Attitude towards Mathematics
Moore (2012) appreciates the fact that learners at all levels have significantly underperformed in mathematics. Moore goes ahead to attribute this consistent underperformance in mathematics to poor attitude by learners, a position which he shares with Benken and colleagues (2015). Indeed, most students at all levels perceive mathematics as a difficult subject area. This fear of mathematics is passed from generation to generation.
The fear of mathematics and related courses is shown best by the work of Hannigan and colleagues (2014). Their study revealed that medical students, who are unarguably among the most brilliant minds in society, had negative attitudes towards statistics, which is part of the curriculum for medicine. Apparently, the poor attitude of these students towards statistics was born by the fact that they associated statistics with mathematics. Eventually, the study found out that medical students performed poorly in statistics as a subject, despite its utmost importance to the increasingly evidence-based medical profession. This underperformance can be heavily attributed to the poor attitude towards mathematics and associated subject areas.
Various researchers and curriculum developers have tried to explain the bad attitude of students towards mathematics. Moore concludes that poor teaching techniques could have a role to play in causing the poor attitude of students towards mathematics (2012). Among the other factors that have been thought to affect the attitude of learners towards mathematics in past studies is the lack of confidence, feeling that the usefulness of mathematics is much less that is protracted, and inability to discover anything in mathematics (Moore, 2012).
Curtis (2006) appreciates the fact that mathematics has been traditionally taught predominantly by use of textbooks and memorization. This method of teaching, which focuses on the learner’s memory rather proper delivery of the content, is not only taxing but also extremely boring to the learner (Rodrigues, 2012). Textbook exercises and many worksheets are never the most stimulating for students. This mode of teaching obviously antagonizes the basics of the perceptual variability principle of learning mathematics (Subong, n.d.). The method, therefore, makes learning mathematics unreasonably difficult.
Additionally, poor experience with the subject in the past has been shown to contribute to a negative attitude toward the subject (Curtis, 2006). Most students leave lower grades with a feeling of failure and thus natural resentment to mathematics. The most sighted previous poor experiences with mathematics include the inability to understand word problems, failure to utilize mathematics in real-life situations, and a feeling of being academically inferior to classmates (Curtis, 2006). Wolfle (2014) also identifies many other causes of a feeling of inferiority that can lead to poor attitude hence poor performance in mathematics. Among the factors identified are black ethnicity, developmental status, and traditional aging. College students who had done a course in developmental mathematics were more likely to have poorer attitude towards college mathematics and likewise were shown to perform poorly compared to college students who did not have to take developmental mathematics. The fact that teaching of pre-college developmental mathematics usually employs traditional techniques maybe a contributing factor in the poor attitudes of the learners who went through developmental mathematics.
Le and colleagues (2011) also relate the struggle that developmental math students go through to their resentment of mathematics in future. Furthermore, Wolfle (2014) showed that female students had better attitudes towards mathematics than their male counterparts. Socioeconomic status is another factor that may affect the confidence of students and their attitude and performance in mathematics (Davidson & Petrosko, 2015). Learners who come from backgrounds with higher socioeconomic statuses are advantaged as they are exposed to technological developments more. Exposure to technology can help learners in grasping various mathematical concepts.
A 2002 study by Lizzio, Wilson, and Simons revealed that learners resented courses with lots of drill and practice assignments. In essence, learners resent traditional teaching techniques. Students better welcomed analytic problem solving and interactive learning techniques. This, therefore, means that learners receive nontraditional learning techniques much better. Interactive learning has also been shown to reduce math anxiety (Beilock & Maloney, 2015); math anxiety is one of the causes of a poor attitude towards mathematics.
Additionally, lack of confidence while solving mathematical problems breeds a negative attitude towards the subject (Curtis, 2006). In a bid to drive away attention from their incompetence of mathematics, learners who lack confidence resort to avoidance strategies. These learners avoid asking questions and expressing their failure to understand certain mathematical concepts. Moreover, these students consistently put in poor effort in their attempt to improve in mathematics.
As earlier alluded to, math anxiety is an important cause of the poor attitude shown by learners towards mathematics (Curtis, 2006). Curtis (2006) defines math anxiety as that irrational fear of solving mathematical problems either in the classroom or even in real-life situations. Moreover, a study by Furner and Berman (2003) found that two-thirds of the American adult population just fear mathematics. Lack of confidence while handling mathematical problems has been incriminating in breeding this anxiety. In the current society, the usefulness of mathematics has been trashed more by the emergence of technology hence the continued poor attitude and lots of math anxiety among students. Mathematics is depicted as a difficult and useless subject that is only reserved for selected few. Prior bad experiences with mathematical problems and with mathematics teachers also contribute to the occurrence of math anxiety (Beilock & Maloney, 2015). Learners reported being disgruntled with teachers and instructors who treated them badly when they failed to understand mathematical concepts.
Cooperative learning has been shown as a way to eliminating math anxiety (Curtis, 2006 p.31). Rapid delivery of math content also contributes to poor understanding of the concepts hence heightening math anxiety. Similarly, this is a reason why math anxiety and the subsequent underachievement in mathematics are far more common in traditionally aged learners than nontraditional students. Apart from being delivered by way of traditional techniques, Bonham and Boylan (2011) assert that the mathematics content of developmental courses is usually delivered in such a short time hence breeding high levels of math anxiety.
The inception of standards-based classrooms was meant to solve these problems of poor attitude and underachievement in mathematics. The standards-based teaching of mathematics employs the use of nontraditional teaching methods in the delivery of mathematics content to learners (Curtis, 2006). Among the methods that are employed in this type of teaching are cooperative learning, incorporation of real-life situations in teaching mathematics, learner-directed learning, and use of technology. Curtis (2006) showed that these nontraditional students had a much better attitude towards mathematics compared to the traditional students. Incorporation of real-life situations made mathematics far more meaningful and helped the student to appreciate the sheer necessity of mathematics in life hence a better attitude and far much more effort and consistency from the students. Strategies like learner-directed learning and cooperative learning made the class more enjoyable and interactive apart from making it easier for teachers to drive concepts home (Curtis, 2006). Furthermore, learner-directed learning allows students to learn at their own pace thus eliminating the rapidity of delivering content that usually breeds math anxiety.
Technology and Mathematics
Use of technology in the mathematics classroom has obviously made mathematics far more enjoyable and easier to understand. Frey and Fisher (2008) showed that learners of the current generations are easily fascinated with technology and thus the introduction of computer technology in the classroom makes the classroom a better environment for learning. Further, the computer can be used effectively to make understanding of math concepts much easier. The ability of computers to show three-dimensional images and to reproduce virtual real-life situations makes them very useful in the math classroom. Moreover, Frey and Fisher (2008) indicated that the incorporation of computer technology in the mathematics classroom could help eliminate the traditional opinion that the computer technology came to substitute mathematics. Indeed, the two complement each other and this aspect of complementation is something that should be cultivated in learners from the earliest possible stage.
A 2008 study by Haines and Gomez-Chacon reveals that even though computer use in mathematics classrooms in Spain and England at the time of the study was somewhat attenuated; there was a strong positive correlation between increased computer use and improved achievements in mathematics. The students in the study revealed that the computers helped them to establish connections between various areas of mathematics. The relationship between algebra and geometry was one of these areas. However, commitment to the use of computers for learning mathematics was determined more by the learners’ attitudes towards computers than their attitudes towards mathematics. The study also confirms that generally, learners are open to using computers in learning mathematics; something, which Ardies and colleagues (2015) also illustrate. Therefore, the teacher should avail the necessary resources that will allow integration of computer technology in the mathematics classroom.
Many gaps are yet to be filled in the study of the attitudes of learners towards mathematics and technology. For instance, inasmuch as it is generally accepted that technology enhances learning mathematics, it is also possible that overuse of technology jeopardizes the learning process and turns the classroom from a learning zone to an entertainment zone. This is a key area, which needs to be addressed in future research. There has to be a research, which reveals the exact relationship between the use of technology and the rates of achievement in mathematics. A study by Cox (2008) did not establish any meaningful relationship between use of technology and achievement in mathematics. Furthermore, the sample size in this particular study was too small for the study to have a good level of statistical significance. A study by Aqda, Hamidi, and Rahimi (2011) speculated that continuous use of technology tended to reduce creativity of learners. Future studies in this area need to improve on sample size so as to increase the statistical significance and thus the applicability of the study results to the rest of the population.
Secondly, future studies need to look into the possibility of having other ways of solving the issue of poor attitude in mathematics apart from the nontraditional means of content delivery. Even on the aspects of nontraditional methods of teaching that are increasingly becoming useful in teaching mathematics, there should be efforts to conduct studies that will quantify the effects that the various strategies that consist nontraditional methods have had on achievement in mathematics. Currently, only a few studies have shown that nontraditional methods are able to have improved student attitude towards mathematics but it is not sufficient to confirm that indeed nontraditional methods of content delivery correlate positively with better performance in mathematics.
Lastly, studies towards attitudes of learners in mathematics will make more meaning and will be more helpful in understanding the genesis of the problem and dealing with it if they were focused on various areas of the subject. This means that, instead of a study focusing on asking learners about their attitudes on mathematics, the study should focus on attitudes towards algebra, geometry, statistics or other areas of mathematics. In this way, the results of the study will be more useful in designing teaching strategies that will enhance achievement in narrower areas. strategies meant for very wide subject areas are likely to less influential than those designed for a narrower subject area as the later will address all probable issues while the former fails to address some pertinent issues.
Adaptive Learning and Technology in the Math Classroom
According to Henson (2014), adaptive learning refers to a method of learning and teaching that is meant specifically to address the specific concerns of the learning. Adaptive learning is one of the many techniques that is being employed in teaching nontraditional college mathematics (Henson, 2014). Murray and Perez (2015) have shown that adaptive learning is more effective than traditional learning. Adaptive learning can be personalized. However, with advancement in technology, there has been increased use of automated teaching. Personalized adaptive learning means that a teacher interacts closely with a student with special focus on the academic needs of the student. In automated adaptive learning, technology is used to design a learning tool that is suitable for students of a certain level. This tool is made to have an interactive interface and to ensure that the student chooses whatever they want to engage in by themselves. Moreover, in the case of mathematics, these tools are designed to give students exercises after an amount of content has been delivered. The exercises can be designed to have different levels of difficulty and the learner is allowed to start with what is most comfortable for them as they advance. This not only ensures proper grasp of content but also encourages students who are weak to push on.
In adaptive teaching, there are various strategies by teachers that are meant to enhance the learning process. First, in interactive teaching, the instructor changes tasks to be performed by the student frequently (Goos, 2010). This is meant to alleviate boredom and maintain the concentration of students in the learning process. Moreover, in adaptive teaching, the teacher aims to increase interactions between learners, which could be achieved by cooperative learning especially in the personalized design of adaptive learning. Past research has shown that cooperative learning and working groups has the ability to enhance achievement in mathematics and enhancing attitude (Boaler, 2002). Mixed ability groups are thought to be the best for mathematics. Ability groups make some students feel humiliated hence an even worse attitude.
In addition, adaptive learning has seen changes in teaching methods and course goals (Goos, 2010). As earlier alluded to, adaptive learning in student-centered and as such, learning is predominantly directed by the learners themselves. This mode of teaching-learning which is learner-directed has been shown to be more effective in ensuring that the learners understand difficult mathematical concepts at a pace which is most comfortable for them (Abrami et al., 2008). The change in course goals has seen more emphasis on mastery of key concepts rather than simple memory and completion of the syllabus.
Moreover, Goos (2010) noted that adaptive learning has seen more alignment of the curriculum with research and practice. This has been made possible through the integration of many real-life situations in mathematical problems that need to be computed in the classroom. Moreover, at the college level, mathematical problems are tailored more towards their future careers and situations that they may encounter in these careers and their mathematical skills called upon (Goos, 2010). This enhances interest in mathematics by emphasizing the importance of this subject area in future careers of the college students.
Automated adaptive learning is not the only use of technology in a math classroom. Technology has been used in various other ways in math classrooms. Increased use of class blogs and wikis is one of these areas in which technology has been married with the classroom. With these, learners can share information freely. Moreover, such technological advancements make it far much easier for learners to access mathematical information (Venkatesh et al., 2014). At college level, use of wireless microphones in the classroom has been used to enhance delivery of content. The microphones enable interaction of individual students with the teacher in a way that will benefit the whole class despite the big size of the class. According to Chilton (2012), video links can be used in teaching to make the learning more experiential even when the students are not in physical contact with the teacher.
Chilton (2012) argues that teaching mathematics has been enhanced greatly by the introduction of whiteboards. These boards enable the learners or the teacher to display and manipulate anything easily on a computer screen. This not only enhances visual learning, but also enables students to understand topics like geometry, linear programming, and statistics much better. Furthermore, utilization of video games in the classroom especially in mathematics has significantly increased the motivation of learners.
Technology has also seen the development of numerous software that are dispensable at college level mathematics. These tools include drawing tools that can be used to develop all kinds of geometrical shapes and charts like graphic calculators, dynamic graphing tools, and dynamic geometry tools. There are also tools for data manipulation and storage like Microsoft excel and Microsoft mathematics. Geo Gebra is a software tool that can assist learners in computing algebraic expressions (Gómez-Chacón, 2011); algebra is one of the most problematic areas in mathematics. MathLab is an all-inclusive software tool that is meant to help learners by making a wide range of mathematical concepts much easier (Pearson Education, 2015). The application is used in the delivery of content and assessment of learners.
Use of technology was first introduced in teaching mathematics for various reasons. First, as one of the key principles of adaptive learning and teaching, a change of scenario is important. Technology is one of the ways in which this change can be achieved. Change of scenario alleviates boredom and enhances concentration and understanding of mathematics. Moreover, use of technology has been lauded for making idea tangible. Increased tangibility and ability to visualize concepts from various angles greatly enhances learning in mathematics is in accordance with the perceptual variability principle (Subong, n.d.). Students to not have to great ability of imagination for them to perform well in mathematics.
Use of technology has effectively enhanced the performance of learners in mathematics (Gómez-Chacón, 2011). Teachers have also benefited from the use of technology in their work. With technology, it is easier for a teacher to plan a lesson and deliver their lesson. Moreover, technology allows for faster communication between the teacher and the learners hence it is possible to save time and for the teacher to access more learners and attend to their specific needs in shorter time. With the inception of adaptive learning, technology has become a necessity in teaching mathematics for nontraditional college-level students (Henson, 2014). This is because adaptive learning requires the teacher to pay close details to the students; this can only be possible in a purely personalized adaptive learning setup if the number of teachers is big enough to give every teacher only a few students with whom they can interact closely. However, with technology and automated adaptive learning tools, it is possible for one teacher to pay attention to the needs of more learners. By extension, this is an advantage to the college boards as they do not have to employ more instructors. Generally, a blended environment that emphasizes on adaptive learning, modern teaching methods, and use of technology enhances learning effectiveness (Chew, 2011).
One controversy with the use of technology in the math classroom is the ability of technology to bridge the gap between the performance of boys and girls in mathematics. Over the years, it has been shown that boys have consistently outperformed girls in mathematics at various levels. Myers (2009) showed that use of GSP technology seemed to bridge the gap between boys and girls in their algebra marks. However, it could not be confirmed that it was this technology which helped in bridging this gap. Moreover, this study was somewhat controversial; the sample size used for this study was less than one hundred participants (Myers, 2009). This sample size is too small to give the study great significance. Moreover, the diversity of the students used in that study was not representative of the situation in the rest of the country. Most importantly, the teacher who participated in the study, both for the control and the study groups, had attended a short in-service training on proper teaching of algebra (Myers, 2009). This is likely to have affected the results.
Inasmuch as it is almost conventionally obvious that technology has helped in improving learners’ attitudes towards mathematics, various studies have proven otherwise. It is even thought the widespread negative attitude towards mathematics is contributed to by the notion that technology has come to replace the necessity of mathematics in life. Future studies should focus on resolving this controversy.
In future, it is important for studies on the influence of technology on mathematics to focus on specific areas of the curriculum rather than on mathematics as a whole. Apart from enhancing the accuracy of the research findings, the usefulness of the findings in enhancing the teaching of that particular subject area will be enhanced. It is also key for such researches to have a good sample size and other aspects of the study that can improve their statistical significance.
Finally, it has been established that indeed technology motivates the learners, more so in a subject like mathematics where poor attitude is so widespread (Berger & Karabenick, 2011). However, there needs to be more research on the way technology affects the teachers. Does technology motivate the teachers too? Do the teachers think that use of technology enhances the delivery of content? A study by Baylor and Ritchie (2002) revealed few factors that the perception of teachers on technology including their off-class computer use. However, this study was not conclusive and further studies will be helpful. More importantly, research should look to establish the prowess of math teachers in matters technology. Teachers cannot teach math using technology when they themselves are poor in technology. Research should establish just how much teachers know about technology and identify the areas that need to be filled by way of in-service training sessions. Moreover, future research should involve more teachers to determine what teachers think are the best ways on integrating technology into the math classroom and the best ways of using this technology to teach math concepts. Niess (2005) says that continuous training of teachers important to develop pedagogical skills at the same pace as technology used in teaching improves. Oliver and Stallings (2014) assert that there is a need for continuous teacher preparation as the challenges and technologies that are utilized in education keep changing.
References
Abrami, P. C., Bernard, R., Wade, A., Schmid, R. F., Borokhovski, E., Tamin, R., … Newman, S. (2008). A review of e-learning in Canada: A rough sketch of the evidence, gaps and promising directions. Canadian Journal of Learning and Technology/La revue canadienne de l’apprentissage et de la technologie, 32(3). Retrieved from https://www.cjlt.ca/index.php/cjlt/article/view/26464
Aqda, M. F., Hamidi, F., & Rahimi, M. (2011). The comparative effect of computer-aided instruction and traditional teaching on student’s creativity in math classes. Procedia Computer Science, 3(1), 266-270.
Ardies, J., De Maeyer, S., Gijbels, D., & van Keulen, H. (2015). Students attitudes towards technology. International Journal of Technology and Design Education, 25(1), 43-65.
Baylor, A. L., & Ritchie, D. (2002). What factors facilitate teacher skill, teacher morale, and perceived student learning in technology-using classrooms?. Computers & education, 39(4), 395-414
Beilock, S. L., & Maloney, E. A. (2015). Math Anxiety A Factor in Math Achievement Not to Be Ignored. Policy Insights from the Behavioral and Brain Sciences, 2(1), 4-12.
Benken, B. M., Ramirez, J., Li, X., & Wetendorf, S. (2015). Developmental Mathematics Success: Impact of Students’ Knowledge and Attitudes. Journal of developmental education, 38(2), 14-31.
Berger, J. L., & Karabenick, S. A. (2011). Motivation and students’ use of learning strategies: Evidence of unidirectional effects in mathematics classrooms. Learning and Instruction, 21(3), 416-428.
Boaler, J. (2002). Experiencing school mathematics: Traditional and reform approaches to teaching and their impact on student learning. Mahwah, N.J: L.Erlbaum.
Bonham, B. S., & Boylan, H. R. (2011). Developmental mathematics: Challenges, promising practices, and recent initiatives. Journal of Developmental Education, 34(3), 2-10.
Chew, L. K., LaBoone, E., Low, S., Attallah, S., Toon, A., & Cheang, P. (2011, March). Learning Effectiveness of an Upper Level Math Course in a Blended Environment for Adult Learners. Global Learn, 2011(1), 1868-1876.
Chilton, M. A. (2012). Technology in the classroom: using video links to enable long distance experiential learning. Journal of Information Systems Education, 23(1), 51-62.
Cox, T. D. (2008). Learning styles and students’ attitudes toward the use of technology in higher and adult education classes. Institute for Learning Styles Journal, 1(Fall 2008), 1-13.
Curtis, K. M. (2006). Improving student attitudes: A study of a mathematics curriculum innovation (Doctoral dissertation, Kansas State University).
Davidson, J. C., & Petrosko, J. M. (2015). Predictors of persistence for developmental math students in a community and technical college system. Community College Journal of Research and Practice, 39(2), 163-178.
Frey, N., & Fisher, D. (2008). Doing the right thing with technology. English Journal, 38-42.
Furner, J. M., & Berman, B. T. (2003). Review of research: math anxiety: overcoming a major obstacle to the improvement of student math performance. Childhood education, 79(3), 170-174.
Gómez-Chacón, I. M. (2011). Mathematics Attitudes in Computerized Environments. In Model-Centered Learning (pp. 145-168). SensePublishers.
Gómez-Chacón, I. Mª and Haines, C.(2008). Students’ attitudes to mathematics and technology. Comparative study between the United Kingdom and Spain. In ICME-11, 11th International Congress on Mathematical Education.
Goos, M. (2010). Using Technology to support effective mathematics teaching and learning: what counts? Retrieved from http://research.acer.edu.au/cgi/viewcontent.cgi?article=1067&context=research_conference
Hannigan, A., Hegarty, A. C., & McGrath, D. (2014). Attitudes towards statistics of graduate entry medical students: the role of prior learning experiences. BMC medical education, 14(1), 70.
Henson, A. R. (2014). The success of nontraditional college students in an IT world. Research in Higher Education Journal, 25, 1.
Le, C., Rogers, K. R., & Santos, J. (2011). Innovations in Developmental Math: Community Colleges Enhance Support for Nontraditional Students. Jobs for the Future. Retried from http://www.jff.org/sites/default/files/publications/MetLife-DevMath-040711.pdf
Moore, N. D. (2012). Alternative Strategies for Teaching Mathematics (Master’s thesis). Retrieved from http://digitalcommons.brockport.edu/cgi/viewcontent.cgi?article=1132&context=ehd_theses
Murray, M. C., & Pérez, J. (2015). Informing and performing: A study comparing adaptive learning to traditional learning. DigitalCommons@ Kennesaw State University.
Myers, R. Y. (2009). The effects of the use of technology in mathematics instruction on student acheivement. FIU Electronic Theses and Dissertations, 136.
Niess, M. L. (2005). Preparing teachers to teach science and mathematics with technology: Developing a technology pedagogical content knowledge. Teaching and teacher education, 21(5), 509-523.
Oliver, K., & Stallings, D. (2014). Preparing teachers for emerging blended learning environments. Journal of Technology and Teacher Education, 22(1), 57-81.
Pearson Education, (2015). MyMathLab. In Pearson Higher Education. Retrieved October 13, 2015, from http://www.pearsonhighered.com/educator/product/MYMATHLAB/9780321527509.page
Rodrigues, K. J. (2012). It does matter how we teach math. Journal of Adult Education, 41(1), 29.
Subong, R. (n.d.). Mathematics learning according to Zoltan P. Dienes. In Teachmath. Retrieved from http://teachmath.yolasite.com
Venkatesh, V., Croteau, A. M., & Rabah, J. (2014, January). Perceptions of effectiveness of instructional uses of technology in higher education in an era of Web 2.0. In System Sciences (HICSS), 2014 47th Hawaii International Conference on (pp. 110-119). IEEE.
Wolfle, J. D., & Williams, M. R. (2014). The impact of developmental mathematics courses and age, gender, and race and ethnicity on persistence and academic performance in Virginia community colleges. Community College Journal of Research and Practice, 38(2-3), 144-153.
