## Editorial Work

Appova, A., Welder, R. M., and Feldman, Z. (2020). Guest editorial: Special issue on supporting mathematics teacher educators’ knowledge and practices for teaching content to prospective (grades K-8) teachers. In A. Appova, R. M. Welder, and Z. Feldman, (Eds.), Supporting Mathematics Teacher Educators’ Knowledge and Practices for Teaching Content to Prospective (Grades K-8) Teachers. *Special Issue: The Mathematics Enthusiast*, ISSN 1551-3440, vol. 17, nos. 2 & 3, pp. 337–365. ScholarWorks: University of Montana. Retrieve (open access) from: https://scholarworks.umt.edu/tme

## Refereed Journal Articles and Book Chapters

Castro Superfine, A., Prasad, P. V., Welder, R. M., Olanoff, D., & Eubanks-Turner, C. (2020). Exploring mathematical knowledge for teaching teachers: Supporting prospective teachers’ relearning of mathematics. In A. Appova, R. M. Welder, and Z. Feldman, (Eds.), Supporting Mathematics Teacher Educators’ Knowledge and Practices for Teaching Content to Prospective (Grades K-8) Teachers. *Special Issue: The Mathematics Enthusiast*, ISSN 1551-3440, vol. 17, nos. 2 & 3, pp. 367–402. ScholarWorks: University of Montana. Retrieve (open access) from: https://scholarworks.umt.edu/tme

Max, B. & Welder, R. M. (2020). Mathematics teacher educators’ addressing the common core standards for mathematical practice in content courses for prospective elementary teachers: A focus on critiquing the reasoning of others. In A. Appova, R. M. Welder, and Z. Feldman, (Eds.), Supporting Mathematics Teacher Educators’ Knowledge and Practices for Teaching Content to Prospective (Grades K-8) Teachers. *Special Issue: The Mathematics Enthusiast*, ISSN 1551-3440, vol. 17, nos. 2 & 3, pp. 843–881. ScholarWorks: University of Montana. Retrieve (open access) from: https://scholarworks.umt.edu/tme

Thanheiser, E., Olanoff, D.,Hillen, A., Feldman, Z., Tobias, J. M., & Welder, R. M.(2016). Reflective analysis as a tool for task redesign: The case of prospective elementary teachers solving and posing fraction comparison problems. *Journal of Mathematics Teacher Education*, 19(2-3), 123-148. DOI: 10.1007/s10857-015-9334-7

Feldman, Z., Thanheiser, E., Welder, R. M., Tobias, J. M.,Hillen, A. F., & Olanoff, D. (2016). When is a mathematical task a good task? In L. C. Hart, S. Oesterle, S. S. Auslander, & A. Kajander (Eds.), *The Mathematics Education of Elementary Teachers: Issues and Strategies for Content Courses *(pp. 9-24). Charlotte, NC: Information Age Publishing. http://www.infoagepub.com/products/The-Mathematics-Education-of-Elementary-Teachers

Yow, J., Eli, J., Beisiegel, M., McCloskey, A., & Welder, R. M. (2016). Challenging transitions and crossing borders: Preparing novice mathematics teacher educators to support novice K-12 mathematics teachers. *Mathematics Teacher Education and Development*, 18(1), 52-69 [last three authors listed alphabetically to indicate equal authorship]. https://www.merga.net.au/ojs/index.php/mted/article/view/222

Jong, C., Hodges, T. E., Royal, K. D., & Welder, R. M. (2015). Instruments to measure elementary preservice teachers’ conceptions: An application of the Rasch rating scale model. *Educational Research Quarterly*, 39(1), 21-48. http://erquarterly.org/index.php?pg=content

Sharp, J. & Welder, R. M. (2014). Reveal limitations through fraction division problem posing. *Mathematics Teaching in the Middle School*, 19(9), 540-547. DOI: 10.5951/mathteacmiddscho.19.9.0540

Tobias, J. M.,Olanoff, D., Hillen, A., Welder, R. M., Feldman, Z., & Thanheiser, E. (2014). Research-based modifications of elementary school tasks for use in teacher preparation*. *In K. King (Ed.), *Annual Perspectives in Mathematics Education: Using Research to Improve Instruction *(pp. 181-192). Reston, VA: National Council of Teachers of Mathematics. http://www.nctm.org/Store/Products/Annual-Perspectives-in-Mathematics-Education-2014–Using-Research-to-Improve-Instruction/

Welder, R. M. (2012). Improving algebra preparation: Implications from research on student misconceptions and difficulties. *School Science and Mathematics*, 112(4), 255-264. DOI: 10.1111/j.1949-8594.2012.00136.x

Cherkas, B. & Welder, R. M. (2012). Interactive web-based tools for learning mathematics: Best practices. In A. A. Juan, M. A. Huertas, S. Trenholm, & C. Steegmann (Eds.), *Teaching Mathematics Online: Emergent Technologies and Methodologies *(IGI Series in Advances in Distance Education Technologies) (pp. 276-310). Hershey, PA: IGI Global [equal authorship]. DOI: 10.4018/978-1-60960-875-0.ch014

Welder, R. M.(2012). Dylan’s multidigit subtraction strategy. *Teaching Children Mathematics*, 18(6), 392-394. DOI: 10.5951/teacchilmath.18.6.0392

Welder, R. M. & Champion, J. (2011). Toward an understanding of graduate preservice elementary teachers as adult learners of mathematics. *Adults Learning Mathematics: An International Journal*, 6(1), 20-40. http://www.alm-online.net/images/ALM/journals/almij-volume6_1_feb2011.pdf

Welder, R. M. & Simonsen, L. M. (2011). Elementary teachers’ mathematical knowledge for teaching prerequisite algebra concepts. *Issues in the Undergraduate Mathematics Preparation of School Teachers: The Journal, *1: Content Knowledge, 1-16.

http://www.k-12prep.math.ttu.edu/journal/1.contentknowledge/welder01/article.pdf

Welder, R. M. (2010). Effects of personality on student performance in collegiate pre-calculus. *The New Jersey Mathematics Teacher: Journal of the Association of Mathematics Teachers of New Jersey*, 68(2), 15-20. http://amtnj.org/wp-content/uploads/2011/09/journal-dec-2010.pdf

## Refereed Publications in Conference Proceedings

Max, B. & Welder, R. M. (2019). Engaging prospective elementary teachers in standards for mathematical practice within content courses for teachers. In S. Otten, A. G. Candela, Z. de Araujo, C. Haines, & C. Munter (Eds.), *Proceedings of the 41st Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education* (pp. 1141-1145). St. Louis, MO: University of Missouri. Retrieve (Open Access) from: https://s3.amazonaws.com/v3-app_crowdc/assets/2/27/2768340edebc9e2c/PMENA19_020_Max.original.1571926683.pdf

Olanoff, D., Welder, R. M., Prasad, P., & Castro Superfine, A. (2018). Fractalization as a Metaphor for Mathematical Knowledge for Teaching Teachers: Synthesizing the Frameworks and Exploring the Consequences. In T. E. Hodges, G. J. Roy, & A. M. Tyminski (Eds.), *Proceedings of the 40th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education* (pp. 500-503). Greenville, SC: University of South Carolina & Clemson University. https://s3.us-east-2.amazonaws.com/pmena2018/documents/public/PMENA+2018+Proceedings.pdf

Olanoff, D., Bajwa, N. P., Feldman, Z.,Thanheiser, E., Welder, R. M., & Tobias, J. M. (2018). Using the Array Model to Develop Prospective Teachers’ Understanding of Multiplication and its Properties. In T. E. Hodges, G. J. Roy, & A. M. Tyminski (Eds.), *Proceedings of the 40th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education* (p. 833). Greenville, SC: University of South Carolina & Clemson University.

https://s3.us-east-2.amazonaws.com/pmena2018/documents/public/PMENA+2018+Proceedings.pdf

Welder, R. M., Prasad, P., Castro-Superfine, A., & Olanoff, D. (2017). Developing a framework for mathematical knowledge for improving the content preparation of elementary teachers. In E. Galindo & J. Newton (Eds.), *Proceedings of the 39th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education *(p. 637). Indianapolis, IN: Purdue University.

https://www.conf.purdue.edu/landing_pages/pme-na/docs/PMENA39_2017_Proceedings.pdf

Welder, R. M., Appova, A., Olanoff, D., Taylor, C. E., & Kulow, T. (2016). Improving preservice elementary teacher education through the preparation and support of elementary mathematics teacher educators. In M. B. Wood, E. E. Turner, M. Civil, & J. A. Eli (Eds.), *Proceedings of the 38th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education *(pp. 1713-1722). Tucson, AZ: University of Arizona. http://www.pmena.org/pmenaproceedings/PMENA 38 2016 Proceedings.pdf

Olanoff, D., Feldman, Z., Welder, R. M., Tobias, J. M., Thanheiser, E., & Hillen, A. (2016). Greater Number of Larger Pieces: A Strategy to Promote Prospective Teachers’ Fraction Number Sense Development. In M. B. Wood, E. E. Turner, M. Civil, & J. A. Eli (Eds.), *Proceedings of the 38th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education *(pp. 799-805). Tucson, AZ: University of Arizona. http://www.pmena.org/pmenaproceedings/PMENA 38 2016 Proceedings.pdf

Welder, R. M., Tobias, J. M., Feldman, Z., Hillen, A., Olanoff, D., & Thanheiser, E. (2015). Modifying children’s tasks into cognitively demanding tasks for preservice elementary teachers. In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez (Eds.), *Proceedings of the 37th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education*(pp. 984-987). East Lansing, MI: Michigan State University. http://www.pmena.org/pmenaproceedings/PMENA 37 2015 Proceedings.pdf

Welder, R. M., Jansen, A., & McCloskey, A. (2014). Preparing and supporting mathematics teacher educators: Opportunities and challenges. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), *Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education *(Vol. 1; p. 248). Vancouver, Canada: PME. http://www.pmena.org/pmenaproceedings/PMENA 36 PME 38 2014 Proceedings Vol 1.pdf

Olanoff, D., Hillen, A. F., Tobias, J. M.,Welder, R. M., Thanheiser, E., & Feldman, Z. (2014). Facilitating prospective teachers’ fraction number sense development through problem solving and problem posing. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), *Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education *(Vol. 6; p. 187). Vancouver, Canada: PME. http://www.pmena.org/pmenaproceedings/PMENA 36 PME 38 2014 Proceedings Vol 6.pdf

Feldman, Z., Tobias, J. M.Olanoff, D., Thanheiser, E., Hillen, A. F., & Welder, R. M. (2014). Prospective elementary teachers’ analysis of student thinking. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), *Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education *(Vol. 6; p. 67). Vancouver, Canada: PME. http://www.pmena.org/pmenaproceedings/PMENA 36 PME 38 2014 Proceedings Vol 6.pdf

Thanheiser, E., Hillen, A., Olanoff, D., Feldman, Z.,Welder, R. M., & Tobias, J. M.(2013). Task design in mathematics content courses for preservice elementary teachers: A collaborative approach. In M. V. Martinez & A. Castro Superfine (Eds.), *Proceedings of the 35th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education*(pp. 893-896). Chicago, IL: University of Illinois at Chicago. http://www.pmena.org/pmenaproceedings/PMENA 35 2013 Proceedings.pdf

Welder, R. M., McCloskey, A., & Searle, S. P. (2013). Teaching to teach without having taught: Mathematics teacher educators preparing elementary teachers of mathematics*. *In M. V. Martinez & A. Castro Superfine (Eds.), *Proceedings of the 35th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education*(p. 969). Chicago, IL: University of Illinois at Chicago. http://www.pmena.org/pmenaproceedings/PMENA 35 2013 Proceedings.pdf

Hart, L., Swars, S., Oesterle, S. Kajander, A., Browning, C. Thanheiser, E., … Yoder, M. (2013). Developing elementary teachers’ mathematical knowledge

for teaching: Identifying important issues. In M. V. Martinez & A. Castro Superfine (Eds.), *Proceedings of the 35th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education *(pp. 1292-1301). Chicago, IL: University of Illinois at Chicago. http://www.pmena.org/pmenaproceedings/PMENA 35 2013 Proceedings.pdf

Welder, R. M. & Jong, C. (2012). Examining connections between mathematical knowledge for teaching and conceptions about mathematics teaching and learning*. *In L. R. Van Zoest, J.-J. Lo, & J. L. Kratky (Eds.), *Proceedings of the 34th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education *(pp. 773-776). Kalamazoo, MI: Western Michigan University. http://www.pmena.org/pmenaproceedings/PMENA 34 2012 Proceedings.pdf

McCloskey, A., Beisiegel, M., Eli, J., Welder, R. M., & Yow, J. (2012). Parallel transitions: Challenges faced by new mathematics teachers and new mathematics teacher educators. In L. R. Van Zoest, J.-J. Lo, & J. L. Kratky (Eds.), *Proceedings of the 34th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education *(pp. 737-740). Kalamazoo, MI: Western Michigan University [last four authors listed alphabetically to indicate equal authorship]. http://www.pmena.org/pmenaproceedings/PMENA 34 2012 Proceedings.pdf

Eli, J., Beisiegel, M., McCloskey, A., Welder, R. M., & Yow, J. (2012). Transitioning to faculty: New mathematics teacher educators’ perceptions of successful doctoral program preparation. *Proceedings of the 12th International Congress on Mathematical Education *(p. 7945). Seoul, Korea [last four authors listed alphabetically to indicate equal authorship]. https://archive.org/details/springer_10.1007-978-3-319-12688-3

Welder, R. M., Hodges, T. E., & Jong, C. (2011). Measuring changes in teachers’ beliefs, attitudes, and dispositions related to experiences in mathematics. In L. R. Wiest & T. Lamberg (Eds.), *Proceedings of the 33rd Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education*(pp. 2118-2125). Reno, NV: University of Nevada, Reno. http://www.pmena.org/pmenaproceedings/PMENA 33 2011 Proceedings.pdf

Beisiegel, M., Eli, J., McCloskey, A., Welder, R. M., & Yow, J. (2011). Transforming practices by understanding connections between new mathematics teacher educators and new K-12 mathematics teachers. In L. R. Wiest & T. Lamberg (Eds.), *Proceedings of the 33rd Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education *(p. 1912). Reno, NV: University of Nevada, Reno [equal authorship]. http://www.pmena.org/pmenaproceedings/PMENA 33 2011 Proceedings.pdf

Welder, R. M. (2006). Prerequisite knowledge for the learning of algebra. *Proceedings of the 5th Annual Hawaii International Conference on Statistics, Mathematics and Related Fields *(pp. 1642-1667). Honolulu, Hawaii.

## Additional Publications

Welder, R. M. (2015). Preparing and Supporting Mathematics Teacher Educators: Opportunities and Challenges. *International Group for the Psychology of Mathematics Education Newsletter*, 19-20.

Welder, R. M. (2010). *Iterated prisoner’s dilemma: A game theory approach to the mathematical study of cooperation*. Saarbrücken: Lambert Academic Publishing AG & Co. KG.