## Invited Talks

Cullen, C. J. (2019). *Exploring Trigonometric Relationships: Is it a function?* Presented for the University of Maine’s Colloquium Series, Orono, ME, April 8, 2019.

Cullen, C. J. (2019). *Exploring Trigonometric Relationships: Is it a function? *Presented for the University of Southern Illinois Colloquium Series, Edwardsville, IL, March 22, 2019.

## Conference Presentations

Cullen, C. J. (2023, October) Does this Look Random? Presented at the Illinois Council of Teachers of Mathematics 73rd Annual Meeting, October 7, 2023.

Cullen, C. J. (2023, April) What Does Random Look Like? Presented at the 69^{th} Annual Western Illinois University Mathematics Teacher Conference, Macomb, IL.

Cullen, C. J. (2023). *Sine, Cosine, Tangent → Sine, Secant, Tangent*. Presented at the

*The 37th Annual Illinois Council of Teachers of Mathematics Conference – Southern Section*, February 16, 2023.

Cullen, C. J. (2022). *Respecting the Transcendental Functions*. Presented at the Illinois Council of Teachers of Mathematics 72^{nd} Annual Meeting, October 29, 2022.

Isaacson, K. J., Cullen, C. J., Betz-Cahill, C. (2022). *Supporting Equity with Technology*. Council of Teachers of Mathematics 72^{nd} Annual Meeting, October 29, 2022.

Cullen, C. J., Ssebaggala, L., & Chávez, O.** **(2022, March). *Why Do we Really Need Radians? *Presented at the 2022 Regional Conference of the National Council of Teachers of Mathematics, Indianapolis, IN.

Martin, T. S., & Cullen, C. J. (2021). *Creative Mathematical Reasoning and Content as an Evaluative Framework For Preservice Teacher Experiences*. Poster session to be presented at PME-NA 42 AMTE. Mazantlan, Sinaloa, Mexico, October 14 – 18, 2020 (Rescheduled for May 27 – 20 & June 5 – 6, 2021).

Martin, T. S., Cullen, C. J., & Day, R. (2020). *Creative Mathematical Reasoning and Key Curricular Content as an Evaluative Framework for Preservice Task Engagement*. Individual session presented at the 24th Annual AMTE Conference. Phoenix, AZ, February 6 – 8, 2020.

Cullen, C. J. (2020). *Leveraging Technology to Support Math Instruction*. Presented at the Illinois Council of Teachers of Mathematics 70^{th} Annual Meeting, October 17, 2020.

Clarkson, K. A., Lawton, C. A., Azimi, K., Martin, T. S. & Cullen, C. J. (2019). *The Role of Creative Reasoning in a Technology-Based Task for Pre-Service Secondary Teachers.* Poster presented at the 41^{st} Annual Meeting of PME-NA, St. Louis, MO, November 14 – 17, 2019.

Roehrig, A. E., VanMeenen, E., Kharel, R. P., Kancharlapalli, N., Cullen, C. J., & Martin, T. S. (2019). *Connecting Data-Claim Relationships Using Toulmin’s Model.* Poster presented at the 41^{st} Annual Meeting of PME-NA, St. Louis, MO, November 14 – 17, 2019.

Martin, T. S., Cullen, C. J., & Day, R. (2019). *Chords and secants and tangents, oh my!* Poster presented at the 2019 Math and Science Conference, Peoria, IL, October 18 – 19, 2019.

Cullen, C. J., & Martin, T. S. (2018). Exploring trigonometric relationships: Is it a function? Research report presented at the 40th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Greenville, SC.

Dimmel, J., Nickels, M., Cullen, C., & Bock, C. (2018). Mathematical making in immersive virtual environments working group. Working Grouppresented at the 40th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.Greenville, SC.

Cullen, C. J. (2017, April) An Introduction to Geogebra. Presented at the 66^{th} Annual Western Illinois University Mathematics Teacher Conference, Macomb, IL.

Cullen, C. J., Klanderman, D., & Barrett, J.(2017, November). *A Pleasure to Measure: CCSSM Activities for K–Grade 5. *Workshop presented at the 2017 Regional Conference of the National Council of Teachers of Mathematics, Chicago, IL.

Cullen, C. J., Barret, J. E., Clements, D. H. (2017) Learning Trajectories to Support the Development of Measurement Knowledge, pre-K through Middle School. Presented at the NCTM Research Conference, San Antonio, TX, April 3–7, 2017.

Cullen, C. J. (2017) A Pleasure to Measure: Tasks for Teaching Measurement in Elementary Grades. Invited talk for Author Presentations at the NCTM Annual Meeting, San Antonio, TX, April 5–8, 2017.

Cullen, A. L., Cullen, C. J., & O’Hanlon, W. A. (2017, October). *Elementary Students’ Reasoning about Angle Constructions*. Research report presented at the 39^{th} Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Indianapolis, IN.

Cullen, C. J., (2016) *The Roles of Technology in the Mathematics Classroom*. Presented at the Illinois Council of Teachers of Mathematics 66^{th} Annual Meeting, Peoria, IL, October 7 – 8, 2016.

Cullen, C. J., & Klanderman, D. B. (2016) *Measurement Activities for CCSS-M. *Presented at the Annual NCTM Conference, San Francisco, C.A., April 13 – 16, 2016.

Cullen, C. J., Barret, J. E., Clements, D. H., & Van Dine, D. W. (2016) Stucturing two- and three dimensional space: A focus on representations. Symposium presented at the NCTM Research Conference, San Francisco, CA, April 11 – 13, 2016.

*Eval**uation of three interventions teaching area measurement as spatial structuring to young children. *Paper presented as part of the symposium *Structuring Two- and Three-Dimensional Space: A Focus on Representation* at the 2016 NCTM Research Conference: San Francisco, CA, April 11 – 13, 2016.

Eames, C. L., Cullen, C. J., Barrett, J. E., Klanderman, D., & Unverferht, R. (2015, April). *Extending the empirical basis of a length measurement learning trajectory*. Paper presented at the Research Session of the 2015 Annual Conference of the National Council of Teachers of Mathematics, Boston, MA.

Barrett, J. E., Cullen, C. J., Beck, P., Eames, C. L., Clements, D. H., & Sarama, J. (2015, April). *Children’s estimation and measurement of area.* Paper presented at the 2015 Annual Meeting of the American Educational Research Association, Philadelphia, PA.

Cullen, C. J., & Klandermann, D. B. (2015) *Measurement Activities for CCSS-M*. Presented at the NCTM Regional Conference, Minneapolis, MN, November 11 – 13, 2015.

Cullen, C. J. (2015) *Flight Planning a Good Lesson.* Presented at the Illinois Council of Teachers of Mathematics 65^{th} Annual Meeting, Tinley Park, IL, October 23 – 24, 2015.

*Meas**urement as a Concrete Introduction to Variable*.Presented at the Illinois Council of Teachers of Mathematics 65^{th} Annual Meeting, Tinley Park, IL, October 23 – 24, 2015.

Beck, P. S., Cullen, C. J., & Rupnow, T. J., (2015) *Measuring the Base and Height of Triangl**es.* Presented at the Illinois Council of Teachers of Mathematics 65^{th} Annual Meeting, Tinley Park, IL, October 23 – 24, 2015.

Cullen, C. J. (2015). *A Geometric Interpretation of Trigonometry*. Presented at the Indiana Mathematics Association of America Section, Westville IN, October 17, 2015.

Cullen, C. J. (2015) *Effectively Incorporating Technology in the Classroom*. Invited discussant at the Indiana Mathematics Association of America Section, Westville IN, October 17, 2015.

Barrett, J. E., Cullen, C. J., Beck, P. S., Eames, C. L., & Rupnow, T. J., (2015) *Building the Base and Attaching the Altitude: Measuring Triangles*. Presented at the Annual Meeting of the National Council of Teachers of Mathematics, Boston, MA, April 15 – 18, 2015.

Martin, T. S., Cullen, C. J., & Day, R. (2015) *Reasoning and Problem Solving in the Common Core Era.* Presented at the Annual Meeting of the National Council of Teachers of Mathematics, Boston, MA, April 15 – 18, 2015.

Cullen, C. J. (2015) *Flight Planning for a Good Lesson*. Presented at the 64^{th} Annual Western Illinois University Mathematics Teacher Conference, Macomb, IL, April 10, 2015.

Cullen, C. J. (2014) *Bringing the Function into Trigonometry. *Presented at the Illinois Council of Teachers of Mathematics 64^{th} Annual Meeting, Tinley Park, IL, October 17 – 18, 2014.

Beck, P. S., Cullen, C. J., Eames, C. L., Barrett, J. E., Clements, D. H., & Sarama, J. (2014) *Turn up the Volume!* Presented at the Illinois Council of Teachers of Mathematics 64^{th} Annual Meeting, Tinley Park, IL, October 17 – 18, 2014.

Miller, A. L., Eames, C. L., & Cullen, C. J. (2014). *Thinking deeply about area measurement*. Research session presented at the 2014 Annual Conference of the National Council of Teachers of Mathematics, New Orleans, LA, April 9 – 12, 2014.

Cullen, C. J., Barrett, J. E., Clements, D. H., Sarama, J. Eames, C. L., Miller, A. L., Klanderman, D. (2014). *Supporting Children’s Learning of Area Measurement: A Microgenetic Study*. Paper presented at the 2014 Annual Meeting of the American Educational Research Association, Philadelphia, PA, April 4 – 7, 2014.

*Using learning trajectories for spatial measurement as tools for teaching*. Invited session presented at the 29^{th} Annual Conference on Teaching Mathematics, Carbondale, IL, February 20, 2014.

Eames. C. L., Miller, A. L., Kara, M., Cullen, C. J., & Barrett, J. E. (2013). The longitudinal development of unit concepts in area and volume measurement contexts: A case study. Research report presented at the 35^{th} Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Chicago, IL, November 14 – 17, 2013.

Eames, C. L., Miller, A. L., Kara, M., Van Dine, D. W., Cullen, C. J., Barrett, J. E., Clements, D. H., Sarama, J. (2013). *The longitudinal development of children’s conceptions of* *spatial measurement*. Paper presented at the 43^{rd} Annual Meeting of the Jean Piaget Society, Chicago, IL, June 6 – 8, 2013.

Van Dine, D., Kara, M., Miller, A. L., Eames, C. L., Sarama, J. Clements, D. H., Barrett, J. E., Cullen, C. J. (2013). *Va**lidating a learning trajectory for volume measurement with* *Rasch modeling*. Poster presented at the 43^{rd} AnnualMeeting of the Jean Piaget Society, Chicago, IL, June 6 – 8, 2013.

Eames, C. L., Miller, A. L., Kara, M., Van Dine, D., Cullen, C. J., Barrett, J. E., Clements, D. H., Sarama, J. (2013). *The longitudinal development of children’s conceptions of* *spatial measurement*. Paper presented at the 43^{rd} Annual Meeting of the Jean Piaget Society, Chicago, IL, June 6 – 8, 2013.

Van Dine, D., Kara, M., Miller, A. L., Eames, C. L., Sarama, J. Clements, D. H., Barrett, J. E., Cullen, C. J. (2013). *Va**lidating a learning trajectory for volume measurement with* *Rasch modeling*. Poster presented at the 43^{rd} AnnualMeeting of the Jean Piaget Society, Chicago, IL, June 6 – 8, 2013.

Barrett, J. E., Cullen, C. J., Miller, A. L., Van Dine, D. W., Eames. C. L., Kara, M., Sarama, J., & Clements, D. H. (2013). *Framing and revising a hypothetical learning trajectory for* *area measurement*. Symposium presented at the Research Presessionof the 2013 Annual Conference of the National Council of Teachers of Mathematics,Denver, CO, April 17 – 20, 2013.

Miller, A. L., Eames, C. L., Kara, M., & Cullen, C. J. (2013). *Hypothetical learning trajectories as dynamic works-in-progress tools: Insights into the revising and refining process*.Individual session presented at the 17^{th} Annual Conference of the AssociationofMathematics Teacher Educators, Orlando, FL, January 24 – 26, 2013.

Hertel, J., Cullen, C., Moore, K., Steckroth, J., & Thompson, P. (2012) *Current research on trigonometry teaching and learning. *Symposium presented at the Research Pre-session of the National Council of Teachers of Mathematics: Philadelphia, PA, April 23 – 25, 2012.

*Trajectories of three students’ learning of area measurement: Grades 2 – 5*. Poster presented at the Research Pre-session of the National Council of Teachers of Mathematics: Philadelphia, PA, April 23 – 25, 2012.

Eames, C. L., Kara, M., Cullen, C. J., & Miller, A. L. (2012). *Implications for the integration of learning trajectories in teacher preparation*. Presented at the Annual Meeting of the Association of Mathematics Teacher Educators: Fort Worth, TX, February 8 – 11, 2012.

Cullen, C. J., & Miller, M. R. (2012). *Dynamic Representations of Polar Graphing. *Poster presented at the Annual Meeting of the Association of Mathematics Teacher Educators: Fort Worth, TX, February 8 – 11, 2012.

Miller, A. L., Cullen, C. J., & Barrett, J. E. (2012). *Extending length measurement into the middle school with CCSSM. *Presented at the Regional Meeting of the National Council of Teachers of Mathematics: Chicago, IL, November 28-30, 2012.

Cullen, C. J., Miller, A. L., & Van Dine, D. W. (2012). *Reaching the measurement objectives in the CCSSM*. Presented at the Annual Meeting of the National Council of Teachers of Mathematics: Philadelphia, PA, April 25 – 28, 2012.

Hertel, J., & Cullen, C. (2011, October). *Teaching trigonometry: A directed length approach.* Presented at the 33^{rd} Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Reno, NV, October 2011.

Kara, M., Eames, C. L., Miller, A. L., Cullen, C. J., & Barrett, J. E. (2011, October). *Developing and understanding of area measurement concepts with triangular units*. Presented at the 33^{rd} Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Reno, NV, October 2011.

Cullen, C. J., Miller, A. L., Barrett, J. E., Clements, D. H., & Sarama, J. (2011, July). *Unit eliciting task structures: Verbal prompts for comparative measures*. Presented at the 35^{th} Conference of the International Group for the Psychology of Mathematics Education, Ankara, Turkey, July 2011.

Cullen, C. J., Miller, A., & Barrett, J. E. (2011, April). *Connecting length, area, and volume tasks through units and comparison*. Presented at the Annual Meeting of the National Council of Teachers of Mathematics: Indianapolis, IN, April 13 – 16, 2011.

Barrett, J. E., Cullen, C. J., Witkowski-Rumsey, C., Miller, A. L., & Klanderman, D. (2011, April). *De**signing integrative learning tasks for unit concepts throughout length, area, and volume measurement (grades 2 – 5). *Poster presented at the American Educational Research Association, New Orleans, LA, April 8 – 12, 2011.

Cullen, C. J., Miller, A. L., Witkowski-Rumsey, C., & Sarama, J. (2011, April). *Area hypothetical learning trajectory: Relating square units to non-rectilinear regions*. Paper presented at the American Educational Research Association, New Orleans, LA, April 8 – 12, 2011.

Cullen, C. & Hertel, J. (2011, February). *A dynamic geometric approach to trigonom**etry.*Presented at the 27^{th} Annual Conference on Teaching Mathematics, Carbondale, IL, February 17, 2011.

Cullen, C. & Hertel, J. (2011, February). *Dynamic exploration of families of functions. *Presented at the 27^{th} Annual Conference on Teaching Mathematics, Carbondale, IL, February 17, 2011.

Miller, A., Cullen, C., & Tobias, J. (2011, January). *Using empirical classroom results to inform modifications on a hypothetical learning trajectory for area.* Presented at the Annual Meeting of the Association of Mathematics Teacher Educators, Irvine, CA, January 27 – 29, 2011.

Cullen, C. J., Witkowski, C., Miller, A. L., Barrett, J. E., Sarama, J. A., & Clements, D. H. (2010, October). *Key components for measurement tasks*. Presented at the 32nd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education: Columbus, OH, October 28 – 31, 2010.

*Strategy use indicative of an understanding of units of length*. (2010, July). Presented at the 34th Annual Conference of the International Group for the Psychology of Mathematics Education, Belo Horizonte, Brazil, July 2010.

Cullen, C. (2010, June). *A comparison of representations of units of length: A microgenetic analysis*. Presented at the Eighth Illinois Education Research Council, Champaign, IL, June 8 – 9, 2010.

Cullen, C., Barrett, J. E., Clements, D. H., & Sarama, J. (2010, April – May). *A comparison of representations of units of length: A microgenetric analysis. *Presented at the annual Meeting of the American Educational Research Association, Denver, CO, April 30 – May 4, 2010.

Barrett, J. E., Witkowski, C., Cullen, C., Klanderman, D., Clements, & D., & Sarama, J. (2010, April). *A longitudinal analysis of unit iteration concepts for length area, and volume (grades 2** – 4)*: San Diego, CA, April 21-24, 2010.

Cullen, C. *Iterating the square root function: Things just got a little complicated!* Presented at the 61^{st} Annual Meeting of the Illinois Council of Teachers of Mathematics: Springfield, IL, October 14 – 16, 2010.

Cullen, C. (2010, October). *Gettin’ triggy with it: I thought I just had to memorize all of these!* Presented at the 61^{st} Annual Meeting of the Illinois Council of Teachers of Mathematics, Springfield, IL, October 14 – 16, 2010.

Witkowski, C., Wilder, R., Maubach, R., Irvin, K., Mueller, M., & Cullen, C. (2010, April). *Wrapp**ing around: Understanding fractions and “super” units*. Presented at 88th Annual Meeting of the National Council of Teachers of Mathematics: San Diego, CA, April 21 – 24, 2010.

Cullen, C., & Thurnau, A. (2010, March). *Iteration of the square root function: Oh the places we will go. *Presented at Annual Western Illinois University Mathematics Teachers Conference, Macomb, IL, March 25, 2010.

Cullen, C. (2010, February). *TI-Npire: Inspirational or the biggest flop since the TI-85?* Presented at Group for Education Research in Mathematics, Normal, IL, February 12, 2010.

St. John, D., Cullen, C., & Lewis, G. (2009, Fall). TI-Nspire workshop: This workshop was presented by Denny St. John, Craig Cullen, and Gary Lewis. This workshop was presented to approximately 40 students over a two-day period. The participants in this workshop received training on the latest Texas Instrument’s calculator the TI-Nspire. Fall, 2009.

Cullen, C., & Barrett, J. (2009, September). *A comparative analysis: Two representational models for units of length.* A report presented at the first meeting of the Measurement Mini-Center held at Michigan State University, Lansing, Michigan, September 17 – 19, 2009.

Barrett, J. & Cullen, C. (2009, September). *T**he children’s measurement project at Illinois State University, 2009*. A report presented at the first meeting of the Measurement Mini-Center held at Michigan State University, Lansing, Michigan, September 17 – 19, 2009.

McCool, J., Cullen, C. & Barrett, J. (2009, April). *From numerals to intervals and back: How young children think about measuring.* Presented at the 87^{th} Annual Meeting of the National Council of Teachers of Mathematics, Washington, D.C., April 22 – 25, 2009.

Barrett, J., Cullen, C., McCool, J, & Witkowski, C. (2009, April). *Children’s abstraction of iterative units to measure linear space: An examination of a learning trajectory as a formative assessment tool for teaching length. *Presented at the Annual Meeting of the American Educational Research Association, San Diego, CA, April, 2009.

McCool, J., & Cullen, C. (2009, March). *From** numerals to intervals and back: How young children think about measuring.* Presented at the Annual Western Illinois University Mathematics Teachers Conference, Macomb, IL, March 27, 2009.

Cullen, C., & McCool, J. (2009, March). *Click and drag geometer’s sketchpad out of your geometry class.* Presented at the Annual Western Illinois University Mathematics Teachers Conference, Macomb, IL, March 27, 2009.

Clements, D., Sarama, J., Barrett, J., Cullen, C., McCool, J., & Schiller, J. Professional Development Seminar (University at Buffalo, August 25, 2008).

Barrett, J., Cullen, C., McCool, J., & Witkowski, C. (2008, October). *It all counts for something: Math strategies for scholastic bowl competition. *Invited talk at the Illinois Elementary School Association (IESA) Annual Scholastic Bowl Workshop, Bloomington, IL, October 24, 2008.

Cullen, C., & McCool, J. (2008, July). *Elementary children’s understanding of units, number, and space on linear measurement tasks: Unpacking strategic knowledge of rulers.* Presented at the Professional Development Seminar at Thomas Metcalf Lab School, Normal, IL, July 15, 2008.

Cullen, C., & McCool, J. (2008). *Assessment of measurement knowledge in elementary grades. *Presented at Group for Education Research in Mathematics, Normal, IL.

Cullen, C. (2007, April). *When Will I Ever Use This? The Simpsons and Other InterestingMathematics*. Invited presentation for pre-service teachers at Illinois State University, Normal, IL, April 13, 2007.

Cullen, C. (2007, March). *Mathematics Education and “The Simpsons.”* Presented at Group for Education Research in Mathematics, Normal, IL, March 5, 2007.

Barrett, J. E., Cullen C. J. (2008, October). *A practical analysis of instructional practices for linear units of measurement with students in grades 2 – 4*. Presented at Metcalf Laboratory School as part of their in-service professional development program, October 10, 2008.

Clements, D., Sarama, J., Schiller, J, Barrett, J., Cullen, C., McCool, J. (2008, August). *Symposium for measurement instruction in early childhood. * Presented at the State University of New York at Buffalo in Amherst, NY as part of their sponsored in-service professional development program, August 25, 2008.

ICTMSS: February 16, 2021 |

Chord and Sine |

Secant and Tanget |

Chord, Secant, Tangent (v1/v2) |