Helping Students Understand Fractions
The Fraction Foundations MOOC-Ed 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 MOOC-Ed. 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 the Fraction Foundations MOOC-Ed 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 MOOC-Ed 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 MOOC-Ed and provide suggestions for improving the MOOC-Ed 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.
Tamar earned her B.A. in Applied Mathematics at the University of California, San Diego, in 1998 and her M.A. in Mathematics at the University of California, Los Angeles, in 2000. She taught in community colleges in both Southern California and North Carolina for four years before joining the faculty at the North Carolina School of Science and Mathematics (NCSSM) in 2004, and received National Board Certification in 2008. In addition to teaching on the residential side at NCSSM, she has been active in teaching through video conference and reviewing, developing and teaching online and blended/hybrid courses. She is currently pursuing her Ph.D. in Mathematics Education at NC State and has worked with the FI Math Ed team since 2012. Her research interests lie in models of online professional development for mathematics teachers.
Sherry Booth Freeman
Sherry is a Senior Research Scholar at the Friday Institute for Educational Innovation and an Adjunct Assistant Professor in the College of Education at North Carolina State University. Sherry’s professional interests center on the development and evaluation of innovative uses of technology to support teaching and learning. Currently, Sherry leads the scale research for a five year “Citizen Science” Math-Science Partnership Project funded by the National Science Foundation. Additionally she co-leads the evaluation of all MOOC-Eds currently being developed and implemented through the Friday Institute. Previously, Sherry led research for the Connected Educators project funded by the U.S. Department of Education. Before coming to the Friday Institute, Sherry had extensive experience as a curriculum developer. At the JASON Foundation for Education, Sherry served as Senior Curriculum Developer for online mathematics professional development courses for teachers. Through her work at Education Development Center in Newton, MA, Sherry developed, implemented, and evaluated numerous technology-enhanced curriculum projects and professional development programs. Sherry holds a B.A. in Mathematics from Sweet Briar College; an Ed.M. from the Harvard University Graduate School of Education; and a Ph.D. in Curriculum and Instruction from North Carolina State University.
Alex Dreier is the Instructional Design Lead for the Friday Institute for Educational Innovation at the NC State University's College of Education. His current work focuses on the instructional design and content development for the Institute’s current series of MOOC-Eds. Prior to joining Institute, Alex managed the online training courses for EdTech Leaders Online, a nationally-recognized online professional development organization housed at Education Development Center, Inc. in Waltham, MA. Among the courses that Alex helped update and maintain were Using Models to Understand Fractions, Examining the Common Core Math Content Standards, and Exploring the Common Core Standards of Mathematical Practice. He holds a B.A. in Psychology from Tulane University and an Ed.M. from the Harvard Graduate School of Education.
Natasha Elliott is a Graduate Research Assistant at the Friday Institute for Educational Innovation. She earned a B.A. in Mathematics in 2001 and a M.A.T. in Math Education in 2003 from UNC Chapel Hill. Natasha taught for three years at the K-12 level before spending seven years teaching mathematics at the community college level. She is now pursuing a Ph.D. in Math Education at NC State University. Natasha's research interest is elementary education and minority students.
Nicole L. Fonger
Dr. Nicole Fonger researches student learning of mathematics across a variety of K-12 settings. A Minnesota native, she earned her B.A. in mathematics from the University of Saint Thomas in Saint Paul, Minnesota. For her graduate coursework, she earned her M.A. in mathematics, M.A. in mathematics education, and Ph.D. in mathematics education from Western Michigan University in Kalamazoo. She has conducted classroom-based teaching experiments, engaged teachers in collaborative research, conducted task-based interviews with students, and worked on a curriculum development team. She has taught at the secondary school and university levels, with a focus on mathematics content courses for elementary and secondary pre-service mathematics teachers. She has also collaboratively designed and conducted face-to-face and online professional development courses for educators. Her research in K-12 mathematics education focuses on characterizing how students learn, and understanding the nature of the curricular and instructional supports for that learning.
Theresa is a Project Coordinator at the Friday Institute for Educational Innovation. She earned her B.S. in Mathematics and in Mathematics Education at Buffalo State College in NY. She has experience teaching Algebra and Geometry to students in grades 8-12 and in academic intervention for mathematics working with students in grades 6-12. Theresa also worked at the community college level as a developmental mathematics instructor. Prior to joining the research team, she worked as a program manager in a title I program to provide tutoring in mathematics and reading to K-8 students throughout North Carolina, South Carolina, and Virginia. In her role as project coordinator, Theresa is interested in providing high quality, accessible resources to educators and supporting a positive relationship with mathematics for both educators and students.
Shaun Kellogg is a Research Scholar at the Friday Institute for Educational Innovation and Teaching Assistant Professor in the College of Education at North Carolina State University. His work centers on evidence-based design to improve online and blended learning systems, and the impact of these systems on teachers and students. Prior to his work in research and evaluation, he spent 10 years in K-12 education, beginning his teaching career as a Peace Corps Volunteer and later teaching in the public school systems of Michigan and North Carolina. In 2009, he was received the NCCTM Outstanding Elementary Math Teacher and was awarded Math Teacher of the Year by his school district. He holds a B.A. from the University of Michigan, teaching certification from Michigan State University, and a Master's Degree in Educational Technology from Western Michigan University. He received his PhD in Curriculum & Instruction at North Carolina State University, with a where his dissertation work focused on modeling mechanisms that influence the development of educator social networks in online learning environments.
Glenn Kleiman, Ph.D., is the Executive Director of the Friday Institute for Educational Innovation and a Professor at the NC State University College of Education. A cognitive psychologist by background (Ph.D., Stanford, 1977), his work in education has spanned basic and applied research, curriculum development, software development, professional development for teachers and administrators, policy analyses, and consulting for schools, districts and state departments of education.
Dr. Kleiman chaired the Teaching and Learning Subcommittee of the North Carolina eLearning Commission and served on the Executive Committee of Governor Perdue’s Education Transformation Commission. He currently leads the Friday Institute’s work developing the North Carolina Digital Learning Plan for K-12 Schools for the State Board of Education.
Prior to joining NC State University in July 2007, Dr. Kleiman was Vice President and Senior Research Scientist at Education Development Center, Inc. in Newton, MA, where he led the development of the NSF-funded MathScape: Seeing and Thinking Mathematically middle school curriculum, published by Glencoe-McGraw Hill. He was also the Director of the Center for Online Professional Education, the Northeast and Islands Regional Technology in Education Consortium (NEIRTEC) and the Regional Education Laboratory for the Northeast and Islands (REL-NEI). Dr. Kleiman was on the faculty of the Harvard Graduate School of Education from 1995-2007 and was education chair of the Harvard/EDC Leadership and the New Technologies Institutes.
Dr. Dung Tran is a current lecturer at Victoria University, Australia, who worked at North Carolina State University for more than two years developing and researching MOOC-Eds. He is a native of Hue city, Vietnam, graduated from the University of Missouri – Columbia, USA with a Ph.D. in Mathematics Education and a Ph.D. Minor in Statistics. He also earned an M.Ed. in Mathematics Education and a B.S. in Mathematics in Vietnam. His interests focus on mathematics curriculum development, more specifically the impact of mathematical modeling and learning trajectories in curriculum design on student learning, with statistics being the focal content area. He has extensive experience in curriculum analysis and development at the middle and high school levels, conducting sizeable clinical interviews with elementary children, and analyzing a diversity of both quantitative and qualitative data. He taught both mathematics and methods courses for preservice high school mathematics teachers at Hue University College of Education in Vietnam for five years.
- 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