Building upon the Foundation: Developing Additive Reasoning and Computational Fluency

Course Number: EDU 5515 C20
Instructor: Loree Silvis
Location: The Howard Dean Center, Springfield, VT
Dates and Times: July 17 - July 21, 2017 from 8:30 am to 4 pm. Course completion date is July 31, 2017
Credits: 3 credits
Tuition: $900 non-members/$810 members (includes materials); optional 3 graduate credits, additional $375

Notes: Please register directly with the Vermont Learning Collaborative (VLC). If you wish to take the course for credit, please notify VLC. VLC will give you the link to Castleton's online registration form. Tuition is payable to VLC.

Course Description

This 3-credit graduate course will focus on examining research with regards to how students construct understanding of addition and subtraction and the relationship between them, analyzing strategies students use, and exploring various ways to assess and promote additive reasoning.

Course Objectives

Examine research with regards to how students construct understanding of addition and subtraction and the relationship between them.

Investigate and analyze how students develop and use strategies for addition and subtraction.

Explore ways to assess and promote a deeper understanding of addition and subtraction as these operations evolve in the Common Core State Standards; and to develop fluency of basic number combinations.

Course Expectations

• Read Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction by Catherine Twomey Fosnot and Maarten Dolk
• Complete all additional readings handed out during class
• Reflect in writing on each assigned reading or chapter
• Maintain a course binder
• Analyze games that promote computational fluency and share during class
• Plan an Additive Reasoning Project to implement with students in the fall
• Active participation and helpfulness to colleagues
• Attendance at all sessions

Game Analysis Assignment

Due Date: Participants choose additive reasoning (addition and/or subtraction) games to analyze and share with colleagues.

This project requires you to choose 2 games that support student understanding of additive reasoning, analyze the game for its mathematical relevance, and present the game to colleagues.

Assignment Details:
1. Choose one game/activity from any program or resource, or create your own, AND choose one online game to share with your colleagues during class.
2. Play the game(s) with a child or another adult to gain insight about your own thinking and strategy use while playing.
3. Analyze the games for mathematical relevance using the form provided in class.
4. Type up the game instructions using the format provided in class include learning expectations, materials needed, procedures, and variations (extensions or simplifications).
5. Share the game during class so we can all play. Please bring all needed materials or make arrangements to use the instructor’s materials.

Case Study Presentation

Due Date: Wednesday, July 19, 2017

Using the case study form provided in the course binder, record concerns regarding student understanding, misconceptions or difficulties student experiences in the classroom. Present your case study in class where colleagues will brainstorm strategies to support student learning.

Minilesson/Problem Strings/Number Talks

Due Date: Thursday, July 20, 2017

Reflect in writing using forms provided regarding the implementation of 2 whole-class minilessons (problem strings, see Chapter 8 in YMAW, or Number Talks) focused on exploring relationships and developing strategies for addition and/or subtraction.

Individual/Group Additive Reasoning Project:

Due Date: Friday, July 21, 2017. This project is intended to be completed in your educational setting in the fall and can be completed on your own or with colleagues. Time and guidance will be provided during class to plan this project.

Project Details:

1. Choose a ‘big idea’ or concept from the landscape of learning found in the Young Mathematician at Work as the topic/focus of your project.
2. Develop an instructional plan, which focuses on this ‘big idea’. This plan should include at least 4-5 different learning opportunities for your students which may include using tools, games and activities discussed during class, something you’ve created yourself, or ones that are included in Young Mathematician at Work or your classroom math program.
3. Create a pre-assessment or a method of collecting evidence of what your students know and understand before implementing your project.
4. Complete a final written plan (2-3 pages) which will include:
a. An overview of why you chose to focus on this concept.
b. A copy of your pre-assessment.
c. An outline of the learning opportunities you have planned, include any additional instructional strategies you will use.

In the fall:
5. Implement your instructional plans for a period of 2-6 weeks.
6. Collect evidence of students’ developing understandings while implementing your plan using anecdotal notes, interviews, questions, or some other formative assessment.
7. Analyze progress made throughout the implementation period, you may use a post-assessment if you’d like.

Required Texts

Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction by Fosnot, C. T., & Jacob, B. (2010). Portsmouth, NH: Heinemann.

For additional course information

Loree Silvis
(802) 434-5080

For additional registration information

Susan Leuchter
(802) 257-8600

Register online now!