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
Why this website?
I want to share with everyone the results of my research because teachers have told me that this research can change how they teach. They also say that when they teach based on how children learn, the children understand so much more than the teachers thought possible. Teachers also can learn more about mathematical ideas because most of us including me did not have a chance to learn with understanding so we need those opportunities now.
What is in this website?
Each of the sections below can be reached by clicking on the links in the top menu.
I have gathered my research-based teaching ideas into visual and audio Teaching Progressions that show the research-based visual supports that enable children to build math ideas. I discuss how these ideas develop through the year and through the grades. 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. I show the teaching approaches I developed in classrooms in the Children’s Math Worlds Research Project and then used in Math Expressions. 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. My development of visual supports was supported by the National Science Foundation and so anyone can use these supports. Click on Teaching Progressions in the menu above. 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 on 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.
I have gathered some of the research that underlies the classroom teaching/learning approaches. Click on the word Publications in the menu above. You can sort the table of publications by math topic or by type of research publication (shorter or longer). You can download a pdf file of a publication for your own educational use. When a publication is a chapter in a book, you might want to look at the whole book for other useful chapters. Authors of these publications include members of the Children’s Math Worlds Project team, my PhD students, post-doctoral students, and colleagues at Northwestern University and elsewhere. Authors who have gone on to faculty positions at a university have emails or that university listed so that you can contact them to follow their other research. You can download the references for all publications available here on this website by clicking here.
I have gathered pdf files of some PowerPoint presentations I have made at conferences because these summarize visually ideas I think are important. Click on the words Presentations in the menu above. Many of these presentations are about math domains, and you can find out more about these domains in the Publications and in the Teaching Progressions for those domains. Sort the Publications list to find papers for that math topic, and look at the column following each Presentation title to see which Teaching Progression to view for more detail and audio to go with the visual. You can download the references for all presentations available here 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.
If you want to find the titles of other things I have written or presentations I have given, you can look here in my Curriculum Vitae.
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.