Effectiveness of PBL (Project-Based Learning) in K-12 Mathematics Heidi Oline Pruett
The purpose of this literature review is to examine the research from 2008 – 2018, on the effectiveness of PBL (project-based learning) in increasing K-12 student academic achievement in mathematics. Project-based learning consists of four components: a driving question, a student generated authentic artifact, student collaborated research and student presentation to an audience of community. The upper primary grades and beyond can also incorporate technology-based cognitive and communication tools. Project-based learning models can be completed either independently or in groups. If a project-based learning environment is rich in opportunities for student achievement in mathematics, both academically and emotionally, then we should prioritize implementation in mathematics classrooms. There is mounting evidence that project-based learning is beneficial for improving student academic achievement and motivation for learning (Holmes, 2016), and furthermore, that it is even more beneficial when students are familiar with the project-based learning environment (Capraro, 2016). Ten empirical studies will be reviewed to address the effectiveness of PBL in primary school, middle school, secondary school and undergraduate education settings.
The Long View: Connecting Primary School to Undergraduate Work
Hao, Branch and Jensen (2016) evaluated the effects of precommitment during goal setting in a project-based learning environment on student performance. The participants of this single-group repeated measure quantitative and qualitative study consisted of 41 undergraduate students (28 women and 13 men) enrolled in a course on instructional technology. The results show that students benefited from the PBL environment at an increased level when precommitment was initiated during goal setting at the onset of the PBL. This result gives evidence that a meta-cognitive approach to student activity enhances performance. The most striking aspect of this study, in relation to this literature review, is the analysis of the data and the discussion. The analysis emphasizes that undergraduate students are frequently asked to monitor their own learning and to engage in active learning processes. Because primary and secondary students are more often taught in a passive learning environment, they often struggle with the meta-cognitive demands of a student driven, collaborative environment. This observation and analysis calls for action to be taken in the early school years so that students can develop the skills necessary to maximize the benefits of PBL. (Hao et al., 2016, p.442-448)
If undergraduate students benefit from experience in project-based learning, then we need to go back to the starting point and seek evidence that primary students benefit from project-based learning. Papancheva (2017) conducted a study to assess if a project-based learning model would increase primary grade level student clarity of understanding and application of conducting survey and presenting results. The study was conducted using a pre-test and post-test model. The total instruction time of the study was 6 hours, distributed as follows: a diagnostic test administered to the students, one teacher’s class of the week, three math classes, and a control test. The student projects were evaluated based on a scale form 0 – 4, corresponding to “weak” to “excellent” work. The indicators used to determine the initial levels of student understanding of data analysis included assessments of working with tabular information and diagrams. The target group consisted of two classes of 40 3rd grade students. The results of Papancheva’s 2017 study show that all the children formed basic statistical literacy through the completion of the project-based learning unit, with 43% of the students showing small inaccuracies and the other 57% of the students successfully completing their own self-studies. Although the investigator indicates a positive result, the methods of statistical data analysis used are unclear. Even with this questionable data analysis, the reports that the fifth-grade participants “are happy to perform their assigned tasks, take them as an interesting game, and imperceptibly create important knowledge and skills to work with data structures.” (p. 6), is encouraging enough to prompt further studies. This publication includes many delightful photos of student work as well as student teams filled with smiling faces. The environment of the classroom appears positive, engaging and productive. When this can be achieved in a mathematical statistics course, we must persevere to prove the academic benefits of this type of positive learning environment. (Papancheva, 2017, p. 1-7)
Firdaus, Wahyudin, and Herman (2017) conducted a study to determine whether there are differences in the mathematical literacy of students who learn in a project-based (PBL) learning environment versus those who learn in a direct instruction (DI) environment. This study also explored the variable of the location of the school and selected samples from rural, city and county transition communities. This was a quantitative research study based on a quasi-experimental method with non-equivalent groups. Pre-test and Post-test assessments were analyzed using statistical quantitative analysis. Participants were selected from the population of all fifth-grade students in primary schools in the county and cities of Bandung, Indonesia. A total of six schools were selected, four representing the rural and transition areas and two representing the urban areas. There were 115 participants in the PBL (Project-Based Learning) group and 105 participants in the DI (Direct Instruction) group. The main results show that the students in a PBL environment showed significantly higher levels of improvement in mathematical literacy than those in a DI environment. Furthermore, regardless of the location of the school, the increase in mathematical literacy of the PBL groups were consistently higher than the DI groups. Although this study provides a good discussion of current thinking regarding PBL in the classroom and the results are encouraging, the grammatical errors sometimes lead to possible misinterpretation of the authors intent. This being stated, the data still demonstrates a greater increase in mathematical literacy in a PBL environment compared to a DI environment. (Firdhaus, 2017, p. 212-219)
PBL in Middle School Mathematics
Cervantes, Hemmer, and Kouzekanani (2015) conducted a causal-comparative study comparing 7th and 8th graders in a PBL environment to those in a traditional classroom setting where PBL was non-existent. High student drop-out rates of 3 out of 10 students is a great concern. The main reason for student drop-out is that students find school boring and become disengaged from high school (p.51). Furthermore, research linking disengagement from school that leads to dropping out often begins in middle school. The results of this ex post facto, casual-comparative research, investigating the differences between the PBL group and the non-PBL group demonstrate that the students participating in the PBL environment showed statistically significant increased performance in both mathematics and reading achievement based on the STAAR standardized test results. (Cervantes 2015, p.50-66) Koparan & Güven (2014) conducted a study to examine the effectiveness of project-based learning on 8th grade students’ improved comprehension of statistics. The study was designed on a quasi-experimental research model using a pre-test and post-test assessment to evaluate levels of improvement in student statistical literacy. Qualitative data based on a statistical literacy test was evaluated using Rasch measurement techniques, which allowed the researcher to evaluate student performance and item difficulty on the same scale. The six levels of statistical literacy assessed include the following progression: idiosyncratic, informal, inconsistent, consistent non-critical, critical, critical mathematical. The study group consisted of 70 8th grade students studying in two different classes. The two classes of 35 students each comprised the control group and intervention group accordingly. The students of the intervention group were placed into heterogenous groups of three or four to complete the project and were guided by the teacher. The results show that all students improved in statistical literacy between the pre-test and post-test assessments, but the intervention group showed a significantly larger improvement. When evaluating the raw scores, the control group tested at 42.1% on the pre-test and 53.6% on the post-test, whereas the intervention group tested 34.8% on the pre-test and 79.2% on the post-test. The Rasch score which compared each item on the statistical literacy assessment, based on both level of difficulty and student performance, shows consistent results with strong reliability scores. The results of this study give further evidence that project-based learning is a beneficial model for improving statistical literacy in middle school students. (Koparan & Güven, 2014, p.145-157)
Cheng, Lam, and Chan (2008) conducted a study to investigate the effects of group heterogeneity and the quality of PBL implementation on student learning. Hierarchical linear modeling was used to analyze the nested data in this qualitative study based on a student-report questionnaire measuring group processes, self-efficacy and collective-efficacy. Evaluation of student academic achievement was based on school examination marks. The participants consisted of 1, 921 students from eight Hong Kong schools, (49.9% males, 50.1% females, 39.8% seventh graders, 33.3% eight graders and 26.8% ninth graders). The result shows that both high-achieving students and low-performing students report higher levels of collective efficacy than self-efficacy when the quality of the PBL implementation is high. When designing project-based learning, it is critical for the teacher to make informed choices in student grouping, based on both knowledge of his or her students and knowledge of grouping that benefits all students. Some argue that while low achievers benefit greatly from group work, high achievers are not sufficiently challenged and therefore would be better served in an academically homogenous grouping. These arguments are supported by Vygotsky’s theoretical framework of the zone of proximal development. (p.209) This research provides evidence that in group work of high quality, higher achievers are not negatively affected. The findings are encouraging for proponents of project-based learning. This study also emphasizes the need for extensive professional development for teachers in the implementation of quality project-based learning. (Cheng, Lam, and Chan, 2008, p.205-221)
PBL in Secondary Mathematics
Holmes & Hwang (2016) conducted a mixed-method longitudinal study to assess the benefits of PBL on both academic skills and strategies for learning for secondary mathematics students. Quantitative statistical analysis was performed on the participants’ standardized test scores. Qualitative analysis was performed based on observations and student interviews. The participants were placed into two designated groups, PBL and non-PBL students. The PBL students attended a PBL high school and the non-PBL students attended the standard high school in the same area. The demographics of the two groups were comparable in all areas except for mathematics, with the PBL group demonstrating mathematics achievement 10% lower than the non-PBL group before the onset of the study. The initial findings showed no significant statistical difference between the two groups when evaluating mastery of mathematical content. However, data disaggregation showed that the achievement gap of at-risk and minority students decreased significantly following participation in the PBL environment. The PBL environment greatly benefited at-risk and minority students in mathematic achievement. Furthermore, “…PBL students were more intrinsically motivated, showed significantly higher critical thinking skills, and appreciated peer learning.” (p. 461), when compared to the non-PBL group. (Holmes & Hwang, 2016, p.449-463)
Han, Capraro, and Capraro (2016) found that high-need high school students in the United States benefit from PBL. Han et al. (2016) hypothesized that STEM (Science Technology Engineering and Mathematics) PBL would have positive impacts on Hispanic students and at-risk students’ mathematics achievement. This was a quantitative research study, evaluating student mathematics performance on the Texas Assessment of Knowledge and Skills (TAKS) over a three-year period. Latent growth model and multiple group analyses were employed. Furthermore, the quality of the STEM -PBL environments were examined and the students were placed into two groups, one with teachers participating in PD (Professional Development) and the other group without this intervention. The intervention consisted of a sustained and well-structured PD program on STEM PBL. A total of 3,394 participants from 56 schools were observed over 3 years. Of the total students, 70.7% were designated as at risk of dropping out of school based solely on state-mandated academic criteria. The results showed that Hispanic students in STEM PBL instruction demonstrated an increase in mathematics achievement. The overall result showed that STEM PBL did not positively influence at-risk students, but that the PBL environment did not show any negative consequences for at-risk students. Given that the Hispanic population showed significant gains in mathematics academic achievement, further inquiries into why the other at-risk students were not able to benefit should be pursued. (Han, Capraro, and Capraro, 2016, p. 157-166)
The purpose Cakiroglu’s, 2014 study was to assess the effect of VM’s (virtual manipulatives) in project-based learning environments on student academic achievement and student attitudes towards mathematics courses. This study was based on a quasi-experimental design with one experimental group (EG) and one comparison group (CG). The study used a pre-test/post-test nonequivalent control group design. Once the two groups were established, both groups received four weeks of direct instruction by the same teacher in the same course of 9th grade mathematics. The projects introduced subject matter of a 10th grade mathematics curriculum. Both groups received the same three projects about Polynomials and Quadratic Equations, each to be completed in two weeks, totaling a six-week project. The experimental group was given access to 15 VM’s and the teacher instructed the students about how to use them for their projects. The comparison group was not instructed in use of the VM’s, but was instructed to use class notes as resources to complete the project. To assess academic achievement, an Achievement Test (AT) was designed based on the opinions of three field experts and was comprised of twenty-five items about the learning outcomes regarding polynomials and quadratic equations. The reliability of the test was tested during a pilot study. To assess changes in students’ attitudes the Mathematics Attitude Questionnaire (MAQ), developed and validated by Duatepe and Ҫilesiz in 1999, was given to both the EG and CG at the beginning and at the end of the study. Both groups consisted of students of the same 9th grade mathematics teacher. The students had only an introductory knowledge of quadratic equations and polynomials and the researchers assume that because of this their backgrounds about the subjects can be considered similar. The experimental group (EG) consisted of 14 male and 16 female students. The comparison group (CG) consisted of 15 male and 15 female students. The results were evaluated using both quantitative and qualitative data. The post-test scores show a statistically significant result that the EG students who received access to VM’s in the PBL outperformed the students in the CG. Both groups however, showed a statistically significant increase in performance on the post-test assessment. These results reflect that all the students participating in the PBL made academic gains, but the EG gained more than the CG. In addition to the 38 response MAQ that was administered, 8 students were interviewed. The interview was broken down into three themes: enhancing learning, attitude toward course, and behaviors during the course. The qualitative analysis of the MAQ did not show a statistical difference between the two groups on either the pre-test or post-test responses. However, the results show a statistically significant difference for both the EG and CG groups between the pre-test and post-test results. Thus, more evidence that PBL learning, whether VM’s are accessed or not, improve student attitudes toward their mathematics courses. The sample is relatively small and seemingly homogenous in terms of racial and socioeconomic status. The results could vary when applying this model in a more diverse setting. More studies need to be administered to better understand if these results would hold true in a heterogenous population. The students felt comfortable with increased independence from the teacher and felt more comfortable learning from their mistakes in the PBL environment. This is beneficial for improved learning in mathematics classes. In the interview, one student shares that the guided independent learning is better because she/he is not concerned and distracted by the teacher being right next to her/him. Both this marked decrease in mathematics anxiety and the positive aspects of student driven learning are beneficial to academic achievement in mathematics. The former “sage on the stage” instructivist pedagogy can increase student anxiety where PBL environments can help to decrease student anxiety in mathematics courses. (Cakiroglu’s, 2014, p.201-222)
Capraro, Capraro, Scheurich, Jones, Morgan, Huggins, Corlu, Younes, and Han (2016) conducted a study to assess the impact of sustained systemic professional development on the effectiveness of PBL in science and math classes in three urban high schools. This study was conducted using both quantitative and qualitative analysis. This longitudinal investigation took place over four years and academic achievement outcomes were based on standardized test performance of the students over time. The Texas Assessment of Knowledge and Skills (TAKS) was the standardized test used to consider student academic achievement in mathematics and science. Teacher observations and reflections on project-based learning were recorded through a series of focus group interviews. The school district where the study took place serves a large low-income population with 83.1% of the students classified as economically disadvantaged. The demographics of the student body include: 34.9% black, 50.9% Hispanic, and 13.6% White. 14.4% of the students were classified as limited English proficient, 11.4% as special education, and 13.14% as bilingual/English as a second language. (Holmes et al., 2016) Participants attended three different district high schools with a total population of 1,185 students. The sample group consisted of sixty students that were randomly selected from this population. The students were all in science and mathematics courses taught by the teachers participating in the study and thus the professional development program. After three years, the quantitative research results showed a marked improvement in mean scores for each of the six categories from baseline observations. The aggregate scores show that student mean scores increased in correlation to the level of PBL implementation. Implementation quality is defined by HS1, HS2 and HS3 in increasing order of quality of PBL implementation in either math or science classes. Overall, the increase in student academic performance is positively correlated to the quality of the project-based learning environment established by the teacher. The qualitative data were based on two types of focus group interviews with one for mathematics educators and one for science educators. Data was collected over six focus group interviews. Teachers consistently reported that there were major positive effects of PBL as well as some significant challenges in implementation. All six-teacher focus groups reported positive effects of PBL on student achievement as well as some significant challenges in implementation of PBL. Increased student engagement was reported by five out of the six focus groups, which is significant in a population where lack of student engagement leads to conflict and student drop-out rates. (Capraro, Capraro, Scheurich, Jones, Morgan, Huggins, Corlu, Younes, and Han, 2016, p.181-196)
Although further research needs to be done to more clearly answer the questions about the benefits of project-based learning across the grade-levels, we see a trend of positive outcomes from PBL implementation from primary school through secondary school and into undergraduate pursuits. It is worth noting that the majority of PBL studies conducted with the primary and middle school populations are centered around statistics. Mathematical statistics is easily adapted into a project-based learning task. It is important that we explore the positive outcomes of PBL when projects are centered around other mathematical concepts. However, in the meantime, if statistical project-based learning can offer a positive introduction to project-based learning, and at the same time improve student conceptions of statistics and mathematics, then we have a positive base of evidence that project-based learning increases student engagement and thus academic achievement. It is also clear in the research that the quality of the project-based learning environment correlates directly to student achievement levels. Attention should be focused on offering teachers access to professional development programs on project-based learning. Further research needs to be conducted to evaluate the benefits of project-based learning on the early primary grades. If the thinking that is involved in project-based learning is beneficial to students, then introducing the model in the foundational years of education should be beneficial as well.
References
Çakiroglu, Ü. (2014). Enriching Project-Based Learning Environments with Virtual Manipulatives: A Comparative Study. Eurasian Journal of Educational Research, 55, 201-221.
Capraro, R. M., Capraro, M. M., Scheurich, J. J., Jones, M., Morgan, J., Huggins, K. S., ... & Han, S.(2016). Impact of sustained professional development in STEM on outcome measures in a diverse urban district. The Journal of Educational Research, 109(2), 181-196.
Cervantes, B., Hemmer, L., & Kouzekanani, K. (2015). The Impact of Project-Based Learning on Minority Student Achievement: Implications for School Redesign. Education Leadership Review of Doctoral Research, 2(2), 50-66.
Cheng, R. W. Y., Lam, S. F., & Chan, J. C. Y. (2008). When high achievers and low achievers work in the same group: The roles of group heterogeneity and processes in project-based learning. British Journal of Educational Psychology, 78(2), 205.
Firdaus, F. M. (2017). Improving Primary Students' Mathematical Literacy through Problem Based Learning and Direct Instruction. Educational Research and Reviews, 12(4), 212-219.
Hao, Q., Branch, R. M., & Jensen, L. (2016). The effect of precommitment on student achievement within a Technology-rich Project-based learning Environment. TechTrends, 60(5), 442-448.
Han, S., Capraro, R. M., & Capraro, M. M. (2016). How science, technology, engineering, and mathematics project-based learning affects high-need students in the US. Learning and Individual Differences, 51, 157-166.
Holmes, V. L., & Hwang, Y. (2016). Exploring the effects of project-based learning in secondary mathematics education. The Journal of Educational Research, 109(5), 449-463.
Koparan, T., & Güven, B. (2014). The Effect of Project Based Learning on the Statistical Literacy Levels of Student 8th Grade. European Journal of Educational Research, 3(3), 145-157.
Papancheva, R. Y. (2017). Data handling and project-based learning at Primary school. Journal of Process Management. New Technologies, 5(4), 1-7.