MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 2 Acknowledgements Many people have helped and encouraged me throughout this project, especially the long-suffering souls on my committee, but several people merit special thanks. First, my amazing husband Dave, for his endless patience, support and practical knowledge, and my daughter Catherine for her confidence empathy and humor. Also, I was very lucky to have Dr. Sheryl Rushton as the chair of my committee. She not only freely gave of her expertise, but her friendship as well. My co-worker, Richard Campos for coming to my rescue many times for all things formatting. Dr. Cora Neal merits special thanks for her invaluable help with the statistics even though she was in no way obligated to work on this project. Last and certainly least, I want to thank my cat Tigger, who often sat by my side and complained loudly and at length when I was too busy to voice the complaints for myself. MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 3 Table of Contents Acknowledgements ......................................................................................................................... 2 Table of Contents ............................................................................................................................ 3 List of Tables ................................................................................................................................. 5 Abstract .......................................................................................................................................... 7 NATURE OF THE PROBLEM...................................................................................................... 8 Literature Review......................................................................................................................... 11 College Level Students Are Struggling with Mathematics ....................................................... 11 The Causes of Mathematics Failure Are Heterogeneous .......................................................... 12 Mathematics is traditionally learned as a series of memorized procedures .......................... 12 Anxiety ................................................................................................................................. 14 Underprepared...................................................................................................................... 14 Learning disabilities .............................................................................................................. 15 Lack of motivation ................................................................................................................ 15 Remediation Is Largely Unsuccessful ...................................................................................... 17 Many colleges are reducing the number of developmental courses needed ......................... 17 The Role that Student Personality plays in Learning................................................................ 18 The Development and Impact of Personality............................................................................ 21 Personality in the Classroom .................................................................................................... 22 The MBTI is a Well-known Personality Assessment ........................................................... 24 The MBTI ............................................................................................................................. 24 MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 4 Validity of the MBTI ............................................................................................................ 28 MBTI concerns ..................................................................................................................... 29 The MBTI as a classroom tool .............................................................................................. 31 A Gap in the Research .............................................................................................................. 33 PURPOSE .................................................................................................................................... 35 METHODS .................................................................................................................................. 37 Overview .................................................................................................................................. 37 Participants ............................................................................................................................... 37 Procedure ................................................................................................................................. 39 RESULTS .................................................................................................................................... 41 DISCUSSION ............................................................................................................................... 52 REFERENCES ............................................................................................................................. 59 MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 5 List of Tables Table 1 Total number of students in each of the 16 MBTI types .................................................. 38 Table 2 Total number of students when sorted into each dichotomy preference………...………38 Table 3 Summary of all chi-squared tests run for this study. ....................................................... 42 Table 4 All MBTI types compared to actual and expected initial placement levels at Weber State...................................................................................................................................... 43 Table 5 All MBTI types compared to actual and expected compressed grades. .......................... 45 Table 6 Extraverted and Introverted types compared to actual and expected initial placement. 46 Table 7 Sensing and Intuitive types compared to actual and expected initial placement. ........... 46 Table 8 Thinking and Feeling types compared to actual and expected initial placement. ........... 47 Table 9 Judging and Perceiving types compared to actual and expected initial placement. ....... 47 Table 10 Extraverted and Introverted types compared to actual and expected compressed grades. .................................................................................................................................. 47 Table 11 Sensing and Intuitive types compared to actual and expected compressed grades. ...... 48 Table 12 Thinking and Feeling types compared to actual and expected compressed grades. ..... 48 Table 13 Judging and Perceiving types compared to actual and compressed grades. ................ 48 Table 14 Heart of Type for Thinking paired with Sensing and Intuitive types compared to actual and expected initial placement.............................................................................................. 49 Table 15 Clearly indicated MBTI for Extraverted and Introverted compared to actual and expected initial placement..................................................................................................... 50 Table 16 Clearly indicated MBTI scores for Sensing and Intuitive types compared to actual and expected initial placement..................................................................................................... 50 MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 6 Table 17 Clearly indicated MBTI scores for Thinking and Feeling types compared to actual and expected initial placement..................................................................................................... 51 Table 18 Clearly indicated MBTI for Judging and Perceiving types compared to actual and expected initial placement..................................................................................................... 51 MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 7 Abstract Many students have great difficulty passing required mathematics courses. These difficulties persist into the college years and cost both students and their institutions billions of dollars and great frustration. This project explores the impact of personality on math achievement, specifically whether any one of the sixteen Myers-Briggs personality types displays an advantage in the study of mathematics, and whether there is a difference between students with Sensing or Intuitive preferences. This was a quantitative study using chi-square analytics to determine statistical significance between various personality types and mathematics success. With IRB approval, the MBTI data for all students (excluding minors) who were enrolled in the First Year Experience course in the Fall of 2018 were obtained. These data were compared to the student’s initial mathematics placement at Weber State University and the student’s performance in mathematics courses if taken, in the Fall of 2018 and Spring of 2019. This study did not reveal any significant differences of MBTI type and mathematics performance or a difference between the Sensing and Intuitive learning preferences. There was, however, a significant difference between the Thinking and Feeling types with Thinking types displaying an overall advantage both in initial mathematics placement and subsequent performance. The implications of this research show that one determinate of success in mathematics lies not in the way a student learns information, but in how the student reaches decisions. Further research on the differences in mathematical thinking for both Thinking and Feeling types is indicated. MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 8 NATURE OF THE PROBLEM Many students have difficulties with mathematics that persist into the college years. The consequences of mathematics failure are serious for the student, as mathematics is a requirement for college graduation. Failure is also serious for the institution, because government funding is often tied to graduation rates (Cafarella, 2016). Developmental mathematics courses are of particular concern because such high numbers of students fail to pass these entry level courses (Bailey, Jeong, & Cho, 2010). The reasons for mathematics failure are varied and complex (Cafarella, 2016). One cause for frustration is simply due to the nature of mathematics, which is a subject that builds upon formerly learned skills (Boylan, 2011). A lack of meaningful understanding at lower grade levels can cause chronic problems as students’ progress to higher levels without adequate understanding. Adding to the difficulty, is that mathematics has traditionally been presented as a series of procedures to be memorized rather than as a subject of deep meaning and intrinsic interest (Murphy, 2018). This type of surface learning, which relies heavily on memorized facts, often results in a fragmented concept of mathematics and is correlated with low pass rates (Murphy, 2018). The consequence being that in some community colleges as many as 75% of students need courses in developmental mathematics (Howard & Whitaker, 2011). In response to the low pass rates, institutes of higher education have poured billions of dollars into developmental mathematics education (Cafarella, 2016). And yet, only “33 % of those referred to developmental mathematics remediation completed their sequence of developmental education” (Bailey et al., 2010, p.259). MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 9 Mathematics instructors at all levels have tried and continue to try various strategies to assist students (Boylan, 2011; Cafarella, 2016; Galbraith & Jones, 2006; Jorgensen, 2010; Stephan, Pugalee, Cline, & Cline, 2016). Today, because remediation has been so unsuccessful, many institutions are reducing the number of developmental courses needed in the hopes that by shortening the sequence of required mathematics courses, students will be more motivated to complete quantitative literacy, and so be more likely to graduate (Cafarella, 2016). The reduction is sometimes made by allowing co-requisite courses and sometimes by simply allowing students to enroll in a gateway course (defined as the course preceding the course that will satisfy the quantitative literacy requirement) regardless of placement (Cafarella, 2016). The results of these programs have been mixed (Cox & Dougherty, 2018; Park, Woods, Hu, Jones, & Tandberg, 2017). Currently at the K-12 level, the common core has instituted a major shift in the way mathematics has been taught in America. No longer as reliant on memorization and rigid procedure, the emphasis is on conceptual understanding and coherence in the way mathematics is presented (National Council of the Teachers of Mathematics [NCTM], 2014). The question of which personal characteristics successful mathematics students have in common has also been explored. Traits such as self-efficacy, and a perception of mathematics as relevant to life, contribute to success (Murphy, 2018); whereas other personality traits, such as an avoidance temperament have been shown to have a significant negative impact on academic performance (Liew, Lench, Kao, Yeh, & Kwok, 2014). The study of personality encompasses individual traits and the impact these traits have on the individual as well as commonalities across the human condition (Myers, McCaulley, Quenk & Hammer, 2003). Educators who understand the differences in how students receive, frame and retain information are better MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 10 equipped to differentiate their instruction in an effective way (Rodriguez, Romero-Canyas, Downey, Mangels, & Higgins, 2013). One well-respected assessment of personality is the Myers-Briggs Type Indicator (MBTI), which measures non pathological patterns of cognition and behavior. Personality is parsed on a continuum of four dichotomies which results in 16 possible combinations of dominant personality traits or types. There has been research conducted on all the MBTI types and how these types correspond with general academic success (Bishop-Clark, Dietz-Uhler, & Fisher, 2007; Conti & McNeil, 2011; Hye-Young, 2015). However, there is very little research on the correlation between MBTI type and mathematics learning specifically. MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 11 Literature Review This review of the literature has four main sections: (a) Causes and consequences of mathematics failure at the college level; (b) The effect of remediation and current changes in the way mathematics is being taught; (c) The role that student personality plays in learning; (d) The validity of the Myers-Briggs Type Indicator (MBTI) and its usefulness in informing instruction. College Level Students Are Struggling with Mathematics The number of students entering college who need developmental mathematics is substantial. More than half of community college students need at least one developmental mathematics course (Bailey et al., 2010), and many students need two or three before they reach the necessary course required to fulfill quantitative literacy in order to graduate (Bonham & Boylan, 2012). In some community colleges, as many as 75% of students need developmental mathematics (Howard & Whitaker, 2011). However, even though developmental mathematics courses are designed to remediate students to enable them to succeed in their required college-level mathematics courses, nationally, only 30% of students complete the entire sequence needed (Cafarella, 2016). Failure in mathematics can have significant consequences; according to the National Center for Education Statistics (NCES, 2017a) most state institutions and universities require some level of mathematics competency for graduation. In 2016-17, 65% of four-year institutions and 76.2% of two-year institutions offered remedial courses (NCES, 2017a). As of September 2018, 32 states have adopted a performance-based model for their higher education (Ziskin, Raybourn, & Hossler, 2018). Performance-based models allocate a certain portion of the money universities receive from the state based on a set of outcome-driven MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 12 metrics such as graduation rates (Morgan, 2019). Forty percent of America’s students in four-year colleges fail to graduate (NCES, 2017b), and nearly 70% of students in Title IV two-year institutions fail to graduate (NCES, 2017b). Therefore, higher educational institutions are strongly motivated to improve graduation rates which means improving student mathematics completion. Significant amounts of money have been poured into developmental programs and trainings designed to increase pass rates in mathematics (Cafarella, 2016). The cost to students is substantial as well. In 2016 students paid approximately 1.5 billion dollars to help fund their own remedial education (Smith, 2016). The Causes of Mathematics Failure Are Heterogeneous Why exactly so many students perform poorly in mathematics is a question many researchers and educators have asked (Ashcraft & Krause, 2007; Boylan, 2011; Cafarella, 2016). Because the population of students needing mathematics is large and diverse, the reasons for student failure likely have multiple causes as well (Cafarella, 2016). Several causes of mathematics difficulty are listed below. Mathematics is traditionally learned as a series of memorized procedures. Although the procedural method of mathematics teaching has been standard in America for many years, many now feel this method is ineffective and largely responsible for the current high levels of student failure. However, the traditional method is not without supporters (NCTE, 2014). For example, there is agreement in the findings of both Vasquez (2003) and Schurter (2002) that there should be a specific structure to teaching a developmental mathematics course. When introducing new concepts, Vasquez (2003) stressed the Algorithm Instructional Technique (AIT). The AIT consists of the instructor initially modeling to the class effective step-by-step strategies to solving mathematics problems of a specific type. Students should then practice the MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 13 material with instructors providing feedback early and often. Practice problems can be completed in small groups. The end goal is for students to be able to complete mathematical problems independently without assistance from peers or their instructor (Vasquez, 2003). However, to succeed in even developmental level mathematics courses, students must master skills that use abstract reasoning (Boylan, 2011), and although Vasquez (2003) intends that independent reasoning skills will be among the desired outcomes of AIT, too often students are not making the leap from memorized procedures to mathematical independence (Cafarella, 2016). Without understanding the why of mathematics processes, learners often struggle to remember how different types of problems are solved. Students will often fail to recognize the same problem when presented in a slightly different way, or to be able to reason how to use the skills they supposedly have learned in story problem settings. (Ross, Perkins, & Bodey, 2013). These deficits often constitute a serious problem in mathematical information literacy (Ross et al., 2013). Mathematics literacy is not only defined as achieving a certain level of competency but also encompasses the ability to recognize when information is needed and where to best find that information. Information literate students tend to display higher levels of self-efficacy and are more motivated to persist through difficulties (Ross et al., 2013). Lack of information literacy is often tied to a deficiency in the skills required to study mathematics (Boylan, 2011), and this, paired with the fact that it is socially acceptable to fail mathematics in America (Boylan, 2011; Rattan, Good, & Dweck, 2012), provides ample reason for some students to avoid studying mathematics altogether. Repeated failure sets the stage for mathematics anxiety as they face increasingly difficult tasks without first mastering foundational skills (Boylan, 2011). MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 14 Anxiety. Anxiety is not merely an uncomfortable emotion. Anxiety can interfere with a student’s working memory, rendering that student less able to learn (Ashcraft & Krause, 2007). In a 2007 study, participants who tested high on anxiety measures also tested worse than their less anxious counterparts as problems increased in difficulty (Ashcraft & Krause, 2007). This result is because the anxious students were focusing both on their emotional state and the task at hand, effectively requiring double effort from their working memory therefore, having fewer mental resources available as they tried to solve complex problems (Ashcraft & Krause, 2007). Underprepared. Some students come to the university severely underprepared (Cafarella, 2016). With a lifetime of struggle and failure behind them, it is difficult for these students to conclude anything other than something must be wrong with them (Cafarella, 2016). It is unsurprising then that these students experience anxiety at the mere thought of completing a sequence of mathematics courses before even beginning college-level work. Often, students have forgotten, or never really learned, basic arithmetic facts (Howard & Whitaker, 2011). This deficit not only slows students down as they endeavor to solve mathematics problems, but also decreases accuracy, especially if a student is trying to rush through an assignment; a common avoidance technique (Howard & Whitaker, 2011). Instructors can help students practice fundamental skills by pinpointing the students’ true placement and then teaching accordingly (Galbraith & Jones, 2006). Students interviewed in one study reported that when they learned they had a measure of control in their ability to get correct answers, it was an eye-opening and powerful experience (Howard & Whitaker, 2011). Their new-found confidence contributed to a new and positive cycle as they became increasingly willing to spend the time necessary to be successful (Howard & Whitaker, 2011). MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 15 Learning disabilities. Other students come into developmental mathematics with not only working memory issues, but one or more other types of processing disabilities as well. These may include troubles with: …auditory processing, processing speed (visual), short-term memory (auditory), visual spatial thinking, long-term retrieval, working memory, comprehension-knowledge (long-term memory), or fluid reasoning (abstract). Fluid reasoning is the processing deficit that causes the most mathematics learning problems and is the most difficult to accommodate. (Boylan, 2011, p. 22) Lack of motivation. Researchers have identified a lack of motivation as a primary problem for developmental mathematics students (Bonham & Boylan, 2012; Galbraith & Jones, 2006; Rattan et al., 2012; Howard & Whitaker, 2011; Thompson & Gaudreau, 2008). When students lack motivation, their attitude can set off a cascade of behaviors that negatively impact their chances for success. For these students, it is all too easy to fall into a pattern of missed homework, subsequent failed tests, then giving up altogether (Cafarella, 2016). Chronic failure builds on itself to create habits of procrastination as a means of protecting self-worth (Middleton & Spanias, 1999). Unfortunately, the temporary emotional benefit of procrastination can produce a habit of learned helplessness (Howard & Whitaker, 2011). Motivation or the lack thereof is a rich topic for research. One approach that has defined certain types of motivation is self-determination theory (SDT), an approach that observes personality development and attempts to understand motivation by defining the driving needs behind student behavior; whether internal satisfaction or external rewards (Ross et al., 2016). Other researchers in the field of education have also explored personality in order to better understand student learning styles and develop effective curriculum (Ashcraft & Krause, 2007; MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 16 Cafarella, 2016; [NCTM], 2014). As far back as the 1800’s, educators were analyzing student response to mathematics as a guide to understanding the internal world of their pupils in order to make changes in their teaching that would improve the student experience (Jorgensen, 2010). One instructor in 1825, John Bonneycastle, shared his opinion that motivation was key to student success. He wrote: To raise the curiosity and awaken the listless and dormant powers of younger minds, we have only to point out to them a valuable acquisition, and the means of obtaining it; the active principles are immediately put into motion, and the certainty of conquest is ensured from a determination to conquer. (as cited in, Jorgensen 2010, p. 27) Modern educators continue to make the same discovery, namely that the student’s point of view and personality are fundamental to how that student will interpret and act on the instruction given. Therefore, it behooves instructors to have some understanding of how their teaching is being received and the reasons behind their students’ response. For example, Rodriguez et al. (2013) conducted a study of student beliefs regarding mathematics and the perceived purpose of mathematics (whether to enable individual discovery or to benefit society as a whole) and found that when mathematics was taught in a way that matched student beliefs, students’ performance increased. Bonneycastle would probably have been very comfortable with the purpose of the study of Rodriguez et al., which was to, “consider how math may be made more motivating to students when it is framed in ways that appeal to their basic values and beliefs about the world” (Rodriguez, et al, p,445). In other words, it is not only the instructor’s expertise that will enable a student to learn mathematics, but the psychological state of the student. The student’s past experiences, their MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 17 motivation, level of interest and perception of the purpose of mathematics all impact the eventual success or failure of the student. Remediation Is Largely Unsuccessful As stated above, developmental mathematics programs designed to help students succeed regardless of their past mathematics history, have shown dismal pass rates. In many cases, the programs designed to help these students have become roadblocks in and of themselves because the length of time to completion is overwhelming (Bonham & Boylan, 2012). Many students, while aware that mathematics is a problem subject, are still unpleasantly surprised when they discover that they must take one or more developmental mathematics courses which they will pay for but for which they will not receive credit (Bailey et al., 2010). The subsequent discouragement results in many students either withdrawing early from courses or simply not enrolling at all (Bailey et al., 2010). In fact, not enrolling in developmental mathematics courses is a more significant problem than failing them (Bailey et al., 2010). One study estimated that 56% of referred students never enrolled in the first course of their sequence; and of students who did enroll, although 63% passed the course, only half of those who passed enrolled in the next course (Bailey et al., 2010). However, when students pass all necessary preparatory courses, the outlook brightens. About two thirds then will progress to the gatekeeper course (typically the course immediately preceding the final required mathematics course), and about three-fourths of those students pass that course (Bailey et al., 2010). Many colleges are reducing the number of developmental courses needed. In response to low mathematics completion rates, there have recently been initiatives to MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 18 reduce or even eliminate developmental mathematics courses for underprepared students (Cafarella, 2016). Some educators feel that students are “quite capable of assimilating course material in a shorter time when the material is presented in a more intense and compressed format” (Sheldon & Durdella, 2010, p.52). Others (Woodard & Burkett, 2010) favor compressed courses both to increase student success and reduce the chances of future burnout for many students. However, the movement to reduce courses has some educators concerned (Mangan, 2014). Some question how students can be expected to solve more complex equations when they lack basic mastery of numbers (Mangan, 2014). Another concern is that the instructors of college-level mathematics courses will be overwhelmed with an influx of low-skill students that will compromise the learning of all the students in the course (Mangan, 2013). Yet another concern is that the movement to compress mathematics courses is being driven by external pressures rather than from educators (Mangan, 2013). For example, The Bill and Melinda Gates Foundation has poured millions into developmental mathematics education, but has also helped to initiate Complete College America (CCA). CCA is a nonprofit advocacy group that urges state lawmakers to reduce or eliminate remedial courses so that students can progress into their college-level courses more quickly (Mangan, 2013). Some see this as a conflict of interest (Mangan, 2013). The Role that Student Personality plays in Learning Whether students are required to pass a few or many mathematics courses, the one idea that has general consensus, is that regardless of the instruction taking place, that instruction needs to be effective (Rodriguez et al., 2013). Currently, the common core standards are bringing about a major shift in the way math is taught in K-12 classrooms. Rather than focusing on MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 19 memorizing procedures and tricks such as, “ours is not to reason why, just invert and multiply,” (NCTM, 2014, p. xxiv) the goal is to teach mathematics in a coherent, meaningful way to build deep conceptual understanding that can be applied in a variety of mathematical tasks (NCTM, 2014). Students are being asked to be creative when solving problems and then be able to defend their reasoning. Shortcuts, such as inverting a fraction and then multiplying are only used after the student has discovered the shortcut for themselves and thoroughly understands why the shortcut works. The major goals for each grade level are outlined, but instructors should connect the content of one grade level to the content of the grade before and the grade to come (Jaciw et al., 2016). Such a shift, so different from the way most of the teachers themselves have been taught, has not been implemented without difficulty (Cogan, Schmidt & Houang, 2013). Parents have been confused and frustrated by what sometimes looks to them like very inefficient ways to solve problems, and teachers have sometimes tried to teach thinking strategies in the way that they themselves were taught, that is to say, in a procedural way (Cogan, Schmidt & Houang, 2013). Despite the difficulties involved in introducing a significant paradigm shift, studies have found that when mathematics is taught as a “complex logical system which could be used to solve complex problems and provide insight used for understanding the real world, students experienced positive outcomes” (Murphy, 2018, p. 576). “Students actually learn mathematics by doing mathematics rather than spending time listening to someone talk about doing mathematics” (Bonham & Boylan, 2012, p.16). Hands-on work with instructor support and encouragement helps students to develop competence, which becomes a step to developing an MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 20 interest in learning mathematics for its own sake (Bonham & Boylan, 2012). Although the current methods for instruction being used in the common core are relatively new, caring instructors have been researching and experimenting with methods to better teach their students probably since the earliest discoveries of mathematics itself. In the present day, teachers at all levels of instruction and using many different styles of teaching, continue to use formal research, trial and error, experience, observation and common sense to provide the most effective instruction possible (Bonham & Boylan, 2012; Cafarella, 2016; Galbraith & Jones, 2006). For example, two effective instruction techniques that can supplement any mathematics course are play and group work (Bonham & Boylan, 2012; Cafarella, 2016). These types of activities help students better understand their own attitudes towards learning as well as support the learning itself (Bonham & Boylan, 2011). Play and group work can be an effective means of varying instruction, encouraging exploration and reaching adult learners as well (Galbraith & Jones, 2006). Students learning and playing together come to realize that they are not alone in their struggles (Cafarella, 2016). Group activities can also aid in the development of critical thinking skills as students work together to solve problems (Cafarella, 2016). Even icebreakers, which frequently lack academic content, help students relax and lower their affective filters making subsequent instruction far more impactful (Galbraith & Jones, 2006). The above methods, including contextual mathematics learning, represent efforts to engage the student in developmentally appropriate ways. Psychologists and educators understand that a person’s development is not complete by the age of 18 (Martinez, 2008). Any person of any age when learning new material is in the process of developing new understanding and must learn the material in ways that are comprehensible to them (Martinez, 2008), including post- MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 21 secondary learners. Since every person is different, the challenge for teachers is to present their material in such a way that every student will be able to progress (Martinez, 2008). Silver, Strong and Perini (2009), in their book The Strategic Teacher: Selecting the Right Research-Based Strategy for Every Lesson, identify reliable teaching methods and divide them into four basic categories, memory, reasoning, imagination and creativity and meaning in relationships. Although each area is important, each student will enjoy some types of learning more than others. This book contains a wealth of activities geared towards each of these areas specifically “to provide teachers with a repertoire of strategies they can use to meet today’s high standards and reach the different learners in their classroom” (Silver, Strong & Perini, 2009. p.2). The Development and Impact of Personality. Personality is a comprehensive word used to describe an individual’s normal response to stimuli; the habits of a person’s thinking and interactions with their world—the “default” setting if you will (Myers et al., 2003). While it is impossible to predict what any given person will do or say in a specific situation, it is possible to observe general characteristics of large groups and test how certain personality types will likely react in a given situation with a surprising amount of accuracy (Myers et al., 2003). There are many theories of personality. According to Feist, Feist, and Roberts (2017), how humans develop personality traits and the impact personality has on the individual has been studied by many. Sigmund Freud believed that much of human personality was driven by unconscious desires which shaped behavior. Alfred Bandura and Walter Mischel developed the Social-Cognitive theory of personality, which postulates that personality grows from both the thoughts of the individual and their social interactions. But an all-encompassing definition of what, exactly, constitutes personality has been difficult to define. Carl Rogers, working in the MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 22 1950’s believed that our personalities were formed from our conscious experiences and that humans are strongly motivated to align their thoughts and behaviors with their concepts of the world around them. Theories such as these shed light on how personality grows. Other scholars were more interested in articulating the ways in which personality manifests itself, by identifying hallmark traits of various personality types (Feist, Feist & Roberts, 2017). Raymond Cattell and Hans Eysenck believed that everyone exhibits certain traits such as being outgoing or being suspicious. These traits were stable, although they could be influenced by outside circumstances. Cattell’s research led to the development of the 16-trait theory. Eysenck’s work overlapped Cattell’s somewhat. Eysenck simplified Cattell’s theories and distilled personality into three distinct types, introversion/extraversion, neuroticism and psychoticism (Feist, Feist & Roberts, 2017). In the late 20th century a trait theory called The Big Five emerged. Not attributed to any one scholar, the Big Five seem a reasonable middle ground to advance the understanding of personality; easier to manage than 16 trait variables, yet diverse enough to encompass most of human thought and behavior. The Big Five are: Openness, Conscientiousness, Extraversion, Agreeableness and Neuroticism (Feist, Feist & Roberts, 2017). Personality in the Classroom Trait theory is valuable to the educator because individual traits are relatively easy to determine, either by test or by observation. Each personality trait has strengths and weaknesses (Myers et al., 2003). Attempting to understand the minds of the students and the subsequent strengths and weaknesses the students are therefore likely to have, enables educators to create programs to capitalize on the best of a students’ nature while developing weaker areas (Myers et al., 2003). The effects of personality and learning have been studied by many (Myers et al., MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 23 2003; Rešic՛, Korda, Palic՛ & Omerovic՛, 2013) pertaining both to learning in general (Martinez, 2008) and learning in specific subjects (Clark & Riley, 2001). The study of personality has important implications in the classroom (Sample, 2017), and the impact of personality is statistically significant (Myers et al., 2003). One group of Romanian researchers studying medical and law students concluded, “…knowing their personality and training them to manage and preserve their physical and psychological health is no longer optional, nor a desideratum” (Răşcanu, Grama, & Botone, 2016). Myers et al. (2003), studying American students, agree that the impact of various personalities on learning is powerful. Every student has preferred habits of mind which can be said to form their cognitive style. For example, one student may show a preference for organizing information and making logical connections, while another will be more apt to trust their feelings and move more quickly to intuitive conclusions (Myers et al., 2003). These habits influence where the student will be more likely to direct their focus when they are presented with new material. In the classroom, students are naturally drawn to certain types of learning environments and interests and tend to avoid (either physically or mentally) those learning situations that are less compatible. For instance, an introverted student will almost always choose to work independently rather than in a group when given a choice (Sample, 2017). Because personality profoundly affects how students think and learn, studying personality can greatly help instructors to understand why one student may be doing well in a given subject, while another is struggling. Such understanding will enable the teacher to differentiate instruction in effective ways rather than to simply repeat and drill procedures in the same way the procedures were originally presented, and to which the student has already demonstrated difficulty in learning (Sample, 2017). MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 24 The MBTI is a Well-known Personality Assessment. The MBTI is one of the best researched and most well-known personality tests in print. “More than 2 million people in the U.S. alone take the Myers-Brigg Type Indicator (MBTI) personality test each year, and it has been translated into more than 30 languages” (Weiler, Keller, & Olex, 2012, p. 234). It is used worldwide in such diverse places as Hong Kong, Iran, and South Korea (Conti & McNeil, 2011). The MBTI. The MBTI differs from other trait-based tests in that it only assesses normal and healthy differences in the way people understand their world and interact with themselves and others. It is not interested in identifying mental pathologies, but rather to promote interpersonal understanding, learning and respect (Myers et al., 2003). It is based on Carl Jung’s theory of psychology (Myers et al., 2003) which postulates that seemingly random variations in human behavior have order and consistency and are therefore predictable. Myers et al, (2003) state: The value of the theory underlying the Myers-Briggs Type Indicator personality inventory is that it enables us to expect specific differences in general types of people and to cope with people and their differences more constructively than we otherwise could. (p.21) In the context of curriculum development and day to day teaching practice, the MBTI is valuable not only to raise awareness of individual differences but as a means for integrating and engaging students in a learning framework (Sample, 2017). The differences among the types that the MBTI identifies are so fundamental to a person’s way of functioning that the person in question often does not recognize that other ways of thinking and functioning can exist (Myers et al., 2003). For example, those who lean toward what is called a sensing orientation often interpret concepts such as fairness, equity and justice to MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 25 mean that everyone should be treated in the same manner and assume that this assumption is universally self-apparent and accepted by others. However, others who lean toward what is called the intuitive orientation are more likely to interpret fairness and equity to mean that the needs of each individual are met even when those needs require a differing response from person to person. When these individuals meet to discuss a solution to a problem without being aware of other interpretations of “fairness,” conflict and confusion can easily result (Myers et al., 2003). Isabel Myers, who created the test based on Jung’s theories, identifies these differences as strengths or “gifts” (Myers et al., 2003). These “gifts differing” describe the self and others and their ways of viewing and experiencing the world, in terms of strength (Sample, 2017, p. 980). Jung believed that every individual is born with innate preferences that influence how one interacts with the world, takes in information, and makes decisions. These preferences can be measured on four dichotomous scales that address both function and attitude (Extraversion– Introversion, Sensing–Intuition, Thinking–Feeling, and Judging–Perceiving), which indicate how an individual is reflexively likely to act in a given situation (Myers et al., 2003). These four scales result in sixteen possible combinations, or types each consisting of four core traits. No type is better or healthier than another, but each type exhibits behaviors and modes of thinking that may be mystifying to those of their opposing preference. A central tenet of type theory is that individuals are far more likely to use their preferred function in each of the four dichotomies. This is usually an unconscious decision and the person in question is thinking and behaving in a manner that is natural to them, much like a person preferring to use their dominant hand. The skills associated with those behaviors naturally improve over time with repeated use. Although individuals differ, the patterns the MBTI MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 26 uncovers demonstrate order and consistency, making behavior somewhat predictable (Myers et al., 2003). To understand the MBTI and the scope of its interpretation, it is necessary to have an idea of the meaning of the four dichotomies. When the MBTI is scored, the subject is given a four letter ‘type’ which indicates where on each of the four dichotomies the subject has a preference. For example, INFP, represents Introverted-INtuitive-Feeling-Perceiving preferences, which are outlined below. The first pairing is Extraversion (E) vs. Introversion (I). This dichotomy does not assess the degree to which a person might be outgoing or reserved. Rather, it is the measure of where a person gathers their energy, from other people and outward experiences (Extraversion) or from one’s own thoughts (Introversion). A rough guide to which preference a person likely has is an individual’s response to the following scenario: imagine coming home after an exhausting day of work and school. As you walk in the door the phone rings—it’s a friend inviting you to come over to play cards with some others. Would you want to go? Generally, an Extravert would answer yes, because being tired, they would find being with friends an energizing experience. An Introvert would most likely answer no, because being tired, having to interact further with others would only be more draining. The next pairing, Intuition (N) vs. Sensing (S) measures how a person collects information and makes sense of their world. An Intuitive person as defined by the MBTI, prefers to receive information in a big-picture context because that enables them to see patterns and draw connections. For this reason, an Intuitive might jump quickly from subject to subject in ways that seem unrelated on the surface. Doing so is the Intuitive’s way of exploring the whole of the information being received, connecting that information with other ideas already in the MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 27 person’s established paradigm, and sorting which concepts are fundamental and which are peripheral. Sensors best receive information in a very different way. Sensors prefer to understand their world in a logical, step by step way. They tend to prefer practical realities and are more interested in the ‘right’ way to do or understand things. For a Sensor it can be difficult to see a pattern until all of the facts have been presented. For an Intuitive, it can be difficult to see individual facts until a framework encompassing the whole is in place. Thinking (T) and Feeling (F) are written next in the four-letter description. It is important to note that ‘thinking’ in this context does not equate to a high level of intelligence. Instead, the Thinking and Feeling dichotomy is a measure of how a person tends to make decisions. A Thinker tends to make decisions based on what seems to them to be the most logical course of action. The ‘right’ decision is the logical decision and is the overarching principle that guides a Thinker’s choices. For a Feeler, the ‘right’ decision is the one that will create the most harmony both internally and externally. For example, in a business setting, a Thinker in a leadership position will work hard to do what makes the best business sense for the company and might be resistant to popular ideas that to them seem inferior. The Feeler in the same setting will be more likely to weigh the impact a decision will have on the morale of the group as well as what is best for the business. A Feeler will be more likely to choose a viable popular opinion, even if they believe the plan to be less effective because they believe that more progress will be made in the long run when all concerned are working happily together to achieve the desired outcome. Lastly, is the Judging (J) and Perceiving (P) scale. Here again, it is important to note that if a person has a Judging preference, it does not mean that the person is judgmental or critical and a person on the Perceiving end of the scale is not necessarily perceptive. The J-P scale is an indicator of the person’s preferred lifestyle. A person with a Judging preference likes to control MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 28 their life and surroundings as much as possible. They tend to use planners and lists, and dislike last-minute decisions and working under time pressure. The Perceivers of the world like to experience all that life has to offer and even enjoy last-minute changes and surprises. Because Perceivers tend to work well under pressure, they may tend to procrastinate (Myers et al., 2003). As much as people prefer living and thinking in the ways that are most comfortable for them, type theory maintains that individuals can, and often must, use less preferred functions as circumstances require, for example, when an introverted person finds themselves in a group setting. Such a person may interact quite well in the group; however, the interaction will require more energy from them than from their extraverted friends because engaging with multiple people at the same time is not their natural setting. With effort, everyone can improve on the skills associated with their non-preferred type (Fornaciari & Dean, 2013). Because of preference differences, various types tend to gravitate toward differing careers and other fields of interest. One study was conducted among 355 high school band, orchestra and choir members to determine if certain types gravitated toward different branches of music. The answer was yes. Extraverted types were more often found in choir rather than instrumental groups. Other personality differences were not statistically significant amongst the music students, however when comparing music students with the general high school population, music students were more likely to have higher scores on the Intuitive and Feeling scale, and the band members leaned toward a perceiving lifestyle (MacLellan, 2011). Validity of the MBTI. The differences demonstrated on the MBTI have been shown to be innate and remarkably stable over a lifetime. There have been various studies of type consistency across different forms of the test as the assessment has evolved. Re-tests given after an interval of greater than nine months consistently found a much higher percentage of type MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 29 agreement than the chance probability (6.25) of the tests resulting in an identical type in all four categories (Myers et al., 2003). This level of consistency is an indicator of the good internal validity of the test. One very interesting test-re-test study was conducted in the early stages by Isabel Myers herself beginning in 1943: She administered one of the first forms of the Indicator to the 87 members of the Swarthmore high school class of 1943. At the 50th reunion of this class, Katharine Myers administered form G to 39 of these same people. Over this 50-year period 8 people (21%) had the same type, 13 (33%) had changed one letter, 16 (41%) had changed two letters, 2 (5%) had changed three letters and no one in the group had changed all four letters of his or her type. Over a 50-year interval, then, 54% changed either none or just one letter. The level of agreement expected by chance would be 6.25%. (Myers et al., 2003, p. 164) The MBTI demonstrates a high level of reliability as well. Subjects taking the questionnaire are instructed not to overthink their answers and to simply use their first impulse. When hesitating between two choices, the advice is to answer according to how they would feel and react in their most natural and relaxed state (Myers et al., 2003). As is to be expected, persons with a very clear preference for any of the types, were more likely to agree with the initial test assessment, and also to demonstrate this same preference at a later date. The greatest variations are to be found amongst those who did not demonstrate a clear preference originally (Myers et al., 2003). MBTI concerns. Although the MBTI can be very helpful when striving to understand others (Myers et al., 2003), in order to save time and effort, results can be interpreted too simplistically. Problems arise when shortcuts are too broadly applied and people are slotted into MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 30 narrow categories rather than viewed as whole and unique individuals (Sample, 2017; Conti & Kolody, 2004). Thus, as with any concepts that have the potential of labeling people, care must be taken in how they are used. However, certain traits that are associated with personality can be useful in providing insights about how people learn. Such knowledge could help learners better understand how they go about the learning process. For the teacher, types of information such as this: …can be beneficial to the selection of appropriate methods and techniques when they are used to focus understanding, discussion, and reflective thought about the learner; however, they can be detrimental if they are used to avoid critical thinking about the learners. (Conti & Kolody, 2004, p. 189) While it is true that the different personality types think and behave in distinct ways, it is not true, when speaking of specific individuals, that a specific person will always demonstrate a certain bias or weakness (Myers et al., 2003). Because the MBTI is so widely used both in business and in education, there is a valid concern that the test may be improperly administered or improperly interpreted: [With] widespread use comes a potential for abuse in the administration and interpretation of an individual’s feedback scores. Instructors are implored to use reliable, valid, and accepted forms of the MBTI and to avoid the temptation to use short forms available from a variety of Internet sources, which are often unreliable and have questionable validity. Further, instructors should not infringe on international copyright laws by making unauthorized copies of the MBTI and scoring forms. (Sample, 2017, p. 990) MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 31 Other researchers have warned against creating stereotypes as well. One study in which over 500 volunteers took both the Assessing the Learning Strategies of Adults (ATLAS) and the MBTI, did not find a significant relationship between type and learning preference groups. The researcher concluded that one could not observe a students’ approach to learning and make assumptions about that student’s personality type (Conti & McNeil, 2011). However, the MBTI does not presume to accurately measure simple equivalencies. One cannot assume an observed behavior (especially an isolated incident) will always equate to a specific MBTI profile (Myers et al., 2003). Instead, the MBTI paints a broader picture and asserts that individuals who identify as a certain type tend to display certain kinds of characteristics. There will always be individual variations. For example, persons with a judging orientation tend to prefer highly organized lifestyles and are likely, when planning a vacation, to create detailed itineraries. Those with perceiving orientations are more likely to enjoy spontaneity and may feel restricted with a planned schedule. However, it is entirely possible for both the judger and the perceiver to make very specific vacation plans, leading a casual observer to conclude that both individuals must be of a judging type. However, it is the motivation behind the behavior that the MBTI seeks to illuminate. The judger will enjoy a detailed itinerary because the judger likes the feeling of knowing exactly what to expect. When a perceiver creates a detailed itinerary, it is likely because the perceiver wants to explore all of the available options to enable the best choice at any given moment as plans change throughout the trip. The MBTI as a classroom tool. Even though each student is a unique individual, the MBTI has often been used very effectively in an educational setting in informing practice (Myers et al., 2003). Fornaciari and Dean (2013) posited an instance in which an Extraverted, Sensing, MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 32 Thinking, Judging (ESTJ) student (an extraverted person who prefers information given in a logical sequence, makes decisions based on logic and enjoys order and predictability in life) is confused about an assignment given by an Introverted, Intuitive, Feeling, Perceiving (INFP) faculty member (an introverted person preferring information being given as a big picture, who makes decisions based on achieving harmony, and enjoys spontaneity). These are opposite types, but the chances for effective communication can still be high if the instructor is aware that the ESTJ student will automatically pay the most attention to logically presented concrete information and less attention to suppositions and ambiguous instructions (Fornaciari & Dean, 2013). A straightforward approach combined with the INFP’S natural warmth, will likely result in success from the point of view of both the instructor and the student. Both the instructor and the student should “flex” to each other’s approach in communicating and resolving a problem to achieve a satisfactory resolution (Allen & Brock, 2000; Sample, 2017). The MBTI has been successfully used to build effective groups for project-based learning. When instructors know beforehand which personality types tend to do well together and where conflicts are likely to arise, a great deal of unnecessary stress, which can inhibit learning, can be avoided (Rodriguez Montequín, Mesa Fernández, Balsera, & Garcia Nieto, 2013). Instructors have long been aware that some students are more outgoing than others. The MBTI offers one cohesive explanation of why some students are much more talkative than others which reaches well beyond the simple labels of “shy” or “outgoing.” Extraverted types (typically talkative) often think out loud. For them, verbalization is a form of thinking itself. Therefore, they tend to do well when given an opportunity to work in groups because the communication group work entails better enables them to think. Alternatively, introverts (generally quieter) MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 33 prefer to be given time and space to think things through internally and make connections on their own and so may have difficulty when suddenly asked for their thoughts before they have had time to establish for themselves what their thoughts actually are (Myers et al., 2003; Sample, 2017). From such examples it might be easy to conclude that the best way for students to learn is to pair them up with instructors of matching type. However, research shows that this does not seem to be the case (Myers et al., 2003). Rather, students benefit when instructors are teaching in ways that are consistent with their own personality but are aware of and are able to adapt to the different characteristics that their pupils bring to the classroom. The MBTI has also played a useful role in developing curriculum and public policy (Myers et al., 2003). Sample (2017) outlines an exercise in which he creates teams of students with differing decision-making preferences, and then asks the team to generate a public policy on a given topic. Once this is accomplished the group must decide exactly how to present that topic to others and lastly, to reflect and outline what biases the individuals may have based on preference type and to discuss how policies can be implemented to be more inclusive. This experience can be eye-opening for students as they first realize that their habits of thinking are far from universal and they then begin to appreciate the strengths and weaknesses of their own thinking patterns and those of others. A Gap in the Research Given the pervasive and long-standing difficulties that so many students encounter in mathematics learning, and the volume of research on the MBTI, it is somewhat surprising that there is very little research on MBTI type and mathematics success. A study correlating each of MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 34 the 16 types and also the Sensing and Intuitive type specifically, as it is this dichotomy that measures how individuals process information, may be enlightening. MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 35 PURPOSE Mathematics is a problem at the college level both for students and institutions. Billions have been spent on remediation, but this has not been successful. In response, there is currently a movement to condense or eliminate developmental mathematics courses. This shortened curriculum has had mixed results. Whether students take many preparatory mathematics courses, or just a few, it certainly behooves educators to teach mathematics as effectively as possible. When instructors are able to improve their understanding of how students organize the learning of new concepts, teachers can better tailor their instruction. Many studies have been done on personality and the influence individual personality has on learning outcomes. The Myers-Briggs Personality Type Indicator (MBTI) is a well-known personality assessment, which assigns people to one of 16 normal personality types based on self-report answers to a questionnaire. Although there is wide variation within each type, each type tends to exhibit certain distinct characteristics that remain stable over a person’s lifetime. A number of studies have been conducted on the MBTI and the correlation of type to academic performance. Research has also been done on the MBTI and broad topics such as science and some on specific subjects such as chemistry. However, there is a gap in the research on MBTI type and mathematics specifically. In addition, there is a gap comparing Sensing and Intuitive types and their success in mathematics and scientific fields in general. Because Sensing types prefer to receive information in an orderly, step by step sequence and because mathematics is traditionally taught in a step by step logical format, one might suppose that Sensors will have an MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 36 advantage in learning mathematics. Studies supporting or detracting from such a supposition are lacking. Given the pervasiveness of mathematics difficulty, these gaps are somewhat surprising. The purpose of this study is to compare MBTI types to mathematics success to determine whether there is a statistically significant correlation. Two primary research questions will direct this study: 1. Is there a correlation between MBTI type and mathematics success? If so, which of the 16 types is the most successful? 2. What are the differences of mathematical success between the Sensing and Intuitive types? MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 37 METHODS Overview Student personality has been shown to influence academic performance. The Myers- Briggs Type Indicator (MBTI) is one of the best known and reliable personality assessments available. However, despite the high percentage of students who fail to pass even remedial mathematics courses, there has been very little research done to compare MBTI types to mathematics performance. This study sought to assess the correlation (if any) of the 16 MBTI types and mathematics success, and the correlation (if any) between the Sensing and Intuitive types specifically. Participants Data were collected from 250 students at Weber State University, a midsized open enrollment institution. The majority of students in these courses were freshman below the age of 25. However, there are also non-traditional students of all ages and the students came from a wide variety of circumstances. Other than class standing (e.g. freshman, sophomore, junior, senior), the demographics of the course mirrored the demographics of Weber State University with roughly the same number of male and female students, who are predominantly Caucasian (74.8 %) and English speaking (Weber State University, 2019). All non-native English speakers must pass an English proficiency test before they are allowed to take mainstream courses such as the First Year Experience. The participants selected for this study contained all the students in the First Year Experience course who took the MBTI in the fall of 2018 (351). Two groups were excluded from this study, minors and those who had zero initial mathematics placement of zero upon MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 38 acceptance to Weber State University. Placement level zero indicated that the university had not yet received the information needed to assign a placement level. These students were excluded for lack of sufficient information. After these exclusions, 250 students remained in the study. The number of students in each of the 16 personality categories and the total number of students in each of the individual preference types as measured by the MBTI are summarized in the tables below. Table 1 Total number of students in each of the 16 MBTI types. ENFJ 15 ENFP 25 ENTJ 2 ENTP 9 ESFJ 20 ESFP 19 ESTJ 8 ESTP 6 INFJ 19 INFP 26 INTJ 2 INTP 8 ISFJ 39 ISFP 16 ISTJ 22 ISTP 13 Note: There were 250 total participants. Table 2 Total number of students when sorted into each dichotomy preference. Extraversion 104 Introversion 146 Sensing 143 Intuitive 107 Thinking 70 Feeling 179 Judging 137 Perceiving 158 Note: There were 250 total participants. Instruments The MBTI assessment, Form M, was used for the First Year Experience course at Weber State University in 2018. “Form M (93 items) [is] the current standard form of the MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 39 MBTI® assessment and is scored for four-letter type and the preference clarity indexes. Online administration and scoring is available through the publisher, The Myers-Briggs Company” ("Versions," 2019). This assessment was administered at various points throughout the semester, depending on teacher planning, and online scoring was utilized. Student records from Weber State University provided both the initial mathematics placement and subsequent grades in mathematics (if taken). Initial placement levels represented the highest mathematics course a student would be allowed to take without further testing. Levels ranged from one to six, level one representing the lowest level course, pre-algebra and level six indicating that the student had completed the quantitative literacy requirement. Procedure In Fall of 2018, 351 students took the MBTI. With IRB approval, these students’ names were entered into an excel spreadsheet housed in a password protected computer, along with their MBTI type as provided by the assessment and individual scores in each of the four dichotomies. Next the students’ initial mathematics placement was entered. Mathematics placement is determined by a number of factors such as ACT scores, Weber State University placement testing, AP scores, or concurrent enrollment courses completed. Because Weber State University is an open enrollment school, occasionally students are admitted before Weber State receives record of previous courses or testing. In these cases, a student is given a placement of zero. For purposes of this study, students with a zero placement were excluded because it was not possible to determine whether more placement data would have been forthcoming. Students who were minors in Fall 2018 were also excluded from the study. MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 40 Transcripts were then checked for all students enrolled for the Fall of 2018 and Spring 2019 semesters. If the student enrolled in a mathematics course at any level in either Fall or Spring or both, the course and the subsequent grade were recorded on an excel spreadsheet. Once the data were entered, both the student name and their Weber identification number were deleted from the spreadsheet, thus permanently erasing any link that would identify an individual student and link them to their data. Chi-squared analytics were used to make a variety of comparisons, beginning with the two research questions: “Is there a correlation between MBTI type and mathematics success and if so, which of the 16 types is the most successful? And, what are the differences of mathematical success between the Sensing and Intuitive types?” As the research progressed, other questions emerged based on the data. Further analytics were run, and those results are also outlined below. MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 41 RESULTS The purpose of the quantitative study was to discover whether there was any correlation between MBTI type and mathematics success both as whole and between the Sensing and Intuitive types specifically. Chi-squared analytics were used to make these comparisons. The results of these comparisons led to other questions and further analysis. The results of all tests run are summarized in Table 3 below. The first question in this study was: Is there a correlation between MBTI type and mathematics success? A chi-squared analysis was run comparing all sixteen MBTI types against the initial mathematics placement of 250 students. There were six possible levels of placement. Level 1 represents placement in Math 950, Pre-Algebra. This is a developmental course, students receive no college credit for completion. Level 2 represents Math 970, Introduction to Algebra, again this is a developmental course and students receive no credit for completion. Level 3 is Math 1010, Elementary Algebra. Although Math 1010 is still considered to be developmental, students do receive college credit. Level 4 is either Math 1030, Contemporary Mathematics or Math 1040, Statistics. These are both terminal classes which satisfy the quantitative literacy requirement for many, but not all, majors at Weber State University. Students may move from Math 970 straight to Math 1030 or 1040. Math 1010 is the pre-requisite course for Level 5, College Algebra. Math 1050 is the pre-requisite for all higher-level mathematics courses. Level 6 indicates that a student has met the quantitative literacy requirement, either by previous course work or a qualifying exam. Table 3 is a summary of all chi-squared tests run for this study. A more detailed table and explanation of each test will follow in this results section. MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 42 Table 3 Summary of all chi-squared tests run for this study. Table Description Significance P value Table 4 All MBTI types and initial placement No .07 Table 5 All MBTI types to compressed grades No .84 Table 6 Extraverted and Introverted types to initial placement No .24 Table 7 Sensing and Intuitive types to initial placement No .52 Table 8 Thinking and Feeling types to initial placement Yes .02* Table 9 Judging and Perceiving types to initial placement No .69 Table 10 Extraverted and Introverted types to compressed grades No .96 Table 11 Sensing and Intuitive types to compressed grades No .24 Table 12 Thinking and Feeling types to compressed grades Yes .04* Table 13 Judging and Perceiving to compressed grades No .18 Table 14 Heart of Type for Thinking paired with Sensing/Intuitive No .29 Table 15 Clear Extraverted and Introverted types to initial placement No .59 Table 16 Clear Sensing and Intuitive types to initial placement No .62 Table 17 Clear Thinking and Feeling types to initial placement Yes .04* Table 18 Clear Judging/Perceiving to initial placement No .46 *p < .05 There was not a significant difference amongst any of the MBTI types and initial level placement. Table 4 shows all participant MBTI types and their actual placement level on arrival at Weber State University compared to the levels predicted by the chi-square analysis to determine whether any differences were of statistical significance. MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 43 Table 4 All MBTI types compared to actual and expected initial placement levels at Weber State. MBTI Type Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 ENFJ (actual) 5 5 2 2 0 1 ENFP (actual) 12 3 4 2 2 2 ENTJ (actual) 1 0 1 0 0 0 ENTP (actual) 4 1 1 3 0 1 ESFJ (actual) 5 4 7 1 2 1 ESFP (actual) 7 4 4 0 3 1 ESTJ (actual) 3 0 0 2 3 0 ESTP (actual) 1 1 1 0 3 0 INFJ (actual) 2 8 3 0 2 4 INFP (actual) 13 5 0 2 5 1 INTJ (actual) 0 1 1 0 0 0 INTP (actual) 1 2 1 1 2 1 ISFJ (actual) 12 10 7 1 6 3 ISFP (actual) 5 5 1 2 0 3 ISTJ (actual) 6 2 4 3 5 2 ISTP (actual) 3 1 2 2 0 5 ENFJ (expected) 4.8 3.13 2.35 1.27 1.99 1.5 ENFP (expected) 8 5.22 3.92 2.11 3.31 2.51 ENTJ (expected) 0.64 0.42 0.31 0.17 0.27 0.2 ENTP (expected) 3 1.88 1.41 0.76 1.19 0.9 ESFJ (expected) 6.4 4.18 3.13 1.69 2.65 2 ESFP (expected) 6.08 3.97 2.98 1.6 2.52 1.91 ESTJ (expected) 2.56 1.67 1.25 0.67 1.6 0.8 ESTP (expected) 1.92 1.25 0.93 0.51 0.8 0.6 INFJ (expected) 6.08 3.97 2.98 1.6 2.52 1.91 INFP (expected) 8.32 5.43 4.07 2.19 3.44 2.6 INTJ (expected) 0.64 0.42 0.31 0.17 0.27 0.2 INTP (expected) 2.56 1.67 1.25 0.67 1.06 0.8 ISFJ (expected) 12.48 8.14 6.11 3.29 5.17 3.92 ISFP (expected) 5.12 3.34 2.51 1.35 2.12 1.61 ISTJ (expected) 7.04 4.59 3.44 1.86 2.91 2.2 ISTP (expected) 4.16 2.71 2.04 1.09 1.72 1.3 Note: The chi square analysis for all MBTI types compared to their initial math placement at Weber State was not significant (p = .07). MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 44 A chi square analysis was run for all MBTI types against all possible grade outcomes. The grades represented courses taken in either or both Fall 2018 and Spring 2019. It is interesting to note that none of the participants who took math courses received a grade of D-. The reason for this is unclear. While running the chi-square analysis the D- column was removed from the data to avoid dividing by zero. During the time period measured in this study, some students took two mathematics courses, some took one course while others did not enroll in mathematics at all. The total number of mathematics courses taken when all student courses were added was186. When all possible grades (including plus and minus grades) of all 16 MBTI types were entered into an excel spread sheet, the result was very low numbers in each of the possible categories. The chi-square test in this case calculated such a high level of significance (p < .00) that it was far more likely that the analysis was compromised by the low numbers than that there was truly significance at the p < .00 level. Table 5 shows all MBTI types compared to all possible actual and expected compressed grade outcomes, meaning that plus or minus grades were grouped together. For example, the B category contains grades of B+, B and B-. This analysis was constructed to increase the numbers for each possible outcome to enable a more accurate result. When calculated in this fashion a non-significant result was returned. MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 45 Table 5 All MBTI types compared to actual and expected compressed grades. MBTI Type A B C D E/UW ENFJ (actual) 3 4 1 2 2 ENFP (actual) 1 6 3 3 7 ENTJ (actual) 0 0 0 0 1 ENTP (actual) 0 1 2 1 2 ESFJ (actual) 5 5 4 0 0 ESFP (actual) 1 4 3 2 2 ESTJ (actual) 1 2 1 2 1 ESTP (actual) 0 3 0 1 0 INFJ (actual) 2 5 5 3 2 INFP (actual) 3 4 4 2 7 INTJ (actual) 0 1 1 1 0 INTP (actual) 0 3 3 1 1 ISFJ (actual) 4 9 7 5 2 ISFP (actual) 2 4 2 2 4 ISTJ (actual) 2 4 2 1 5 ISTP (actual) 3 2 1 1 0 ENFJ (expected) 1.74 3.68 2.52 1.74 3.87 ENFP (expected) 2.9 6.13 4.19 2.9 3.87 ENTJ (expected) 0.15 0.31 0.21 0.15 0.19 ENTP (expected) 0.87 1.84 1.26 0.87 1.16 ESFJ (expected) 2.03 4.3 2.93 2.03 2.71 ESFP (expected) 1.74 3.68 2.52 1.74 2.32 ESTJ (expected) 1.02 2.15 1.47 1.02 1.35 ESTP (expected) 0.58 1.23 0.84 0.58 0.77 INFJ (expected) 1.16 5.21 3.56 2.46 3.29 INFP (expected) 2.9 6.13 4.19 2.9 3.87 INTJ (expected) 0.44 0.92 0.63 0.44 0.43 INTP (expected) 1.16 2.45 1.68 2.03 1.55 ISFJ (expected) 3.91 8.27 5.66 3.92 5.23 ISFP (expected) 2.03 4.3 2.94 2.03 2.71 ISTJ (expected) 2.03 4.3 2.94 2.03 2.71 ISTP (expected) 1.02 2.15 1.47 1.06 1.35 Note: The results of this analysis were non-significant (p = .84). MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 46 Tables six through nine assess the difference between each of the four dichotomies compared to initial math placement. The tables are ordered according to the established norm in listing MBTI type (Extraversion/Introversion, Sensing/Thinking, Thinking/Feeling, Judging Perceiving). The same order is kept in Tables nine through thirteen). Table 7 attempts to answer the second research question: Is there a significant difference in mathematics success between the Sensing and Intuitive preferences? Because the result of that analysis was non-significant (p = .52), the same analysis was run for each of the other dichotomies with the following result: of the four dichotomies only Thinking/Feeling yielded a significant result (p = .01). Table 6 Extraverted and Introverted types compared to actual and expected initial placement. MBTI Type Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Extraverted (actual) 37 18 20 10 13 6 Introverted (actual) 43 34 19 11 20 19 MBTI Type Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Extraverted (expected) 33.28 21.63 16.22 8.74 13.73 10.4 Introverted (expected) 46.72 30.37 22.78 12.26 19.27 14.6 Note: The comparison between Extraverted and Introverted types for initial placement is non-significant (p = .24). Table 7 Sensing and Intuitive types compared to actual and expected initial placement. MBTI Type Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Sensors (actual) 42 27 26 11 22 15 Intuitive (actual) 38 25 13 10 11 10 Sensors (expected) 45.76 29.74 22.31 12.01 18.88 14.3 Intuitives (expected) 34.24 22.26 16.69 8.99 14.12 10.7 Note: The comparison between Sensing and Intuitive types for initial placement is non-significant (p = .52). MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 47 Table 8 Thinking and Feeling types compared to actual and expected initial placement. MBTI Type Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Thinking (actual) 19 8 11 11 13 9 Feeling (actual) 61 44 28 10 20 16 Thinking (expected) 22.72 14.62 10.96 5.9 9.28 7.02 Feeling (expected) 56.79 37.38 28.03 15.09 23.72 17.98 Note: The comparison between Thinking and Feeling types for initial placement is significant (p = .02). Table 9 Judging and Perceiving types compared to actual and expected initial placement. MBTI Type Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Judging (actual) 16 16 15 6 9 7 Perceiving (actual) 23 13 7 6 8 4 Judging (expected) 40.64 26.42 19.81 10.67 16.76 12.7 Perceiving (expected) 39.36 25.58 19.19 10.33 16.24 12.3 Note: The comparison between Judging and Perceiving types is non-significant (p = .69). Tables ten through thirteen show the four dichotomies measured against compressed grade performance. Again, only the Thinking/Feeling dichotomy showed significance. Table 10 Extraverted and Introverted types compared to actual and expected compressed grades. MBTI Type A B C D E Extravert (actual) 11 25 14 11 15 Introvert (actual) 16 32 25 16 21 Extravert (expected) 11.03 23.29 15.94 11.03 14.7 Introvert (expected) 15.97 33.71 23.06 15.97 21.29 Note: The comparison between Extraverted and Introverted compressed grades is non-significant (p = .96). MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 48 Table 11 Sensing and Intuitive types compared to actual and expected compressed grades. MBTI Type A B C D E Sensing (actual) 18 33 20 14 14 Intuitive (actual) 9 24 19 13 22 Sensing (expected) 14.37 30.34 20.76 14.37 19.16 Intuitive (expected) 12.63 26.66 18.24 12.63 16.83 Note: The comparison between Sensing and Intuitive compressed grades is non-significant (p = .24). Table 12 Thinking and Feeling types compared to actual and expected compressed grades. MBTI Type A B C D E Thinking (actual) 6 16 10 8 10 Feeling (actual) 21 41 29 19 26 Thinking (expected) 7.26 15.32 10.48 7.26 9.68 Feeling (expected) 19.74 29.98 21.22 19.74 19.01 Note: The comparison between Thinking and Feeling types is significant (p = .04). Table 13 Judging and Perceiving types compared to actual and compressed grades. MBTI Type A B C D E Judging (actual) 17 30 21 14 13 Perceiving (actual) 10 27 18 13 23 Judging (expected) 13.79 29.11 19.92 13.79 18.39 Perceiving (expected) 13.21 27.89 19.08 13.21 17.61 Note: The comparison between Judging and Perceiving types is non-significant (p = .29). The Thinking and Feeling dichotomy was the only test to show a statistically significant difference in mathematics success when measured against initial placement and compressed grade achievement. Would the difference between these two types have an impact on other MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 49 MBTI types? Table 14 measures the “heart of type,” which are the central two letters of each person’s four-letter MBTI type. The preferences indicated by the central letters greatly impact a person’s style of thinking and behavior (Myers et al., 2003). The analysis for the central letters compared to initial placement did not reveal a significant result (p =.18) but was somewhat closer to significance than Sensing compared to Intuitive types alone (p =.24). Because thus far initial placement has yielded higher levels of significance than compressed grades, an analysis for heart of type and compressed grades was not calculated. Table 14 Heart of Type for Thinking paired with Sensing and Intuitive types compared to actual and expected initial placement. MBTI Heart of Type Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Sensing/Thinking (actual) 10 8 8 8 4 4 Intuitive/Thinking (actual) 17 5 8 9 17 7 Sensing/Thinking (expected) 10.8 5.2 6.4 6.8 8.4 4.4 Intuitive/Thinking (expected) 16.2 7.8 9.6 10.2 12.6 6.6 Note: The comparison between Heart of Type involving Thinking paired with Sensing and Intuitive types is non-significant (p = .18). All of the participants in this study came from the First Year Experience course in the Fall of 2018. Most of the participants were traditional first-time college students between the ages of 18 and 22. It is possible that, being young, some students did not take care to answer the MBTI questionnaire accurately. The researcher hypothesized that scores indicating a moderate to strong preference (10 or higher on a 1-30 point scale), would be more likely to represent true patterns of thinking and behavior that may influence mathematics performance. Only 15 participants scored less than 10 across all four dichotomies. Tables 15 through 18 evaluate the four moderate to high scoring MBTI dichotomies compared to initial placement. The total n varies in these calculations because it is possible that any individual student may have a high MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 50 score in more than one category. The following analysis considered all those who demonstrated a clear preference in the specific dichotomy in question without regard to high or low preference scores in other areas. Table 15 Clearly indicated MBTI for Extraverted and Introverted compared to actual and expected initial placement. MBTI Type Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Extraverted (actual) 16 13 11 7 9 3 Introverted (actual) 31 24 16 7 14 14 Extraverted (expected) 16.81 13.23 9.65 5 8.22 6.08 Introverted (expected) 30.19 23.77 17.35 8.99 14.78 10.92 Note: The comparison between clearly indicated Extraverted and Introverted types is non-significant (p = .59). Table 16 Clearly indicated MBTI scores for Sensing and Intuitive types compared to actual and expected initial placement. MBTI Type Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Sensing (actual) 11 7 11 2 9 7 Intuitive (actual) 17 8 8 3 5 5 Sensing (expected) 14.15 7.58 9.6 2.53 7.08 6.06 Intuitive (expected) 13.85 7.42 9.4 2.47 6.92 5.94 Note: The comparison for clearly indicated Sensing and Intuitive types is non-significant (p = .62). MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 51 Table 17 Clearly indicated MBTI scores for Thinking and Feeling types compared to actual and expected initial placement. MBTI Type Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Thinking (actual) 8 3 11 8 7 4 Feeling (actual) 33 28 20 7 14 8 Thinking (expected) 11.13 8.42 8.42 4.07 5.7 3.25 Feeling (expected) 29.87 22.58 22.28 10.93 15.29 8.74 Note: The comparison for clearly indicated Thinking and Feeling types is significant (p = .04). Table 18 Clearly indicated MBTI for Judging and Perceiving types compared to actual and expected initial placement. MBTI Type Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Judging (actual) 16 16 15 6 9 7 Perceiving (actual) 23 13 7 6 8 4 Judging (expected) 16 16 15 6 9 7 Perceiving (expected) 23 13 7 6 8 4 Note: The comparison for clearly indicated Judging and Perceiving types is non-significant (p = .46). MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 52 DISCUSSION History: This project has deep personal roots. From an early age I have struggled and continue to struggle with mathematics. However, through people very close to me, I have glimpsed the beauty, fascination and creativity of mathematics. In consequence, I have made sincere efforts on multiple occasions to overcome this limitation, but despite being an able student in every other subject, the door to mathematics has until recently, remained firmly closed to me. While working as a secretary for the Weber State mathematics department I saw many students for whom mathematics was the only subject preventing graduation. Many studies (Bailey et al.,2010; Bonham & Boylan, 2012; Cafarella, 2016) confirm that failure in mathematics is not an isolated personal issue or one limited to Weber State alone. And yet, the instructors did not seem to be at fault. I knew firsthand of the depth of their caring, their competence and the many extra hours they habitually put in. When I became acquainted with the MBTI, it seemed to me that at least one part of the mathematics failure mystery might be explained. I have a very clear Intuitive preference. Perhaps because the mathematics courses I had taken thus far did not present an overall objective, I was unable to build the mental framework necessary to retain and understand the concepts being taught. This theory was later born out when I took a mathematics course for teachers. It was the first time I had experienced mathematics taught in context and it was the first and only time I have done well in a mathematics course. MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 53 Hypothesis The hypothesis in developing this study was that those with a Sensing orientation would naturally have higher mathematics placement and higher pass rates than Intuitive types. The Sensing/Intuitive dichotomy measures the way in which an individual receives and organizes information. Those with Sensing preferences best understand information when it is presented in a logical style, moving step by step with little extraneous information. Mathematics is traditionally taught in this fashion. Those with an Intuitive disposition understand better when they can see facts in relation to a big overall picture. In this study, the analysis for Sensors and Intuitives compared to their initial placement scores at Weber State University, showed no significance. Not only did the p value fail to show statistical significance, there was virtually no difference between the groups with a p value of .51. Clearly, for students who were evaluated for this study, there was no advantage to being either a Sensor or an Intuitive. The Extraverted/Introverted and the Judging/Perceiving dichotomy also showed no significance. However, the Thinking/Feeling pairing showed significance both when measured both initial placement and actual grade performance. Thinkers and Feelers In the present study Thinkers outperformed those with a feeling preference. Because Thinkers have a natural inclination toward the logical solution for any given problem, at first glance it would not seem surprising that Thinkers have a distinct edge in the study of mathematics. However, those with a thinking disposition are not necessarily better at logical thinking or deduction, and there is no overall difference in the intelligence levels of thinkers or MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 54 feelers. The Thinking/Feeling dichotomy only measures decision making preferences, not greater reasoning faculties. An example from the First Year Experience class illustrates the difference very well. Students self-select themselves into Thinking and Feeling groups and are given the following scenario: You are all on a sinking ship. The only possible way to survive is to throw one person in your group overboard to lighten the load. Whom do you choose? The discussion that follows is enlightening. Often students in both groups will volunteer to jump to save the others. When this happens the instructor prompts the group to assume that no one is volunteering, what would they do then? Invariably the Feeling groups begin by asking value driven questions of one another. Who has children? Is anyone likely to make a large positive contribution to the world? The Thinkers begin with non-emotional or practical solutions. Who is the best swimmer? Does anyone have a terminal illness and will die soon anyway? How about drawing straws? In the end both groups find a logical solution. The Thinkers will almost always make a disinterested decision based either on random selection or a better chance at survival. The Feelers make a logical decision based in equity. Each person’s individual circumstances are considered and by process of elimination the one who has lived the longest or has the fewest people depending on them, is the one elected to go overboard, almost always with the selected person in full agreement. The difference between the two groups is value based, not logic based. This opens a number of questions as to how and why Thinkers demonstrate stronger performance in mathematics. MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 55 The MBTI Manual (Myers, 2003) discusses the differences in type by pairing functions of type together. The type combinations that deal with mental functions are the Sensing/Thinking (ST), Sensing/Feeling (SF), Intuitive Thinking (NT) and Intuitive Feeling (NF). Each type and each combination of type exhibit characteristics that may be perceived in certain situations as positive or negative. The MBTI manual lists a number of these strengths and weaknesses. ST types “Maintained high interest throughout a production simulation that required learning well-defined, structured procedures” (Myers, 2003 p. 42). Whereas NT types, “Lost interest rapidly and ‘dropped out’ in a production simulation that required learning well-defined structured procedures” (Myers, 2003 p.45). The natural ability of ST types to maintain focus in learning structured procedures would suggest that these types might enjoy traditionally taught mathematics more than their peers of another preference type leading Sensors to better performance. In the present study, ST types did show a slight advantage over NT types, although not one of statistical significance. However, according to the MBTI manual (Myers, 2003), ST types are also the most risk averse. Should an ST student be uncomfortable in a mathematics course, they may be apt to shut down more quickly than other types. Limitations This study had several limitations. It had 250 participants and evaluated the 186 mathematics classes taken among them. This was not a large enough sample size to produce an accurate result when considering all possible grade outcomes. A larger sample size would also be more likely to represent the population as a whole. All of the participants were students who had enrolled in the First Year Experience course. Although this course is highly recommended, it is not a required course. It is possible that the course attracts a disproportionate number of certain personality types. MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 56 The First Year Experience course is open to all students of any age and at any point in their education, however the course primarily attracts traditional students between the ages of 18- 20 who are in their freshman year of college. It is possible that younger students may not have taken the assessment as seriously as more experienced students and that careless answers may have skewed the results. Recommendations Future quantitative studies with a larger more randomized pool of participants could help to verify whether those with a Thinking disposition are in fact, more likely to do well in mathematics. Several qualitative studies that examine both Thinkers and Feelers to discover common patterns of thinking and behavior that contribute to their math success would be enlightening. Conversely, the same kind of study examining both Thinkers and Feelers who struggle in math might help to uncover common poor habits of thinking that might be able to be corrected with intervention. It would be especially helpful if the research that studies the students who struggle, could focus on students whose only academic problem area is mathematics. By selecting otherwise able students, the researcher could eliminate some confounds due to broad learning disabilities or overall poor study habits. In 2011, a qualitative study was conducted by Laurel Howard and Martha Whitaker that questioned adult learners who had poor histories in mathematics but were now successful in their mathematics courses. In every case, the key factor in their new-found success was powerful outside motivation. These students had reached a point in their lives where they had no choice except to be successful in mathematics or be unable to support their families because of underemployment or complete loss of employment. In these circumstances, the students in this MYERS-BRIGGS TYPE INDICATOR AND MATHEMATICS SUCCESS 57 study began to devote the time necessary to learn the content in their coursework. They attended all of their classes, turned in all homework and sought help immediately when difficulties arose. In consequence, they began to perform well in mathematics. Although several voiced that they enjoyed their mathematics courses, none indicated any area of particular mathematical interest or plans to pursue mathematics beyond the minimum required. While it is good that all of these students were eventually able to overcome their difficulties in mathematics, it would obviously have been better if the difficulties could have been addressed and corrected much earlier without the stress of financial catastrophe as a motivator. A better understanding of the different habits of mind presented by different personality types, will help educators to correct problems in the early stages before the student becomes discouraged and decides that they “hate math,” and long before the student reaches adulthood and only learns mathematics when it is forced upon them. Humans are complex and solutions to human difficulties will therefore also be complex. 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