Assessment and Learning Models

Possible Project-Based Learning Scenario

Project Title: Creating  Real-World Fraction Division Situations for Students

Description: Mathematics educators will be given access to a student activity for Dividing Whole Numbers by Unit Fractions on Desmos to review and try for themselves.  They will then review the activity, Dividing Whole Numbers by Unit Fractions, on Geogebra.  Educators will then write an original real-world fractions division problem and create their own original Geogebra activity that models the mathematics when students engage with the activity. This project assumes that educators are already proficient in creating activities and interactives in Geogebra. 

Purpose:  Creating real world scenarios that require fraction division are traditionally quite challenging for many upper elementary and middle school math teachers. Many teachers know the procedure for dividing by fractions, but struggle to come up with a solid example of a real world application as well as a way to digitally model the mathematics in a way that makes sense to students. This project helps educators engage with digital fraction division models and then provides them with an opportunity to create their own scenario and digital interactive for students in grades 4 and 5 who are just learning to divide whole numbers by fractions. Many educators will use trial and error to figure out a problem and a model and then tweak their design to push students to think deeper. 

Objectives: 

1. Educators will review the activity in Desmos and answer the "Teacher Moves" questions from the perspective of their students.

2. Educators will write a new real world scenario that requires students to divide a whole number by fractions. The whole number can be either in the dividend or the divisor. 

3. Educators will create a Geogebra interactive activity that works in conjunction with the real world scenario and provides feedback to students that helps them successfully solve the problem, based on the rubric criteria provided.

4. Optional: Educators may challenge themselves to write a scenario and create an interactive where non-unit fractions are used instead of unit fractions. They may optionally choose to write an activity where both the dividend and divisor are fractions instead of one being a whole number.

Assessment:

Formative: Educators will submit their drafts of their real-world division problems and describe their ideas for a Geogebra interactive activity on the course discussion board for other educators enrolled in this professional learning to review. Discussion threads will be encouraged as a way for peers to provide feedback on one another's proposed problems. This will also provide a way for the instructor(s) to monitor drafts of problems and interactives before educators start building their Geogebra activities, which can be time consuming and frustrating if the problem and the model don't mathematically support each other. 

Authentic Assessment:

Educators will be evaluated by submitting their final Geogebra products for peer and instructor review. A rubric will be provided that prompts designers and reviewers to examine the following elements of their Geogebra activity design and the degree to which they have met each element:

1. Is the division problem well-written, understandable for 4th and 5th grade students, and mathematically correct?

2.  Does the model appropriately help students conceptually "see" how fraction division works? Does it help students understand why division is the operation needed to solve the problem? Does the activity help students connect to the fractions division algorithm?

3. Is the model engaging and interesting for students who are in 4th and 5th grades? Is the problem motivating and interesting for 4th and 5th grade students?

4. Does the activity provide thoughtful questions for the educator to ask students in order to both assess and advance student understanding of fraction division?

5. Does the activity provide suggestions for how educators can use the activity in their classrooms, taking into consideration a variety of ways in which students can interact with the activity?

Learning Theories at Work:

This project primarily follows a constructivist learning theory. Educators are faced with a challenge of writing a fractions division problem and creating an interactive to model the problem. Geogebra has a lot of capability for creating interesting interactives for students. Educators may find themselves having a great idea that doesn't work out and having to either tweak the idea or learn from it and start over with a new idea. This project may provide a lot of opportunities for educators to "try it and see if it works." It will be rare that the the first idea they have will be the one that works best. Educators are also provided with a venue to collaborate with other learners through the discussion board, and then given time to work on their fractions division problem and interactive based on feedback from the discussion board (which follows a connectivist theory of learning).