Algebraic Thinking in the Elementary School
This course provides elementary teachers with resources and opportunities to work with activities that promote algebraic thinking in the elementary math classes. Participants will learn how to integrate strategies and instructional procedures to help students think about mathematics at an abstract level, reason about real-life problem scenarios and make sense of their thinking. Participants will explore three components of algebraic thinking: making generalizations, thinking about “equals” and being able to reason about unknown quantities.
Participants will consider how to integrate algebraic tasks into their classroom instruction, how to utilize various media resources and how to engage in mathematical problem solving to promote algebraic thinking of elementary school students laying the foundation of future success of students.
This is an introductory course for teachers, particularly elementary teachers of mathematics, technology specialists, curriculum specialists, professional development specialists and administrators. Participants are expected to have regular access to computers. Although not a requirement, high speed Internet access definitely enhances the online experience. Participants should be proficient with using email, browsing the Internet, and navigating through computer files. Access to Microsoft Office is recommended. Participants who do not have access to Microsoft Office should download Open Office documents (a free download from Microsoft) to enable them to read and send word documents throughout this course.
This course will enable participants to:
learn how children in grades 3-5 can think about basic algebraic concepts,
appreciate the importance of algebraic thinking in the upper elementary curriculum,
read and discuss relevant research on the importance of algebraic thinking in elementary school instruction,
explore a variety of problems that can be used with students to develop their algebraic thinking,
understand student misconceptions about the sign “=” and why this is such a pivotal concept in elementary mathematics,
identify generalization as a strategy for solving some, but not all, algebraic problems,
appreciate the role of “unknown quantity” problems in the development of algebraic reasoning,
learn how to design and “algebrafy”** activities that encourage algebraic thinking,
create a collection of activities which promote algebraic thinking that can be integrated into classroom practice and
promote a “learning-by-doing” methodology, which is applicable to students at all ages.
Assessment and Course Requirements
Each session includes readings, activities and a discussion assignment, which participants are required to complete. High-quality, active participation in the online discussions is vital to the understanding and completion of the course. Additionally, participants will develop portions of a final project during each week’s session. Weekly assignments address sections of this project and a midterm check will occur during Session Three.
The project for this course is a collection of classroom activities that promote algebraic thinking which include activities, follow-up questions, and a brief reflection piece where the teacher describes his/ her expectations in terms of what students will know and be able to do upon completion of each activity.
Participants will be evaluated weekly on the frequency and quality of their participation in the discussion forum. Participants are required to post a minimum of three substantial postings each session, including one that begins a new thread and two that respond to existing threads. Postings that begin new threads will be reviewed based on their relevance, demonstrated understanding of course concepts, examples cited, and overall quality. Postings that respond to other participants will be evaluated on relevance and the degree to which they extend the discussion. Participants are to read all original messages by course colleagues and enough additional responses to make a total of 50% of the messages posted for that session.
Session One: What is Algebraic Reasoning?
During this session, participants will learn why algebraic reasoning is important in elementary math instruction and what exactly “algebraic reasoning” means. Participants will utilize knowledge of the NCTM Algebra strand goals and will investigate activities such as identifying patterns, analyzing change, representing situations and using math models to understand relationships such as algebraic thinking.
Session Two: Understanding Algebraic Representations and Patterns
In this session, participants explore two algebraic problems and compare their methods for solving them. Participants learn that different methods of solving problems contribute much to the understanding of the problem and that there is no “one right” way to solve these problems. This session focuses on “doing the math”.
Session Three: The Meaning of Equality
In this session, participants focus on “equality/ equals/=” and consider why youngsters have a difficult time solving algebraic problems of the sort “3=5=__+4” and “__ =2=3+6. The idea that the equals sign should be introduced as a balance and not as an operator, will be investigated. During this session, participants will interview a student about his/ her thinking about this topic.
Session Four: Using Algebra to Think About Unknown Quantities
During this session, participants will consider ways to solve algebraic problems when multiple possibilities exist for a number n. Participants will explore problems that compare two quantities in order to think about students’ understanding of algebraic tasks. This session is designed to illustrate that algebraic thinking does not always involve finding a missing quantity; sometimes it’s more about relating two quantities that happen to have an element in common.
Session Five: “Algebrafying” Elementary Math Instruction
In this session, participants will learn how to “algebrafy” their math instruction by applying new questioning techniques to delve into student thinking. They will also think about what types of problems they can algebrafy and which types of questions are not appropriate for that. Attention will be given to identifying math problems which are algebraic in nature and how to bring out algebraic ideas in these problems. Participants will also consider how to ask questions that promote algebraic thinking.
Session Six: What is the Value of Algebra in Elementary School?
In this session, participants will continue to work with algebrafying their instruction and will consider the deeper importance of incorporating algebra into their instruction. Participants will also continue working on problems that were introduced in Session 5, and will complete work on their Final Project.