Editorial Work
Guest Editor (with Appova, A. & Feldman, Z.). (2020) 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. 325-937. ScholarWorks: University of Montana. Retrieve (open access) from: https://scholarworks.umt.edu/tme/vol17/iss2/
Refereed Journal Articles and Book Chapters
Kwok, M., Welder, R. M., Moore, J., & Williams, A. M. (2022). Beyond keywords: Applying systemic functional linguistics to unpack the language of additive word problems. International Journal of Science and Mathematics Education. Advance online publication. https://doi.org/10.1007/s10763-022-10290-6
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/vol17/iss2/
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/vol17/iss2/
Appova, A., Welder, R. M., & 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/vol17/iss2/
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
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.
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
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. Retrieve (Open Access) from: 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. Retrieve (Open Access) from:
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.
Refereed Publications in Conference Proceedings
Olanoff, D., Bajwa, N. P., Tobias, J. M., & Welder, R. M. (2023). Reflecting on and evaluating tasks: What happens when learning goals are not met? In Lamberg, T., & Moss, D. (Eds.), Proceedings of the Forty-Fifth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1) (pp. 546-550). Reno, NV: University of Nevada, Reno. (Open Access) from: http://www.pmena.org/proceedings/
Welder, R. M., Castro Superfine, A., Prasad, P. V., & Olanoff, D. (2022). Conceptualizing mathematics teacher educator knowledge: Comparing and contrasting existing frameworks. In Lischka, A. E., Dyer, E. B., Jones, R. S., Lovett, J. N.., Strayer, J., & Drown, S. (Eds.), Proceedings of the Forty-Fourth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 737-747). Nashville, TN: Middle Tennessee State University. Retrieve (Open Access) from: https://doi.org/10.51272/pmena.44.2022
Welder, R. M., Burton, M., & Eisenreich, H. (2022). Using mindfulness to support the well-being of preservice K-8 teachers during a pandemic. In Lischka, A. E., Dyer, E. B., Jones, R. S., Lovett, J. N.., Strayer, J., & Drown, S. (Eds.), Proceedings of the Forty-Fourth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1321-1326). Nashville, TN: Middle Tennessee State University. Retrieve (Open Access) from: https://doi.org/10.51272/pmena.44.2022
Welder, R. M., Kwok, M., Williams, A. M., & Moore, J. (2022). Supporting preservice K-8 teachers’ conceptions of addition using a linguistics approach to analyzing word problems. In S. Bateiha, & G. Cobbs. (Eds.), Proceedings of the 49th Annual Conference of the Research Council on Mathematics Learning (pp. 77-85). Grapevine, TX. Retrieve (Open Access) from: https://www.rcml-math.org/assets/Proceedings/RCML%202022%20Proceedings.pdf
Welder, R. M., Williams, A. M., Kwok. M., & Moore, J. (2021). Applying systemic functional linguistics to unpack the language of additive word problems. In D. Olanoff, K. Johnson, & S. Spitzer (Eds.), Proceedings of the 43rd Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1011-1015). Philadelphia, PA. Retrieve (Open Access) from: http://www.pmena.org/pmenaproceedings/PMENA%2043%202021%20Proceedings.pdf
Foran, A., Welder, R. M., & Williams, A. M. (2021). Task development to address error patterns in prospective elementary teachers’ posing of multi-step word problems. In D. Olanoff, K. Johnson, & S. Spitzer (Eds.), Proceedings of the 43rd Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 918-927). Philadelphia, PA. Retrieve (Open Access) from: http://www.pmena.org/pmenaproceedings/PMENA%2043%202021%20Proceedings.pdf
Foran, A., & Welder, R. M. (2020). Error patterns in prospective K-8 teachers’ posing of multi-step addition and subtraction word problems. In A. I. Sacristán, J. C. Cortés-Zavala, & P. M. Ruiz-Arias (Eds.), Proceedings of the 42nd Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1601-1605). Mazatlán, Sinaloa, Mexico. Retrieve (Open Access) from: https:/doi.org/10.51272/pmena.42.2020-252
Bajwa, N. P., Tobias, J. M., Olanoff, D., & Welder, R. M. (2020). Developing prospective teachers’ representational fluency of whole number multiplication using array representations. In A. I. Sacristán, J. C. Cortés-Zavala, & P. M. Ruiz-Arias (Eds.), Proceedings of the 42nd Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1712-1713). Mazatlán, Sinaloa, Mexico. Retrieve (Open Access) from: https:/doi.org/10.51272/pmena.42.2020-272
Max, B., & Welder, R. M. (2020). Textbook use of children’s thinking to support prospective elementary teachers’ geometric understanding. In A. I. Sacristán, J. C. Cortés-Zavala, & P. M. Ruiz-Arias (Eds.), Proceedings of the 42nd Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1738-1739). Mazatlán, Sinaloa, Mexico. Retrieve (Open Access) from: https:/doi.org/10.51272/pmena.42.2020-285
Olanoff, D., Prasad, P. V., & Welder, R. M. (2020). Exploring mathematics teacher educators’ avenues for professional growth: A review of the research literature. In A. I. Sacristán, J. C. Cortés-Zavala, & P. M. Ruiz-Arias (Eds.), Proceedings of the 42nd Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 895-897). Mazatlán, Sinaloa, Mexico. Retrieve (Open Access) from: https://doi.org/10.51272/pmena.42.2020-136
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. Retrieve (Open Access) from: 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. Retrieve (Open Access) from: 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. Retrieve (Open Access) from:
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. Retrieve (Open Access) from: 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. Retrieve (Open Access) from: 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. Retrieve (Open Access) from: 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. Retrieve (Open Access) from: 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. Retrieve (Open Access) from: 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. Retrieve (Open Access) from: 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. Retrieve (Open Access) from: 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. Retrieve (Open Access) from: 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. Retrieve (Open Access) from: 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. Retrieve (Open Access) from: 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. Retrieve (Open Access) from: 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. Retrieve (Open Access) from: 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. Retrieve (Open Access) from: 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. Retrieve (Open Access) from: 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., Olanoff, D., Tobias, J. M., Bajwa, N. P., & Thanheiser, E. (2020). Tasks for teachers: Approaches to the design of tasks for preservice and inservice learners. Journal of Mathematics Teacher Education in Texas, 10(3), 6-7.
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.