# Counting and Additive Situations: Unit Construction

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 AIMS research 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.

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 move 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 is allowing us to collect a video library of children demonstrating the different stages as identified by Dr. Steffe. These videos will be used to help us share the research findings with classroom teachers. Our intention is that information gained as a result of this project will be used to continue our pursuance of research that can address the difficulties in understanding the concept of fractions.

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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.

Darrell Blanks – Research Associate
dblanks@aimsedu.org — (559) 453-3679

Darrell Blanks, a Research Associate at the AIMS Center for Math and Science Education, has worked in public education for 26 years with 23 of those working in inner city schools in the Fresno Unified School District. He has experience teaching grades 2 through 8, including bilingual dual immersion and departmentalized math settings. Mr. Blanks served in roles outside of the classroom including that of a district math coach and a site principal. Currently a faculty member of the Teacher Education Division at Fresno Pacific University, he serves as the director of the Multiple Subjects program and teaches courses in elementary and secondary mathematics instructional methods. Darrell holds graduate degrees in Math Education and Educational Administration.

Grace Florez – Research Associate
gflorez@aimsedu.org — (559) 453-8118

Grace Florez is a Research Associate at the AIMS Center. She has worked in education for the past 12 years as a kindergarten, 1st, 3rd, and 5th grade teacher. As a teacher, Grace has been on various curriculum adoption teams as well as teacher mentoring committees. Grace earned her Bachelors Degree in Agricultural Business from California State University, Fresno. Soon after receiving her BS she worked for Texas A&M Extension Center, Robstown, assisting in the Agricultural Financial Risk Department. Upon moving back to California she earned her teaching credential at Chapman University. In 2015, Grace earned her Masters Degree in Educational Administrative Leadership from National University.

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 14 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.

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 Van Vleet – Research Associate
evanvleet@aimsedu.org — (559) 453-8112

Elin Van Vleet 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.