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SMT 506
Integrated Approaches in Mathematics Education II
Spring, 2015, Wednesday 4:10 - 6:30
Eric Pandiscio, Associate Professor
301 Shibles Hall, 581-2452
eric.pandiscio@umit.maine.edu
Office Hours: Tuesday 8:30 - 9:30; Wednesday 3:30 - 4:00; or by appointment
Course description:
Applications of mathematics education research to the teaching of mathematics concepts and problem solving in introductory courses. Students will explore guided inquiry approaches to teaching, methods of curriculum assessment, and research based teaching strategies.
Overview of course content and format:
As part of a two-course sequence, SMT 506 will address large issues in mathematics education. The following topic areas will receive particular emphasis:
The Teaching and Learning of Number and Operation
The Teaching and Learning of Geometry
The Teaching and Learning of Algebra
These content strands are three of the five major areas delineated by the National Council of Teachers of Mathematics (2000) in their visionary document Principles and Standards for School Mathematics [PSSM]. Major concepts within the content areas will be the focus of our deliberations and mathematical work. Discussions will focus on the outcomes of learning: what do we expect students to know and be able to do as a result of instruction relative to these concepts?
Two other themes will permeate the course: the processes of mathematical inquiry, and research on mathematics education. The processes of mathematical inquiry will be approached from the perspective of the five process standards of the PSSM: problem solving, reasoning & proof, communication, connections, and representation as well as from the Standards for Mathematical Practice section of the Common Core State Standards. Research on mathematics education will be approached through the close reading of a variety of studies using different methodologies and across different grades and topics.
As part of a course reform initiative supported by grant funding, this course will include a unit of mathematical content on transformational geometry at a level of sophistication that is deeper than what is expected of secondary students as a means of enhancing prospective teachers content knowledge.
Learning Outcomes
Students will gain proficiency with the following topics:
an understanding of the nature and origin of the desired outcomes of learning in K-12 mathematics classes
a grasp of what we expect students to know and be able to do as a result of concept-based instruction
the processes of mathematical inquiry, and research on mathematics learning
the use of NCTMs five process standards: problem solving, reasoning & proof, communication, connections, and representation
Layout
This course will involve reading, writing, and discussion. It is intended to operate as a seminar, which means, among other things, extensive involvement by the students. Students will also work on numerous mathematical tasks, both in class and outside class. These will be gathered from a variety of sources, including large-scale assessments such as Smarter Balanced, Praxis 2, and TIMSS. As a class participant you will be expected to read all articles handed out.
Blackboard site
We will make use of a course Blackboard site. You can access it from http://www.courses.maine.edu. The site is where you will find assigned readings, and make posts to the discussion forums. Additional information about the site and how to use its various features will be discussed in more detail in class.
Assignments:
1. Full and active participation in class. There will be reading assignments for most classes. One goal of having assigned readings is for you to become familiar with educational literature. Another, equally important goal, is for you to become savvy consumers of educational research and other kinds of articles related to mathematics teaching and learning. We will focus comparing, contrasting, and critiquing various forms of manuscripts. Students should be prepared to discuss readings meaningfully in class.
2. Forum Postings
For most of the readings, you will post at least one question or comment in the appropriate Discussion Forum on Blackboard. This serves several purposes. First, it provides structure and focus for you as you read the assigned articles. Second, it gives me information about what ideas were of particular interest to the class and what questions or issues came up as people did the readings You can ask a question about something that the author(s) of the article were not clear about, ask how something the author(s) said applies to a particular situation your familiar with, express an opinion about the views expressed by the author(s), or anything else related to the issues that comes to mind as you are reading the article.
Your questions/comments are due by midnight-ish on Monday. On Tuesday, read the questions and comments posted by your classmates and reply to at least one question/comment. This means you will be making a total of at least three postings this week. Post your replies by 8am on Wednesday.
To post a question/comment, go to the appropriate forum and click on the Thread icon. This will open a new window where you can write the subject of your post and the text of your post. Be sure to click Submit at the bottom of the page.
To view and reply to posts, go into the Forum, click on one of the messages, click Reply and write and then Submit your response.
3. Transformational Geometry unit and accompanying assessments. The broad outline of the purpose of this initiative follows:
We will work with a unit of instruction in Transformational Geometry, as described in the Common Core State Standards for Mathematics (CCSSM). Transformational Geometry is a topic that receives more emphasis in the CCSSM than it has in other standards and curriculum frameworks that have guided K-12 mathematics instruction over the past several decades. To address the need to enhance the prospective teachers content and pedagogical content knowledge related to this topic, this module will provide students with an opportunity to study the mathematical content of transformational geometry at a level of sophistication that is deeper than what is expected of secondary students as a means to enhancing the prospective teachers content knowledge. Assessment will be a series of mathematical tasks an understanding of transformational geometry at a sophisticated level. These tasks will be designed from the perspective of a college geometry curriculum yet be applicable to secondary mathematics.
Another aspect of course reform will utilize assessment items from Smarter Balanced and PARCC to evaluate each others mathematical thinking on topics drawn directly from the Common Core. This work has multiple purposes: a) to enhance students ability to assess mathematical reasoning, b) to Construct Viable Arguments and Critique the Reasoning of Others, one of the Standards for Mathematical Practice in the CCSSM, and c) to become familiar, through direct experience, with the nature of the evaluation items that secondary students will be expected to know and be able to do. Students in the course will use each others work samples, and to the extent feasible, the mathematical work of other participants that can be recruited to complete the Smarter Balanced and PARRC items (e.g. other MST students, MAT 103 students, etc.).
4. Content Problems and other prompts. We will engage in mathematical explorations, some of which will be turned in, and others of which will be less formal.
5. Final Synthesizing Project. This assignment will be arranged individually with the instructor. The overarching theme is for each student to focus on a single idea of significance in mathematics education. For those concentrating in mathematics, and who are ready, this can connect with the thesis. For other students, I envision a brief exploration of an aspect of mathematics education (curriculum, research, instruction, assessment, etc.) that connects to your particular work or school setting.
Evaluation
Weekly Participation 20 %
Discussion Forums 20 %
Transformational Geometry work 20 %
Content Problems/Prompts 20 %
Final Synthesizing Project 20 %
Required Texts:
Kilpatrick, J., Martin, W. G., & Schifter, D. (Eds.). (2003). A research companion to principles and standards for school mathematics. Reston: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. Principles and Standards for School Mathematics. Reston, Virginia: 2000.
Online at:
http://standardstrial.nctm.org/triallogin.asp
(need to register for a free, 120-day student version)
Common Core State Standards (free, online)
http://www.maine.gov/education/lres/math/standards.html#ccss
(these are available in a variety of formats; we'll talk about which ones to read in class)
Selected articles will be available on Blacboard.
Academic honesty
Academic dishonesty included cheating, plagiarism and all forms of misrepresentation in academic work, is unacceptable at the University of Maine. As stated in the University of Maine's online "Student Handbook," plagiarism (the submission of anothers' work without appropriate attribution) and cheating are violations of the University of Maine Student Conduct Code. An instructor who has probable cause or reason to believe a student has cheated or plagiarized may act upon such evidence and report the case to an Associate Dean.
Special Accommodations
If you have a disability for which you may be requesting an accommodation, please contact Ann Smith, Director of Disabilities Services, 121 East Annex, 581-2319, as early as possible in the term.
Contingency Plan:
In the event of disruption of normal classroom activities due to unexpected circumstances, the format for this course along with assignments and grading procedures may be modified to enable completion of the course. In that event, an addendum to this syllabus will be provided that will supersede this version.
Incomplete grades:
A grade of I (Incomplete) is assigned if a student has been doing work of acceptable quality but, for reasons satisfactory to the instructor, has not completed all of the work required to earn credit by the end of the semester or session.
The work must be completed and submitted to the instructor by the date agreed to with the instructor, but not later than one year (i.e., 12 months) from the end of the semester or session in which the incomplete was granted.
An I remains on the transcript permanently if not resolved or if a written request for an extension is not approved within the allotted time period for removing the incomplete. The request for an exception to regulation, listing the circumstances necessitating the extension, the work that remains unfinished and a specific deadline for completion, must be approved by the instructor, the students advisor (for degree students), Graduate Program Coordinator, and Dean. An extension will be granted only under unusual circumstances. For grades of I, it is the student's responsibility to reach and maintain an understanding with the instructor concerning the timely completion of the work.
Sexual Discrimination Reporting
The University of Maine is committed to making campus a safe place for students. Because of this commitment, if you tell a teacher about an experience of sex discrimination which includes sexual assault, sexual harassment, stalking, or relationship abuse involving members of the campus, your teacher is required to report this information to the campus Office of Sexual Assault & Violence Prevention or the Office of Equal Opportunity.
If you want to talk in confidence to someone about an experience of sexual discrimination, please contact these resources:
For confidential resources on campus: Counseling Center: 207-581-1392 or Cutler Health Center: at 207-581-4000.
For confidential resources off campus: Rape Response Services: 1-800-310-0000 or Spruce Run: 1-800-863-9909.
Other resources: The resources listed below can offer support but may have to report the incident to others who can help:
For support services on campus: Office of Sexual Assault & Violence Prevention: 207-581-1406, Office of Community Standards: 207-581-1409, University of Maine Police: 207-581-4040 or 911. Or see the OSAVP website for a complete list of services at HYPERLINK "http://www.umaine.edu/osavp/" http://www.umaine.edu/osavp/
Schedule of Topics, Readings, and Assignments:
January 14 Introduction
January 21 Read the Five Process Standards for grades 9-12 in Principles and Standards for School Mathematics. Available on-line. (pages 334- 364)
Read Standards for Mathematical Practice from Common Core State Standards
January 28 Read the Numbers and Operations, Algebra, and Geometry Standards for grades 9-12 (pages 287- 318) in Principles and Standards for School Mathematics.
Read Motivating Students by Teaching for Understanding (Kazemi & Stipek)
Read Mixed-Ability versus Same-Ability Grouping in Mathematics (Linchevski & Kutscher)
February 4 Read Secondary Options and Post-Secondary Expectation: Standards-based Mathematics Programs and Student Achievement of College Mathematics Placement Exams
February 11 Read Chapter 2 in Research Companion
What Research says about the NCTM Standards (Hiebert)
Read Chapter 6 in Research Companion
Developing Mathematical Power in Whole Number Operations (Fuson)
February 18 Read Chapter 7 in Research Companion
Fractions and Multiplicative Reasoning (Thompson & Saldahna)
Read Technology Integration in Secondary Mathematics Classrooms: Effect on Students Understanding
February 25 Transformational Geometry Unit, Part 1
Read Connecting Science and Mathematics Instruction: Pedagogical Context Knowledge for Teachers
March 4 Spring Break: No Class
March 11 Spring Break: No Class
March 18 Transformational Geometry Unit, Part 2
Read Chapter 8 in Research Companion
Facts and Algorithms as Products of Students' Own Mathematical Activity (Gravemeijer & van Galen)
Read Abstract or Concrete Examples in Learning Mathematics?
March 25 Read Chapter 9 in Research Companion
On Appreciating the Cognitive Complexity of School Algebra (Chazan & Yerushalmy)
April 1 Read Students' Understanding of Three-Dimensional Cube Arrays (Battista & Clements)
Read Students Understanding of the Cartesian Connection: An Exploratory Study (Knuth)
April 8 Transformational Geometry Unit, Part 3
Read Chapter 11 in Research Companion
Teaching and Learning Geometry (Clements)
Read Assessing Justification and Proof in Geometry Classes Taught Using Dynamic Software (Galindo)
April 15 Read Chapter 15 in Research Companion
Reasoning and Proof (Yackel & Hanna)
Read Transforming Secondary Mathematics Teaching: Increasing the Cognitive Demands of Instructional Tasks Used in Teachers Classroom
April 22 Read Chapter 16 in Research Companion
Representations in School Mathematics: Children's Representations of Problems (Smith)
Read Teaching Mathematics for Understanding: An Analysis of Lessons Submitted by Teachers Seeking NBPTS Certification
* Final Synthesizing Project Due
April 29 Last Class: Tying up loose ends
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