An investigation of assessment and feedback practices in fully asynchronous online undergraduate mathematics courses

References

• Bakia M, Shear L, Toyama Y, Lasseter A. Understanding the implications of online learning for educational productivity. Washington, DC: U.S. Department of Education Office of Educational Technology Center for Technology in Learning; 2012.
   Google Scholar
• Miller B. The course of innovation: using technology to transform higher education. Washington, DC: Education Sector; 2010.
   Google Scholar
• Campbell M. Online schooling is exploding in US. New Sci. 2012;215(2881):6–8.
   Web of Science ®Google Scholar
• Allen IE, Seaman J. Going the distance: online education in the United States, 2011. Newburyport, MA: The Sloan Consortium; 2011.
   Google Scholar
• Selden A. New developments and trends in tertiary mathematics education: or, more of the same? Int J Math Educ Sci Technol. 2005;36(2):131–147.
   Google Scholar
• Maltempi MV, Malheiros APS. Online distance mathematics education in brazil: research, practice and policy. ZDM. 2010;42(3):291–303.
   Google Scholar
• Zinger VA. Challenges and rewards of distance education in Alaska: experience in teaching web-based courses in mathematics in Alaska. In: Uskov V, editor. Proceedings of the 5th IASTED International Conference on Web-Based Education; 2006 January 23–25; Puerto Vallarta. Anaheim, CA: ACTA Press. p. 361–364.
   Google Scholar
• Engelbrecht J, Harding A. Teaching undergraduate mathematics on the internet: part II. Educ Stud Math. 2005;58(2):253–276.
   Google Scholar
• Sumler DE. Distance learning in Maryland colleges and universities, academic year 2000. Annapolis, MD: Maryland State Higher Education Commission; 2001.
   Google Scholar
• Kirkman E. Statistical abstract of undergraduate programs in the mathematical sciences in the United States: fall 2010 conference board of mathematical sciences (CBMS) survey. Providence, RI: American Mathematical Society; 2012.
   Google Scholar
• Glass J, Sue V. Student preferences, satisfaction, and perceived learning in an online mathematics class. J Online Learn Teach. 2008;4(3):325–338.
   Google Scholar
• Lokken F. 2010 distance education survey results – trends in e-learning: tracking the impact of e-learning at community colleges. Washington, DC: Instructional Technology Council; 2011.
   Google Scholar
• Philip D. Internet-based tools for mathematics learning: making math add up on the internet in learning technology innovation in Canada. A supplement to the journal of distance education. J Distance Educ. 2003;17(3):38–39.
   Google Scholar
• Smith GG, Ferguson D, Caris M. The web versus the classroom: instructor experiences in discussion-based and mathematics-based disciplines. J Educ Comput Res. 2003;29(1):29–59.
   Google Scholar
• Smith GG, Ferguson D. Student attrition in mathematics e-learning. Australas J Educ Technol. 2005;21(3):323–334.
   Google Scholar
• Bernard RM, Abrami PC, Lou Y, Borokhovski E, Wade A, Wozney L, Huang B. How does distance education compare with classroom instruction? A meta-analysis of the empirical literature. Rev Educ Res. 2004;74(3):379–439.
   Web of Science ®Google Scholar
• Shachar M, Neumann Y. Twenty years of research on the academic performance differences between traditional and distance learning: summative meta-analysis and trend examination. J Online Learn Teach. 2010;6(2):318–334.
   Google Scholar
• Zhao Y, Lei J, Yan B, Lai C, Tan S. What makes the difference? A practical analysis of research on the effectiveness of distance education. Teach Coll Rec. 2005;107(8):1836–1884.
   Web of Science ®Google Scholar
• Davis L, Harrison M, Palipana A, Ward J. Assessment-driven learning of mathematics for engineering students. Int J Electr Eng Educ. 2005;42(1):63–72.
   Web of Science ®Google Scholar
• Houston K. Assessing undergraduate mathematics students. In: Holton D, editor. The teaching and learning of mathematics at university level: an ICMI study. Dordrecht, The Netherlands: Kluwer Academic Publishers; 2002. p. 407–422.
   Google Scholar
• Marriott P, Lau A. The use of on-line summative assessment in an undergraduate financial accounting course. J Account Educ. 2008;26(2):73–90.
   Google Scholar
• Smith G, Wood L. Assessment of learning in university mathematics. Int J Math Educ Sci Technol. 2000;31(1):125–132.
   Google Scholar
• Biggs J, Tang C. Teaching for quality learning at university. 3rd ed. Maidenhead: Open University Press; 2007.
   Google Scholar
• Ramsden P. Learning to teach in higher education. 2nd ed. London: RoutledgeFalmer; 2003.
   Google Scholar
• Hattie J, Timperley H. The power of feedback. Rev Educ Res. 2007;77(1):81–112.
   Web of Science ®Google Scholar
• Taras M. Assessment summative and formative: some theoretical reflections. Brit J Educ Stud. 2005;55(4):466–478.
   Web of Science ®Google Scholar
• Ramaprasad A. On the definition of feedback. Behav Sci. 1983;28(1):4–13.
   Google Scholar
• Sadler DR. Formative assessment: revisiting the territory. Assess Educ Princ Policy Pract. 1998;5(1):77–84.
   Google Scholar
• Knight PT. Summative assessment in higher education: practices in disarray. Stud High Educ. 2002;27(3):275–286.
   Web of Science ®Google Scholar
• Kluger AN, DeNisi A. Effects of feedback intervention on performance: a historical review, a meta-analysis, and a preliminary feedback intervention theory. Psychol Bull. 1996;119(2):254–284.
   Web of Science ®Google Scholar
• Goodman JS, Wood RE, Hendrickx M. Feedback specificity, exploration, and learning. J Appl Psychol. 2004;89(2):248–262.
   PubMed Web of Science ®Google Scholar
• Butler DL, Winne PH. Feedback and self-regulated learning: a theoretical synthesis. Rev Educ Res. 1995;65(3):245–281.
   Web of Science ®Google Scholar
• Entwistle N. Concepts and conceptual frameworks underpinning the ETL project. Edinburgh: Enhancing Teaching-Learning Environments in Undergraduate Courses, Higher and Community Education, School of Education, University of Edinburgh; 2003. (Occassional Report No. 3).
   Google Scholar
• Shute VJ. Focus on formative feedback. Rev Educ Res. 2008;78(1):153–189.
   Web of Science ®Google Scholar
• Tobin K. Effects of teacher wait time on discourse characteristics in mathematics and language arts classes. Am Educ Res J. 1986;23(2):191–200.
   Web of Science ®Google Scholar
• Simmons M, Cope P. Angle and rotation: effects of different types of feedback on the quality of response. Educ Stud Math. 1993;24(2):163–176.
   Google Scholar
• Zerr R. A quantitative and qualitative analysis of the effectiveness of online homework in first-semester calculus. J Comput Math Sci Teach. 2007;26(1):55–73.
   Google Scholar
• Butler M, Pyzdrowski L, Goodykoontz A, Walker V. The effects of feedback on online quizzes. Int J Technol Math Educ. 2008;15(4):131–136.
   Google Scholar
• Trigwell K, Prosser M, Waterhouse F. Relations between teachers' approaches to teaching and students' approaches to learning. High Educ. 1999;37(1):57–70.
   Web of Science ®Google Scholar
• Moreno R. Decreasing cognitive load for novice students: effects of explanatory versus corrective feedback in discovery-based multimedia. Instr Sci 2004;32(1):99–113.
   Web of Science ®Google Scholar
• Laurillard D. Rethinking university teaching: a conversational framework for the effective use of learning technologies. 2nd ed. London: RoutledgeFalmer; 2002.
   Google Scholar
• Merrill DC, Reiser BJ, Ranney M, Trafton JG. Effective tutoring techniques: a comparison of human tutors and intelligent tutoring systems. J Learn Sci. 1992;2(3):277–305.
   Google Scholar
• Taras M. Using assessment for learning and learning from assessment. Assess Eval High Educ. 2002;27(6):501–510.
   Google Scholar
• van der Kleij FM, Theo JHM, Timmers CF, Veldkamp BP. Effects of feedback in a computer-based assessment for learning. Comput Educ. 2012;58(1):263–272. doi: 10.1016/j.compedu.2011.07.020.
   Web of Science ®Google Scholar
• Kvale S. Contradictions of assessment for learning in institutions of higher learning. In: Boud D, Falchikov N, editors. Rethinking assessment in higher education: learning for the longer term. 1st ed. Oxford: Taylor & Francis; 2007. p. 57–71.
   Google Scholar
• Sadler DR. Formative assessment and the design of instructional systems. Instr Sci. 1989;18(2):119–144.
   Web of Science ®Google Scholar
• Entwistle N. Teaching for understanding at university. Deep approaches and distinctive ways of thinking. Basingstoke: Palgrave Macmillan; 2009.
   Google Scholar
• Ramsden P. Improving learning: new perspectives. London: Kogan Page; 1988.
   Google Scholar
• Anderson TD, Garrison DR. Critical thinking in distance education: developing critical communities in an audio teleconference context. High Educ. 1995;29(2):183–199.
   Web of Science ®Google Scholar
• Roper W. Feedback in computer assisted instruction. Program Learn Educ Technol. 1977;14(1):43–49.
   Web of Science ®Google Scholar
• Singh R, Saleem M, Pradhan P, Heffernan C, Heffernan N, Razzaq L, Mulcahy C. Feedback during web-based homework: the role of hints. Artif Intell Educ Lect Notes Comput Sci. 2011;6738(2011):328–336.
   Google Scholar
• Baker S, Gersten R, Lee DS. A synthesis of empirical research on teaching mathematics to low-achieving students. Elem Sch J. 2002;103(1):51–73.
   Web of Science ®Google Scholar
• Arend BD. Course assessment practices and student learning strategies in online courses. J Asynchronous Learn Netw. 2007;11(4):3–13.
   Google Scholar
• Gaytan J, McEwen BC. Effective online instructional and assessment strategies. Am J Distance Educ. 2007;21(3):117–132.
   Google Scholar
• Liang X, Creasy K. Classroom assessment in web-based instructional environment: instructors' experience. Pract Assess Res Eval. 2004 [cited 2012 Dec5];9(7). Available from: http://PAREonline.net/getvn.asp?v = 9&n = 7.
   Google Scholar
• Robles M, Braathen S. Online assessment techniques. Delta Pi Epsil J. 2002;44(1):39–49.
   Google Scholar
• Walker DJ. Principles of good online assessment design. In: Nichol D, editor. From the Re-Engineering Assessment Practices in Scottish Higher Education (REAP) International Online Conference on Assessment Design for Learner Responsibility, 2007 May 29–31. Glasgow, Scotland: University of Strathclyde. p. 1–6.
   Google Scholar
• Anderson T. Towards a theory of online learning. In: Anderson T, Elloumi F, editors. Theory and practice of online learning. Athabasca: Athabasca University; 2008. p. 45–74.
   Google Scholar
• Jarmon C. Testing and assessment at a distance. In: Boaz M, Elliott B, Foshee D, Hardy D, Jarmon C, Olcott Jr D, editors. Teaching at a distance: a handbook for instructors. Los Angeles, CA: League for Innovation in the Community College, a Division of Harcourt Brace & Company; 1999. p. 55–65.
   Google Scholar
• Gikandi JW, Morrow D, Davis NE. Online formative assessment in higher education: a review of the literature. Comput Educ. 2011;57(4):2333–2351.
   Web of Science ®Google Scholar
• Shuey S. Assessing online learning in higher education. J Instr Deliv Syst. 2002;16(2):13–18.
   Google Scholar
• Speer NM, Smith III JP, Horvath A. Collegiate mathematics teaching: an unexamined practice. J Math Behav. 2010;29(2):99–114. doi: 10.1016/j.jmathb.2010.02.001
   Google Scholar
• Iannone P, Simpson A. The summative assessment diet: how we assess in mathematics degrees. Teach Math Appl. 2011;30(4):186–196.
   Google Scholar
• Ross SC. What happened to tests? Assessment practices in undergraduate mathematics. MAA Notes. 1999;49:77–79.
   Google Scholar
• Solomon Y. Not belonging? What makes a functional learner identity in undergraduate mathematics? Stud High Educ. 2007;32(1):79–96.
   Web of Science ®Google Scholar
• Wood LN, Smith GH. Flexible assessment. In: Spunde W, Cretchley P, Hubbard R, editors. The challenge of diversity. Laguna Quays, AU: University of Southern Queensland Press; 1999. p. 229–233.
   Google Scholar
• Trenholm S. An investigation of assessment in fully asynchronous online math courses. Int J Educ Integ. 2007;3(2):41–55.
   Google Scholar
• Evia GB. Distance learning today. In: Proceedings of the International Congress of Mathematicians; Madrid, Spain; 2006. p. 1752–1757.
   Google Scholar
• Sakshaug LE. Research on distance education: implications for learning mathematics. Focus Learn Prob Math. 2000;22(3/4):111–124.
   Google Scholar
• Lingefjärd T, Holmquist M. Mathematics, technology and examination in distance education: working group 2. European research in mathematics education II. Mariánské Lázně: 2002. p. 193–202.
   Google Scholar
• Comeaux P. Assessing online learning. Bolton, MA: Anker Publishing; 2005.
   Google Scholar
• Austin G. A review of: ‘Assessing online learning’. Community Coll J Res Pract. 2007;31(1):79–81.
   Google Scholar
• Semião P. Strategies for a web-based mathematics course. In: Méndez-Vilas A, Solano Martín A, Mesa González JA, Mesa González J, editors. Research, reflections and innovations in integrating ICT in education. Badajoz: Formatex; 2009. p. 436–439
   Google Scholar
• Mandernach BJ, Gonzales R, Garrett AL. An examination of online instructor presence via threaded discussion participation. J Online Learn Teach. 2006;2(4):248–260.
   Google Scholar
• Swan K. Learning effectiveness online: What the research tells us. In: Bourne J, Moore JC, editors. Elements of quality online education, practice and direction. Needham, MA: Sloan Center for Online Education; 2003. p. 13–45.
   Google Scholar
• Trenholm S. A review of cheating in fully asynchronous online courses: A math or fact-based course perspective. J Educ Tech Syst. 2007;35(3):281–300.
   Google Scholar
• Boud D. Assessment and the promotion of academic values. Stud High Educ. 1990;15(1):101–111.
   Web of Science ®Google Scholar
• Wormald BW, Schoeman S, Somasunderam A, Penn, M. Assessment drives learning: an unavoidable truth? Anat Sci Educ. 2009;2(5):199–204.
   PubMed Web of Science ®Google Scholar
• Allen GD. A survey of online mathematics course basics. Coll Math J. 2003;34(4):270–279.
   Google Scholar
• Gadanidis G, Graham L, McDougall D, Roulet G. On-line mathematics: visions and opportunities, issues and challenges, and recommendations. White paper based on the Fields Institute for Research in Mathematical Sciences Mathematics Online Working Meeting. Toronto: Fields Institute; 2002.
   Google Scholar
• Everson MG, Garfield J. An innovative approach to teaching online statistics courses. Technol Innov Stat Educ. 2008;2(1):1–18.
   Google Scholar
• Pomper M. Building community in an online upper-division mathematics course. Int J Instr Technol Dist Learn. 2007;4(12):45–61.
   Google Scholar
• Tsvigu C, Breiteig T, Persens J, Ndalichako J. Promoting the learning of mathematics: on the use of learning styles in a distance education calculus course. In: Holtman L, Julie C, Mikalsen O, Mtetwa D, Ogunniyi M, editors. Some developments in research in science and mathematics in sub-Saharan Africa: access, relevance, learning, curriculum research. Somerset West: African Minds; 2008. p. 133–156.
   Google Scholar
• Galante D. Web-based mathematics: an examination of assessment strategies implemented in the online mathematics classroom [ PhD dissertation]. Normal, IL: Illinois State University; 2002.
   Google Scholar
• Smith GG, Heindel AJ, Torres-Ayala AT. E-learning commodity or community: disciplinary differences between online courses. Internet High Educ. 2008;11(3–4):152–159.
   Web of Science ®Google Scholar
• Greenberg W, Williams M. New pedagogical models for instruction in mathematics. In: Konaté D, editor. Mathematical modeling, simulation, visualization and e-learning: proceedings of an International Workshop Held at Rockefeller Foundation's Bellagio Conference Center; 2008 November 20–26; Milan, Italy. Berlin, Germany: Springer-Verlag; p. 361–371.
   Google Scholar
• Lowe T, Hasson R. Assessment for learning: using moodle quizzes in mathematics. In: Green D, editor. CETL-MSOR Conference 2010 September 6–7; University of Birmingham, Birmingham, UK. Birmingham (UK): Maths, Stats & OR Network; 2011. p. 39–45.
   Google Scholar
• Varsavsky C. Can online weekly quizzes contribute to learning in mathematics? In: Yang W-C, Chu S-C, de Alwis T, Ang K-C, editors. Proceedings of the 9th Asian Technology Conference in Mathematics: Technology in Mathematics; 2004; Singapore: ATCM; p. 161–168.
   Google Scholar
• Griffin F, Gudlaugsdottir S. Using online randomised quizzes to boost student performance in mathematics and operations research. Proceedings of the 7th International Conference on Information Technology Based Higher Education and Training, ITHET 2006; Sydney; 2006. p. 21–29.
   Google Scholar
• Pitcher N, Goldfinch J, Beevers C. Aspects of computer-based assessment in mathematics. Active Learn High Educ. 2002;3(2):159–176.
   Google Scholar
• Paterson JS. Linking on-line assessment in mathematics to cognitive skills. In: Danson M, editor. Proceedings of the 6th International CAA Conference; 2002 July 4–5. Loughborough (UK): Loughborough University. p. 295–304.
   Google Scholar
• Morrison GR, Ross SM, Gopalakrishnan M, Casey J. The effects of feedback and incentives on achievement in computer-based instruction. Contemp Educ Psychol. 1995;20(1):32–50. doi: 10.1006/ceps.1995.1002.
   Web of Science ®Google Scholar
• Hrastinski S, Stenbom S. Student–student online coaching: Conceptualizing an emerging learning activity. Internet High Educ. 2013;16:66–69.
   Web of Science ®Google Scholar
• Skemp RR. Relational understanding and instrumental understanding. Math Teach. 1976;77:20–26.
   Google Scholar
• Dubinsky E. Reflective abstraction in advanced mathematical thinking. Adv Math Think. 1991;11(2):95–126.
   Google Scholar
• Sangwin C, Cazes C, Lee A, Wong KL. Micro-level automatic assessment supported by digital technologies. In: Hoyles C, Lagrange JB, editors. Mathematics education and technology-rethinking the terrain. New York: Springer; 2010. p. 227–250.
   Google Scholar
• Mascuilli AB. Comparing an online course to its classroom counterpart. Int J Instr Technol Dist Learn. 2004;1(5):29–31.
   Google Scholar
• Smith GG, Torres-Ayala AT, Heindel AJ. Disciplinary differences in E-learning instructional design. J Dist Educ. 2008;22(3):63–88.
   Google Scholar
• Flesch M, Ostler E. An analysis of how proctoring exams in online mathematics offerings affects student learning and course integrity. Int J Math Teach Learn. 2011 [cited 2012 Feb 5]. Available from: http://www.cimt.plymouth.ac.uk/journal/flesch.pdf
   Google Scholar
• Yates RW, Beaudrie B. The impact of online assessment on grades in community college distance education mathematics courses. Am J Dist Educ. 2009;23(2):62–70.
   Google Scholar
• Englander F, Fask A, Wang Z. Comment on ‘The impact of online assessment on grades in community college distance education mathematics courses’ by Ronald W. Yates and Brian Beaudrie. Am J Dist Educ. 2011;25(2):114–120.
   Google Scholar
• Trenholm S. Adaptation of tertiary mathematics instruction to the virtual medium: Approaches to assessment practice. Unpublished PhD. East Midlands (UK): Loughborough University; 2013 [cited 2015 Apr 17]. Available from: https://dspace.lboro.ac.uk/2134/12561
   Google Scholar
• Trenholm S, Alcock L, Robinson CL. Assessment and feedback in fully online tertiary mathematics: The instructor perspective. J Rese Math Educ. (Forthcoming).
   Google Scholar
• Trigwell K, Prosser M. Development and use of the approaches to teaching inventory. Educ Psychol Rev. 2004;16(4):409–424.
   Web of Science ®Google Scholar
• Prosser M, Trigwell K. Confirmatory factor analysis of the approaches to teaching inventory. Br J Educ Psychol. 2006;76(2):405–419.
   PubMed Web of Science ®Google Scholar
• Stes A, De Maeyer S, Van Petegem P. Approaches to teaching in higher education: validation of a Dutch version of the approaches to teaching inventory. Learn Environ Res. 2010;13:59–73.
   Google Scholar
• Juan AA, Huertas MA, Trenholm S, Steegmann C. Teaching mathematics online: emergent technologies and methodologies. Hershey, PA: IGI Global; 2011.
   Google Scholar
• Radford AW. Learning at a distance: undergraduate enrollment in distance education courses and degree programs. Washington, DC: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics; 2011. ( NCES Report No. 2012–154).
   Google Scholar
• Evans JR, Mathur A. The value of online surveys. Internet Res. 2005;15(2):195–219.
   Web of Science ®Google Scholar
• Duda MD, Nobile JL. The fallacy of online surveys: No data are better than bad data. Hum Dimens Wildl. 2010;15(1):55–64.
   Google Scholar
• Burn RP, Appleby JC, Maher P. Teaching undergraduate mathematics. London: Imperial College Press; 1998.
   Google Scholar
• Engelbrecht J, Harding A. Teaching undergraduate mathematics on the internet: part I. Educ Stud Math. 2005;58(2):235–252.
   Google Scholar
• Brookhart SM. Assessment theory for college classrooms. New Direct Teach Learn. 2004;100:5–14. doi: 10.1002/tl.165
   Google Scholar
• Yorke M. Formative assessment in higher education: moves towards theory and the enhancement of pedagogic practice. High Educ. 2003;45(4):477–501.
   Web of Science ®Google Scholar
• Havnes A, Smith K, Dysthe O, Ludvigsen K. Formative assessment and feedback: making learning visible. Stud Educ Eval. 2012;38(1):21–27. doi: 10.1016/j.stueduc.2012.04.001
   Google Scholar
• Kirkman E, Lutzer KJ, Maxwell JW, Rodi SB. Statistical abstract of undergraduate programs in the mathematical sciences in the united states: fall 2005 conference board of mathematical sciences (CBMS) survey. Providence, RI: American Mathematical Society; 2007.
   Google Scholar
• Finnegan C, Morris LV, Lee K. Differences by course discipline on student behavior, persistence, and achievement in online courses of undergraduate general education. J Coll Stud Retent Res Theory Pract. 2009;10(1):39–54.
   Google Scholar
• Illowsky BS. Effects of discussion postings in online elementary statistics community college classes [ PhD dissertation]. Minneapolis, MN: Capella University; 2007.
   Google Scholar
• Lowrie T, Jorgensen R. Teaching mathematics remotely: changed practices in distance education. Math Educ Res J. 2012;24(3):371–383.
   Google Scholar
• Anderson T, Elloumi F. The theory and practice of online learning. Alberta: AU Press; 2008.
   Google Scholar
• Moore MG. The theory of transactional distance. In: Moore MG, Anderson WG, editors. Handbook of distance education. 2nd ed. Mahwah (NJ): Lawrence Erlbaum; 2007. p. 89–104.
   Google Scholar
• Larreamendy-Joerns J, Leinhardt G, Corredor J. Six online statistics courses: examination and review. Am Stat. 2005;59(3):240–251.
   Web of Science ®Google Scholar
• Brown S, Knight P. Assessing learners in higher education. London: Kogan Page Ltd; 1994.
   Google Scholar
• Gill M, Greenhow M. How effective is feedback in computer‐aided assessments? Learn Media Technol. 2008;33(3):207–220.
   Web of Science ®Google Scholar