Kirkpatrick Model Level 2

Course Learning Objectives Addressed in this Assessment:

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 this Assessment:

• 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 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.  

• 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: It has been a little while since I wrote an assessment! My current role in my company has focused on other projects and it was refreshing to get back to writing a good, valid assessment that aligns to objectives and hopefully produces the responses I would like to see. It also reminds me how challenging this task is. Assessment should always be meaningful. The purpose of assessment is to provide the teacher or course admin with data around the learning. Sometimes instructors approach assessment as a means to putting a grade in a grade book. But that rationale is secondary to the meaningful data it can collect when it is well written and well aligned to course objectives and learning content. If I didn't build in a learning activities that directly connect to every assessment question, I cannot reliably ask the question because I have not offered a learning path. 

The data from this assessment should tell me whether or not participants have internalized how to use pattern blocks for fraction addition and subtraction, and to what degree they understand the underlying properties. Ultimately, the pattern blocks are a tool to help visualize fractions but those visualizations should become more general when we work with fractions that are not represented by pattern blocks. If I see participants consistently failing a question or having to retake it, then I know I need to revisit the content and/or the assessment question to determine where there is a mismatch. I might also find in some incorrect responses that participants are forming misconceptions about the material that I did not anticipate. That means that something in the content needs a revision to make the learning "take away" more clear. 

Side note, unfortunately Canvas has been having a number of problems in the last week- likely because higher ed is going back to school right now. I was struggling to get this assessment loaded into Canvas so for now, it's housed outside the LMS. Eventually I will move it into Canvas when the issues have been resolved by the Canvas tech team.