Instructional Strategies for Reducing Student Math Anxiety

Abstract

In order to create citizens able to compete in a technologically-driven global market, it is critical that education supports and prepares all students in mathematics. Math anxiety greatly affects student performance in math. Math anxiety is negatively correlated with working memory. There are several versions of a survey that measures math anxiety. Instructional strategies that address working memory on the items in the survey should reduce math anxiety. Introduction

According to the US Department of Education (2007) 75% of the fastest growing occupations require significant science and mathematics training (STEM). Our education system needs to prepare all students to compete in a global market dominated by STEM. Students know this world is their future. And many students are keenly aware they are not succeeding in the mathematics classroom. There are lots of people writing lots of papers and editorials pointing lots of fingers. The job of the teacher is to meet the students where they are and move them forward in their education. Research has shown that math anxiety greatly affects student performance in math (Ashcraft, 2007). Reducing a student’s math anxiety should result in an increase in that student’s learning and achievement. The secondary math teacher seeking to improve his or her teaching and helping their students achieve must focus on those instructional strategies that can be accomplished within the constraints of teaching math to one hundred twenty high school students seen for fifty minutes per day, five days per week, for thirty-six weeks per year. Math anxiety interferes with my students’ achievement of their dreams for themselves. Anything that is an obstacle to my students’ learning is something that needs to be addressed. Literature Review

A recent editorial (Large, 2013) described a principal who changed his approach to student discipline based on how early childhood trauma can affect brain development. The tool mentioned in the editorial for quantifying traumatic childhood events is known as the Adverse Childhood Experience Survey (ACES). I noticed that many of my students who struggle with math tend to have higher ACES scores. I began this literature review seeking research that would correlate ACES with math achievement. I could find no research linking them. Instead of research correlating ACES with math achievement, I found abundant literature about math anxiety and classroom instructional strategies that interested me as a high-school math teacher. I found many articles written by neurologists for other neurologists about how the brain learns. I found many articles written by educators for other educators about classroom instructional strategies.

I found few articles written by neurologists for educators and few articles written by educators for neurologists that connected how the brain works to classroom instructional strategies. Most of the articles that did bridge these two disciplines were not applicable to the high school math classroom. The purpose of this literature review is to investigate classroom instructional strategies that reduce math anxiety. One emergent theme is that instructional strategies targeting working memory and/or cognitive load should work to lower math anxiety. The research for this review revealed several versions of a tested survey that accurately measures math anxiety. A second theme of this paper will focus on instructional strategies that target the items on one version of this survey. This literature review will conclude by identifying three possible avenues for future research. Math Anxiety

Most people would define math anxiety as being anxious about math. Math anxiety is most often considered when examining student math performance. Ashcraft (2002) defines math anxiety as a feeling of tension, apprehension, or fear that interferes with math performance. Kagan (1987) defines math anxiety as feelings of tension that interfere with the manipulations of numbers and the solving of math problems. Math anxiety is not something specific like a broken bone where we see the fracture or the measles where we confirm the presence of a virus. A working analogy for math anxiety might be depression where a person is given a list of symptoms and the person self-reports how many symptoms and how severely the symptoms manifest in the person’s life. Just as a person who feels sadness over the death of a loved one would not be diagnosed with clinical depression neither would a person who merely gets nervous before taking an algebra final be diagnosed with math anxiety. Are certain people genetically or neurologically predisposed to math anxiety (the “nature” argument)? Does math anxiety arise from certain environmental factors that can be prevented or overcome (the “nurture” argument)? There is evidence to support both nature and nurture. On the “nature” side of the argument, we know that some people are born with or are deeply embedded with learning disabilities. Krinziger (2009) found that mathematical learning disabilities are often associated with math anxiety. Sweller (2011) assumed that working memory is a fixed trait and that working memory strength predicts a child’s cognitive flexibility. Blackwell (2009) correlated this flexibility to mathematical aptitude. The evidence that math anxiety is related to differences in the spatial reasoning abilities found in men and women also strongly suggests a genetic component for math anxiety (Robert, 2003).

Perhaps most telling is the suggestion from Maloney (2010) that the deficit in counting, but not subitizing1, demonstrates that the problem of math anxiety “exists at a level far more basic than would be predicted from the extant literature.” To summarize, having a brain that is not good at math will cause math anxiety, just as having a body that is not good at tennis will cause anxiety when one is told to play tennis. However, there is a great deal more research that math anxiety comes from environmental factors. Kagan’s research (1987), which demonstrated that numeric anxiety could not be distinguished from text anxiety, implied that math anxiety is unrelated to math ability. Seyler’s study (2003) demonstrated that problems and strategies can become associated regardless of the correctness of the strategy. Ben Zeev (1998) discovered a taxonomy of rule-based errors in mathematical reasoning that illustrates how a few basic mental processes might be responsible for generating a whole host of different math errors. Ben Zeev’s finding further disconnects math anxiety from innate math ability. Perhaps most indicative that math ability and math anxiety can be traced to environmental factors are the studies that link math anxiety with learned helplessness. Akin, Dweck, and Ozgen were all cited by Stevens (2006) as having the same conclusion: self-efficacy, the sources of self-efficacy, and emotional feedback are all stronger predictors of math performance than general mental ability. These findings suggest that students with adequate math ability will not automatically succeed in math if the same students are impaired by math anxiety. Cognitive Load Theory

Research into math anxiety has consistently demonstrated a strong negative correlation with working memory. Cognitive Load Theory (CLT) is an instructional theory based on human cognitive architecture (Sweller, 2011). CLT is based on research into memory. A person’s long-term memory is assumed to be extremely large but working memory is extremely limited in both capacity and duration (Sweller, 2011). Foundational to CLT is the interaction between long-term memory and working memory. According to CLT learning can only occur when the total demand on working memory does not exceed the working memory capacity of the learner (Sweller, 2011). A person’s amount of working memory is a deeply embedded trait, so deeply embedded that it appears to be a fixed item of a person’s ability (Imbo, 2007). Because working memory is deeply embedded it seems highly impractical for a secondary teacher to attempt to increase a student’s amount of working memory. Therefore, the strategy of the secondary teacher should be reducing the cognitive load of instruction.

The research into the neuroscience of CLT has demonstrated that teacher strategies which conform to the principles of CLT can have a great impact on student learning (Takir, 2012). “Cognitive Load Theory uses evolutionary theory to consider human cognitive architecture and uses that architecture to devise novel instructional procedures. Secondary knowledge, unlike primary knowledge, is the subject of instruction. It is processed in a manner that is analogous to the manner in which biological evolution processes information. When dealing with secondary knowledge, human cognition requires a very large information store, the contents of which are acquired largely by obtaining information from other information stores.” (Sweller, 2011, p. 37) In another article, Sweller (2009, p. 22) wrote that “instructional design that does not take human cognitive architecture into account is likely to be random in its effectiveness.” There are five instructional strategies that can commonly and easily be taken into account when designing lessons based on Cognitive Load Theory: worked example, goal-free, split-attention effect, modality effect, and redundancy effect (Sweller, 2009). Worked Example

According to Sweller (2011, p. 64),

“Learners may be presented with the problem (a + b)/c = d, solve for a, for which they are required to find a solution. This problem-solving condition can be compared with a worked example condition in which learners are presented with the same problem along with its worked solution: (a + b)/c = d

a + b = cd

a = cd – b”

Research has consistently shown that having students learn from worked examples is a far superior way to have students learn math. Students learn more from studying worked examples than from solving problems (Loring, 2003, and Pawley, 2005). According to Cognitive Load Theory, this is because students are able to learn the method of solving separate from the actual calculation of solving. It is this separation that reduces the cognitive demand on working memory. For those teachers who insist on giving students problems to solve, student achievement increases when the problem solving is paired with a worked example. Student achievement also increases if the student studies the worked example before they attempt problem solving (van Gog, 2011). Worked examples are so effective at increasing student learning that learning goes up even when the worked example includes isolated elements of problem solving (Ayres, 2012). Goal-Free

According to Sweller (2011, p. 64), “goal-free problem solving only requires learners to consider their current problem state and any operator that can alter that state.” Students who are provided problems without a conventional goal outperform students presented with conventional problems on subsequent tests (Sweller, 2011). Wirth (2009) found that nonspecific problem solving goals resulted in a lower cognitive load and better learning that specific problem solving goals. Nonspecific problem solving goals allow students to choose the problem solving strategy rather than naming which specific problems solving strategy they are to use. Wirth (2009) also found that providing students with nonspecific goals decreases cognitive load and, thus, enables students to learn with less effort. An example of a non-specific goal would be to have students measure the interior angles of a triangle and have them to write about their observations. The instructor can

provide some general questions to guide the student observations (what is the sum of the angles?) but not specific problem solving questions (what is the measure of angle A?). Split-Attention Effect

Sweller (2011, p. 66) wrote:

“Consider a typical geometry worked example. It usually consists of a diagram and a set of statements next to or under the …, as indicated above, can be expected to involve a large number of elements of information and processing these elements imposes an unnecessary working memory load—an extraneous cognitive load…Alternatively, if the statements are placed at appropriate locations on the diagram or if arrows link the statements with appropriate diagram locations, a search for referent locations no longer is necessary, reducing extraneous cognitive load due to the elimination of the need to use the randomness as genesis principle to process the statements.” Illustrations and statements must be used and combined with care. Illustrations can have a detrimental effect on performance of arithmetic word problems (Berends, 2009). If the purpose of the problem is to have the students correctly label and mark the illustration with the given statements, then give them the statements in the text of the problem. But if the purpose of the problem is to have the students calculate the value of the missing piece, then place the statements in their proper place on the illustration. Modality Effect

Sweller (2011, p. 67) wrote, “Two sources can be presented in different modalities. One source can be presented visually, while the other source can be presented aurally. Dual modality presentation should increase effective working memory and so decrease cognitive load.” But modalities must be mixed carefully: additional modalities should not merely repeat the same information as the first modality. Merely repeating the same information could result in a higher cognitive load (Sweller, 2011) because of the redundancy effect. The new modality should present new information or present the same information in a different way. For example, Ostad (2008) wrote that classroom teachers should be encouraged to talk out loud their internal problem solving strategy as a valuable and potentially powerful tool. This technique would have teachers solving a problem while

simultaneously talking about how and why they are solving that problem. But there can be drawbacks to how and when the spoken word is used: Kalyuga (2012) recommended teachers pay particular attention to pacing and the degree of complexity of the spoken word. Another modality that shows promise is kinesthetics. “Students translate body movement into the flexible virtual worlds of math data through a performance with interactive elements in the classroom environment…This more personal exploration of math and movement becomes a learning model for students in other aspects of their world” (Mickelson, 2010). Redundancy Effect

Sweller (2011, p. 68) wrote, “The redundancy effect occurs when the addition of additional information interferes with learning … the sources of information are intelligible in isolation and do not need to be integrated in order to be understood.” Improperly combined text and illustrations or improperly combined visual and aural information can lead to detrimental performance (Berends, 2009). An example of improperly combined text and information would be if the text repeated the information also given in the illustration. An example of improperly combined visual and aural information would be having someone read aloud at the same time students are reading to themselves. In both instances there is nothing new being given to the students. Redundant information increases cognitive load because the working memory is seeking something new in the redundancy (Sweller, 2011). This same research demonstrated that giving students a supplemental text or diagram will not be helpful if the supplement repeats the information the student was already given. Measuring Math Anxiety

In addition to designing instruction according to the principles of Cognitive Load Theory, there are other ways to address student math anxiety. A psychometric test developed by Robert Suinn in 1972—the Mathematics Anxiety Rating Scale (MARS)—suggests other instructional strategies. MARS has been the subject of multiple studies and has been shown to correlate with the factors of math anxiety. The original MARS has ninety-eight items for which students self-report their anxiety on a five-point Likert scale of “not at all” to “very much” (Suinn, 1982). Suinn and a colleague developed a thirty item abridged version of MARS to address concerns that the original was too

lengthy to administer (Suinn, 2003). Another twenty-five item version, the Revised Mathematics Anxiety Scale (rMARS), was developed and tested by Professor Mustafa Balo?lu in 2007. This review will not be addressing the original or abridged version but the revised version as developed by Professor Balo?lu. The premise of using the psychometric tool as an intervention tool is quite simple: if a teacher addresses the item in the tool, then the math anxiety will be reduced. The items on the various versions of the MARS have been repeatedly shown to correlate with math anxiety; therefore, instructional strategies that address the items on the MARS should be effective strategies for reducing math anxiety. But which items to address? The primary filter of this literature review is classroom instructional strategies. This filter divides the items into two categories: (1) those items that cannot be addressed with classroom instructional strategies, and (2) those items that can be addressed with classroom instructional strategies. Several items on the rMARS relate to the legality and logistics of being enrolled in a mathematics course: the number of math courses a student is required to take, receiving grades in the mail, checking out a textbook, etc. The teacher in the classroom cannot change or influence the number of math courses a student is required to take in order to graduate. The teacher is not responsible for the manner in which course grades are distributed to the student and their family by the school. These are examples of items that cannot be addressed with classroom instructional strategies. The remaining items from the rMARS are items that the teacher can address with instructional strategies: how to use a math textbook, how to study for a math quiz or test, how to work at the board in front of the class, etc. The teacher can design new instructional strategies and adjust existing instructional strategies with the goal of reducing student math anxiety. rMARS and Assessment

The items on the rMARS (Balo?lu, 2007) with the highest correlation to math anxiety (the measured variable loading ranged from 0.70 to 0.88) relate to assessment (formative or summative). This high correlation between assessment and math anxiety suggests a high need to address these items with classroom instructional strategies. These assessments might be created by the teacher or by a testing corporation (ACT, SAT, the exams currently being

written for the Common Core Standards, etc.). One research-based avenue for reducing math anxiety is to expose students to humor before a test. Ford (2012) demonstrated that exposing students to a funny cartoon before administering a test improved student performance on the test. Another strategy is to incorporate student culture into the exams. Using names of musicians and authors and characters familiar to students pulls them into the question and reduces the sense that math is something “other” or outside the student’s life. This is similar to Beal’s (2012) research which is discussed in greater detail later. rMARS and Textbook

Several items on the rMARS (Balo?lu, 2007) relate to student interaction with the textbook. Research has shown several avenues for reducing math anxiety associated with the textbook. One possible research-based avenue is for students to create their own problems. Beal (2012) suggested there are motivational and cognitive benefits for students from creating their own problems. Having students create their own problems situates the learning and problem solving directly with the student rather than the perception that mathematical problem solving exists “somewhere else.” Another research-based avenue is to frame the problems in the textbook as learning opportunities, rather than specific goals that must be achieved. Wirth (2009) replicated the findings of other researchers that nonspecific problem solving goals lead to lower cognitive load and better learning than specific problem solving goals. Offering other modalities (auditory, kinesthetic, etc.) for accessing the information found in the textbook was found to reduce the cognitive load and thereby reduce math anxiety (Kalyuga, 2012). One kinesthetic-based approach deals with the student’s physical relationship with the textbook. Some students approach their textbook as if it were a toxic substance or fear it as if it were a poisonous snake. Isbister (2012) suggested that teaching students “power” poses to place them in physical positions of authority and power over their textbook should reduce student anxiety. rMARS and Teacher Talk

One item on the rMARS (Balo?lu, 2007) asks about watching a teacher work out an algebraic problem. Research has suggested that having the teacher demonstrate interest in, and enjoyment of, math reduces student anxiety

(Bagaka, 2012). Bagaka’s research also suggested that teachers need to be seen as humans who make mistakes and fix them. Showing students mistake-free examples increases student anxiety because the student will make mistakes. One instructional strategy that can be easily implemented in the classroom is to use humor in the lesson. Ford (2012) demonstrated that humor inhibits anxiety. Teaching geometry involves naming shapes (triangle ABC, trapezoid ABCD, etc.). Using texting acronyms (OMG, WTH, LMAO, etc.) that students understand can reduce the tension in the classroom. Other research suggests that having the teacher talk through their problem solving process reinforces correct schema acquisition in the student and allows students to see the teacher as a problem-solver like them (Ostad, 2008). rMARS and Group Work

One item on the rMARS (Balo?lu, 2007) asks about listening to another student explain their work. The correlation of this item to math anxiety (variable load of 0.62) is higher than any activity involving a textbook. Some recent research has indicated that participating in group work increases a student’s anxiety and that group work has a negative relationship with student interest, effort, and perception of mathematics (Bagaka, 2012). This appears to contradict the contemporary pedagogical practice of encouraging students to work in groups and collaborate with others in their learning. Unfortunately, the rMARS and the other versions of MARS do not ask students about their anxiety level when working alone. Summary

The purpose of this literature review was to investigate instructional strategies that reduce math anxiety. Ashcraft (2002) provided one definition of math anxiety as feelings of tension that interfere with math performance. A working analogy for math anxiety would be depression as a cluster of symptoms with varying degrees of severity. Math anxiety has been shown to be negatively correlated with working memory which is a foundational component of Cognitive Load Theory. This literature review investigated classroom instructional strategies that conform to the design principles of Cognitive Load Theory. This literature review also investigated the several survey tools shown to correlate with math anxiety. The premise is that classroom instructional strategies that address the item in the survey will reduce

math anxiety. Avenues for Future Research

One avenue for future research is suggested by the rMARS: ask students to self-report their anxiety when working alone versus when working as part of a group. A second avenue for future research is to compare MARS scores with ACES scores. This literature review found no published articles linking MARS and ACES. It is my hypothesis that there is a positive correlation between MARS and ACES. A correlation between MARS and ACES could potentially demonstrate a link between specific childhood experiences, the age at which these experiences occur, and math anxiety. A third avenue for future research is to examine who so little educational research is conducted using high school students. In order for research-based classroom instructional strategies to be implemented they need to be relevant to that classroom. Very little educational research is relevant to my high school math classroom. Conclusion

The research is clear: there are cognitive and global consequences of math anxiety (Ashcraft, 2007). The research is also clear: there are research-based classroom instructional strategies that teachers can implement that will decrease a student’s math anxiety. Decreasing a student’s math anxiety removes one more obstacle between that student and their success in the mathematics classroom. Even a secondary math teacher who sees one hundred twenty high school students for fifty minutes every day for one hundred eighty days wants his or her students prepared to compete in a global market dominated by STEM that is their future. References

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