Dr. Karen C. Fuson
For 50 years I have been studying how children understand math ideas, designing teaching materials based on how children learn and understand, and working in schools to help teachers teach in new ways to support all children to learn. For much of this time I was a professor at the School of Education and Social Policy and Department of Psychology at Northwestern University. I published over eighty research articles on mathematics teaching and learning including children’s counting and their developing understanding of addition and subtraction methods, multiplication and division, fractions, ratios, and proportion. I spent over ten years in a range of different classrooms developing the NSF-funded math program, the Children’s Math Worlds Research Project. I worked with many wonderful fellow researchers and teachers. I resigned from my position in 2002 to have more time to devote to my research and to national service in math education. I am now a Professor Emerita at Northwestern University continuing to do my research and writing at home.
I was a member of the National Research Council’s Mathematics Learning Study Committee that wrote Adding It Up and the Committee on Early Childhood Math that wrote Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity. I wrote the chapter on whole numbers for the NCTM Research Companion to the 2000 Standards and wrote the introductory chapter for the National Research Council’s How Students Learn: Mathematics in the Classroom. I am the author of the K-6 math program Math Expressions published by Houghton Mifflin Harcourt. This program is based on my research in classrooms in the Children’s Math Worlds Project, on earlier and later research I carried out, and on research by others in the NRC reports and on aspects of international math programs (Dr. Sybilla Beckmann is my co-author for the Grade 6 books). I am a co-author on five of the NCTM grade-level books for teachers about the focal points (PK, K, G1, G2, G5). I worked on the Common Core State Standards-Math and on the learning progressions for these standards and advised PARCC and Smarter Balance on their math test design and items.
About This Website
Visual representations of mathematical concepts are crucial for student understanding. The videos and papers on this website show children in PK, K, and 1 using manipulatives and explaining how these manipulatives support specific math concepts. These extensive resources also show students in grades 1 through 6 using math drawings for many math topics, discussing how to develop these math drawings and use them in problem-solving.
The Teaching Progressions show the research-based teaching approaches I developed in classrooms in the Children’s Math Worlds Research Project and then used in the Math Expressions program. These Teaching Progressions can help people using any program understand more deeply how visual supports support math teaching and learning and can enable viewers to see the progressions of math teaching and learning in action. I organized these Teaching Progressions by math topic using the topics in the Common Core State Standards (CCSS) and explain the progression of the standards for each math topic. This organization fits other high-level state standards and so can be used by anyone. My research was supported by the National Science Foundation and so anyone can use any ideas in these progressions. Click on Teaching Progressions in the menu above to view the Teaching Progression videos. You can download the description of all Teaching Progressions available here on this website by clicking here.
The National Science Foundation funded a video research report of the Children’s Math Worlds Research Project to show the levels of learning possible by children from backgrounds of poverty who experience good teaching. The Classroom Videos were taken in four public schools, three high-poverty urban schools with some to most students speaking a native language other than English, and a suburban school with immigrants from many countries. The classrooms you will see were built by the continuing efforts of many dedicated teachers, students, parents, school administrators, and members of the Children’s Math Worlds research team. Language and ideas of students, teachers, and parents were woven into the curriculum as it was revised each year. The project had a strong emphasis on children explaining their thinking and on using math drawings developed in the project to support student thinking and explaining. None of our teachers had learned math in this way, so they were all brave pioneers in learning how to create such classrooms. All classrooms are complicated places, and no teaching segment can be perfect. We can all have ideas about how to change things the next time. I am enormously proud of and grateful to these teachers for being willing to share their classrooms so that everyone can see what students can do if we support them in their thinking. The Teaching Progressions show in more detail the learning progressions students experienced to reach the points shown in these Classroom Videos. To view the Classroom Videos, click on the words Classroom Videos in the menu above. You can download the description of and more information about the Classroom Videos available here on this website by clicking here.
Many of my research papers about classroom teaching/learning approaches are available on this website. Click on Publications in the menu above to view the table containing my research papers. You can download any paper for your own educational use by clicking on the last column in the table. You can download the references for all publications available here on this website by clicking here.
In this section you will find presentations I have made at conferences. These were selected because they summarize ideas I think are important. Click on Presentations in the menu at the top to view the table containing my presentations at conferences. You can download any presentation for your own educational use by clicking on the last column in the table. You can download a list of all of the presentations available on this website by clicking here.
Remote Teaching Materials
Visual representations of mathematical concepts are crucial for student understanding. The videos and papers on this website show children in PK, K, and 1 using manipulatives and show students in grades 1 through 6 using math drawings for many math topics. When covid resulted in many schools teaching remotely, I realized that teachers needed digital versions of these learning environments that could support children to move manipulatives and to draw and to write. As in the classroom, the teacher needs to see what all children are making so that feedback is possible, and the teacher can select examples to discuss with all children. Supporting teachers as much as possible to orchestrate a Nurturing Math Talk Community in the classroom even when teaching remotely is vital for student and teacher emotional and conceptual functioning.
Therefore, I worked with two experienced Math Expressions teachers and coaches, Robyn Decker and Shannon Kiebler. They have worked with many districts supporting teachers in developing and using a Nurturing Math Talk Community in the classroom. What did we make that you can use now?
The Quick Practices in all grades Kindergarten through Grade 6 and the Daily Routines in Kindergarten, Grade 1, and Grade 2 are crucial for building complex and central math concepts and for creating a sense of community as children engage in these practices together. We created digital slide decks in Google Slides for teachers to use in leading these Quick Practices and Daily Routines remotely or in the classroom. We made colorful visuals with interactive sentence stems from increasing the ease of use and comprehension of the mathematical aspects of the Daily Routines and Quick Practices. The Student Leader shares their screen and has the microphone on so that all students can see and hear the Student Leader lead the Quick Practice or Daily Routine.
Students also need the special large Math Expressions MathBoards that contain specific grade-level learning supports and the grade-level manipulatives including the strategy/fluency cards. These manipulatives and cards can be given to students to use at home for remote teaching. But it is difficult for the teacher to see what a student is doing, and younger students require help with organizing and using the manipulatives. So we also made the crucial grade-level manipulatives on Google Slide decks and made the Math Expressions MathBoards on Jamboards, a free app from Google that has a good writing function.
Practice materials are also important. I developed conceptual fluency cards that students can use individually to focus on the additions, subtractions, multiplications, and divisions with which they are not yet fluent. All of the conceptual fluency cards for Grades 1, 2 and 3 are available for online practice for teacher-led activities in the whole class and for individual practice at home. There are also other fluency practice materials for Grades 2 and 3 available.
There are Pre-Kindergarten Teaching, Home Activity, and Daily Routine Google slide decks for teachers and parents. These can be used to catch up students who did not have prekindergarten or are just not ready for kindergarten.
This is a research-based website that is for everyone, not just for users of Math Expressions. Anyone is welcome to use these Remote Teaching Materials. And please visit other parts of my website including the Teaching Progressions, which are 22 hours of visual and verbal explanations of the learning paths in the Common Core State Standards organized by math domain and using the research-based visual supports in Math Expressions.
You can see the file with the description of all of these Remote Teaching Materials and the links to get to these materials by
Math Expression Users
This page has available for downloading some papers I have written especially for Math Expressions teachers, coaches, administrators, and parents. These papers discuss teaching, assessments, frequently asked questions, and other issues. This page also has reminders about the free Google resources I made with colleagues Robyn Decker and Shannon Kiebler. These classroom resources for teachers are described and available on the Remote Teaching Materials page. Anyone is welcome to use the resources on that page or the page for Math Expressions Users.
Contact me using the Contact Form, where you can leave me a message about this website. I will try to check messages once a week and reply as soon as possible. Sometimes, I am traveling and cannot get back right away. Thanks for your interest.