Helping Students Understand Fractions
Fraction Foundations will help you teach fractions concepts and skills more effectively through understanding students' thinking and implementing research-based approaches in your classroom. It will help you address rigorous curriculum standards for fractions, whether from the Common Core State Standards or from other up-to-date standards.
The course is organized around the recommendations of the Practice Guide on Developing Effective Fractions Instruction for Kindergarten Through 8th Grade, from the U.S. Department of Education's Institute of Education Sciences (published in Sept 2010).
- Develop a deeper understanding of the fractions content standards, and relevant practice standards, that apply in their own schools.
- Investigate common student misconceptions about fractions and why fractions are hard for children (and adults) to understand.
- Analyze students' thinking about fractions to inform instruction.
- Address students' learning differences when teaching fraction concepts and skills.
- Learn to effectively use:
- Fair-sharing activities to help students understand key concepts of fractions, such as fractions representing the relationship between parts and wholes, equivalent fractions and comparing fractions. (Focus of Unit 2)
- Measurement and number line activities to help children understand fractions as part of the number system and key concepts such as equivalent fractions, comparing fractions, and the relationship of fraction and integer operations. (Focus of Unit 3)
- Activities to help students understand why procedures for computations with fractions make sense. (Focus of Unit 4)
Unit 1: The Foundations for Understanding Fractions
This unit will explore why fractions are hard for children and even adults, recommendations for effective fraction instruction, curriculum standards for fractions concepts and operations, and the concept of deeper learning. You will discuss successes and challenges of your current approaches to teaching fractions and begin to plan your project. The essential questions for this unit are:
- Why are fractions so challenging to learn?
- What misconceptions about fractions and fraction operations are common among students?
- What informal strategies and language do students use to solve fraction problems and how can teachers build upon those to help students learn the mathematics of fractions?
Unit 2: Fair Sharing Activities
This unit introduces several instructional strategies for meaningful fractions learning, including building on students’ understanding of fractions in the context of fair-sharing and analyzing students’ thinking to inform instructional decisions. The essential questions for this unit are:
- What are fair-sharing activities and why are they recommended to help students build a foundation for understanding fractions?
- How can fair-sharing activities be used to address misconceptions?
- How can fair-sharing activities be used with students with different levels of understanding and different learning strengths?
Unit 3: Measurement and Number Line Activities
This unit focuses on interpreting fractions as numbers through partitioning and iterating (repeatedly using) fractions. Fractions as measures on a number line, as emphasized in the Common Core State Standards, and measures of area and sets, will be explored. The essential questions for this unit are:
- What are measurement activities and why are they important?
- How can the number line activities be used to help students understand fractions within the number system?
- How can measurement and number line activities be used to address students’ misconceptions?
- How can measurement and number line activities be used to help students with different levels of understanding and different learning strengths?
Unit 4: Understanding Procedures for Computing with Fractions
This unit engages in building students' understanding of fraction computation. Different visual models to help students understand fraction operations will be considered. The essential questions for this unit are:
- How can students be introduced to operations with fractions in ways that form a good foundation for using fractions to solve problems?
- How can you identify and address students’ misconceptions about operations with fractions?
- How can fair-sharing and number line activities be used to support an understanding of computations with fractions?
Unit 5: Wrap-up and Next Steps
This unit will allow you to reflect on, assess, and share the knowledge gained throughout the course, provide feedback for the work posted by colleagues and share what you have learned and your ideas for improving the course. The essential questions for this unit are:
- How has your own understanding of teaching fractions changed?
- What strategies/skills have you found most valuable?
- What are your next steps after the course?
- How can Fraction Foundations be improved for future participants?
A certificate of completion for 30 hours of professional development will be provided on request to participants who: (1) spend at least 30 hours participating in the course; (2) participated in the discussions, posting at least one new discussion or one reply to a discussion in each unit of the course; (3) submitted a project; and (4) provided feedback on at least one other project. You can submit the certificate to your local agency with a request for CEUs. Granting of CEUs will be subject to the policies and procedures of your state and local agency.
Participants are expected to do the following within their 30 hours of participation:
- Complete the course pre- and post- assessments.
- Review the core resources for each session. These will provide some common background, frameworks and language to inform the discussions, tasks and peer feedback. There will be additional recommended resources that participants can choose to review.
- Complete the final project.
- Review and provide constructive feedback to other participants on their projects.
- Contribute to the Fraction Foundations course by asking questions, responding to others' questions and sharing ideas in the discussion forum; suggesting resources that will be useful to others; and sharing your expertise in other ways.
- Complete the unit feedback surveys and a post-course survey about the course and provide suggestions for improving the course in the future.
Additional Credit Options
There are also opportunities to participate in performance assessments to demonstrate your competency with ideas presented in the course and apply them to your educational practices. These performance assessments, called micro-credentials, can allow you to earn additional professional development hours. Our Fraction Foundations micro-credentials are portable and stackable. Once you demonstrate a competency and earn a micro-credential, you will receive a certificate and a virtual badge recognizing your accomplishment. We have created two stacks of micro-credentials that are purposefully stacked to help support you as you deepen your knowledge and competence in specific areas of teaching fraction foundations. The micro-credentials can help you earn 5-10 professional development hours. Note that you can earn hours by successfully completing micro-credentials even if you choose to not complete the requirements for the 30-hour certificate.
- Self-directed learning, through personalizing your experience by identifying your own goals, selecting among a rich array of resources, and deciding whether, when, and how to engage in discussions and activities to further your own learning and meet your goals.
- Peer-supported learning, through engaging in online discussions, reviewing your colleagues' projects, rating posted ideas, recommending resources, crowdsourcing lessons learned, and participating in twitter chats and other exchanges appropriate to the individual course.
- Job-embedded learning, through the use of case studies, classroom and school related projects; developing action plans; and other activities that center your work on critical problems of practice and data-informed decision-making in your own classrooms, schools or districts.
- Multiple voices, through learning about the perspectives of other teachers and administrators along with those of students, researchers and experts in the field. Our courses are purposefully not designed around one or two experts who present online lectures. They provide exposure to a rich set of perspectives presented within the context of course elements that reflect these core principles.
You will see these design principles implemented in our courses through the following instructional elements:
- Conceptual Frameworks
- Resource Collections
- Asynchronous Discussions and Twitter Chats
- Student Scenarios
- Expert Panels
- Participant Projects and Peer Feedback
- Professional Learning Community (PLC) Guides