TEACHERS' FEEDBACK STRATEGIES IN STUDENTS' MATHEMATICAL
THEORITICAL FRAMEWORK
Feedback is a process, which helps to modify and improve the succeeding action based on the outcome of a current action. In this study, feedback means teachers’ feedback to their students based on their educational activities.
Teachers' feedback needs to use to empower students as self-regulated learners and high performer/achiever (Nicol &
Macfarlane-Dick, 2006). Feedback is also an integral part of instructional activities, which is necessary for students to be aware of status of their learning. Furthermore, feedback needs to be timely and specific to the criteria, corrective nature and include suggestions for ways to improve future performance (CERI, 2008). Similarly, Banerjee (2014) found in her research study that teachers’ feedback is one of the key turning points in effecting students’ learning. Therefore, the quality of feedback is a mainstay of students’ learning progression. In context of Nepal, National Early Grade Reading Program 2014/15-2019/20 (2014) clearly states that the teachers’ feedback (remedial support) will be made available to students lagging behind in meeting minimum learning competency.
Teachers' feedback is a powerful component of ongoing assessment, which de/motivates the learners to learn progressively. It may be very powerful if carried out well. The power of formative feedback lies in its double-barrelled approach, addressing both cognitive and motivational factor at the same time (Brookhart, 2008). Teachers' feedback should be informative so the students get opportunities to know their status of learning as well as what to do next learn.
According to Gilbert (1978) the improper guidance and feedback is the single largest contributors to incompetence in the world of work, and a principal culprit at school (as cited in Banerjee, 2014). So, the way to guide and provide feedback properly may be challenging for every teacher and stakeholder of education. The effective feedback of ongoing assessment may vary in feedback strategies; time of feedback, amount of feedback, mode of feedback, and audience of feedback (Brookhart, 2008). Not every feedback may be effective for a particular action.
Therefore, there should be an effective connection between action of learners and teachers' feedback. The researcher only examined the significant differences of two strategies of teachers' feedback; audiences of teachers' feedback and modalities of teachers' feedback in the study.
The researcher used Carol Ann Tomlinson's Differentiated Classroom Instruction and Assessment: Philosophy of Differentiation and Lev Vygotsky's Sociocultural Learning Theory: Zone of Proximal Development (ZPD) as the theoretical frame of the study. Tomlinson (1999) states that the philosophy of differentiation in classroom instruction provides multiple approaches to content, process and product based on students' needs and interests. Furthermore, the content, process and product means the input or what students learn, how students go about making sense of ideas/information and output or outcomes respectively (Tomlinson, 2001).
Vygotsky's ZPD shows that there is distance between what a student does alone and with the help of others in their learning (Vygotsky, 1978). Learners have some expectation of remedial support from senior or capable peer to choose the right way in the span of their learning improvement. In such condition, the support from teachers or capable peer has significant influences in students' learning achievement which is called scaffolding in ZPD. According to Wood et al. (1967), the scaffolding provided by an expert or adult “enables a child or novice to solve a problem, to carry out a task or to achieve a goal, which would be beyond his unassisted efforts" (as cited in Khaliliaqdam, 2014). The Zone of Proximal Development (ZPD) is the area where learning takes place through a process of scaffolding and Scaffolding occurs when the more expert provides support through a process of interaction (Heritage, 2010) and in addition, the teacher’s scaffolding helped students to engage creatively and independently with mathematical tasks (Goos, 1999).
METHOD OF STUDY
This research study followed survey research design for both primary and secondary data. Creswell (2012) states that the survey research provides a quantitative or numeric description of trends, attitudes, or opinions of a population by studying a sample of the entire population. The researcher collected the required information by administrating contingency questionnaire to the sample students and their answers that creates the data to be analyzed (Fowler, 2009).
How can we select the appropriate sample for the study? Which sample size is suitable for the research? These are the common questions in case of research. Cohen, Manion, and Morrison (2011) state that there is no clear-cut answer for the correct sample size, which depends on the purpose of study and the nature of the population under scrutiny. The researcher took 232 number of sample students by using Yamane (1967), 1 where, n= required sample size, N= total population size, acceptable sampling error (as cited in Polonia 2013, p.8). The determination of sample size and procedure for sample selection, the researcher based on sampling frames designed by Ross (2000) for designing the national sample for data collection. The sampling frame suggested selecting at least 20 students from each sample school for the research. Therefore, the researcher followed Ross’s sampling guideline and selected 232 students’
samples because all schools have above 25 students in grade 8 (District Education Office [DEO], 2014). Furthermore, the researcher used contingency questionnaire as a research tool with the value of Cronbach's Alpha 0.74, which is optimal (Singh, 2007).
TEACHERS' FEEDBACK STRATEGIES AND STUDENTS' ACHIEVEMENT
The researcher examined the significant difference of teachers' feedback strategies (i.e. Audiences: individual, group and Modalities: written, oral, demonstration) on mathematics learning process (i.e. classwork, homework, project work and tests) and students' achievement in mathematics.
Audience of Teachers' Feedback and Students' Achievement
The researcher studied the significant differences between audience of teachers' feedback of formative assessment and students' achievement. Furthermore, he examined the significant difference of audiences (i.e. individual and group/class) of teachers' feedback on four forms of formative assessment in students' achievement in mathematics.
Table 1. Feedback in Classwork and Students' Achievement
Audience of feedback Achievements' Score
Category N Mean SD CV Sig.
Individual 120 38.78 10.91 28.13
.929
Group/Class 96 38.65 11.58 29.96
(Field Survey, 2015) The mean difference between two groups of students is in point (0.13). Standard Deviation shows that the scores in mathematics obtained by students are not widely dispersed on the basis of audience of teachers' feedback. The first group (who received teachers' feedback most of the time in individually on the classwork) of students' achievement was found higher than second group (who received teachers' feedback most of the time in group/class on the classwork) of students. The Coefficient of Variance also shows that the achievement score of first group was more consistent than that of their counterparts. While testing the hypothesis or significant test of the differences, the researcher employed independent sample t–test because the audience of feedback of classwork has two independent variables; individual and group/class. According to t–test, there was no significant difference between audience of teachers' feedback on students and students' achievement at p=0.05 < 0.929. The finding shows that there is equivalent strength of teachers' feedback on students whether it is provided individually or in group/class.
Table 2. Feedback in Homework and Students' Achievement
Audience of Feedback Achievements' Score
Category N Mean SD CV Sig.
Individual 75 39.36 12.56 31.91
.310
Group/Class 127 37.72 10.12 26.83
(Field Survey, 2015) The average achievement score of the students who received teachers' feedback individually on their homework frequently is higher than that of those students' who received feedback in group/class. However, the Coefficient of Variance shows that the achievement score of the students who received teachers' feedback in group/class was found more stable than that of their counterparts. By testing the significant differences between mean scores of two groups through independent sample t-test, the researcher found that there is no significant difference between audience of teachers' feedback based on homework and students' achievement in mathematics at p=0.05 < 0.31. The finding also shows that there is equivalent strength of teachers' feedback whether it is provided to individual student or to the group/class on their achievement in mathematics.
Table 3. Feedback in Project work and Students' Achievement
Audience of Feedback Achievements' Score
Category N Mean SD CV Sig.
Individual 27 36.67 8.87 24.19
.176
Group/Class 95 40.38 13.35 33.06
(Field Survey, 2015)
Comparing achievement scores, the second group of students who received teachers' feedback in group/class frequency is higher than the first group of the students who got feedback individually. SD values shows that the achievement scores of second group of students are widely deviated from the mean score than the achievement scores of first group. According to the Coefficient of Variance, the result shows that the first group of students who received teachers' feedback individually on their project work is highly reliable than the second group of students. According to the independent sample t-test, the value of p was found 0.176 with 0.05 level of significance. According to the p value,
the alternative hypothesis "there is significant difference between teachers' feedback based on students' project work and the achievement of mathematics students" is not sustained. It shows there is no significant difference of audience of teachers' feedback on the basis of students' project work on the students' achievement.
Table 4. Feedback in Tests and Students' Achievement
Audience of Feedback Achievements' Score
Category N Mean SD CV Sig.
Individual 35 37.03 14.14 38.19
.471
Group/Class 179 38.54 10.72 27.82
(Field Survey, 2015) The achievement score of mathematics students is highly deviated among the students who received teachers' feedback individually than their counterparts. The average achievement score of second group of students who received teachers' feedback on different test papers/answer sheet in group/class is higher than the first group of the students. The same result was found in Coefficient of Variance (CV). According to CV the achievement score of the second group of students is highly steady than the first group of students who received teachers' feedback individually most of the time.
To test significance, the researcher employed independent sample t–test with 0.05 level of significance. According to the result of t-test, the value of p was found 0.471, which is greater than the level of significance. The result shows that
"there is no significant difference between audience teachers' feedback on the students' answer sheet of different tests and achievement of mathematics students" is sustained. It is clear that there is no relationship between audience of teachers' feedback of test and students' achievement.
Mode of Teachers' Feedback and Students' Achievement
The researcher found out the relationship between mode of teachers' feedback on the basis of different forms of formative assessment and students' achievement. Furthermore, he examined the significant difference of modalities (i.e.
oral, written and demonstration) of teachers' feedback on the basis of forms of formative assessment and students' achievement in mathematics.
Table 5. Feedback in Classwork and Students' Achievement
Mode of Feedback Achievements' Score
Category N Mean SD CV Sig.
Oral 41 40.39 12.95 32.06
Written 140 37.64 9.80 26.03 .147
Demonstration 35 41.11 13.68 33.28
(Field Survey, 2015) The average achievement of students who received teachers' feedback on their classwork through demonstration most of the time is higher than other two groups of students who received teachers' feedback orally and in written. To check the significance of the mean difference among these different groups, the researcher employed the one way ANOVA test. According to the ANOVA table, the difference between mode of teachers' feedback based on students' classwork and students' achievement was not found statistically significant at 0.05. In the table, F-ratio is 1.933 at p=0.147. This is higher than the alpha value 0.05. So, the hypothesis "there is no significant difference between mode of feedback of classwork and students' achievement in mathematics" is sustained. Therefore, there is no significant difference of mode of teachers' feedback of classwork in students' achievement in mathematics.
Table 6. Feedback in Homework and Students' Achievement
Mode of Feedback Achievements' Score
Category N Mean SD CV Sig.
Orally 35 38.69 12.39 32.02
Written 120 38.20 10.18 26.64 .974
Demonstration 47 38.38 12.48 32.52
(Field Survey, 2015) There is not higher difference between the achievement scores of three groups who received teachers' feedback based on homework orally, in written and demonstration. The value of standard deviation represents that the scores of mathematics is not widely deviated. Similarly, the second group of students' mathematics score is more consistent than other two groups which is shown by the value of Coefficient of Variance. The researcher proceeded with one-way ANOVA test for the significance of the mean score of modalities of teachers' feedback on students' homework.
According to the table of ANOVA the F-ratio 0.027 at p=0.974 is greater than the value of alpha 0.05. Therefore, the
hypothesis "there is no significant difference between mode of feedback of homework and students' achievement in mathematics" is accepted.
Table 7. Feedback in Project work and Students' Achievement
Mode of Feedback Achievements' Score
Category N Mean SD CV Sig.
Orally 18 38.94 12.05 30.94
Written 53 35.81 6.70 18.71 .005*
Demonstration 51 43.67 15.92 36.46
*P<0.05 (Field Survey, 2015)
The trend of teachers' feedback on students' project work and students' level of achievement in mathematics has been found different. The students who received teachers' feedback on project work in written form scored less. The Coefficient of Variance is also found higher while comparing mode of teachers' feedback on students' project work through demonstration. While comparing the achievement score of three groups, the third group of students who received teachers' feedback on project work through demonstration is higher than other two groups. To find the significance difference, one way ANOVA was employed. According to the table of ANOVA F- value between mean score of three groups of students is 5.487 at p=0.005 which is less than level of significance value 0.05. The mean score obtained through different mode of feedback of project work is statistically significant. Therefore, the alternative hypothesis "there is significant difference between mode of teachers' feedback on students' project work and students' achievement in mathematics" is sustained. The finding shows that there is a significant difference between the modalities of teachers' feedback based on students' project work and students' achievement in mathematics. There might be several reasons behind it.
Table 8. Multiple Comparisons (Post Hoc Test) of Modes of Feedback
Mode of feedback Mode of feedback Sig.
Oral Written .345
Demonstration .158
Written Oral .345
Demonstration .001
Demonstration Oral .158
Written .001
*. The mean difference is significant at the 0.05 level.
(Field Survey, 2015) However, to conduct the multiple comparison of significant difference, the researcher employed the Post Hoc Test. The result of Post Hoc Test shows that there is significant difference between written mode of teachers' feedback and demonstration mode of teachers' feedback on students' project work.
Table 8. Feedback in Tests and Students' Achievement
Mode of Feedback Achievements' Score
Category N Mean SD CV Sig.
Orally 35 39.40 15.45 39.21
Written 125 37.89 10.01 26.42 .774
Demonstration 54 38.52 11.26 29.23
(Field Survey, 2015) The descriptive statistical findings show three group of students' achievement in mathematics. Comparing these groups, the first group of students, who received feedback orally based on the answer sheet of tests, is higher than other two groups. In comparison between remaining two groups of students, demonstration mode of feedback is better than written. According to the coefficient of variance, the first group of students' achievement scores is less consistent than other two groups and oppositely the second group of students' achievement scores is more consistent than other two groups. So based on students' answer sheet the written mode of teachers' feedback is better than other modes according to the CV. To check the significance the researcher employed the one way ANOVA test. According to the ANOVA table the F-value is 0.256 and p=0.774 which is greater than 0.05 level of significance. The result shows that the alternative hypothesis "there is difference between teachers' feedback based on students' answer sheet of different tests and students'
achievement in mathematics" is not accepted. Therefore, there is no significant difference of modalities of teachers' feedback on students' answer sheet of different tests in achievement of mathematics students.
DISCUSSION
Regarding students' motivation in learning Brown (1994) states that effective learners operate best in their learning when they have insight into their own strengths and weaknesses (cited in Tomlinson, 2013). It may raise the question; how do the teachers can know and inform the students' strengths and weaknesses of particular subject matter?
As an answer to this question Tomlinson (1999) suggests to create multiple approaches in process of classroom instruction and assessment, which also supports the findings of the study. Therefore, it is influential if the teachers' administrate multiple forms of students' assessment in classroom instruction to analyze the students' strengths and weaknesses.
Informing students about their strengths and weaknesses in particular subject matter and the teachers' feedback strategy (i.e. time of feedback) play important role in improving learning achievement of the students (Ajogbeje et al., 2013), which is also found in the study. The use of effective feedback provides the foundations for learner autonomy and a framework for high achievement and addition it is essential as the scaffolding that enhances the students' learning (Gould & Day 2013 as cited in McCarthy, 2015). The effective feedback always varies on its delivering strategies (Brookhart, 2008). Therefore, this study examined the significant difference of teachers' feedback strategies (i.e.
audiences and modalities) on the forms of formative assessment (i.e. classwork, homework, project work, and tests) in students' achievement in mathematics. The researcher found mixed results.
In audience of teachers' feedback, the researcher tested the significant difference of group audience and individual audience in students' learning achievement. It is better to provide the feedback individually to motivate to modify the existing behavior of every learner and it helps to become effective role performer (Ilgen, Fisher , & Taylor , 1979). On contrary it is better to provide the teachers' feedback in group of peers which helps to promote students' learning achievement through the collaborative teaching and learning activities (Kio, 2015). However, with classwork and homework, the research findings according to the mean score of students' achievement depicts that it is better to provide teachers' feedback individually. It is not same with project work and tests. Furthermore, it is more productive to provide teachers' feedback in class or group of students on students' mathematics project work and tests.
Nonetheless, these all results were not statistically significant. Therefore, there is no significant difference among audience of teachers' feedback (i.e. teachers' feedback in group of students and teachers' feedback in individual or in person to person) on the four forms of formative assessment in students' achievement in mathematics. So the findings oppose the controversial results by Ilgen et. al. (1979) and Kio (2015) for improving students' learning achievement. However, the teacher's scaffolding (i.e. remedial support or feedback) is necessary for students in the stage of ZPD because the scaffolding occurs when the more expert other provides support through a process of interaction with the learners (Heritage, 2010). Therefore, it is essential to provide positive and motivational feedback (Erturan-İlker, 2014) but not necessary to prefer specific receiver like group/class or individual to improve students' achievement in mathematics.
Another strategy of teachers' feedback is the modalities (i.e. oral, written, and demonstration). The researcher checked the significant difference modalities on the forms of formative assessment in students' learning achievement.
Different research found different results on teachers' feedback modalities. Ice, Curtis, Phillips , and Wells (2007) found that the oral/audio feedback is more supportive than others to improve students' level of understanding. Furthermore, the research findings according to mean value of students' achievement portrays that it is better to provide teachers' feedback to students' on their homework and answer sheet of tests orally or through audio modality. The most interesting part is that one minute of audio feedback was equivalent to approximately 100 words and provided more in-depth and detailed review of students work than other modalities of feedback (Emery & Atkinson, 2009 as cited in McCarthy, 2015).
However, the modalities of feedback based on the homework and answer sheet of tests were not statistically significant i.e. there was no significant difference of modalities of teachers' feedback on students' homework and answer sheet of tests in students' achievement in mathematics. Therefore, the teachers may provide effective feedback on the homework and answer sheet of tests through any modalities which does not affect in students' learning achievement.
Regarding level students' perception McCarthy (2015) found that the majority of participants use the demonstration or video mode of feedback. Similarly, this research also depicts that the demonstration or video mode of teachers' feedback according to the mean value of achievement, is better in students' mathematics classwork and project work. Demonstration model of teachers' feedback can be easier to comprehend and act upon (West & Turner, 2015) and in addition video-based feedback are more individulised and personalised than text-based feedback (Henderson &
Phillips, 2015). However, the significant difference of modalities of teachers' feedback in classwork is not statistically sustained i.e. there is no significant difference of modalities of teachers’ feedback on students' mathematics classwork in students' learning achievement. So, to deliver effective feedback on students' mathematics classwork, teacher may use any modalities because the modalities does not affect in students' learning achievement. However, it is not same with project work. There is statistically significant difference of modalities of teachers' feedback on students' mathematics project work and their learning achievement.