Abstract
A study researching differences in IB SL Mathematics students’ understanding of trigonometry was conducted in an international boarding school in Switzerland. The sample size was made up of 18 randomly selected students, divided into two groups. The intervention group integrated peer-reviewed video-recording activities in their lessons while the comparison did not. The research design was experimental and the researcher assumed the null hypothesis (no significant different outcome).
Prior to the beginning of the implementation phase, a pre-test was undertaken, following a treatment phase where the innovative teaching practice was implemented. A post-test was carried out three weeks later. Data was statistically analyzed, including a T-test between the two columns of change percentages, which was applied in order to reject or confirm the null hypothesis. Qualitative results are also presented. Background Study Location The following study was conducted at LAS, a boarding private secondary school in Leysin, a small village with a medium-size ski resort in the French-speaking part of Switzerland. LAS follows the American Advanced Placement (AP) as well as the International Baccalaureate (IB).
The student body is made up of approximately 350. Around 50% of LAS students join the school for just one year, as they want to have a short experience in a boarding school or travel around Europe.
Students staying in boarding house
Factors Affecting the CPU-AT Students’ Preference in choosing Boarding Houses/Dormitories. In today’s academic society, students aim for higher degree of education to improve their respective socio-economic status and of their society as a whole. As they enter colleges, it is given that some, if not most, are away from their homes. As a result, students tend to seek for temporary residences such ...
Student Demographics Participants in this research were students from two different groups of the same level (Pre-Calculus).
They all attended three long 85-minute block-period lesson and nine 50-minute periods of Mathematics. They followed the exact same syllabus and were taught by the same teacher. The Researcher This study was carried out by a Mathematics teacher with eight years of experience in education, most of which working in international schools. Importance of the Study Reasons for Undertaking this Project The researcher attempts to improve students’ understanding of trigonometry by means of adding motivating, interesting and innovative pedagogical activities.
This project intends to find out if integrating video recording has an impact on the students’ achievements as measured by teacher generated pre/post tests. Significance for the Researcher In general, teachers use videos in class as a substitution of a lecture (teacherstudent interaction).
This project includes the use of videos as a full student-centered activity (students actively recording videos, sharing them with their peers and reviewing each other’s videos).
Therefore, class dynamics are changed, and it is expected that this change will generate an improvement in the motivation of students as well. Please note that motivation is not a variable directly studied in this project even though students’ motivation, as well as their relationship with their teachers, appears to be related to their achievement (Midgley, Feldaufer & Eccles, 1989).
Significance for the School Like many schools, LAS is interested in having motivated students achieving high scores on external exams and engaged teachers striving for improving their practices with innovative activities. The school promotes the development of innovation as clearly shown in its mission statement: “Developing innovative, compassionate and responsible citizens of the world” (Leysin American School in Switzerland, n.d., para.1).
LAS offers its students the possibility of studying digital imaging in lower grades. As part of that course, students create and edit videos using iMovie (a video editing software application sold by Apple for the Mac and iPhone, which all LAS students have).
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This activity gives students the opportunity to use their skills in a practical way, making that way a powerful link in the school’s horizontal curriculum. Significance for the Mathematics department.
The Mathematics department encourages teachers and students to use problem – based learning (PBL).
PBL activities require a non-linear process with a constant movement between problem, solution and reflection. It has been discussed whether the process (reflection) is more important than the product (solution) as “ it is this back and forth process that stimulates intellectual work and ensures better learning” (Freiman et al., 2012, p.150).
Video-recording activities might stimulate this process and therefore enhance learning. Significance for the Students Leysin American School students are particularly motivated to obtain high scores and most of them welcome innovation as part of their ideals as well as their school’s mission statement. They understand that “both video viewing and production are becoming routine practices within our media-rich society” (Spires et al., 2012, p. 483).
In addition, new and motivating content is always welcome among LAS students. Through this project, they experienced new ways of learning. As the school’s website states “ The use of IT in math classes helps to break down the barriers that many students experience in this subject” (Leysin American School in Switzerland, n.d., para.8).
Literature Review Similar investigation results show very interesting applications of this type of innovative activities: “recordings allow students to replay the video as many times as they need; so, they can make self-evaluation of themselves as well as their fellow friends. As a consequence, students become self-critical, because they can see their problems and trace their improvements” (Kirkgöz, 2011, p.2).
Jarvinen, Jarvinen and Sheehan (2012) claim that hands-on activities such as video-recording are beneficial for students; and Martin, Parker, and Deale (2012), found results which suggested that student interaction, and hence learning, was aided by the live communication that occurred through the virtual classroom in their investigation. Kecik et al. (2012) assert that e-portfolio applications can meet the majority of the planning, teaching, and reflection needs in the teaching process. Holotescu and Grosseck (2012) mention in their article that development of portfolios is necessary for acceding on a mobility-dominated job market. “Flipped classroom teachers almost universally agree that it’s not the instructional videos on their own, but how they are integrated into an overall approach, that makes the difference” (Tucker, 2012, p1).
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Walling (2012) warns us that integrating various forms of technology from personal devices, school devices and Internet is a challenge.
Finally, Spires et al. (2012) found that “Knowledge representation is critical to knowledge construction and meaning making” (p. 484).
Video production has an artistic component that could, as Goodman suggests, improve education (“History of Project Zero,” n.d.).
Statement of the Issue The researcher has observed over a number of years that students’ communication skills in Mathematics could be improved and believes this exercise can be beneficial. Please note that the students’ communication skills level is not a variable directly studied in this project. However, it indirectly affects students’ scores on their tests, since one of the aims of the Mathematics I.B. Diploma Program is to enable students to “communicate clearly and confidently in a variety of contexts” (Diploma Programme Mathematics SL, 2006, p. 2).
Research Question What happens to Students’ understanding of trigonometry as measured by a teacher generated pretest-posttest when peer-reviewed video-recorded presentations are integrated in their lessons? Integrating video-recording in the lessons includes the production of videos using screen cast software and/or a webcam to show how to solve Mathematics problems, editing them, publishing them online (with privacy restrictions) and referencing them within the online portfolios of participating students. In addition to that, students will also peer-review each other’s videos and provide feedback using online Google forms and spreadsheets. The researcher assumed the null hypothesis, i.e., he expected no evidence of significant change in both comparison and intervention groups´ results for pre-test and post-test.
Research Methodology Sample Two grade 11 classes with 8 students participating in each class constitute the sample. Participants attend 50-minute lessons 3 times a week, and an 85-minute lesson once a week. LAS students generally come from financially rich backgrounds and have a wide variety of nationalities. English is used by most of the students as a second language, being the two most common mother tongues Spanish and Russian. Materials LAS supports innovation, and students already possess the materials needed for these activities: “ Upon arrival at LAS, students are issued a MacBook and iPhone as part of the ATLAS program, Advancing Technology at LAS” (Leysin American School in Switzerland, n.d., para.1).
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In addition to that, there is wireless internet access available in all classrooms and students’ dorms. Therefore, there were no costs for the school in terms of materials supplied, as no extra equipment is needed. Instruments The researcher will use the same teacher-generated test in both the pre-test and post-test.
He creates tests using an IB Mathematics SL question bank database, so that students get used to the type of questions that come up in the external IB exam (which is useful for students interested in obtaining the IB diploma. The reliability of such tests is permanently validated by the International Baccalaureate Organization (IBO) (Diploma Programme Mathematics SL, 2006).
This test can be seen in appendix 1. The researcher used an open-ended questionnaire to study how the use of peerreviewed-videos affect student’s attention, motivation and satisfaction. This is very important as these are three basic psychological processes in education.
Procedures At the beginning of the study, the researcher informed participants of the randomly chosen intervention group and ask them their opinion about the possibility of implementing such an innovative tool in their lessons. Upon approval of that change he communicated both intervention and comparison groups that they were going to participate in an investigation into effective innovative teaching strategies. The researcher informed students that this investigation would not affect the classroom dynamics, their assignments or their assessment. He will inform students that their participation in the investigation consists in their anonymous test scores being studied using statistical analysis. He then informed them and their parents (see appendix 3), that they could opt out the investigation, in which case their scores would be withdrawn without modification, as required by the Swiss Ethic Code of Research (Code d’éthique, n.d.).
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No students were withdrawn from the study. Intervention and comparison group took the same pre and post-tests and equivalent open-ended questionnaires. Since the groups are randomly selected, the study design is considered experimental. (See the following table for an overview of the experimental design).
R R O1 O1 X O2 O2
In the table above, the O1 represents the pretest, the O2 the posttest and the X represents the intervention. Students participated in the study for 3 weeks (15 periods), including pre and post-test.
Calendar plan The whole implementation process of the research project took place during the first term of the school year (from August to December).
Following a detailed agenda as depicted below: August 22nd- 24th. Meet Head of Department and ask for permission. Meet digital imaging teacher and discuss possibilities of collaboration (horizontal curriculum).
August 24th – September 14th. Plan and create intranet structure to share online portfolios and peer assessment within privacy restrictions. September 16th – October 1st. Plan and create intranet structure so that other teachers can share their results for an extended data collection. October 2nd. Meet participants and explain project (see procedures section).
October 8th. Pre-test and open-ended questionnaire. October 8th – November 12th. Treatment. November 12th. Post-test and open-ended questionnaire. November 12th – 19th. Data analysis. November 19th -30th. Complete and submit report.
Data Collection and Analysis Four sets of data were collected from the pre and post-test (see appendix 1).
The four sets of data were analyzed using measures of central tendency (mean, mode and median) and of spread (variance and standard deviation).
In addition, the percentage of the difference from pre-test to post-test was individually computed. In order to reject or confirm the null hypothesis, i.e., to find out if the results are significantly different, a ttest between the two columns of change percentages was applied. The researcher used a t-test for independent samples because the groups are independent of each other. The researcher selected the two tails option, as the difference could have been positive or negative (the use of videos could be detrimental).
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A type 2 t-test was applied as the variances of the differences were similar. The results, as we can see in the tables below, show probability values over 0.05, and therefore the null hypothesis is retained. Acording to Ravid, as cited in O’Gara (2008), “A p value of .05 is the most commonly used benchmark to decide whether to consider the results statistically significant” (p. 162).
In addition to this, the researcher also applied a t-test between the pretest and post test values of each group. The results, as shown in the tables below, show probability values well under 0.05, and therefore supporting the hypothesis that the pre-test and post-test scores are significantly different for both control and intervention groups.
The researcher also analyzed the data from the open-ended questionnaire in the following three categories: attention, motivation and satisfaction. Results The scores obtained are computed in table 1. Group 1 is the control group whereas group 2 is the intervention group. Table 1: Student Raw Scores and Percentage Change on Pre-Test and Post-Test Group1 Student 1 Student 2 Student 3 Student 4 Student 5 Student 6 Student 7 Student 8 Pre 13.6 13.6 20.3 58.8 6.80 15.3 8.50 11.9 Post 52.5 84.7 84.7 74.6 54.2 71.2 50.8 81.4 % Change 118 145 123 37.8 156 129 143 149 Group 2 Student 1 Student 2 Student 3 Student 4 Student 5 Student 6 Student 7 Student 8 Pre 10.2 18.6 3.40 25.4 6.80 1.00 5.08 5.08 Post 62.7 47.5 52.5 93.2 37.3 66.1 64.4 79.7 % Change 144 87.2 176 114 138 194 171 176
Data above was processed using a spreadsheet package. These processed results are shown in table 2. Table 2: Measures of Central Tendency and the Standard Deviation from the Data. Group 1 Mean Mode Median Pre 17.6 13.6 13.6 Post 69.3 84.7 72.9 14.6 Change* 125 N/A 136 37.6 Group 2 Mean Mode Median St. Dev. Pre 9.45 5.08 5.93 8.40 Post 62.9 N/A 63.6 17.8 Change* 150 N/A 158 36.1
* Please note that this change has been calculated using the difference over the mean result and not the difference over the pre-test result as the latter is very small.
As we can see from the results as published in the table above, the results of the post-test are higher than those of the pre-test for both the control and experimental group. A t-test was conducted to find out if this difference was significative. The values found were 4.87 10-5 and 4.25 10-5 for the control and intervention groups respectively. Since these results are much smaller than the critical value (0.05) we can consider the difference as significative. Finally, the researcher conducted the t test as described in the data collection and analysis above and compared his results with the critical value, 0.05. The researcher found a p value of 0.195, which is bigger than the critical value. Therefore the null hypothesis cannot be rejected, as the differences are not significant enough. Qualitative data (see appendix 4) show that students’ motivation to use videorecorded presentations increased with use. Some students were concerned about their ability to produce videos and this concern disappeared as they learned the new skills and/or discovered their peer’s abilities to do so.
Extraneous Influences This is the second year that the school is implementing the advanced technology program (see significance for the school section above).
The availability and quality of resources (such as high speed internet connection) plays an important role in the development of this investigation. There were no critical technical problems during the entire duration of this investigation. The level of skills and motivation of the students in digital imaging is also important. In addition, students’ concentration might be affected by their emotional status, time of the day, weather, noises from builders or other classrooms, other subjects’ tests and extra-curricular activities happening that week. All these factors and many others could significantly have had an impact in the results. Conclusion This study has found a difference in the results of pre-post tests, which is significant.
This result is relevant for this investigation as it shows that students have improved their mathematical skills using both teaching methodologies. With regards to the research question (What happens to Students’ understanding of trigonometry as measured by a teacher generated pretest-postest when peer-reviewed video-recorded presentations are integrated in their lessons?), the researcher found that the results improve slightly more using the innovative teaching method (150% change compared to a 125% change), but that these changes are not significant enough to reject the null hypothesis. We can conclude that the use of peer-reviewed video-recorded presentation help the learning process, but many other teaching techniques can help as well. As Tucker (2012) suggests, the difference in the learning process is made when these innovative techniques are used with others.
The researcher does not discard the possibility of publishing his results so that other Mathematics teachers and teachers of other subjects can benefit from his results. Limitations of the Study The main limitation of this study is the fact that there were only two groups of 8 students involved constitutes a major limitation. In order to minimize these limitations, the investigation proposal was sent to many other professionals and published in specialized social media with an invitation to participate. As a result, this investigation can count with the results from three other groups as shown in the following section. Extended investigation This investigation was extended with other sample groups: 41 students from another mathematics course at LAS (28 in the control group and 13 in the intervention group), 12 students from Colegio Juan de Lanuza in Zaragoza (Spain) (5 in the control group and 7 in the intervention group) and 36 students from Munich International School (Germany) (16 in the control group and 20 in the intervention group).
The there schools involved are private international schools and therefore all students have a similar background.
This extended investigation was carried out by three teachers: Eli Durmer (Mathematics teacher at LAS), Pilar Garcia (Mathematics teacher at Colegio Juan de Lanuza) and Philip Kurbis (Mathematics Department Chair at MIS).
The results of this investigation can be seen in appendix 5. As we can see in none of the cases the differences were significant enough. In fact in Durmer’s and Garcia’s groups the differences were negative, suggesting a rather more slow learning process when using the innovative techniques. This might be because this was a very new technique for both students and teachers and considerable lesson time was spent in learning technology and not mathematics.
