# Additive and Multiplicative Situations: Units Coordination

The concept of fractions has been a challenge for children for many years. Researchers at the AIMS Center for Math and Science Education turned to the research of Dr. Leslie Steffe to find out why. The Units Coordination team learned that the difficulties with fractions are related to children’s understanding of whole number and how students can think about whole numbers in more than one way at a time. It became apparent through the work done by Les Steffe that the process of coming to understand whole number is far more sophisticated than adults may realize.

The goal of this team is to learn how children’s additive schemes lead to multiplicative schemes once a child is numerical, and how those schemes relate and contribute to the development of children’s fractional knowledge. A key element in this development is the construction of a composite unit that can be used flexibly by children in addition, multiplication, and in recognizing fractions as numbers. This work adds to our understanding of the continuum that Steffe has identified.

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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 23 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.

Brook Lewis – Research Associate
blewis@aimsedu.org — (559) 453-8116

Brook Lewis is a Research Associate at the AIMS Center for Math and Science Foundation, working with a team investigating research on how children come to know mathematics. Prior to her work with AIMS, she began as a High School mathematics teacher in the Central Valley, and has taught middle school math as well. Brook also gained experience in the public education system as a department leader, instructional coach, education consultant, and curriculum developer. She is determined to understand and translate current research in mathematics education in order to support students in learning, and teachers in the classroom. Although Brook has experience teaching most math courses in High School, her focus was with students that struggled with mathematics which has fueled her passion to work in the realm of research, in order to address the needs in math education. As a graduate from Fresno State University, Brook earned a BA in Mathematics and an MA in Education.

David Pearce – Research Associate
dpearce@aimsedu.org — (559) 453-8119

David Pearce is a Research Associate at the AIMS Center. He has worked in math education for 19 years as a middle school math teacher in Central Unified (California). During this time he was part of the District’s Math Vertical Team, Math Adoption Committee, District Math Committee for Course Alignment and Implementation, as well as the Math Department Chairperson at Rio Vista Middle School and Director of Soccer. David is interested in math education and improving student learning in this area. Through his study of educational research, his work will help in supporting teachers in their efforts to create and facilitate exceptional mathematical learning experiences for all students. He anticipates the completion of his MA in Math Education through Fresno Pacific University by May 2018.

Elin Anderson – Research Associate
evanvleet@aimsedu.org — (559) 453-8112

Elin Anderson is currently a Research Associate for the AIMS Center. She has passion for understanding how students construct their understanding of math concepts. For the past twenty years she has worked as a classroom teacher, mathematics coach, instructional coach, and as a TSA in elementary mathematics for the Fresno Unified School District. In 2015 she participated on the CA Department of Education Expert Panel for the correspondence of the California English Language Development Standards to the Mathematics and Science Standards. She received her BA from Santa Clara University in multidisciplinary studies, and her teaching credential and MA in Math Education from Fresno Pacific University. She also holds an Administrative Credential in Educational Leadership from Fresno State University. Elin is currently a member of the Smarter Balanced State Network of Educators.