# Counting and Additive Situations: Unit Construction

Students often struggle with mathematics and many teachers feel that they are spending too much time “re-teaching” math rather than teaching new mathematical concepts to their students. Researchers at the AIMS Center for Math and Science Education turned to the research of Dr. Leslie Steffe to find out why. The difficulties students experience are related to their conceptual understanding of number whether they can think about numbers in more than one way at a time. Students perceive mathematical situations differently than adults and their ways are meaningful and powerful. Students don’t have misconceptions, they have understandings built on prior experiences that have (so far) worked. The process of coming to understand whole number is far more sophisticated than adults may realize.

This team explores Dr. Steffe’s research on how children develop a sense of whole number in additive situations, which progress along a continuum from concrete material toward a completely abstract concept of number, and Dr. Steffe has identified specific stages of this development. Our goal is to design student experiences that teachers can use to adapt their instruction to the mathematics of their students in an effort to advance their students along this continuum as they begin to form an understanding of additive reasoning.

Observing and recording students at different places along the continuum and identifying specific indicators of the stages has allowed us to collect a video library of children demonstrating the different stages as identified by Dr. Steffe. These videos are used to help us share the research findings with classroom teachers. Information gained as a result of this project will be used to continue our pursuance of research that can address the difficulties students and teachers have in mathematics.

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Tiffany Friesen, Ph.D. – Senior Researcher
tfriesen@aimsedu.org — (559) 453-8121

Tiffany Friesen is a Senior Researcher at the AIMS Center for Math and Science Education, leading teams involved in translating research on how children learn mathematics. She has worked in public education for the past 25 years – the first ten as a High School Mathematics teacher, followed by 13 years at the Community College. Her position at the college afforded her the opportunity to teach a full range of math courses, with a passion for developmental courses and math courses for pre-service elementary teachers. Dr. Friesen has also worked for the Fresno County Office of Education as a facilitator of professional development and as a tutor for their Math On Call homework hotline. She is a member of the San Joaquin Valley Math Project, was selected as her district’s Teacher of the Year in 1997, and has served as a Mentor and Supervisor for student teachers. Dr. Friesen is an alumnus of Fresno Pacific College and received her Ph.D. from Curtin University in Perth, Australia.

Jason Chamberlain – Research Associate
jchamberlain@aimsedu.org — (559) 453-8117

Jason Chamberlain is a Research Associate for the AIMS Center. His experiences in education include: being a father of two school-age, math-loving children, Holly and Luke; designing off-the-wall math experiences for enthusiastic 3rd grade and less enthusiastic (at least, initially) 8th grade students at Caruthers Elementary School, where he also worked to form a K-8 teacher team for vertical articulation; and facilitating math workshops for the San Joaquin Valley Mathematics Project, California Mathematics Council, and the National Council of Teachers of Mathematics. Jason is a graduate of CSU, Fresno, holds a teaching credential, and anticipates receiving a Master of Arts in Curriculum & Teaching from Fresno Pacific University in 2019. At AIMS, he is currently working to translate research related to the development of the understanding of number in young children.

Beverly Ford – Research Associate
bford@aimsedu.org — (559) 453-8128

Beverly Ford, a Research Associate at The AIMS Center for Math and Science Education, has worked in education for the last 16 years as a teacher, math specialist, coach, professional developer, and educational consultant. She is passionate about engaging with educational research that can empower teachers to equip all students to understand mathematics. She is driven to understand the educational research, so that the findings of the research can be utilized by teachers and empower them to teach mathematics in a way that equips students to utilize their mathematical knowledge. Her Bachelors degree, California teaching credential, and Masters degree in Math Education were completed at Fresno Pacific University.

Scott Nielsen – Research Associate
snielsen@aimsedu.org — (559) 453-8140

Scott Nielsen serves as a Research Associate at the AIMS Center. Scott has 20 years of classroom teaching experience in upper-elementary and middle school grades, most recently teaching 8th grade mathematics and woodworking in Kingsburg, CA. As a musician, Scott is always interested in math/music connections and utilizing music in the classroom. He earned his Bachelors Degree and Masters Degree in Mathematics Education at Fresno Pacific University.