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Purpose & Context
Student test scores for mathematics in Ontario have been on the decline for years. Although math is something that all students in Ontario are required to take throughout their elementary and secondary education, many students struggle to get by and never truly understand the concepts taught. It is possible the reason for this is in the way material is presented, instead of the students’ capacity to learn it. The way that mathematics is taught in secondary school is not reflective the way students learn or the way that math is approached beyond high school.
By learning how effective new teaching methods are in terms of student success will help shape the future of mathematics education for the better. This study will compare the success of students exposed to a Problem-Based Learning (PBL) approach to the success of students exposed to traditional methods (TM) to determine whether PBL is an effective approach to improving student success.
This study focuses on students in secondary school enrolled in mathematics, particularly students in the senior grades (grade 11 or 12). This study would take place in the classroom(s) of a teacher or an in-school team of teachers who have been using traditional lecture-style methods in their classroom with limited student success. The particular students in these classrooms would have high to middle past mathematical ability.
Problem-Based Learning (PBL): PBL is a student-centered style of teaching. PBL uses specially constructed problems to encourage students to learn through exploration by solving “real world problems”. Students work collaboratively in small groups, play an active role in learning have the opportunity to direct their own learning. Teachers do not demonstrate material to students but instead facilitate learning.
Traditional Methods (TM): TM of teaching include lecture-style lessons where teachers deliver information to students, take them through the steps of solving a problem and have students practice similar problems. Most problems students solve cannot be easily applied to “real-life” situations and collaboration with peers does not often happen.
Student Success: A students’ ability to not only achieve desirable marks, but also the ability to understand the material. Student success also requires a student to have a positive attitude, interest and high self-efficacy towards mathematics.
Academic Achievement: Academic achievement in math is measured by grades and completion, with high grades corresponding to high achievement.
Review of Literature
Student attitude and interest. A students’ attitude and interest towards math plays a crucial role in their achievement. Classroom atmosphere and teaching style can have a big effect on a students’ attitude and motivation. Fatade, Arigbabu, Mogari, & Awofala (2014) found that there was a statistically significantly difference (p < .001) in the mean scores of a Belief about Further Mathematics Questionnaire between students who were exposed to PBL and those exposed to TM, in favour of the PBL group. These results indicate that students who are exposed to PBL have stronger positive beliefs about mathematics than those exposed to TM. Laforce, Noble, & Blackwell (2017) found that a students’ ratings of PBL significantly predicted their interest in pursuing STEM (p < .001), also noting that the quality of PBL instruction is essential to success. However, Laforce et al. also found that although PBL does have a significant effect on interest in a students’ attitude towards STEM, this effect is small when compared to other variables such as race and gender.
Academic achievement. Academic achievement among students’ in mathematics is something all teachers and schools strive for. Although student effort and ability play a major role in the level of achievement a student obtains, the role of the teacher also has a big effect. The main tool for measuring student success is by testing. Fatade, Mogari, & Arigbabu (2013) tested students before and after being exposed to either PBL or TM. They found that there was a significant difference (p < 0.05) between pre and post test scores between the two groups of students. The mean difference on the pre-tests between both groups was 2.60, where the mean difference of the post-test scores was 8.83, in favour of PBL. A study by Ojaleye & Awofala (2018) also concluded that a students’ achievement was enhanced when PBL strategies (as well as blended learning) were used in teaching when compared to TM.
The way that PBL is used in the classroom can also effect student achievement. Badru (2016) compared PBL in small groups, large groups, a modified group as well as a control (TM) group. Badru found that PBL where students work in small groups (~4 students) is the most effective and that these groups do not need to be based on ability or gender. Ajai & Imoko (2015) studied the effect of PBL on both male and female students finding that achievement and retention scores did not significantly differ between both groups, demonstrating that the use of PBL in the classroom can enhance student achievement in mathematics regardless of gender.
Higher-order-thinking (HOT) and critical thinking (CT) skills. The ability for students to complete HOT questions separates those students who truly understand the material from those who simply memorize enough to get by. HOT and CT prepare all students for the future, regardless of the field they choose to pursue. Napitupulu, Suryadi & Kusumah (2016) found that although mathematical reasoning was low overall, students in a PBL classroom did achieve higher in this category than students in a TM classroom. They also found that using PBL to achieve HOT in students was most successful in classrooms that had middle or high ability students, although mathematical reasoning was still higher among low ability students exposed to PBL than those exposed to TM. Surya & Syahputra (2017) saw significant improvement in students’ problem-solving ability through every cycle of PBL they were exposed to and claimed that the PBL approach can improve a students’ HOT ability.
Widyatiningtyas, Kusumah, Sumarmo, & Sabandar (2015) also found that students who follow a PBL approach have better CT than those who follow TM and that learning approach has a significant impact on these skills. However, Widyatiningtyas et al. also found that a students’ early mathematical ability also influences mathematical CT. So, although PBL can help improve or enhance these valuable skills, previous experience also plays a role.
Challenges. If a PBL approach proves to be more effective in mathematics education, then why is it not adopted by more educators? Jailani & Retnawati (2016) found that many teachers lack an understanding of PBL and have difficulty developing effective problems. Fatade et al. (2013) claim that for teachers to adopt PBL, significant changes would have to take place in the classroom as well as changes to curriculums, time-tables and assessment strategies. Jailani et al. also found that students are not accustomed to this style of learning and lacked the self-confidence and ability to persevere that is necessary for this type of learning to be effective.
The main limitation to this study is measuring the quality of PBL being applied to each situation, as Laforce et al. noted, the quality of PBL is essential to its success. Comparing low-quality PBL to high-quality TM could drastically change results, and vice versa. The teachers’ ability to be an effective facilitator plays a big role in the quality of PBL. Significant training and restructuring of course materials would also be necessary.
The willingness of students to participate is also a limitation, as students are generally more comfortable with the TM of teaching, and have learned to take a passive role in their learning. Students must be willing to be active participants for PBL to be effective.
- Ajai, J. T., & Imoko, B. I. (2015). Gender Differences in Mathematics Achievement and Retention Scores: A Case of Problem-Based Learning Method. International Journal of Research in Education and Science (IJRES),1(1), 45-50. doi:10.21890/ijres.76785
- Badru, A. K. (2016). Problem – Based Instructional Strategy and Numerical Ability as Determinants of Senior Secondary Achievement in Mathematics. Journal of Education and Practice,7(13), 89-95. Retrieved from https://eric.ed.gov/?id=EJ1102799.
- Fatade, A. O., Mogari, D., & Arigbabu, A. A. (2013). Effect of Problem-Based Learning on Senior Secondary Students’ Achievements in Further Mathematics. Acta Didactica Napocensia,6(3), 27-44. Retrieved from https://eric.ed.gov/?id=EJ1053664.
- Fatade, A. 0., Arigbabu, A. A., Mogari, D., & Awofala, A. O. (2014). Investigating Senior Secondary School Students’ Beliefs About Further Mathematics in a Problem-Based Learning Context. Bulgarian Journal of Science & Education Policy,8(1), 5-47.
- Jailani, J., & Retnawati, H. (2016). The Challenges of Junior High School Mathematic Teachers in Implementing the Problem-Based Learning for Improving the Higher-Order Thinking Skills. The Online Journal of Counselling and Education,5(3), 1-13.
- Laforce, M., Noble, E., & Blackwell, C. (2017). Problem-Based Learning (PBL) and Student Interest in STEM Careers: The Roles of Motivation and Ability Beliefs. Education Sciences,7(4), 92. doi:10.3390/educsci7040092
- Napitupulu, E. E., Suryadi, D., & Kusumah, Y. S. (2016). Cultivating Upper Secondary Students’ Mathematical Reasoning -Ability and Attitude towards Mathematics Through Problem-Based Learning. Journal on Mathematics Education,7(2), 117-128. doi:10.22342/jme.7.2.3542.117-128
- Ojaleye, O., & Awofala, A. O. (2018). Blended Learning and Problem-Based Learning Instructional Strategies as Determinants of Senior Secondary School Students’ Achievement in Algebra. International Journal of Research in Education and Science,486-501. doi:10.21890/ijres.428286
- Surya, E., & Syahputra, E. (2017). Improving High-Level Thinking Skills by Development of Learning PBL Approach on the Learning Mathematics for Senior High School Students. International Education Studies,10(8), 12. doi:10.5539/ies.v10n8p12
- Widyatiningtyas, R., Kusumah, Y. S., Sumarmo, U., & Sabandar, J. (2015). The ımpact of problem-based learning approach to senior high school students’ mathematics critical thinking ability. Indonesian Mathematical Society Journal on Mathematics Education,6(2), 30-38.
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