Christine Pries
Self-efficacy: The Missing Link in Math Education
Problems in Math Education and Necessary Reforms
Adviser: Mr. Logsdon
One’s individual education can determine much in their life. A country’s education of its people as a whole can similarly determine the success of that country. Therefore, countries which best educate their people become the superior countries in the world. “The nation’s capacity to innovate for economic growth and the ability of [its] workers to thrive in the global economy depend on a broad foundation of math and science learning” (The Opportunity Equation). To be a world leader, a world superpower, a country needs of population of intelligent, creative, capable people, trained through a good education to handle the world’s challenges. Of course the US is considered a world superpower, but to retain this position the nation must see a turnaround in its students’ success, particularly in math and science. Proper education systems as well as high student motivation combine to create an effective education. The United States used to be up on top. Now, however, the United States' education system has fallen behind other leading countries in the world, specifically in mathematics. Reform in the education system is necessary, but a reform must also occur in students' mentality rather than simply increased spending in new education programs.
The United States is currently stuck in a lull of educational mediocrity. Local math teacher David Alger calls math education in our country “outdated.” We have not been truly improving the system to keep up with advancements in the world. Many countries are swept up in a fierce, worldwide race to show off the best strategy for school success, and the US is far from leading this race. To exemplify, “only 7 percent of [United States] students reached the advanced level in eighth-grade math, while 48 percent of eighth graders in Singapore and 47 percent of eighth graders in South Korea reached the advanced level. As those with superior math and science skills increasingly thrive in a global economy, the lag among American students could be a cause for concern” (Rich). The deficiencies are easy to identify; how to solve the problem is less easy. The US needs major reform rather than simply increased funding, as there is little correlation between expenditures and achievement in education. Student achievement stays at the same level, or can even lower, despite drastic increases in education spending (Joecks). The problems with where this increased spending is being directed will be addressed throughout this paper. While new education reforms in the US have good intentions, they may actually be working against what this country needs.
Low levels of advanced achievement are occurring in the US because classrooms are essentially turning into test-prep centers. Schools want their students to be able to pass the mandatory tests for students to be able to graduate and for the school to get funding. This baseline system does not provide support for the students who are able to, and are looking to, go above and beyond. It also does not provide a thorough education which allows for creative problem solving and future ingenuity, rather just the knowledge necessary to pass some standardized tests. Education is faulted when “depth and cohesion are abandoned for isolated skills found on standardized tests” (Steen). As an example, one can look to the No Child Left Behind policy. Students must pass a minimal proficiency bar in reading and math. Once students are able to do so, there are little means available to follow or analyze progress. No Child Left Behind's accountability metrics do not provide any useful information about schools once most of the students achieve the policy’s modest aims. No Child Left Behind had a noble-sounding goal, to get every child past a basic level of education. The result was not helpful, however. Because of “the lack of demonstrable progress in improving educational performance in mathematics...some people view the problem as inherently unsolvable within a system of public education” (Steen). The ideas are coming from the right place, and it is highly agreed upon that we need educational reform, but reforms that do not actually achieve anything cause the success of the US education system to seem even less achievable.
There are many clear gaps where reform is needed. An overarching need is for wider measures of excellence. When there is just one minimum bar that students must pass, students with the ability to really achieve higher standards are not supported while most efforts and resources become dedicated to getting everyone up to the minimum level. More personalized education methods fit into this model. “Children fortunate enough to have math teachers who allow them to build on their own understanding and experiences have outperformed children who are products of rote drill on mathematical problem-solving tasks and on traditional standardized tests” (Curcio). Not all students will succeed by simply following a standardized education plan characterized by this rote drilling. Advanced students have different needs than students who are struggling to catch up to the minimum proficiency level. A school, and a country’s whole education system, cannot focus on either group at the expense of the other. Struggling students cannot be left behind, but advanced students should not be forgotten either. A more personalized education system would also support independent learners. Independent learners have the motivation to learn, but are not provided the resources in the current classroom settings. Reform efforts supporting independence in education will foster long term success for the students in this nation.
As would be expected, much reform will have to come from teachers. Professional development is vital, especially in terms of teachers learning new technologies, but also in realizing the psychological needs of students in order to succeed. “Educators must feel confident in their mathematical abilities so that they can instill this confidence in their students. Students will pick up on the confidence the teacher feels and will be better positioned to successfully complete mathematical problems assigned to them. Students need to feel capable, confident, and comfortable with mathematics. One way to instill this confidence is to help students understand that they often use mathematics in their daily lives already” (Scarpello). Teachers must be concrete with their content knowledge in the subjects that they plan to teach. “Data [collected in a survey by Susan Haag and Colleen Megowan] revealed that the majority (60%) of 324 in-service teachers are interested in pursuing additional education, beyond that reflected on their current transcript, as a route to becoming more competent in teaching and integrating science and mathematics” (Haag). Teachers are aware that they need more developed content knowledge to be successful math teachers. When the teacher really knows their subject, they will be confident when teaching the material to the students. This confidence will carry over to produce confidence in the students learning from the teachers. Confidence in subject matter also leads to a positive classroom environment. Current Manchester Essex Regional High School math student Michael Chlumecky says that his favorite part of Pre-Calc class with Mr. Alger is the “relaxed classroom environment.” This comfortable classroom environment allows Mike to feel “ready to do math.” Confidence and comfort are both necessary when trying to solve tricky math problems, and both can be felt by students if they have a teacher which portray these in their classroom.
Right now, the country has a lack of teachers with the capabilities to do what needs to be done. The US is not lacking capable people to become teachers, but is lacking the incentive for these capable people to choose teaching as their career. Programs such as Teach For America are good, but “surveys suggest there are tens of thousands of other talented grads every year who also might be inclined to teach, albeit in less demanding circumstances and with less emphasis on a mission to ‘close the gap.’ Rather than recruiting such candidates, reformers have ignored or dismissed them. Plenty of promising candidates might be enticed into teaching by starting salaries that average close to $40,000 for ten months' work, the chance to make a difference, and the substitution of focused TFA-style preparation for vacuous ed-school courses. In a nation that scrambles to hire 300,000 new teachers a year, it's hard to think of a more pressing educational priority than tapping new sources of teaching talent” (Hess). Various conspicuous shortages of teachers have been recognized in the country, and many are trying to address the problem. For example, “the nation's middle schools suffer from a shortage of qualified science and mathematics teachers. To address this need, one university in the southwest has developed the Modeling Institute, a master's degree program for in-service elementary educators interested in teaching science and mathematics at the middle school level” (Haag). Efforts are being made to increase the number of teachers available to schools. If the US wants to really make a reform and improve its education system, the country will need to reevaluate how to make a teaching career appealing to qualified people.
A final prominent reason for the lack of success in the US education system lies in the educational aspirations of students, or lack thereof. An education can only be successful and meaningful in a curious student who is intrinsically motivated to learn. The student must, at least to some degree, want to learn and want to succeed. Attached onto this crucial mindset for students is a necessary amount of self-confidence. Students will not have the motivation to learn if they do not view themselves as capable of doing well in school. Math is a particularly vulnerable subject for those students with lower self-esteem because of Math’s association with being a very difficult subject. “Math anxiety forms early in elementary school. In some cases, this anxiety starts as early as grade four for students. For some teachers, there is also a level of anxiety since math is a challenging subject to teach and many lack the confidence necessary to teach it” (Lazaros). A continuation of the same idea, “students learning math” have been referred to as “one population especially vulnerable to frustration, distraction and misery” (Gulli). This is where self-efficacy comes into play. “Self-efficacy is a personal belief in one’s capability to organize and execute courses of action required to attain designated types of performances” (Artino). Famous psychology Albert Bandura summarized the importance of self-efficacy in the following way:
“People make causal contributions to their own psychosocial functioning through mechanisms of personal agency. Among the mechanisms of agency, none is more central or pervasive than beliefs of personal efficacy. Unless people believe they can produce desired effects by their actions, they have little incentive to act. Efficacy belief, therefore, is a major basis of action. People guide their lives by their beliefs of personal efficacy” (Bandura).
Without this personal belief in oneself, which often couples with an intrinsic motivation to learn, schools will not see significant success. This favorable mindset is far from impossible to achieve, “a positive attitude toward mathematics and toward teaching math is salient. Pupils feel this attitude coming from the teacher and it becomes a part of the repertoire of learners in the classroom” (Ediger). Students’ motivation is so tied to achievement that fostering self-efficacy and developing students’ curiosity and desire to learn is more important than any other factors in education reform.
It is intuitive that motivation is tied to success in learning. Having a motivation to learn causes students to take initiative within their education and really understand material. Self-efficacy has been a key component in theories of motivation and learning in varied contexts, but in the context of education, self-efficacy easily takes a prominent role. “People who have low self-efficacy for accomplishing a specific task may avoid it, while those who believe they are capable are more likely to participate” (Artino). An active participation in one’s education takes it to the next level. It is interesting to note that “Bandura argued...that the most useful efficacy judgments are those that slightly exceed one’s actual capabilities, as this modest overestimation can actually increase effort and persistence during difficult times” (Artino). The research of Bandura is a major source of information about self-efficacy. The self-efficacy component of Bandura’s social-cognitive theory has had a profound impact on the study of motivation and achievement in academic settings. According to Sources of Middle School Students’ Self-Efficacy in Mathematics: A Qualitative Investigation, “teaching structures, course placement, and students’ self-regulated learning also emerged as important factors related to self-efficacy” (Usher). Since self-efficacy is so tied to motivation, and motivation is so tied to education success, then reform must be focused around these specific areas that will foster self-efficacy in students. Cultivating this confidence, a mentality of capability, in students is more important to this country’s education system than other reforms that the country has been implementing. Self-efficacy, a boosted psychological edge in students, is what schools really need in order to yield successful students.
Students’ motivation to really dive into their education allows their education to have a more lasting impact. When students are motivated to take a hold of their own education, their mind can make more meaningful connections with the information learned. Dan Meyer, a high school math teacher, in a lecture for the series TED Talks, stated, “I sell a product to a market that doesn't want it, but is forced by law to buy it. I mean, it's just a losing proposition...I could give you guys [the audience] an algebra-two final exam, and I would expect no higher than a 25 percent pass rate. And both of these facts say less about you or my students than they do about what we call math education in the U.S. today.” The whole system would change, however, if students wanted the ‘product’ that math teachers are ‘selling.’ Students who take a more active role in their education will be able to, as adults, still pass that Algebra exam. In fact, Meyer went on in his lecture to detail lack of initiative as the first problem students have in the math classroom. It has been proven by major psychologists that “any information or skill one doesn’t actively use tends to be forgotten” (Saphier). A motivated student, however, actively uses what they learn in further studies or in applications in their daily life. Alger agrees that students need to become more proficient at “authentic problem solving.” When students can work with problems in terms of real world applications, they will see more success from their education, affirms Alger. This allows them to retain the information. Once students initiate a commitment to their education, they will see success. Any small successes add to a student's’ sense of self-competence. All of these factors lead to a positive feedback loop, keeping students interested in their studies, actively seeking and using information.
Increased self-efficacy in students should be one the highest goals in educational reform. This is going to mostly come from the teacher changing the environment within a classroom. When established properly, school can be an agency for cultivating self-efficacy. “A fundamental goal of education is to equip students with self-regulatory capabilities that enable them to educate themselves. Self-directedness not only contributes to success in formal instruction but also promotes lifelong learning” (Bandura). Students, once equipped with the proper efficacy beliefs, will feel the motivation to pursue the intrinsic interests that are needed to educate themselves throughout their life. When teachers deliver efficacy information to their students through both verbal and social persuasion, students come to the belief that they can overcome difficult problems and situations. “Pupils need encouragement to be creative in finding their own best way to solve problems. There are different algorithms to use in finding answers to many problems” (Ediger). Encouragement is necessary for self-confidence within students. Too much encouragement runs the risk of becoming too false, however. A word of warning to teachers is that “overly optimistic persuasive comments tend to be ineffective, particularly if the individual being persuaded ultimately fails—a result that acts to discredit the persuader and undermine the recipient’s efficacy beliefs” (Artino). The main idea is that all teachers need to pay attention to the individual situations of their students. It is very important for teachers to have an understanding of what concepts students are likely know before instruction on a certain topic, and what typical difficulties for students occur on a given concept or topic so that the teacher can foresee trouble areas and be ready to provide support for certain students. Especially in mathematics, analogies or alternative methods of explanation can really be utilized by teachers. Drawings, diagrams, or real world applications of certain problem types may help students grasp the concept or information in a more indepth way. Current MERHS student, Sofia Del Valle, wishes that real world problems were discussed more in math classes. She wishes to learn about “loans, mortgages, or any problems that we will have to deal with once we are out in the world living on our own.” If students like Sofia were learning about mathematical issues that they were curious about, they would take a greater interest in their education. Real world applications are great because they keep students interested, help students to see why there is a greater meaning to what they are learning, and help students to make more meaningful connections in their brain with the information being presented in the classroom; “and because this is the 21st century and we would love to talk about the real world on its own terms, not in terms of line art or clip art that you so often see in textbooks, we go out and we take a picture of it” (Meyer). It is important to keep in mind, though, that “Demonstrating the use of subject matter must be in proper order, developmentally appropriate, challenging, and assist in achieving successful learners” (Ediger). Teachers must be able to know how to choose between different instructional methods for a given topic for a given class or even a given individual student. An entire curriculum cannot be standardized because it will not work with each student’s learning capabilities. Furthermore, Alger discussed the flaws of a standardized curriculum because not every single student needs to know the same information. Students want to, and should, follow different paths in their education as they follow different paths through their lives. When the curriculum or class work and the student’s learning capabilities do not mesh, then the student will lose motivation.
Moving forward, it must be understood that curiosity can take students into a far more thorough education. This curiosity cannot exist without some intrinsic motivation to work on their education, which is fueled by self-efficacy. If self-efficacy is really nurtured in classrooms, this country will see more success than any other single reform efforts in education. One student’s individual exploration into their education will take him or her from the level of passing a minimum proficiency test to become a curious, smart, possibly inventive member of the US society. The key is to “empower students with the realization that mathematical knowledge (not to mention much else that we learn in school) does not come predigested from teachers and books, but is a product of their own thought and exploration” (Rubin). Especially in this day and age, with vast technological resources, a little curiosity can take a student a long way. “As information technologies continue to revolutionize teaching [and] learning...it seems likely that strong, resilient efficacy beliefs will become even more critical for individuals...as they attempt to exercise control over their own learning in progressively more independent, technology-mediated learning environments” (Artino). Math teacher Dan Meyer “encourage[s] math teachers...to use multimedia, because it brings the real world into [their] classroom in high resolution and full color.” The potential for learning information is immense, greater than ever before because of technology, but students will never take advantage of it without self-efficacy and a little motivation.
Previous and current education reform efforts have a solid basis, and should be continued. Specifically, President Obama’s education reforms can continue to be developed; focus should be less on lessening the gap between successful and struggling students, however, and instead be on improvement by every student. The US has been lagging behind while “the swift competition and progress in a globally changing economic and technological environment have been one of the driving forces for enhancing educational accountability in many countries” (Suthar). It is time for the US, too, to become accountable for the dropping standards in its education and improve students performance before this country loses its place as a world superpower. “Educators, students, parents, leaders of universities, museums, and the business and professional communities, scientists and mathematicians, and public officials at all levels will need to embrace a new understanding that the world has shifted dramatically—and that an equally dramatic shift is needed in educational expectations and the design of schooling. As a society, we must commit ourselves to the proposition that all students can achieve at high levels in math and science...and that we owe it to them to structure and staff our educational system accordingly” (The Opportunity Equation). Teaching that improves self-efficacy in students will result in more success in mathematics, as well any other area of schooling. “Math makes sense of the world. Math is the vocabulary for your own intuition. So I just really encourage you, whatever your stake is in education -- whether you're a student, parent, teacher, policy maker, whatever -- insist on better math curriculum. We need more patient problem solvers” (Meyer). Money that is being poured into educational reform programs could be essentially wasted if students are not taking advantage of all that their education has to offer. An effort to really change the psychological mindset of students, in conjunction with current educational reform efforts, will bring the United States back up in the charts as a world leader.
Much of the research compiled to construct this paper is idealistic. Traditional teaching methods must be in part retained because there are basic sets of facts and knowledge that later schooling will assume that all students have memorized, basic math facts and the like that are drilled into students from the beginning of schooling. Furthermore, some goals for education reform presented in this paper are impractical because of the limit of money and other resources. Education, public education particularly, simply can never be so individualized because of the limit of the number of teachers, number of classrooms, and limit of all resources involved in schooling. In the end, however, and increased focus on the confidence of students, and the increased future success of all students, is necessary. Self-efficacy in this nation’s students is the key to turning around the downward slope that US finds itself in in comparison to other nations. Education reforms centered around closing the gap between students, with all students attempting to reach just a minimum proficiency level, will not raise the US up as a continued world power. Motivated students who take a real interest in their education will become the engineers, inventors, and smart citizens that this country needs, and psychological reforms are needed in classrooms to encourage students to be this way.
Works Cited
Alter, Jonathan. "Obama's class project." Newsweek 20 Sept. 2010: 58. General OneFile. Web.
14 Mar. 2013.
Alger, David. Personal interview. 22 May. 2013.
Artino, Anthony R. "Academic Self-efficacy: From Educational Theory to Instructional
Practice." Perspectives on Medical Education 1.2 (2012): 76-85. www.ncbi.nlm.nih.gov.
Springer Open Choice, 11 Apr. 2012. Web. 14 Mar. 2013.
Bandura, Albert. Self-efficacy: The Exercise of Control. New York: W.H. Freeman, 1997. Print.
Chakrabarti, Rajashri. "Program design, incentives, and response: evidence from educational
interventions." Federal Reserve Bank of New York Economic Policy Review Oct. 2010: 1+.General OneFile. Web. 14 Mar. 2013.
Chlumecky, Michael. Personal interview. 23 May. 2013.
Curcio, Frances R. "Research Backs Reform." New York Times 17 Aug. 1997. Global Issues In
Context. Web. 8 May 2013.
Del Valle, Sofia. Personal interview. 22 May. 2013.
Ediger, Marlow. "Quality teaching in mathematics." Education 133.2 (2012): 235+. Student
Edition. Web. 7 May 2013.
"Education secretary will waive key education reform requirement." American School &
University [Online Exclusive] 8 Aug. 2011.General OneFile. Web. 14 Mar. 2013.
Gabriele, Anthony J., and Elana Joram. "Teachers' Reflections on Their Reform-Based Teaching
in Mathematics: Implications for the Development of Teacher Self-Efficacy." Action in
Teacher Education (2007). Academic OneFile. Web. 14 Mar. 2013.
Gulli, Cathy. "'Emotional' computers: high-tech tutors encourage, empathize with math students."
Maclean's 29 Mar. 2010: 53. Global Issues In Context. Web. 8 May 2013.
Haag, Susan, and Colleen Megowan. "Beyond the transcript: factors influencing the pursuit of
Science and mathematics coursework." School Science and Mathematics 112.8 (2012): 455+. Student Edition. Web. 7 May 2013.
Hess, Frederick M. "Excellence for all: getting past the minimum-standards mentality." National
Review 31 Oct. 2011: 48. General OneFile. Web. 14 Mar. 2013.
Joecks, Victor. "Analysis Shows Little to No Correlation between Education Spending and
Student Achievement Nevada Policy Research Institute." Http://www.npri.org/. Nevada Policy Research Institute, 17 May 2012. Web. 05 May 2013.
Joo, Young-Ju, Mimi Bong, and Ha-Jeen Choi. "Self-efficacy for Self-regulated Learning,
Academic Self-efficacy, and Internet Self-efficacy in Web-based Instruction."Educational Technology Research and Development 48.2 (2000): 5-17. Print.
Lamb, Evelyn. "Too cool for school." Scientific American 307.6 (2012): 22. Student Edition.
Web. 7 May 2013.
Lave, Jean. Cognition in Practice: Mind, Mathematics, and Culture in Everyday Life.
Cambridge: Cambridge UP, 1988. Print.
Lazaros, Edward J. "Promoting the study of mathematics by using Internet resources in the
technology and engineering classroom." Children's Technology and Engineering Mar.
2013: 10+. Student Edition. Web. 7 May 2013.
Meyer, Dan. "Math Class Needs a Makeover." TEDxNYED. 21 May 2013. Ted.com. TED, May
2010. Web. 21 May 2013. <http://www.ted.com/talks/dan_
MC Wong, TC Lau, and A. Lee. "The Impact of Leadership Programme on Self-esteem and Self-
efficacy in School: A Randomized Controlled Trial." PLOS One 7.12 (2012): n. pag.
Pubmed.gov. 18 Dec. 2012. Web. 14 Mar. 2013.
"McGraw-Hill Education Comes to an Agreement with Vibal Publishing to Adapt K-12 Math
Program for Schools in Philippines."Entertainment Close-up 8 Oct. 2012. General OneFile. Web. 14 Mar. 2013.
McManus, John F. "Math and science scores show U.S. students far behind many others." The
New American 21 Jan. 2013: 9. General OneFile. Web. 14 Mar. 2013.
Rich, Motoko. "U.S. Students Still Lag Globally In Math and Science, Tests Show."Nytimes.com.
The New York Times, 11 Dec. 2012. Web. 05 May 2013.
Rubin / TERC, Andee. "Technology Meets Math Education: Envisioning a Practical Future
Forum on the Future of Technology in Education." CIMM.UCR.ac.cr. Universidad De
Costa Rica, n.d. Web. 14 Mar. 2013.
Saphier, Jon, and Robert R. Gower. The Skillful Teacher: Building Your Teaching Skills. Acton,
MA: Research for Better Teaching, 1997. Print.
Scarpello, G. (2010). Tips for teaching math to elementary students. The Education Digest,
76(1), 59-60.
Steen, Lynn A. "Math Education at Risk." Issues in Science and Technology 19.4 (2003): 79-81.
Stolaf.edu. National Academy of Science. Web. 14 Mar. 2013.
Suthar, Velo, and Rohani Ahmad Tarmizi. "Effects of students' beliefs on mathematics and
achievement of university students: regression analysis approach." Journal of Social Sciences Apr. 2010: 146+. Global Issues In Context. Web. 8 May 2013.
"Testing times; Exam reform." The Economist [US] 22 Sept. 2012: 33(US). General OneFile.
Web. 14 Mar. 2013.
The Opportunity Equation: Transforming Mathematics and Science Education for Citizenship
and the Global Economy. Rep. New York: Carnegie Corporation, 2009. Print.
Usher, Ellen L. "Sources of Middle School Students' Self-Efficacy in Mathematics: A Qualitative Investigation." American Educational Research Journal (2009). Academic OneFile. Web. 14 Mar. 2013.
