## David J. Carrejo, PhD

### David J. Carrejo, Ph.D.

Associate Professor, Mathematics Education

**UT System Regents Outstanding Teaching Award Recipient 2015**

Department of Teacher Education/STEM Education Division

College of Education, EDUC 802

Phone: 915-747-5856

E-mail: dcarrejo@utep.edu

### Scope of Research Interests and Activities:

*Theories of learning*

- Constructivism
- Genetic epistemology

*Knowing and learning mathematics*

- Model-based reasoning in mathematics
- Foundations of analytic geometry
- History of mathematics in mathematics education

*Teacher preparation (curriculum design and field experiences)*

- University-school partnerships
- Early STEM for pre-service elementary teachers

*Research methodologies*

- Design-Based Implementation Research (DBIR)
- Mixed methods
- Grounded Theory

## Welcome!

**David J. Carrejo, Ph.D.**, is an *Associate Professor of Mathematics Education and former Associate Dean of Undergraduate Studies and Educator Preparation* in the College of Education at UTEP. After graduating from Cathedral High School, he earned both a Bachelor of Science in Mathematics and a Master of Arts in Teaching Mathematics from UTEP as well as a doctorate in Mathematics Education from the University of Texas at Austin. He has taught secondary algebra and pre-calculus as well as algebra, pre-calculus, and mathematics for preservice elementary teachers at UTEP. He currently teaches elementary and middle-school math and science methods courses for pre-service teachers as well as graduate and doctoral courses in a wide array of areas in mathematics education. In 2015, Dr. Carrejo received the prestigious University of Texas System Regents' Outstanding Teaching Award.

He's conducted professional development at several local campuses across two districts that focused on such topics as integrating mathematics and science in the elementary and middle school curricula, instructional design in secondary teaching, aligning middle school and secondary mathematics curricula with state and national standards, and engaging elementary and middle school learners through activity-based instruction for mathematics and science. He also has a close working relationship with the College of Engineering and the Department of Engineering Education and Leadership.

His research interests are teaching and learning mathematics through mathematical modeling; knowing and learning algebra; history of mathematics in mathematics education, and integrated STEM education. Dr. Carrejo is currently a member of the College of Education's Paso del Norte Partnership Education Research, a network of partnerships between the College of Education, K-12 school districts, and area non-profits that work together to positively affect student outcomes for the diverse communities in El Paso and Hudspeth Counties. His wife, Denise, is the current Assistant Director of the Center for Institutional Evaluation, Research, and Planning at UTEP.

### education/te/people/_Files/Carrejo_ELED-4310_Syllabus_Spring21_W.pdfUndergraduate Courses

### ELED 4310 Teaching Mathematics in Elementary Schools

Students enrolled in this course will explore the methods of teaching mathematics in elementary grades. Emphasis is placed on the equity principle (mathematics for all) and development of conceptual understanding of topics such as real numbers and operations on real numbers, quantitative reasoning, geometry, and early algebra. Students will reflect upon their own experiences and beliefs about mathematics. The course looks at mathematics as a discipline, and compares more traditional ideas about what it means to ‘know’ and ‘do’ mathematics to the vision of mathematics advocated by the reform movements as well as what it means to ‘know’ and ‘do’ mathematics relying on constructivist principles of learning and teaching.

### ELED 4311 Teaching Science in Elementary Schools

This course examines various instructional strategies including organizing, planning, writing and implementing elementary science lessons and units as well as experiments, materials, resources, and using technology/equipment to teach science concepts in a safe elementary science classroom environment. It provides students an opportunity to review the scope and sequence of the National Science Standards, TEKS, and text materials, to understand experiencing science in the classroom, to apply this information when selecting the most appropriate strategies and materials to meet the needs of elementary students in groups and individually, and to participate in hands-on, minds-on science activities, experiments, and investigations.

### MSED 4310 Teaching Mathematics in Intermediate and Middle Grades

Students enrolled in this course explore the methods of teaching mathematics in intermediate and middle grades. Emphasis is placed on the equity principle (mathematics for all) and development of conceptual understanding of topics such as real numbers and operations on real numbers, measurement and estimation, geometry, algebra (patterns, variables, and functions) and probability and statistics. Students reflect upon their mathematics learning experiences and beliefs about mathematics. Students look at mathematics as a discipline and compare more traditional ideas about what it means to ‘know’ and ‘do’ mathematics to the vision of mathematics advocated by the reform movements as well as what it means to ‘know’ and ‘do’ mathematics relying on constructivist principles of learning and teaching.

### MSED 4311 Teaching Science in Intermediate and Middle Grades

This course examines various instructional strategies including organizing, planning, writing and implementing middle school science lessons and units as well as experiments, materials, resources, and using technology/equipment to teach science concepts in a safe middle school science classroom environment. It provides students an opportunity to review the scope and sequence of the National Science Standards, TEKS, and text materials, to understand experiencing science in the classroom, to apply this information when selecting the most appropriate strategies and materials to meet the needs of students in groups and individually, and to participate in hands-on, minds-on science activities, experiments, and investigations.

### Graduate Courses

### MTED 5318 Current Topics in Mathematics Education

__Learning Theory (K-12)__ -- Students enrolled in this course explore some fundamental theories (including those of Jean Piaget, Lev Vygotsky, and current scholars) that lie at the heart of learning mathematics. These theories will focus on critical concepts in mathematics -- number sense (including whole number and place value development as well as measurement), ratio and proportion, function-based reasoning, and mathematical modeling (primarily involving the mathematics of change). Driving questions include: 1) How do children make sense of certain mathematics concepts? 2) What makes a ‘good mathematical task’, and how can a good task support students’ learning? and 3) How can tools (including manipulatives, calculators, and other technology) assist children in their thinking and problem-solving?

__Teaching and Learning with Technology in the Mathematics Classroom__ *--* Students enrolled in this course will be exposed to different theories about using technology (in various forms) to teach mathematics. Basing their ideas on research and practitioner literature as well as theories of learning mathematics, students will participate in discourse on the use of technology in the mathematics classroom. Students will determine appropriate roles for technology in teaching key concepts within specified mathematical domains (e.g. algebra, geometry, and statistics) through their own inquiry-based experiences. The key objectives of the course are: 1) To study current research trends and issues in the use of technology for teaching and learning of mathematics, 2) To become familiar with and adept at using various types of interactive software and devices (e.g. graphing calculators, probes), 3) To identify and discuss problems associated with the use of technology for teaching and learning mathematics, 4) To incorporate technology, including web-based resources and open-source materials, into classroom practice (i.e. curriculum planning and lesson planning), and 5) To define areas of technology education research most applicable to advancing the teaching and learning of mathematics.

### MTED 5320 Research-Based Practices in the Mathematics Classroom

Students enrolled in this course will focus on what teachers can learn from current trends in mathematics education research and how to bridge this research with practice in the mathematics classroom. Students will develop a conceptual discourse on current research related to teaching, learning, curriculum, and assessment in school mathematics. The key objectives of the course are: 1) to study research trends and issues in the teaching and learning of mathematics, 2) To identify and discuss problems associated with different research designs, 3) To synthesize and re-conceptualize research in mathematics education, 4) To describe areas of research most useful to advancing the teaching and learning of mathematics, and 5) To incorporate areas of mathematics education research into classroom practice.

### MTED 5322 Pedagogy and Content in Teaching Mathematics

__Fostering Algebraic Thinking__ -- Students enrolled in this course are offered a research-based and multi-faceted look at issues regarding the learning and teaching of algebra. Based on recent scholarly work, the course is organized around three major themes: 1) the nature of algebra as a domain of mathematics (including historical perspectives), 2) a constructivist-based analysis of math students’ algebraic reasoning and learning, and 3) the critical challenges faced by teachers to foster robust algebraic reasoning in K-12 mathematics classrooms. Driving questions include: 1) What are the most powerful algebraic concepts, ideas, and methods (including modeling techniques) that are accessible to learners? and 2) How can we link theory and practice in the teaching and learning of algebra across the K-12 mathematics curricula?

__Fostering Geometric Reasoning__ -- Students enrolled in this course are offered a research-based and multi-faceted look at issues regarding the learning and teaching of geometry in the K-12 curriculum. The course will focus on the development of geometric reasoning through the mathematics of “space” -- spatial reasoning, measure, estimation, dimension, form (shape), and proof. A key objective of the course is for students to understand and appreciate how geometry is integrated into other mathematical domains such as numeracy and algebra. Based on scholarly work, the course is organized around four major themes: 1) the nature of geometry as a domain of mathematics (including historical perspectives), 2) a constructivist-based analysis of math students’ geometric reasoning and learning, 3) the role of technology and mathematical modeling in fostering geometric reasoning, and 4) the nature and role of geometric proof across grade levels.

__Developing Quantitative Reasoning__ -- Students enrolled in this course are offered a research-based and multi-faceted look at issues regarding the development and enrichment of quantitative reasoning across K-12 classrooms and its importance in developing mathematical literacy. The course will focus on developing quantitative reasoning through several domains of mathematics -- numeracy, probability, and statistics. Another key objective of the course is for students to understand and appreciate how quantitative reasoning is also integrated into other mathematics domains such as discrete mathematics and algebra. Based on scholarly work, the course is organized around three major themes: 1) the nature of quantitative reasoning (including historical perspectives), 2) a constructivist-based analysis of math students’ quantitative reasoning and learning, which forms the basis of sound pedagogical practice for developing quantitative reasoning, and 3) the role of mathematical modeling (including technology) in fostering quantitative reasoning, beginning with math students’ investigating real data in the classroom.

### MTED 6320/MTED 5326 Cultural-Historical Epistemology and Didactics of Mathematics

The purpose of this course is for students to encounter a wide variety of historical situations and contexts which have given rise to mathematical concepts that now form the basis of our required high school mathematics curriculum (grades 9 - 12). There will be a special emphasis on the mathematical and scientific developments that occurred in seventeenth-century Europe, the period of the Scientific Revolution. This course will attempt to allow students to gain some insight into why seventeenth-century European mathematics has become enshrined in our society, particularly in our school curricula. Social, technological, military, and political history will all be brought to bear on questions of why certain mathematics was first developed, and why much of that mathematics remains central in our educational system. Our driving questions include: 1) What were the scientific, social, religious, political and economic intentions of the people who created these mathematics? 2) When and why were these mathematical ideas made into mandatory curriculum? 3) Why do we still teach this curriculum? and 4) How could our curriculum be transformed by new technology? Students will be provided readings and a variety of projects which will allow them to investigate original source materials and draw their own conclusions about the direction of this historical genesis. Herein lies our discussions of “genetic epistemology.” Such historical analysis will help students rethink (critically) the current high school mathematics that is central in our current culture. Furthermore, students will discuss the implications that such historical analysis has on our rethinking the EC-8 mathematics curriculum. Herein lies our discussion of “didactics” (or the teaching) of mathematics.

__Grants__

### 2017 - 2020

Co-PI, *Assessing the Impact of Texas Science, Technology, Engineering, & Mathematics Academies on Students: Learning Environments, Educational Outcomes, and Career Path Decisions*, sponsored by the National Science Foundation **(Award: $590,000)**

### 2017

PI, *Building Capacity for Elementary Environmental Science and Engineering Education*, sponsored by Boeing. **(Award: $27,000) **Partnership with Reyes Elementary School, Canutillo ISD

### 2013 - 2016

Co-PI, Co-Project Director, *Local Educational Agencies Partnership (LEAP) Project*, sponsored by the Department of Education, Transition to Teaching **(Award: $3,200,00)**

### 2014 - 2015

Co-PI, *Building Capacity for Preparing Teacher-Engineers for 21st Century Engineering, *sponsored by the National Science Foundation **(Award: $287,703)**

### 2009 - 2010

PI for Teachers for a New Era (TNE) exploratory study, *Developing a Theoretical Framework for Novice Mathematics Teacher Induction: A Case Study of a University-School Partnership*, sponsored by the Carnegie Foundation **(Award: $4,000)**

### 2008 - 09

Co-PI, *Strategic Learning Opportunities for Promoting Earth Science (Project SLOPES*), sponsored by the Texas Higher Education Coordinating Board **(Award: $70,133)**

### 2007 - 08

Co-PI, *The Science Academy*, sponsored by the Texas Higher Education Coordinating Board **(****Award: $86,999)**

### 2006 - 07

Faculty Research Associate for Texas Engineering and Technical Consortium (TETC) grant, *Reaching Out Across Disciplines: Learning from Each Other to Produce More Graduates in Computer Science ***(Award: $284,882)**

### Doctoral Students

### 2017, Spring

**Mayra Ortiz-Galarza****, Ph.D.** *The Influence of Multiple Representations on Secondary Students' Understanding of Trigonometric Functions*

### 2017, Fall

**Oscar Salcedo***, Ph.D. Towards a Unified Theory of Engineering Education*

**Abdelghani Setra***, Ph.D. Investigating Mathematics Self-Efficacy Beliefs of Elementary Pre-Service Teachers in a Reform-Based Mathematics Methods Course*

### Master's Students

### 2017, Summer

**Michael Strange**, **M.A. ***The Effects of a Covariational Approach to Functions through Computer Programming on Students' Understanding of Rate of Change*

### Publications

**Carrejo, D.,** & Reinhartz, J. **(2014).** Facilitating conceptual change through modeling in the middle school science classroom. *Middle School Journal, 46*(2),10 - 19.

**Carrejo, D., **& Reinhartz, J.** (2014).**Teachers fostering the co-development of science literacy and language literacy with English Language Learners. *Teacher Development: An International Journal of Teachers’ Professional Development*, *18*(3), 334-348.

**Carrejo, D.**, & Reinhartz, J. **(2012, October)**. Exploring innovative approaches to teaching light and shadows through modeling. *Science and Children*, 78 - 80.

**Carrejo, D.,** & Reinhartz, J. **(2012)**. Exploring the synergy between science literacy and language literacy with English Language Learners: Lessons learned within a sustained professional development program. *Journal of Southeastern Regional Association of Teacher Educators, 21*(2), 33 - 38*.*

**Carrejo, D.****,** & Reinhartz, J. **(2012)**. Connections between science teacher learning and designing quality professional development. *The Teacher Educator's Journal***, ***19,* 23 - 41.

**Carrejo, D., **& Robertson, W.H. **(2011).** Integrating mathematical modeling for undergraduate pre-service science education learning and instruction in middle school classrooms. *US-China Education Review, *8*(4), *499-509*. *

**Carrejo, D.,** Cortez, T., & Reinhartz, J. **(2010)**. Exploring principal leadership roles within a community of practice to promote science performance of English Language Learners. *Academic Leadership, 8*(4)*.*

**Carrejo, D.**, & Reinhartz, J. **(2010). **Exploring connections between learning science and mathematics content and English language acquisition: A literacy framework for English Language Learners. In Duschl, R.A., Zeidler, D.L., Kyle, Jr., W.C., & Sondergard, T.A. (Eds.), *The Proceedings of the Annual International Conference of the National Association for Research in Science Teaching (NARST) [CD-ROM]*. Philadelphia, PA.

Marshall, J., & **Carrejo, D. (2008).** Students' mathematical modeling of motion. *Journal of Research in Science Teaching 45*(2), 153 - 173.

**Carrejo, D.****,** & Marshall, J. **(2007).** What is mathematical modeling? Exploring prospective teachers’ use of experiments to connect mathematics to the study of motion. *Mathematics Education Research Journal 19*(1), 45-76.

Confrey, J., & **Carrejo, D.** **(2005).** Ratio and fraction: The difference between complementarity and conflict, v1.0 [Videopaper]. In *Medium and Meaning: Video Papers in Mathematics Education Research, Journal for Research in Mathematics Education Monograph, Vol. 13*. 11.5 min.video (38.6 MB), 21 pages text (65.1 KB), 20 images (556 KB), 13 animations(92.6 KB).

**Carrejo, D.**, & Marshall, J. **(2004).** Motion and mathematical modeling: A study of emerging themes and their impact on science education. *In the Proceedings of the annual meeting of the National Association for Research in Science Teaching (NARST)* [CD-ROM]. Reston, VA: National Association for Research in Science Teaching.

Confrey, J., & **Carrejo, D.** **(2002).** A content analysis of exit level mathematics on the Texas Assessment of Academic Skills: Addressing the issue of instructional decision-making in Texas. In D.S. Mewborn, P. Sztajn, D.Y. White, H.G. Wiegel, R. L. Bryant, and K. Nooney (Eds.), *Proceedings of the twenty-fourth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 539-550).* Columbus, OH: ERIC Clearinghouse.

Confrey J., & **Carrejo, D.** **(2002).** Can high stakes testing in Texas inform instructional decision-making? In D. S. Mewborn, P. Sztajn, D.Y. White, H.G. Wiegel, R. L. Bryant, and K. Nooney (Eds.), *Proceedings of the twenty-fourth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 551-564)*. Columbus, OH: ERIC Clearinghouse.

### Presentations

### 2015

**Carrejo, D.**, Williams, M., & Hernandez, S. *Taking the LEAP: A Multi-dimensional STEM Project.* 8th annual Texas STEM Conference of the Texas STEM Coalition, Austin, TX.

### 2013

**Carrejo, D.**, & Reinhartz, J. *Fostering Science Literacy and Its Role in Developing Language Literacy for English Language Learners: A Study in Teaching for Understanding.* Paper presented at the annual meeting of the American Educational Research Association (AERA), San Francisco, CA.

### 2011

**Carrejo, D.**, & Reinhartz, J. *Integrating Science and Mathematics Within an Engineering Context to Foster STEM Literacy Among Middle School Students.* Paper presented at the annual meeting of the American Educational Research Association. New Orleans, LA.

### 2010

**Carrejo, D. **(June). *Developing a Theoretical Framework for Mathematics Teacher Induction: A Case Study of a University/School Partnership.* Paper presented at the Teachers for a New Era Education Research Symposium. El Paso, TX.

**Carrejo, D.,** & Reinhartz, J. (March). *Exploring Connections Between Learning Science and Mathematics Content and English Language Acquisition: A Literacy Framework for English Language Learners.* Paper presented at the annual international conference of the National Association for Research in Science Teaching (NARST), Philadelphia, PA.

Robertson, W., & **Carrejo, D**. (March/April). *Science Teachers Integrating Mathematical Modeling in Undergraduate Learning for Instruction in Schools.* Paper presented at the annual conference of the Society for Information Technology and Teacher Education, San Diego, CA.

### 2009

**Carrejo, D.** **,** Cortez, T., & Reinhartz, J. (April) *Developing Leadership Roles Within a Community of Practice for Promoting Academic Performance of ELL Students.* Paper presented at the annual meeting of the American Educational Research Association (AERA), San Diego, CA.

**Carrejo, D.****,** & Reinhartz, J. (February) *Producing Teachers Who Meet the Needs of English Language Learners in Middle School Science: Integrating Content with Language Development (ICLD).* Paper to be presented at the 61st annual meeting of the American Association of Colleges for Teacher Education (AACTE), Chicago, IL.

### 2008

Soto-Mas, F., Villaverde, G., **Carrejo, D.****,** & Balcázar, H. (May). *Health Literacy Among College Students.* Poster accepted to the Seventh Annual Health Literacy Conference: Health Literacy in Primary Care: Best Practices and Skill Building*. *Irvine, CA.

**Carrejo, D.****,** & Reinhartz, J. (February). *An Innovative Professional Development Plan for Implementing Best Teaching Practices in Middle School Science and Mathematics.* The 60th annual meeting of the American Association of Colleges for Teacher Education (AACTE), New Orleans, LA.

### 2007

**Carrejo, D.** **,** & Reinhartz, J. (April). *Promoting Middle School Science and Mathematical Reasoning through Modeling*. Paper presented at the annual meeting of the American Educational Research Association (AERA), Chicago, IL.

**Carrejo, D.****,** & Reinhartz, J. (February). *From Vision to Action: Serving Diverse Learners Through a Systemic Approach to Teaching and Learning. *Paper presented at the 59th annual meeting of the American Association of Colleges for Teacher Education (AACTE), New York, NY.

### 2004

Marshall, J., & **Carrejo, D.** (October). *Pre-college teachers: Construction of the velocity concept.* American Physical Society (APS), Texas Section. Waco, TX.

**Carrejo, D.**, & Marshall, J. (April). *Motion and Mathematical Modeling: A Study of Emerging Themes and Their Impact on Science Education.* Paper presented at the annual international conference of the National Association for Research in Science Teaching (NARST), Vancouver, British Columbia.

### 2002

Confrey, J., & **Carrejo, D.**(October). *A Content Analysis of Exit Level Mathematics on the Texas Assessment of Academic Skills: Addressing the Issue of Instructional Decision-Making in Texas.* The 24th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME), Athens, GA.

### 2001

Confrey, J., Bell, K., & **Carrejo, D.** *Systemic crossfire: What implementation research reveals about urban reform in mathematics. *Paper presented at the annual meeting of the American Educational Research Association (AERA). Seattle, WA.

### education/te/people/_Files/Carrejo_faculty_vitae_Fall_2021.pdfEducation

2004 Ph.D., Mathematics Education, University of Texas at Austin

1998 M.A.T., Mathematics, University of Texas at El Paso

1995 B.S., Mathematics, University of Texas at El Paso

__Appointments__

### Current

Member, Paso del Norte Partnership in Education Research, College of Education

Member, PhD in Teaching, Learning, and Culture, Department of Teacher Education

Member, Graduate Programs Committee, Department of Teacher Education

Member, Undergraduate Curriculum Committee, Department of Teacher Education

### 2018 - 2019

Member, University Honors Program Vision Committee, Office of the Provost, UTEP

### 2017 - 2018

Member, UT System Educator Preparation Policy Advisory Committee, Office of Academic Affairs, University of Texas System

### 2015 - 2018

Associate Dean, Undergraduate Studies & Educator Preparation, College of Education

Member, Teacher Preparation Advisory Council (TPAC), College of Education

### 2012 - 2015

Assistant Chair, Department of Teacher Education

### 2013 - 2016

Member, UTEP Graduate Council

### 2010 - 2017

Member, UTEP Institutional Review Board

__Professional____ Experie____nce__

### Current

Reviewer, *Mathematics Education Research Journal*

Reviewer, *Investigations in Mathematics Learning*

Reviewer, *Journal for Research in Mathematics Education*

Member, Editorial Review Board, *Sage Open Journal*

Reviewer, *Journal of STEM Education*

Reviewer, *Middle School Journal*

Reviewer, *The Teacher Educator*

Reviewer, *Statistics Education Research Journal*

### 2014

Co-Facilitator of professional development for pre-service STEM teachers, sponsored by the Science, Engineering, Mathematics, and Aerospace Academy (SEMAA), College of Engineering, University of Texas at El Paso.

### 2012

Facilitator of continuing professional development in secondary mathematics for in-service teachers, grades 9 - 12, Cathedral High School, El Paso, TX

### 2011

Facilitator of professional development sessions in quantitative reasoning for in-service teachers, grades K – 5, Ysleta Independent School District

### 2010 - 2011

Co-facilitator of professional development sessions in mathematics and science for in-service teachers, grades K - 5, Capistrano Elementary School, Ysleta Independent School District

### 2007 - 2010

Facilitator of continuing professional development in mathematics for in-service teachers, grades 6 – 8, Jose Alderete Middle School, Canutillo Independent School District