworks, Graduation Rule, objectives, methods, and materials.
Prerequisite:	ED 3110 or consent of instructor.
Professional Education Mission Statement	Bemidji State University prepares teachers through inquisitive, involved, reflective practice. The framework outlining our program sets a standard that is rigorous, exemplary and innovative. The curricular structure is research based and organized around the Standards of Effective Practice. Graduates are proficient, collaborative, technologically literate and environmentally aware teachers, who work effectively in various settings with diverse learners.
Text:	Principles and Standards for School Mathematics (Book and E-Standards CD)(NCTM) Navigating Through Algebra in Grades 9-12 (NCTM)
Recommended:	NCTM Curriculum and Evaluation Standards (CS) NCTM Professional Standards (PS) NCTM Assessment Standards (AS) NCTM Addenda Series 5-12 NCTM Navigations Materials Minnesota K-12 Mathematics Curriculum Framework NCTM Focus in High School Mathematics: Reasoning and Sense Making NCTM Curriculum Focal Points NCTM 100 years Steen Article
Technology:

Homework: Homework assignments will be made in class. You should come prepared to discuss the various reading assignments and compare contrast them with what you have observed in schools.

Class participation and quizzes: Class participation is expected and in order to participate you need to be present.

Exams: Projects will take the place of quizzes and exams. Students are expected to participate in all projects and discussions. The final exam/personal interview will be scheduled for the final week of exams.

Grades: Grades for this course will be based upon participation, projects, and a personal portfolio. Assignments will be given in class. The following grading scale will be used to determine grades:

A 90% - 100%

B 80% - 89%

C 70% - 79%

D 60% - 69%

A grade of C or better indicates that the student has successfully met the competencies measured in this class through discussion, homework, and projects.

Incomplete: An incomplete (I) grade will only be given in documented emergency situations. BSU policies will be followed.

NOTE: Upon request, this document and others distributed in this course can be made available in alternate formats.  If you have a documented disability and need accommodations for this course please contact the instructor, the Disability Services Office in 202 Sanford Hall, Bemidji State University or Kathi Hagen in the Office for Students with Disabilities at 755-3883 for assistance.. Any other questions about this course should be directed to the instructor.

Change in Course Syllabus: The Instructor reserves the right to change this syllabus as this course proceeds if the need arises. Should a change be required the class will be notified.

Goals and objectives of the course:

Students will:

1. read and report on the NCTM’s PSSM and other standards documents.
2. see the difference between learning a mathematical skill and understanding a mathematical concept.
3. re-familiarize themselves with secondary level mathematics.
4. work with reform curriculum materials and contrast these with traditional.
5. design lesson plans for a mathematics lesson in a secondary school classroom.
6. construct a bulletin board for a mathematics classroom.
7. create a notebook of helpful materials for mathematics teachers.
8. Create a portfolio of relavant materials that could be used for a job interview

• NOTEBOOK - you are required to establish and maintain a loose-leaf notebook. Entries in the notebook will include a synopsis and analysis of NCTM Standards documents, related articles and their photo copies, related WWW sites, and related JAVA applets.

• A mathematical bulletin board will be constructed. The bulletin board should be mathematically informative. In addition it should draw students in and provide opportunities for active interaction or participation.

• During this course students will participate in at least 20 hours of observation of high school or middle level mathematics classes. They may observe additional college mathematics classes. As part of their public school observations, they will prepare and present at least two instructional lessons. These presentations will be coordinated with and made under the supervision of a cooperating classroom teacher.

• Students will be expected to develop lesson plans and present lessons to their peers. Their peer presentations will include secondary topics. Their lessons will include appropriate best practices, manipulatives, and technology.

• This course will be offered at the same time as other content methods courses. In cooperation with these courses, teams will be formed to take part in instructional activities.

• The NCTM curriculum, assessment, and professional standards will be discussed at length. This will include their history and impact on mathematics instructional practices of these standards. The impact of technology on teaching and learning mathematics will also be discussed.

• NOTEBOOK will include the following entries:

PSSM Number include:

* summary

* reatcion

* JAVA applet

* Mathemtics Teacher article

* activities from class

PSSM Algebra include:

* summary

* reatcion

* JAVA applet

* Mathemtics Teacher article

* activities from class

PSSM Geometry include:

* summary

* reatcion

* JAVA applet

* Mathemtics Teacher article

* activities from class

PSSM Measurement include:

* summary

* reatcion

* JAVA applet

* Mathemtics Teacher article

* activities from class

PSSM Probability & Statistics include:

* summary

* reatcion

* JAVA applet

* Mathemtics Teacher article

* activities from class

Journal from practicum include:

* log of hours and observations

* signed and completed teacher evaluation

Course Outline;

Mathematics Education history unit :

WW II to present. Topics included; textbook development evolution and development, NCTM and Minnesota state standards, No Child Left Behind Legislation, TIMSS results, NAEP results, BSU freshmen data, BSU graduation data.

Assignments: define mathematics, describe your perfect teaching job, where do you want to teach, construct standards notebook.

Mathematics Education – Educational Psychology foundations unit:

including Bruner, Lesh, CGI, Polya, and van Hiele models. The role of tracking in students mathematical development.

Assignments: tracking articles

Lesson Plan development unit:

standards, units, daily planning, written curriculum, intended curriculum, delivered curriculum, teachers beliefs.

Assignments: observe cooperating teacher 20 hours, present at least 2 instructional lessons

Technology & Manipulatives unit:

the role of facts and automatized routines; manipulatives, film, calculators, applets and computers. The development of concepts and use for practical purposes.

Assignments: Integrate instructional materials into peer presentations.

Model Lesson Plan development unit:

Trigonometry Unit: Right triangle trigonometry and unit circle trigonometry

Complex Number Unit: rectangular and polar coordinates, addition, subtraction, multiplication, division, and roots of numbers; graphical/geometric interpretation of operations.

Current Research unit:

NCTM Focus in High School Mathematics: Reasoning and Sense Making, Curriculum focal points and Steen article, University of Minnesota NSF research, BSU freshmen and graduation research.

Assignment: Reflect on current high school curriculum and organization.

Professional Materials unit:

Professional Standards and professional organizations, journals, and conferences.

Assignments: Read, review, summarize, and react to 6 professional standards.

Assessment Standards unit

Assignments: Read, review, summarize, and react to 6 assessment standards.

Connections with other disciplines:

Assignment possibilities: tower, Bridge, Trebuchet, Robot car

NSF/Traditional Curriculum unit:

NSF Curriculum review and peer presentations:

Assignments: prepare peer presentation that incorporates, technology and best practices.

Local Communities unit:

resources, expectiations, limitations, administrators, and parents

Instructional Strategies used by instructor in course:

Polya’s problem solving steps

1. Understand the problem

2. Devise a plan
3. Carry out the plan
4. Reflect

Lesson Sequencing

Intuitions Þ Concrete Û Semi-Concrete Û Abstract

Glen’s Teaching/Learning Principles

1. Teach the way students learn

2. Use group work, heterogenous, 3-4, change monthly

3. Communication student Û student

4. Communication teacher Û student

5. Multiple solution paths

6. Use contextual settings / problem solving

7. Assessment

a. Grading

b. To inform instruction

Updated by Glen Richgels

February 26, 2010

TENTATIVE Daily Course Outline

Day 1	Course overview: volunteer 20 hrs in classroom, PSSM - for each standard: summary, reaction, journal activity, www activity/lesson & JAVA.  Play PIG – next class bring your own math game. Mathematics Education history unit.
Day 2	Project with science teachers – lesson plan format on website.  Build a structure to support a ping pong ball with marshmallows & noodles
Day 3	Match with BHS teacher – want 2 – 3 lessons taught do it THEIR way.  TIMSS & “Nation at Risk” lead to reform mathematics. Navigations Number Sense, Mod 7 OR Water World. Mathematics Education – Ed Psych unit
Day 4	Compare game lesson plans to MN Standards. Lesson Plan development unit.
Day 5	Sections of PSSM read.
Day 6	Discuss PSSM.  Put 0-million on chalkboard.  Where is 1,000?…  x10=2x is easy on spreadsheet but difficult with algebra. Technology and Manipulative unit.
Day 7	Build a bridge with science students
Day 8	Discuss observations and student teaching (visit other classrooms).  Discuss PSSM.
Day 9	Model Lesson Plan development unit.
Day 10	People who write math textbooks design it around mathematics, not around how people learn.  Measurement, Data & Prob  EX: If 2 coins then P(HH)=.25, P(HH|1st was H) = .5, P(HH|1 was H) = .3333…  Consider 100 athletes where 10% use drugs and a test that is 90% accurate.
Day 11	Problem solving: 1+2+3+…+99+100=? takes time.  Tetris (Tetromino = four blocks) how many possible shapes?  Pentomino? (12 possible)  Hexomino? …  Geometric proof of a(b+c) = ab + ac (area model)
Day 12	Van Hiele levels: Level 0 – visualiztion (gr 0-2); Level 1 analysis/definitions (gr K-6); Level 2 informal deduction (gr 5-9); Level 3 deduction proof (gr 8 - ?); Level 4 rigor/axiomatics (gr college?)  Assign Professional Standards & Assessment Standards.  Check for progress on volunteering, bulletin boards, portfolio, …
Day 13
Day 14	Student lesson presentations
Day 15	Student lesson presentations
Day 16	Student lesson presentations
Day 17	Student lesson presentations
Day 18	NCLB changed math focus from how many take calc to how many pass basic skills tests.  Who needs calc? Who needs stats? Interviewing skills & questions.  Worthwhile mathematical tasks vs. exercises.  Teacher's role in discourse (wait time, names vs everyone, "guide on the side rather than the sage on the stage.)  Learning environment to encourage intellectual risk takers.
Day 19	Robotics – superlab
Day 20	Robotics – superlab
Day 21	Professional Materials unit. Assessment Standards unit. Assessment standards (math, equity, openness, inferences, coherence)
Day 22	NSF/Traditional Curriculum unit. Differences / similarities Core +, Arise, SIMMS, IMP
Day 23	What’s in the portfolios
Day 24	Research on mathematics learning
Day 25	Student lesson presentations
Day 26	Student lesson presentations
Day 27	Student lesson presentations
Day 28	Student lesson presentations
Day 29	TIMSS video. Local Communities unit.
Day 30	TIMSS video – debrief on math ed major
Day 31	1) first three digits of phone # times 80 || 2) add 1 || 3) multiply by 250 || 4) add the last four digits of your phone # || 5) add the last four digits of your phone # - AGAIN || 6) subtract 250 || 7) Divide by 2.  Do you recognize the answer?  Why does this work??
Day 32	IMAP video clips
Day 33
Day 34

Board of Teaching Standards

Professional Education Program	EVIDENCE OF LEARNING & ASSESSMENT OPPORTUNITIES
8710.4600 Teachers of Mathematics		Course ID Number	Activity or Unit	Assessment
Subp. 3. Subject matter standard. A candidate for licensure as a teacher of mathematics must complete a preparation program under subpart 2, item C, that must include the candidate's demonstration of the knowledge and skills in items A to I.
C. A teacher of mathematics understands that number sense is the underlying structure that ties mathematics into a coherent field of study, rather than an isolated set of rules, facts, and formulae. The teacher of mathematics must demonstrate knowledge of the following mathematical concepts and procedures and the connections among them:
(6) geometric and polar representation of complex numbers and the interpretation of complex solutions to equations;		ED3440 M4350	Unit on complex numbers	Students derive product, quotient, and root formula for complex numbers. Derivations become part of their notebook.
D. A teacher of mathematics understands geometry and measurement from both abstract and concrete perspectives and is able to identify real world applications and to use geometric learning tools and models, including geoboards, compass and straight edge, rules and protractor, patty paper, reflection tools, spheres, and platonic solids. The teacher of mathematics must demonstrate knowledge of the following mathematical concepts and procedures and the connections among them:
(15) extend work with two-dimensional right triangles including unit circle trigonometry.		ED3440	Unit on trigonometry	Students connect right triangles, unit circles, and real numbers. These connections are part of their course notebook.
H. A teacher of mathematics must:
(2) recognize that there are multiple mathematical world views and how the teacher's own view is similar to or different from that of the students;		ED3440	Unit on reform and traditional curriculum.	Students will write a reflection essay on mathematical world views.
(4) understand the role of technology, manipulatives, and models in mathematics.		M3560 ED3440	Several computer software packages (e.g. Geometer’s Sketchpad, Cinderella), a number of manipulatives and two and three-dimensional models are used to explore geometric ideas.	In M3560 these are assessed through in class activities and homework assignments. Lesson plans will include manipulatives or software.
I. A teacher of mathematics must demonstrate an understanding of the teaching of mathematics that integrates understanding of mathematics with the understanding of pedagogy, students, learning, classroom management, and professional development. The teacher of mathematics to preadolescent and adolescent students shall:
(1) understand and apply educational principles relevant to the physical, social, emotional, moral, and cognitive development of preadolescents and adolescents;		ED3440	Mathematics Education – Educational Psychology Foundations unit	Students will write a reflection essay.
(2) understand and apply the research base for and the best practices of middle level and high school education;		ED3440	Mathematics Education – Educational Psychology Foundations unit Technology & Manipulatives unit Current Research unit Reform/Traditional Curriculum unit	Students will write a reflection essay.
(3) develop curriculum goals and purposes based on the central concepts of mathematics and know how to apply instructional strategies and materials for achieving student understanding of this discipline;		ED3440	Mathematics Education – Educational Psychology Foundations unit Technology & Manipulatives unit Current Research unit Reform/Traditional Curriculum unit	Demonstrated in student developed lesson plans.
(4) understand the role and alignment of district, school, and department mission and goals in program planning;		ED3440	Lesson Plan development unit	Demonstrated in student developed lesson plans.
(5) understand the need for and how to connect students' schooling experiences with everyday life, the workplace, and further educational opportunities;		ED3440	Current Research unit	Demonstrated in student developed lesson plans.
(6) know how to involve representatives of business, industry, and community organizations as active partners in creating educational opportunities;		ED3440	Local Communities unit	Students will write a reflection essay.
(7) understand the role and purpose of co-curricular and extracurricular activities in the teaching and learning process;		ED3440	Current Research unit	Students will write a reflection essay.
(8) understand the impact of reading ability on student achievement in mathematics, recognize the varying reading comprehension and fluency levels represented by students, and possess the strategies to assist students to read mathematical content materials more effectively; and		ED3440	Reform/Traditional Curriculum unit Current Research unit Reading unit	Students will write a reflection essay.
(9) apply the standards of effective practice in teaching students through a variety of early and ongoing clinical experiences with middle level and high school students within a range of educational programming models.		ED3440	Lesson Plan development unit	Practicum experience and students will write a reflection essay.

Student writing will be evaluated using the following rubric

1. Writing is incomplete. No indication of progress toward standard.

2. Writing completed. Indication of progress toward standard at beginning level.

3. Writing completed. Demonstrable progress toward standard at satisfactory level.

4. Writing completed. Exemplary progress toward standard beyond level expected.

Professional Education Mission Statement

Bemidji State University prepares teachers through inquisitive, involved, reflective practice. The framework outlining our program sets a standard that is rigorous, exemplary and innovative. The curricular structure is research based and organized around the Standards of Effective Practice. Graduates are proficient, collaborative, technologically literate and environmentally aware teachers, who work effectively in various settings with diverse learners.

The mathematics teacher from BSU will graduate will be a collaborative professional in two aspects. They will use collaborative learning in the classroom to help students learn more. A collaborative environment benefits all students, not just the top students or a subgroup of the class. Also the teachers will understand the benefits of collaboration between colleagues, locally and distant. Sharing of ideas electronically and through conferences enhances a teachers experiences for the benefit of their students. Proficiency in a teacher is developed through a development of content knowledge and an understanding of pedagogy. The math teacher from BSU will understand that good pedagogy will provide students the best opportunity to learn.

Best practices for math teachers are studied in the review and discussion of the NCTM documents, Principles and Standards for School Mathematics, Professional Standards, Assessment Standards, and the Navigations series. During the class these practices will be modeled in the Trigonometry Unit and the Complex Number Unit. Students will be critiqued in their lesson plan development, class mini-lessons and in their class presentations.