Relational Thinking in the Primary Grades: Foundations for Algebra, Silvis, Spring 2020

Course Number: Newport: EDU 5626 C03 or Bellows Falls: EDU 5626 C02
Instructor: Loree Silvis
Location: Newport OR Bellows Falls
Dates and Times: Newport: January 6 - May 31, 2020 OR Bellows Falls: January 9 - May 21, 2020
Credits: 3 Graduate Credits
Tuition: Set by and payable to Cornerstone Mathematics Consulting, LLC

Note: Please register directly with the Cornerstone Mathematics Consulting, LLC using the link provided below. Cornerstone Mathematics Consulting will then give you the link to Castleton's online registration form. Payments are due to Cornerstone Mathematics Consulting.

Course Description

This 3-credit graduate course explores the Common Core State Standards for Mathematics (CCSSM) and their role in improving instruction and student understanding in primary-level classrooms.  How can teachers present opportunities for students to make sense of and make connections between counting, operations, symbolic notation and quantitative relationships? How can teachers develop a culture of learning where flexible thinking and sense making are at the core of all learning? How can teachers encourage students to extend and generalize the relationship they are discovering? What role do the Standards for Mathematical Practice have in deepening student understanding? How can assessment be used to guide instruction and support student understanding?

Course Objectives/Goals

During this 3-credit course teachers will...

  •  Explore instructional strategies for connecting arithmetic to algebra and building relational thinking in the primary grades.
  • Examine the Common Core State Standards for Mathematics and the supporting cognitive research in developing relational thinking.
  • Analyze the Standards for Mathematical Practices from the CCSSM and develop ways to incorporate these standards in our daily instruction and encourage our students to develop these practices.
  • Explore best instructional practices (wait time, questioning, classroom management techniques, assessment, feedback, private think time, facilitating discussions, partner share, active listening, metacognition, building confidence and persistence, motivation, differentiation) for engaging students in thinking deeply and making sense of problems.
  • Examine ways of creating a classroom culture in which students develop a confidence in their abilities, a willingness to engage in and explore problems, communicate solutions and persevere when faced with challenging problems.
  • Develop, analyze and adapt tasks from our published programs to engage students in thinking deeply about big mathematical ideas.

Course Expectations

Course Requirements

  • Read and reflect on all required readings
  • Reflect in writing on your role in supporting student understanding and in developing the Mathematical Practices
  • Collect evidence of student understanding using various techniques
  • Record students solving problems using video
  • Analyze collected evidence of student understanding
  • Compile documentations of student progress using a course binder
  • Create, implement and share a set of problems designed to elicit relational thinking
  • Active participation and helpfulness to colleagues
  • Attendance at all sessions

Ongoing Formative Assessment Project

Due Date: Each class

Each week you will be required to collect and analyze evidence of student understanding for at least 3 students using specific tasks developed or shared during class.

         Assignment Details:

  1. Create and maintain a system for collecting evidence of student understanding and for monitoring student progress.
  2. Choose at least 3 students each week to assess and monitor using the interview assessment guidelines.
  3. Analyze each task prior to implementing task with students (what are the possible solutions, student responses, common errors, misconceptions).
  4. Meet with each student, pose the task and record student response (using video at least 2 times).
  5. Analyze student responses using reflection guidelines discussed in class:
    1. What was successful?
    2. Which strategies were used?
    3. Were there any challenges? Explain.
    4. Do you notice any error patterns? Are there any misconceptions?
    5. What are the next instructional steps?
  • Share results during class and collect additional ideas for instructional strategies
  1. Implement instructional strategies designed to increase student relational understanding.
  2. Continue to monitor student progress to analyze effectiveness of instruction, changing instruction as needed. 

Journal Reflections

Due Date: Each Class

Each class you will be required to reflect on specific questions or prompts provided during class.  Entries will be shared with others during class.

Problem Strings

Due Date: Sign up during first class 

Design, implement, and present to colleagues a set of related problems that have specific focus and encourage relational thinking.    

         Assignment Details:

  1. Design a set of problems including one or two foundational problems followed by several problems to extend thinking and move toward generalizations (total number of problems may range from 5-7).
  2. Implement this problems string with students.
  3. Record anecdotal observations and reflect and analyze student responses.
  4. Present to colleagues in the course your problems string as you did in your classroom and collect feedback from others.
  5. Share your observations of what happened in your classroom and share ideas about next steps.

Required Texts

Costs, if any, for the required readings are not included in the course tuition.


Connecting Arithmetic to Algebra Strategies for Building Algebraic Thinking in the Elementary Grades, Russell, Schifter, Bastable, Heinenmann, 2011

Course Resources:

Adding it Up ,NRC

Algebra For All: Purple Level, Elizabeth Warren – Origo Publications, 2006

Contexts for Extending Addition and Subtraction, Fosnot & Uittenbogaard, Heinenmann, 2007

Contexts for Learning: Minilessons for Early Addition and Subtraction, Fonot & Uittenbogaard, Heinenmann, 2007

Contexts for Learning, Trades, Jumps, and Stops, Fosnot, Heinenmann, 2012

Elementary and Middle School Mathematics Teaching Developmentally, Van de Walle, Karp, Bay-Williams,  Pearson, 2010

Essential Understandings of Mathematical Reasoning Pre-K- 8, Lannin, Ellis, Elliott, NCTM,

Lesson for Algebraic Thinking, von Rotz & Burns, Math Solutions, 2002

Principals and Standards for School Mathematics, NCTM, 2003

Putting Research into Practice in the Elementary Grades, NCTM, 2002

Thinking Mathematically, Carpenter, Franke, Levi, Heinenmann, 2003

Young Mathematicians at Work Constructing Algebra, Fosnot & Jacob, Heinemann, 2010

For additional course and registration information

Loree Silvis

Register online now!