Mathematics Education

The Department of Mathematical Sciences has a very active group of mathematics educators whose research interests lie in the areas of cognition, curriculum development, foundational issues of mathematics education, interdisciplinary mathematics, history and philosophy of mathematics and mathematics education, models and modelling research, mathematics gifted education, assessment, and technology education. The primary focus of mathematics education is the undergraduate program, but there is a graduate component. This component includes a mathematics education option in the Master of Arts degree and the Doctor of Philosophy degree.
Typically, there is at least one seminar in mathematics education per semester open to graduate students and faculty. The Mathematics education faculty is involved in many major National Science Foundation grants: the Systemic Initiative for Montana Mathematics and Science (SIMMS), Six Through Eight Mathematics (STEM) Project, Systemic Teacher Excellence Preparation (STEP), the ShowMe Project, and The Center for Learning and Teaching in the West (CLT West). Because of the NSF grants, there are frequent mathematics and science education visitors to campus.

Faculty

James Hirstein, Ed.D., University of Georgia, 1978
Matt Roscoe, Ph.D., University of Montana, 2009
Bharath Sriraman, Ph.D., Northern Illinois University, 2002Z
Ke Wu, Ph.D., University of Minnesota, 2008


Rick Billstein, Ed.D., University of Montana, 1972, Professor Emeritus
Johnny Lott, Ph.D., Georgia State University, 1973, Professor Emeritus
Mark Lutz, M.A., University of Dayton, Adjunct Instructor
Bonnie Spence, M.A., The University of Tulsa, Lecturer


Faculty in the School of Education often participate in the activities of the math department:
Georgia Cobbs, Ph.D., Ohio State University, 1995
David Erickson, Ph.D., Ohio State University, 1994

Publications by Mathematics Education Faculty

 Walen, S. B. and Hirstein, J. Restructuring Mathematics Assessment: Suggestions from the Classroom. Needham Heights, MA: Simon & Schuster Custom Publishing, 1995.
 Hirstein, J. "Student Assessment in the Pilot Study." In The SIMMS Project. Monograph 4: Assessment. Missoula, MT: The SIMMS Project, 1998, pp. 112.
 Day, Roger; and others (including J. Hirstein). Navigating through Geometry in Grades 912. Reston, VA: National Council of Teachers of Mathematics, 2001.
 Lott, J. W.; and others (including J. Hirstein). "Curriculum and Assessment in SIMMS Integrated Mathematics." In S. Senk & D. Thompson (Eds.), StandardsBased School Mathematics Curricula: What Are They? What Do Students Learn? Mahwah, NJ: Lawrence Erlbaum Associates, 2003, pp. 399423.
 Burrill, J. (Ed.); and others (including J. Hirstein). Mathematics Assessment Sampler Grades 68: Items Aligned with NCTM's Principles and Standards. Reston, VA: National Council of Teachers of Mathematics, 2005.
 "Assessment and Mathematical Modelling", Sloyer, Blum & Huntley (Eds.), Advanced and Perspective in the Teaching of Mathematical Modelling and Applications, Yorklyn, DE: Water Street Mathematics, 1995, pp. 163174.
 "Classroom Vignette: An Alternative Assessment Tool", (with S. Walen), Teaching Children Mathematics, v1 n6, Feb. 1995, pp. 362365.
 "Integrated Mathematics Interfaced with Science", (with J.D. Austin, S. Walen), School Science and Mathematics, 97, 1 Jan. 1997, pp. 4549.
 "Student Assessment in the Pilot Study", Monograph 4: Assessment, The SIMMS Project, 1998, pp. 112.
 "Restructuring Mathematics Assessment: Suggestions from the Classroom", (with S. Walen), Simon & Schuster Custom Publishing, 1995.
 "Views on High School Mathematics Education", Notices of the Amer. Math. Society, 44, February 1997, 197206
 "The Mathematics Education Doctorate Requires Definition", Teaching, Learning, and Learning Teaching, Proceedings of the conference held at California State Polytechnic Univ.Pomona, (eds. J. Price and J. Jacobs). Reston, VA: NCTM, 1997
 "Curriculum Sampler: MCTM/SIMMS Integrated Mathematics: A Modeling Approach Using Technology. Simon & Schuster Custom Publishing Co., Needham Heights, MA: The Company, 1997.
 "1996 Report to the Public: The Present Reforms in Montana Mathematics and Science Education", MCTM, Missoula, MT: The Council, 1996.
 "The SIMMS Project Position Papers Monograph 2", MCTM, Montana Science Teachers Assoc., Montana Mathematics and Science Society, Missoula, MT: The Councils, 1996.
 Middle Grades MATHThematics, Book 1, 2 & 3 (with Jim Williamson), McDougal Littell Publishing Co., 2002.
 A Problem Solving Approach to Mathematics for Elementary Teachers with J. Lott and S. Libeskind, Addison Wesley Longman Publishing. Co., 2004.
 Billstein, R. and J. Williamson, "Middle Grades MATH Thematics: The STEM Project", chapter in Standardsbased Mathematics Curricula: What are they? Do They Work?, Lawrence Erlbaum Associates, 2003.
 Barrett, G and R. Billstein, G. Burrill, H. Kranendock, R, Peck, M. Shaughnessey,
Navigating through Probability in Grades 912. National Council of Teachers of
Mathematics in 2004.
 Billstein, R. "Middle Grades MATHThematics", Developments in School Mathematics Education Around the World , National Council of Teachers of Mathematics, 1999, pp. 36667.
 Lesh, Richard & Sriraman, Bharath (2005). John Dewey Revisited Pragmatism and the modelsmodeling perspective on mathematical learning. In A. Beckmann et al [Eds.], Proceedings of the 1st International Symposium on Mathematics and its Connections to the Arts and Sciences. May 1821, 2005, University of Schwaebisch Gmuend: Germany.Franzbecker Verlag, pp. 3251.
 Sriraman, Bharath. (2005) (with Guenter Toerner & Miriam Sherin] Videobased research on mathematics teaching: Research in the context of video. Proceedings of XXVII Annual meeting of the Psychology of Mathematics Education North America, Roanake, Virginia, [cdrom].
 Sriraman, Bharath & Günter Törner (2005). Beliefs about mathematics and teaching scripts from the perspective of Schoenfeld’s theory of TeachingInContext. Proceedings of XXVII Annual meeting of the Psychology of Mathematics Education North America, Roanake, Virginia, [cdrom].
 Sriraman, Bharath (2005). Videos in collegiate mathematics teaching. Proceedings of XXVII Annual meeting of the Psychology of Mathematics Education North America, Roanake, Virginia, [cdrom].
 Sriraman, Bharath. (2005) Quasiempirical Approaches to mathematics: Recreating the Lakatosian Classroom. Proceedings of XXVII Annual meeting of the Psychology of Mathematics Education North America, Roanake, Virginia, [cdrom].
 Sriraman, B. (2005). (in press) Polya revisited: The cognitive links between mathematical and analogical reasoning. Major Book Review of Lyn English (Ed). Mathematical and Analogical Reasoning of Young Learners. New Jersey: Lawrence Erlbaum & Associates, 2004, 224 pages, ISBN 0805849459. International Reviews on Mathematical Education, vol37,no.6,pp.506508.
 Sriraman, Bharath. (2005). Letter to Editor: Commentary on A first person perspective on problem solving in a History of Mathematics Course. Mathematical Thinking and Learning: An International Journal. Vol7, no.4, pp. 345348.
 Sriraman, Bharath. (2005). Extracognitive creative behaviors of gifted high school students and research mathematicians. In Developing Hearts and Minds: Proceedings of the 15th Annual meeting of the Society for the Advancement of Gifted Education (SAGE), Calgary, Canada, pp.102108.
 Sriraman, Bharath & English, Lyn. (2005) On the teaching and learning of Dienes’ Principles. International Reviews on Mathematical Education, vol. 37, no.3, pp.258262.
 Sriraman, Bharath. (2005). Demystifying the mathematicians craft: Chasing the elusive or a researchable commodity. Book Review of L. Burton (2004) Mathematicians as Enquirers [Kluwer Academic Publishers]. Mathematical Thinking & Learning: An International Journal. vol.7, no.2, pp.171180.
 MorenoArmella, L & Sriraman, Bharath (2005). Structural Stability and Dynamic Geometry: Some Ideas on Situated Proof. International Reviews on Mathematical Education. vol. 37, no.3, pp. 130139.
 Sriraman, Bharath (with C. Christou, N. Mousoulides, M. Pittalis & D. PittaPantazi) (2005). An empirical taxonomy of problem posing processes. International Reviews on Mathematical Education, vol. 37, no.3, pp.149158.
 Lyn English & Sriraman, Bharath (2005). Theories of Mathematics Education. In H. Chick & J.L. Vincent (Eds). Proceedings of the 29th Annual meeting of the International Group of Psychology of Mathematics Education, Melbourne, Australia, vol.1, pp. 170172.
 Günter Törner & Sriraman, Bharath. (2005). Issues and tendencies in German Mathematics Didactics: An epochal perspective. In H. Chick & J.L. Vincent (Eds). Proceedings of the 29th Annual meeting of the International Group of Psychology of Mathematics Education: Melbourne, Australia, vol.1, pp. 197202.
 Sriraman, Bharath. (2005). The impediments to formulating generalizations. In H. Chick & J.L. Vincent (Eds). Proceedings of the 29th Annual meeting of the International Group of Psychology of Mathematics Education: Melbourne, Australia, vol.1, pp. 280.
 Sriraman, Bharath. (2005). Problem solving as a precursor to Mathematical Proof(feature article). Mathematics in School, vol.34, no.1,pp.48.
 Sriraman, Bharath & Adrian, Harry. (2004/05) The Pedagogical Value and the Interdisciplinary Nature of Inductive Processes in Forming Generalizations. Interchange: A Quarterly Review of Education, Vol. 35, no.4, pp. 407422
 Sriraman, Bharath & Strzelecki, Pawel. (2004). Playing with powers. The International Journal for Technology in Mathematics Education, Vol 11, no.1, pp.2934.
 Sriraman, Bharath (2004). Reflective Abstraction, Uniframes and the Formulation of Generalizations. The Journal of Mathematical Behavior, vol.23, no.2, pp. 205222.
 Sriraman, B. (2004). Gifted ninth graders' notions of proof. Investigating parallels in approaches of mathematically gifted students and professional mathematicians. Journal for the Education of the Gifted, Vol. 27, no.4, pp. 267292.
 Sriraman, Bharath & Benesch, Walter (2005). Consciousness and Science: An AdvaitaVedantic perspective on the TheologyScience dialogue. Theology and Science, vol.3, no.1, pp. 3954.
 Sriraman, Bharath & English, Lyn. (2004). Combinatorial Mathematics: Research into practice. Connecting Research into Teaching. The Mathematics Teacher, vol.98,no.3,pp.182191.
 Sriraman, B. (2004). Understanding Mathematical Creativity: A Framework for Assessment in the High School Classroom. In McDougall, D.E & Ross, J.A. (Eds.). Proceedings of the twentysixth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Toronto, Canada, Vol. 1, pp. 350352.
 Sriraman, Bharath (2004). The Characteristics of Mathematical creativity. The Mathematics Educator, vol. 14, no.1, pp. 1934.
 Sriraman, Bharath (2004). Discovering Steiner Triple Systems through Problem Solving. The Mathematics Teacher, vol. 97, no. 5, pp. 320326.
 Sriraman, Bharath (2004). Reflective Abstraction, Uniframes and the Formulation of Generalizations. The Journal of Mathematical Behavior, vol.23, no.2, pp. 205222.
 Sriraman, Bharath (2004). Can problem context be an obstacle to proof? Mathematics in School (UK), vol.33, no.4, pp.25.
 Sriraman, Bharath (2004). Differentiating mathematics via use of novel combinatorial problem solving situations: A model for heterogeneous mathematics classrooms. In Contributions to E. Barbeau, H. Shin et al., TSG 4: Activities and programs for gifted students. Proceedings of the 10th International Congress of Mathematics Education, Copenhagen Denmark, pp.3538.
 Sriraman,Bharath . (2004). Recreating the Renaissance. In Contributions to M. Anaya, C. Michelsen at al., TSG21: Relations between mathematics and others subjects of art and science. Proceedings of the 10th International Congress of Mathematics Education, Copenhagen, Denmark. 6pp.
 Sriraman, Bharath . (2004). The role of affect in the process of generalization. In Contributions to P.C. Clarkson, M. Hannula et al., TSG 24: Students' motivation and attitudes towards mathematics and its study. Proceedings of the 10th International Congress of Mathematics Education, Copenhagen, Denmark, 8pp.
 Sriraman, Bharath. (2003). Mathematics and Literature: Synonyms, Antonyms or the Perfect Amalgam? The Australian Mathematics Teacher, vol. 59, No.4, pp.2631.
 Sriraman, Bharath. (2004). Discovering a Mathematical principle: The case of Matt. Mathematics in School (UK), vol.33, no.2, pp.2531.
 Sriraman, Bharath. (2004). The Influence of Platonism on Mathematics Research and Theological Beliefs. Theology and Science, vol 2, no. 1, pp. 131147.
 Sriraman, Bharath. (2004). Mathematics and Literature (the sequel): Imagination as a pathway to Advanced Mathematical Ideas and Philosophy. The Australian Mathematics Teacher, vol. 60, no.1, pp.1723
 Sriraman, Bharath & Adrian, Harry (2004). The Use of Fiction as a Didactic tool to examine Existential Problems. The Journal of Secondary Gifted Education. vol. 15, no.3, pp. 96106.
 Sriraman, Bharath (2002). How do mathematically gifted students abstract and generalize mathematical concepts. NAGC Research Briefs, Vol. 16, pp.8387.
 Sriraman, Bharath (2002). Generalization processes in combinatorial problem solving situations. Proceedings of XX1V Annual meeting of the Psychology of Mathematics EducationNorth America. Vol.3, pp.14111414.
 Sriraman, Bharath (2003). Mathematical giftedness, problem solving, and the ability to formulate generalizations. The Journal of Secondary Gifted Education, Vol. XIV,.3,, pp.151165.
 Sriraman, Bharath (2003). Can mathematical discovery fill the existential void? The use of Conjecture, Proof and Refutation in a high school classroom. Mathematics in School, (United Kingdom), No.2, pp.2  6.
 Sriraman, Bharath (2003). Discovering mathematical generalizations via problem solving. Beiträge zum Mathematikunterricht (Dortmund, 2003). Proceedings of the 37th Annual Conference of the Gesellschaft für Didaktik der Mathematik (GDM); Dortmund, Germany. pp. 613616.
 Billstein, R, J. Hirstein, and J. Lott, "A Proportion Problem Informs Teaching and Learning", Texas Mathematics Teacher, Vol. XLVIII, Issue 2, Spring 2001, pp.912.
 Billstein, R. " Development of the MATHThematics Curriculum", Perspectives on Curricular Change, Education Development Center, Newton, MA, 2001.
 "The STEM Experience: Some Things We've Learned and Their Implications for Teacher Preparation and Inservice", Mathematics Education Leadership Journal of the National Council of Supervisors of Mathematics, April, 1997, pp. 38.
 "Cleared to Land", Mathematics Teaching in the Middle School, National Council of Teachers of Mathematics
 "Assessment: The STEM Model", Mathematics Teaching in the Middle School, National Council of Teachers of Mathematics
 Billstein, Rick. "Drops Begone", Washington Mathematics, Washington State Mathematics Council, Winter 1997, pp. 15.
 Billstein, Rick. "Squeeze Across America", Montana Science and Mathematics, Montana Council of Teachers of Mathematics, Spring 1997, pp. 1721.
 Billstein, Rick. "The Hunting Game", Washington Mathematics, Washington State Mathematics Council, Spring 1997, pp. 1116.
 Billstein, Rick. "In Thin Air", The Texas Mathematics Teacher, Texas Council of Teachers of Mathematics, Spring 1997, pp. 822.
 Billstein, Rick. "The STEM Experience: Some Things We've Learned and Their Implications for Teacher Preparation and Inservice", Mathematics Education Leadership, National Council of Supervisors of Mathematics, April 1997, pp. 38.
 Lott, Johnny W. "SIMMS Integrated Mathematics: A Modeling Approach with Technology", Simon & Schuster Custom Publishing Co., 19968.
 Lott, Johnny W., Rick Billstein and James Hirstein. "A Perplexing Proportion Problem", School Science and Mathematics, in press.
 Lott, Johnny W., and Mazie Jenkins. "By Way of Introduction", Teaching Children Mathematics,.1 (February 1995): 32021.
 Hirstein, James, and Sharon Walen. "Classroom Vignette: An AlternativeAssessment Tool", Teaching Children Mathematics 1 (February 1995): 362365.
 Lott, Johnny W., and Maurice J. Burke. "Systemic Initiative for Montana Mathematics and Science", The Mathematics Teacher, 87 (September 1994): 46265.
 Billstein, R., J. Lott, and S. Libeskind A ProblemSolving Approach to Mathematics for Elementary Teachers with Benjamin/Cummings Publishing Company; 1981. Second edition, 1984. Third edition, 1987. Fourth edition, 1990. Fifth edition with AddisonWesley Publishing Company, 1993, Sixth edition with AddisonWesley Publishing Co., 1997.
 Billstein, R., and J. Lott. "Golden Rectangles and Ratios", Reprinted in Teaching with Student Math Notes, Vol. 2, edited by E. Maletsky. Reston, VA: National Council of Teachers of Mathematics, 1993, pp. 16.
 Beal, J., D. Dolan, J. Lott, and J. Smith. Integrated Mathematics: Definitions, Issues, and Implications: Report and Executive Summary. ERIC Clearinghouse for Science, Mathematics and Environmental Education. The Ohio State University, Columbus, OH: 1992, 115 pp.
 The SIMMS Project, Level 1, Vol. 14. Great Falls, MT: Montana Council of Teachers of Mathematics, 1993. (Field Test Version Partially edited by J. Lott and J. Hirstein)
 IMPACT's Window on Graphing: Levels 1 and 2 by Anderson, Billstein, et al, Sunburst Communications, 1991.
 Billstein, R. and Lott, J. "Once Upon a Time", Student Math Notes, National Council of Teachers of Mathematics, March 1991.
 Billstein, R. and Lott, J. "On the Mathematical Preparation of Elementary Teachers", Arithmetic Teacher, Vol. 39, No. 3, November 1991.
 Hirstein, James. "Assessment and Mathematical Modelling" in Advances and Perspectives in the Teaching of Mathematical Modelling and Applications, papers from the Sixth International Conference on Teaching Mathematics and its Applications (in press).

