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**Feedback **is defined as information about the gap between the actual level and the reference level of a system parameter which is used to alter the gap in some way (Ramaprasad, 1983). This is compared to *feed out* where the gap in student learning is simply measured with no specific intention to address any learning needs.

**Formative assessment **is linked with feedback practices that are concerned with closing any gap in learning.

**Summative assessment **is linked with the idea of feed out where the gap in student learning is simply measured with no specific intention to address any learning needs.

(Trenholm, Alcock, Robinson, 2015)"Despite its stated potential, the possible effects of feedback on learning should not be oversimplified as wide variability has been reported, with some feedback found to produce no or debilitating effects." |

Trenholm, Alcock, and Robinson (2015) reviewed the literature on feedback in assessment and found the following:

**Feedback Timing:**

The greater the need for students to process the material to gain understanding, the more they may benefit from delayed feedback. (Kluger & DeNisi, 1996)

The benefit of immediate feedback may be limited to lower level 'procedural skills' and providing motivation (Shute, 2008).

Higher mathematics achievement and improvements in the quality of teacher and student discourse may be associated with average feedback timing between 3 to 5 seconds (Tobin, 1986).

Simmons and Cope (1993) found that immediate feedback inhibits moves to high order thinking by enabling procedural to the detriment of conceptual, knowledge, and understanding.

However, others have claimed that immediate feedback is linked with gaining a thorough understanding of mathematics (Zerr, 2007) and may increase grade performance (Butler et al., 2008).

**Types of Feedback:**

The poorest kind of feedback is related to solely consisting of a grade or mark. However, it is widely found and least beneficial to student learning (van der Kleij et al., 2012).

The most beneficial feedback is hints and comments directed at the learning process. This feedback is directed at the learning task and the development of student understanding (Entwistle, 2009).

An intermediate level of feedback consists of providing the correct answer or a full solution.

**Feedback practices in online mathematics:**

More research is required for online feedback practices in mathematics.

It is vital for directing student learning and mediating online courses where students and instructors are separated in both space and time.

Good feedback is considered as a means to stimulate or maintain interactions (Gikandi et al., 2011)

It can keep students engaged with the process of learning (Semião, 2009).

**Online Assessment Practices:**

Tests and quizzes represent the largest portion of a student's final grade and in some cases the only form of assessment (Galante, 2002).

There is a growing body of literature on the use of different formative instruments such as peer assessment, group work or projects, discussion, and journal writing.

Online mathematics courses use tests and question pools more than other disciplines (Smith et al, 2008).

Replacing a traditional summative assessment with a formative style assessment may not be related to improving student learning (Trenholm, 2007).

There is little evidence that there is much if any feedback in online mathematics practices. Feedback tends to fulfill a formative assessment role (Trenholm et al., 2015).

Immediate feedback within assessments may only benefit lower procedural levels of learning (Trenholm et al., 2015).

With evidence of learning generally limited to only a single answer, and not steps, may reinforce incorrect interpretations, trial-and-error, or strategies with no underlying mathematical understanding (Trenholm et al., 2015).

**References**

Butler M., Pyzdrowski L., Goodykoontz A., Walker V. (2008). The effects of feedback on online quizzes. *International Journal of Technology in Mathematics Education*. 15(4), 131–136.

Entwistle N. (2009). *Teaching for understanding at university. Deep approaches and distinctive ways of thinking*. Basingstoke: Palgrave Macmillan.

Galante, D. (2002). *Web-based mathematics: an examination of assessment strategies implemented in the online mathematics classroom* [Doctoral dissertation, Illinois State University].

Gikandi, J.W,, Morrow D., Davis, N.E. (2011). Online formative assessment in higher education: a review of the literature. *Journal of Computer Education*. 57(4), 2333–2351.

Kluger AN, DeNisi A. (1996). Effects of feedback intervention on performance: a historical review, a meta-analysis, and a preliminary feedback intervention theory. *Psychological Bulletin Journal*. 119(2), 254–284.

Ramaprasad A. (1983). On the definition of feedback. *Journal of Behavioral Science*. 28(1), 4–13.

Semião, P. (2009). Strategies for a web-based mathematics course. In Méndez-Vilas, A., Solano Martín, A., Mesa González, J.A,. Mesa González, J. (Eds.), *Research, reflections and innovations in integrating ICT in education*. 436-439. Badajoz: Formatex.

Shute VJ (2008). Focus on formative feedback. *Review of Educational Research*. 78(1), 153–189.

Simmons M, Cope P. (1993). Angle and rotation: effects of different types of feedback on the quality of response. *Educational Studies in Mathematics*. 24(2), 163–176.

Smith, G.G., Heindel, A.J., Torres-Ayala, A.T. (2008). E-learning commodity or community: disciplinary differences between online courses. *The **Internet and Higher Education Journal*. 11(3–4), 152–159.

Tobin K (1986). Effects of teacher wait time on discourse characteristics in mathematics and language arts classes. *American Educational Research Journal. *23(2), 191–200.

Trenholm, S. (2007). A review of cheating in fully asynchronous online courses: A math or fact-based course perspective. *Journal of Educational Technology Systems*. 35(3), 281–300.

Trenholm, S., Alcock, L., & Robinson, C. (2015). An investigation of assessment and feedback practices in fully asynchronous online undergraduate mathematics courses. *International Journal of Mathematical Education in Science and Technology*, 46(8), 1197–1221.

van der Kleij, F.M., Theo, J.H.M., Timmers, C.F., Veldkamp, B.P. (2012).Effects of feedback in a computer-based assessment for learning. *Jounarl of **Computer Education*. 58(1):, 263–272.

Zerr R. (2007). A quantitative and qualitative analysis of the effectiveness of online homework in first-semester calculus. *Journal of Computers in Mathematics and Science Teaching*. 26(1), 55–73.

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