International Conference on Education in Mathematics, Science & Technology (ICEMST) 19 – 22 May 2016, Bodrum, Turkey
EXPLORING THE GRAPHS OF FUNCTIONS USING THE JIGSAW APPROACH Vijayanthi Vijayan1, Masitah Shahrill2, Nor‘Arifahwati Abbas2, Abby Tan3 1 Pg.
Jaya Negara Pg. Hj. Abu Bakar Secondary School, Ministry of Education, Brunei Darussalam 2 Sultan Hassanal Bolkiah Institute of Education, Universiti Brunei Darussalam, Brunei Darussalam 3 Faculty of Science, Universiti Brunei Darussalam, Brunei Darussalam
Introduction • Students worldwide generally performed poorly in Mathematics (Naomi & Githua, 2013). There is a lack of student engagement in Mathematics lessons.
• SPN21, an education reform in Brunei Darussalam, was enforced to develop 21st century skills amongst students (Ministry of Education, 2013). • The current education system in Brunei Darussalam focuses more on a studentcentred teaching and learning method, such as cooperative learning. One such approach is the jigsaw approach. • The graphs of functions is a topic prone to students’ misconceptions.
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The Study 1. Purpose 2. Literature Review i. Cooperative Learning ii. Jigsaw Approach iii. Students’ Misconceptions on Graphs
3. Methods i. Instruments ii. Data Collections and Analysis 4. Results and Discussions 5. Conclusions i. Limitations of the Study 6. 3
Recommendations
Purpose of the Study • Purpose - To investigate the benefits of cooperative learning (jigsaw approach) in helping secondary school students to draw and interpret the graphs of functions. • Teachers need to find interesting ways to teach the basics of the topic of graphs of functions to ensure that students can interpret them at a higher level. • Results of this study will be beneficial to the students, educators and school leaders. • Research Questions: 1. How effective is the jigsaw approach in improving students’ performance in graphs of functions? (RQ1) 2. What are the students’ perceptions on cooperative learning? (RQ2)
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Review of the Literature 1. Cooperative Learning
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Cooperative learning is when a group of individuals work together towards achieving a common goal (Smith, 1996; Gillies, 2004).
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According to Johnson et al. (1998), cooperative learning comprises five basic elements.
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Cooperative learning promotes great leadership, organisational and teamwork skills (Keikhavani et al., 2015).
Review of the Literature 2. Jigsaw Approach •
Invented by Professor Aronson and his graduate students in 1971 (Aronson, 2000).
Figure 1. Jigsaw Group Diagram (taken from Reilley, 2010)
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A study conducted by Zakaria and his colleagues (2013) in Indonesia showed that secondary school students preferred using the jigsaw approach to learn Mathematics.
Review of the Literature 3. Students’ Misconceptions on Graphs
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According to You and Wiest (2009), students can have either an iconic or symbolic interpretation of graphs.
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The use of activities in the classroom also helps in students’ understanding of graphs (Wallace-Gomez, 2014).
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When students become active learners in the classroom, they tend to understand the lesson’s content more (Freeman et al., 2014).
Methodology i.
Mixed method approach
ii.
Cycles:
Cycle 1
Cycle 2
Location
School A, Brunei-Muara District
School B, Belait District
Sample size
19 students (5 boys, 14 girls)
25 students (16 boys, 9 girls)
iii. Instruments: • RQ1 – pre-test – post-test design with an intervention lesson in between • RQ2 – feedback forms
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Methodology iv.
Data Collection and Analysis
• Permissions had to be sought from relevant authorities before the study was conducted. 1. Pre-test • Validity of test questions was sought from teachers • Individual work to be completed in 1 hour 2. Intervention lesson • Discussion with ‘expert’ group – 30 minutes • Discussion with ‘home’ group – 45 minutes • Sharing of solution between ‘home’ groups – 45 minutes 9
Methodology 3. Post-test • Same as pre-test • Mean scores of the pre-test and post-test were compared. • A simple t-test was used to test the level of significance of the results. 4. Students’ feedbacks • 6 open-ended questions based on the jigsaw approach 1. 2. 3. 4.
What do you think cooperative learning is? Have you done it before? How do you feel about it? How do you find the topic of graphs of functions? You had a chance of learning graphs of functions using the jigsaw approach, how did you find the lessons? 5. Did learning through the jigsaw approach help your understanding on graphs of functions? 6. How would you feel if the jigsaw approach was applied to other topics or subjects? 10
Results and Discussions 1. Effectiveness of the jigsaw approach in the students’ performances • Paired samples t-test with confidence interval at 95% was conducted. Cycle 1
Cycle 2
Difference in mean scores between post-test and pre-test
1.42
1.800
p value
0.036
0.000017
• Since the p values for both Cycle 1 and 2 are less than 0.05, the results obtained are significant. Therefore, the jigsaw approach did have a positive effect on the students’ performance levels.
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Results and Discussions 2. Students’ perceptions on cooperative learning • Students’ feedback was categorised into 3 aspects: positive feelings, negative feelings and mixed feelings. • Cycle 1 15.8% disliked cooperative learning. Students stated that the jigsaw approach helped to improve their understanding of the graphs of functions. 57.9% of the students would like to use the jigsaw approach in other topics. • Cycle 2
20% of the students disliked working in groups. 56% of the students gave positive feedback regarding their experience of using the jigsaw approach to learn graph of functions. 12
Conclusions • The jigsaw approach does have a positive effect in improving students performance levels despite absence of real-life examples. • Not every student was keen on working in groups due to the lack of familiarity of such an approach. • Teachers should be well accustomed and trained to implement new pedagogies in the classrooms. • Limitations of the Study This study was conducted in local government schools and therefore cannot be used to generalise all secondary schools in the nation. The jigsaw approach was only used on one topic in Mathematics.
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Recommendations • Studies can be done to make comparisons between government and private schools due to the possible difference in teaching environments. • The jigsaw approach can adopted in other mathematics topics at different levels to check its effectiveness.
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References Aronson, E. (2000). The Jigsaw Classroom. Jigsaw.org. Retrieved from https://www.jigsaw.org Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., & Wenderoth, M. P. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences, 111(23), 8410-8415. Gillies, R. (2004). The effects of cooperative learning on junior high school students during small group learning. Learning and Instruction, 14(2), 197-213. Johnson, D. W., Johnson, R. T., & Smith, K. A. (1998). Cooperative learning returns to college what evidence is there that it works? Change: The Magazine of Higher Learning, 30(4), 26-35. Keikhavani, S., Soheili, S., Mirzaei, M., Ahmadpanah, M., Haghighi, M., & Bajoghli, H., Holsber-Trachsler, E. & Brand, S. (2015). A comparison of cooperative and traditional learning methods on learning mathematics in the 4th and 5th grades in Holaelan, Ilam, Iran. British Journal of Education, Society & Behavioural Science, 7(2), 129-136. Ministry of Education. (2013). The National Education System for the 21st Century: SPN21 (Revised ed.). Ministry of Education, Brunei Darussalam. Naomi, M. W., & Githua, B. N. (2013). Effects of jigsaw cooperative learning strategy on students’ achievement in secondary school mathematics in Laikipia East District, Kenya. Science, 2(3), 177-188. Smith, K. A. (1996). Cooperative learning: Making “groupwork” work. New Directions for Teaching and Learning, 1996(67), 71-82. Wallace-Gomez, P. (2014). Algebraic activities aid discovery lessons. Mathematics Teacher, 107(5), 354-358. You, Z., & Wiest, L. R. (2009). Take time for action: how students interpret graphs. Mathematics Teaching in the Middle School, 15(4), 188-190. Zakaria, E., Solfitri, T., Daud, Y., & Abidin, Z. Z. (2013). Effect of cooperative learning on secondary school students’ mathematics achievement. Creative Education, 4(02), 98-100.
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Ms. Vijayanthi Vijayan (
[email protected]) Dr. Masitah Shahrill (
[email protected]) Ms. Nor‘Arifahwati Abbas (
[email protected]) Dr. Abby Tan (
[email protected])
