COURSE TITLE:  Fractions Operations for Elementary School Math Educators

INTENDED AUDIENCE: Mathematics Educators of Grades 3, 4, and 5

Course Learning Objectives addressed in these discussion prompts and assignment:

1. Educators will explain and demonstrate their understanding of the fundamental, underlying mathematics behind addition, subtraction, multiplication and division of fractions.

2. Educators will explain and demonstrate how the use of properties of operations (the Identity, Associative, Commutative, and Distributive Properties) can be used as tools to understand and teach fraction operations.

Module 1 Learning Objectives Addressed in these discussion prompts and assignment:

• By the end of this module, participants will demonstrate their understanding of how the Identity Property plays a crucial role in operations with fractions.

• By the end of this module, participants will model addition and subtraction of fractions and mixed numbers with pattern blocks and connect their representations to the algorithms.  

Learning Activities and Materials are listed below in sequence. The Discussions and Assignment are in enlarged font to show how these align and fall into the sequence of the Learning Activities and Materials. 

Learning Activities and Materials in Module 1:

• Short video: (<5 minutes) of why we, as teachers, need a deep understanding of the underlying math in operations with fractions. Video will also set the stage for the purpose and what teachers can expect from this course including articulating course learning outcomes.  

• Professional Reading: Participants engage in a brief professional reading about the importance of developing conceptual understanding of fractions operations both for themselves and for their students. Specific reading to be determined. 

• Formative Assessment: Reflection Question for Discussion Board 

  • • Why do you think that as teachers, we benefit our students when we own the task of having a deep understanding of fractions concepts?

• Interaction: Intro to Pattern Blocks. Participants will use pattern blocks to identify fractional values and flexibly change the values of the pattern blocks (eg. the hexagon represents 1 whole in the first interaction, but represents 2 wholes in the next interaction). Participants will have to go through a set number of interactions but can "play" with those as long as they would like. 

• Short video: (<5 minutes) of how the Identity Property plays a crucial role in operations with fractions. 

• Interaction: Participants model addition and subtraction of fractions and mixed numbers with pattern blocks and connect their representations to the algorithms.  

• Short video: (<5 minutes) of how the Associative, Commutative and Distributive Properties are at work in addition and subtraction of fractions and mixed numbers. 

• Interaction: Participants again model addition and subtraction of fractions and mixed numbers with pattern blocks and connect their representations to the properties of operations.  

• ASSIGNMENT: Finding the Sum

• Formative Assessment: Reflection Question for Discussion Board 

  • • How did knowing the properties of operations serve as a tool to help you make sense of the fraction addition and subtraction algorithms?

    • What are the similarities between adding and subtracting fractions? What are the differences?

• Short video: (<2 minutes) Reiterates how the Associative, Commutative and Distributive Properties are at work in addition and subtraction of fractions and mixed numbers. Also addresses the similarities/differences between addition and subtraction. 

Reflection

Creating assignments and discussions in Canvas was extremely easy. I was also able to create a rubric to assist with the grading and set an "auto assign" feature for Canvas to assign 2 peer reviewers to each student. The features were easy to find. I am curious to see what the assignment submissions look like to the teacher. 

This assignment is one I have done with children on multiple occasions. They have articulated that they found it fun and felt like they weren't really doing math (they were!). Adults often don't get many chances for creative freedom. This assignment lends itself to to artistic and creative freedom while prompting them to apply their learning of adding fractions with the properties of operations. 

I did wonder about putting an example alongside the assignment for educators to refer to. Sometimes having a model of what is expected can help students better understand and complete the assignment. This is a strategy I use with young students but not always needed with adult learners. One way I can determine whether or not it's worth my time to create a sample is when I get submissions of the assignments, I can see where misunderstandings or misconceptions of the instructions took place. Then I can determine whether the instructions need clarification or whether I need to create a sample for educators to examine to help them understand the assignment.  

Additionally, the discussion questions can allow me to see what misconceptions might come up. I can address those misconceptions in future iterations of this course. I also wonder if educators will be able to clearly see and apply the properties of operations. For that, I will need to make sure the learning activities are really clear and concise. I have found it to be true of myself as an educator, as well as educators I have coached, that it can be hard to overcome biases and habits in instruction. I am hoping that the discussion boards might reveal some of those biases as well as trends in which ones are common so I can address those in future iterations of this course.