Course Learning Objectives & Outcomes

UPDATE 9/19/2024: At this time, multiplication and division will not be built into the mini-course. The Course Learning Objectives (CLOs) and Module Learning Objectives (MLOs) have been updated to reflect these changes but the language of multiplication and division will remain in this document for consideration when the project is built out out to include those 2 operations as well. 

Course Learning Outcomes

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.

3. Educators will demonstrate how different models can support their conceptual understanding and articulate how those models can support student understanding during classroom instruction.

4. Educators will articulate why it is important to spend instructional time helping students understand the underlying mathematics of fraction operations and the use of properties.

5. Educators will explain how and why a deep understanding of fractions operations is important for students' future mathematics learning, particularly in middle school when ratios and proportions rational numbers are taught by providing at least one concrete example. 

Course Summary

• Module 1: Mathematics at Work: Deep Dive Into the Algorithms for Operations Adding and Subtracting with Fractions

• Module 2: Models that Support A Conceptual Understanding of Operations Addition and Subtraction with Fractions

• Module 3: Teaching Operations Addition and Subtraction with Fractions for Long Term Understanding 

• Apply It in Real Life: Teaching Fractions Operations Addition and Subtraction to Students and Reflecting on the Results

Module Learning Objectives

Module 1:  Mathematics at Work

• By the end of this module, participants will demonstrate their understanding of how the Identity Property plays a crucial role in operations with fractions. (aligns to CLO1, CLO2)

• 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.  (aligns to CLO1, CLO3)

• By the end of this module, participants will model multiplication of fractions and mixed numbers with pattern blocks and connect their representations to the algorithm. (aligns to CLO1, CLO2)

• By the end of this module, participants will model division of fractions and mixed numbers with pattern blocks and connect their representations to the algorithms. (aligns to CLO1, CLO2)

Module 2:  Models that Support A Conceptual Understanding of Operations with Fractions

• By the end of this module, participants will explain the strengths and limitations of the pattern blocks as a model. (aligns to CLO3)

• By the end of this module, participants will use and describe a variety of models that are more universal than pattern blocks. (aligns to CLO3, CLO4)

Module 3:  Teaching Operations with Fractions for Long Term Understanding

• By the end of this module, participants will explain why students need to understand the underlying math behind fractions operations instead of memorizing the steps of the algorithms. (aligns to CLO4, CLO5)

• By the end of this module, participants will describe how strong fractions operations knowledge will support students in middle school and high school math. (aligns to CLO5)

• By the end of this module, participants will describe how strong fractions operations knowledge will support students in daily life and in their careers. (aligns to CLO4, CLO5)

Apply It In Real Life:  Instructional Coaching Support in the Mathematics Classroom

• By the end of one coaching cycle, participants will use a variety of models with students and describe their observed benefits and drawbacks. (aligns to CLO3, CLO4)

• By the end of two coaching cycles, participants will analyze student work in PLCs (Professional Learning Communities) and discuss as a team how student understanding was increased as a result of teaching students the underlying mathematics of fractions operation. (aligns to CLO4)

• By the end of the school year, participants will have filmed one classroom lesson with fractions operations and discuss with the instructional coach where there is evidence of student strengths and limitations in understanding. Participants will develop a plan for "next steps" in instruction with the guidance of the instructional coach. (aligns to CLO4 and CLO5)