EDCI5XX. Math Thinking for Instruction for Grades 6-12 (MTI 6 - 12)
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This course provides an opportunity to study fundamental mathematical theory underlying the content area of number and operation and structures of algebraic thinking. Topics will include working with qualitative and quantitative change and the need to describe and predict variation, the use of mathematical models and the understanding student thinking. Emphasis will be given to developing ideas about algebraic reasoning.

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

The College of Education envisions being a leading, diverse, nationally recognized educational community. Our caring faculty members and innovative curriculum are:

  • Preparing professionals through integrated programs grounded in research
  • Generating and evaluating knowledge through disciplinary and interdisciplinary scholarship
  • Informing professional practice and community life through the exchange and utilization of knowledge

Together, our college community is achieving this vision through a culture of openness, innovation, and collaboration.

College Mission

The College of Education enriches lives by advancing excellence in research and practice in education, leadership, and applied human arts and sciences (adopted January 27, 2005).

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 Practice; and,
Engaging in Community Building & Partnerships.

Course Description

Participants in this course will develop a deep understanding of the topics in number and operations that are taught in grades 6-12 and of the way that children develop an understanding of these ideas. In particular, participants will explore topics important to the mathematical experiences of students in grades 6-12 classrooms including addition, subtraction, multiplication, division, place value, rational number, rational number operations and connections to algebraic reasoning. The focus of the course will be teachers’ understanding of these mathematical ideas as well as students’ reasoning and development of these topics. An investigative approach involving representations, problem solving, reasoning and proof, connections and communication will be emphasized.

Course Goal and Expectations

Goals/Objectives

The following goals and objectives guide this course. Specifically, participants will have opportunities to:

Learn the five big ideas for developing mathematical thinking and how to apply them in a classroom

Become knowledgeable about instructional practices emphasizing mathematical reasoning, communication, connections, and problem-solving

Learn the content, methods, and materials necessary to teach mathematics at the middle and high school level

Develop knowledge of the goals of mathematics curriculum and instruction for grades 6-12 as reflected in the NCTM Standards and Idaho Mathematics Content Standards

Become familiar with assessing and using students’ thinking as a guide to planning instruction

Examine personal assumptions, beliefs and values about middle and high school mathematics instruction

Become more confident in one’s ability to do mathematics

Goals of Curriculum and Instruction

  • Philosophy and Educational Organizations – CI Masters degree graduates have a comprehensive understanding of the philosophical, historical, social, political and cultural understanding of schools and society.
  • Curriculum – CI Masters degree graduates understand that curriculum should be relevant, engaging, challenging, and integrative for the learner. They know how to select, adapt and reflect on theories and engage in reflective practices in light of curriculum standards, theories, models and learners.
  • Instruction– CI Masters degree graduates understand the principles of instruction know a wide variety of teaching strategies and learning theories and incorporate relevant technologies while teaching core concepts, skills of inquiry, problem posing/solving, collaboration, and communication to facilitate student learning.
  • Assessment and Evaluation – CI Masters degree graduates analyze and understand the various roles of multiple types of assessments for monitoring, evaluating and responding to student learning; they understand, develop, use and critique formal, informal, and performance assessment techniques, including local, state, and national assessment systems to improve student learning.
  • Research – CI Masters degree graduates, as critical consumers of educational research, appreciate the role of educational research for informing practice. M.Ed. graduates develop the skills to conduct classroom research. M.S. graduates, as producers of educational research, collect and analyze data, and formally share their research findings.
  • Diversity– CI Masters degree graduates understand human diversity as a valued component of educational systems; understand how to appropriately engage with diverse population; effectively structure learning experiences with diverse population; and effectively engage with diverse populations of students, parents, and colleagues.
  • Subject Knowledge – CI Masters degree students demonstrate their knowledge of the content that they teach through the admissions requirements and/or through content coursework that is included in the degree.

Required Readings and Learning Resources

Driscoll, M. (1999). Fostering algebraic thinking: A guide for teachers, grades 6-10. Portsmouth, NH: Heinemann

Note: Please bring paper, pencil and a simple calculator.

Suggested Additional Resources & Reading Materials

·NCTM Membership.

·Driscoll, M. (2007). Fostering geometric thinking: A guide for teachers, grades 5-10. Portsmouth, NH: Heinemann.

·Van de Walle, J. A. (2006). Teaching student-centered mathematics: Grades 5-8. Boston, MA: Pearson Education Inc.

Learning Activities and Assignments

Major Topics (for Five Full Day Course Format)

Date / Topics / Reading Material
Day 1 / •Introduction
-Math Initiative
-Teaching for Understanding (Seeds Problem)
-Modes of Representation (Choc. Milk Problem)
-Realistic Mathematics Education
• Whole Number Operations Development
-Context (Problem Types, Strategies)
-Addition/Subtraction Progression / •Hiebert (Chp 1) – Attached in initial email.
*All reading assignments and homework are to be completed prior to date listed. All reading materials will be provided in workbook or via dmt.boisestate.edu
Day 2 / • Algebraic Reasoning
-Generalization and Justification
-Equivalence and Relational Thinking
-Modeling
•Multiplication and Fact Fluency / Reading
•Workbook - Session 1: Introduction to Teaching for Understanding
•Workbook - Session 2: Addition and Subtraction
Homework
•Problem Type Table (End of Session 2)
•Use multiple models to solve two +/- problems (End of Session 2)
Day 3 / Algebraic Generalization and Modeling Part 1
Division
-Problem Types and Context
-Progression
Fractions Part 1 - Structural Components / Reading
•Workbook - Session 3: Developing Algebraic Thinking
•Workbook - Session 4: Multiplication
Homework
•Use multiple models to solve two multiplication problems (End of Session 4)
Day 4 / Algebraic Generalization and Modeling Part 2
Fractions Parts 2 & 3
-Situations
-Operations / Reading
•Workbook - Session 6: Division
•Workbook - Session 8 Part 2- Fraction Concepts and Operations
Homework
•Use multiple models to solve two ÷ problems (End of Session 6)
•100’s grids activity (End of Session 8)
Day 5 / • Ratio and Proportional Reasoning
-Problem Types
-Extensions and Applications
•Modeling Real-World Contexts / Reading
•Workbook - Session 9: Ratio and Proportional Reasoning
Homework
•Write a context for 2 ½ ÷ ¾ (End of Session 8)
•Recording Students’ Strategies (Session 8, before Multiplication of Fractions Task)

Course Requirements/Assignments/Projects:

  1. Attend the MTI 6-12 course meetings
  2. Complete assigned readings
  3. Complete class project to consist of:

Design a 2-week instructional unit plan, that consists of ~8 lessons with a pre/post test. The lessons must use key ideas developed in the course and align with the 5-part Teaching for Understanding framework that is developed in the course.

Use the TLSG Task Design Template for each lesson.

Attendance Policy

All participants are expected to attend all class meetings. If you must miss a class meeting, please make arrangements ahead of time with the instructor as soon as possible. Two half-day class absences or one full-day class absence will result in the participant having to withdraw from the course and take it at a later date.

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.

Nondiscrimination Policy

The University of Idaho has a policy of nondiscrimination on the basis of race, color, religion, national origin, sex, age,disability or status as a Vietnam era veteran. This policy applies to all programs, services, and facilities, and includes, butis not limited to, applications, admissions, access to programs and services, and employment. Such discrimination isprohibited by titles VI and VII of the Civil Rights Act of 1964, title IX of the Education Amendments of 1972, sections 503and 504 of the Rehabilitation Act of 1973, the Vietnam Era Veterans' Readjustment Assistance Act of 1974, the AgeDiscrimination Act of 1975, the Age Discrimination in Employment Act Amendments of 1978, the Americans WithDisabilities Act of 1990, the Civil Rights Act of 1991, the Rehabilitation Act Reauthorization of 1992 and other state andfederal laws and regulations. Sexual harassment violates state and federal law and policies of the Board of Regents, andis expressly prohibited, as stated in Faculty Staff Handbook (FSH) 3220. The University of Idaho also prohibitsdiscrimination on the basis of sexual orientation, as stated in FSH 3215. The entire FSH can be accessed online at Questions or concerns about the content and application of these laws, regulations orUniversity policy may be directed to: April Preston, Human Rights Compliance Officer (885-4213); GloriaJensen, Coordinator of Disability Support Services (885-7200); Regional Office for Civil Rights, U.S. Department ofEducation 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 UI Human RightsCompliance Office (885-4212 or ). Retaliation for bringing forward a complaint is prohibited by FSH3810.

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 liaisonlibrarian with questions: Rami Attebury, 885-2503, . 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 for email or IM assistance.

Library Resources (Distance Education/Centers 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 access to personalized assistance from the librarians. If you have assignments or research questions and aren’t sure how to make the most of library resourcesfrom off campus, feel free to contact the College of Education liaisonlibrarian with questions. Help may be obtained via email or phone. RamiAttebury, 208-885-2503, . As always, you may also callthe main reference desk anytime Monday to Thursday 9 to 9, Friday 9 to 5,and Sunday 1-9, 208-885-6584, or visit for email or IM assistance.