# Toward Improving the Mathematics Preparation of Elementary Preservice Teachers

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<ul><li><p>Toward Improving the Mathematics Preparation of ElementaryPreservice Teachers</p><p>Fabiana CardettiUniversity of Connecticut</p><p>Mary P. TruxawUniversity of Connecticut</p><p>Research suggests the importance of mathematics knowledge for teaching (MKT) for enabling elementary schoolteachers to effectively teach mathematics. MKT involves both mathematical content knowledge (M-CK) and mathemati-cal pedagogical content knowledge (M-PCK). However, there is no consensus on how best to prepare elementarypreservice teachers (PSTs) to achieve M-CK and M-PCK. This study builds on research related to MKT by investigatinginfluences of mathematics content courses designed specifically for elementary PSTs (IMPACT coursesImpact ofMathematics Pedagogy and Content on Teaching) on their attitudes (i.e., confidence and motivation) toward M-CK andM-PCK. Results suggest that the PSTs who participated in these IMPACT courses not only acquired high levels ofconfidence and motivation toward M-CK, but also showed significant and greater gains in attitudes toward M-PCK,after taking the required mathematics methods course, than their counterparts. Further, the findings suggest that theseIMPACT courses provided a mathematical foundation that allowed the PSTs to engage in mathematics teaching methodsbetter than those PSTs who did not have such a foundation. These results suggest potential course experiences that mayenhance M-CK and M-PCK for elementary PSTs.</p><p>It has been noted consistently that, in order for elemen-tary school teachers to teach mathematics effectively,mathematics knowledge for teaching (MKT) is necessary.MKT is different from mathematics knowledge learnedfor other purposes. MKT involves an intersection of math-ematical content knowledge (M-CK) and mathematicalpedagogical content knowledge (M-PCK). While therehave been increasing numbers of studies investigatingMKT (e.g., Ball, Lubienski, & Mewborn, 2001; Hill,2010; Hill et al., 2008; Ma, 1999), what has not beenuncovered clearly is how preservice teachers (PSTs) mayacquire MKT. Further, it has been acknowledged that fewcollege-level mathematics courses serve to promoteappropriate MKT for elementary PSTs (Ball, 2003).</p><p>This study investigated elementary PSTs attitudestoward M-CK and M-PCK. We focused on PSTs attitudesfor four reasons: (a) this focus would help to flesh out workof other researchers who are investigating MKT from acontent perspective (e.g., Ball et al., 2001; Hill, 2010; Hillet al., 2008); (b) this focus would build from longstandingand consistent research recognizing that attitudes influ-ence motivation and capacity to learn mathematics (e.g.,Aiken, 1974, 1976; Evans, 2011; Fennema & Sherman,1977); (c) this research would help to uncover specificcourses that might influence attitudes aligned with learn-ing of MKT (Cardetti, 2011; Cardetti, Truxaw, & Bushey,2011; Truxaw, Cardetti, & Bushey, 2010); and (d)acknowledging research that suggests that teacher atti-tudes influence student learning, this focus would connectindirectly to future student learningthe coin of the</p><p>realm for educational studies (e.g., Evans, 2011; Henson,2001).</p><p>With this study, we seek to better understand how PSTsattitudes toward mathematics and its teaching changeaccording to their content course experiences and howthese changes compare across different groups. In particu-lar, we investigate influences of mathematics courseworkthat has been designed specifically with elementary PSTsin mindmathematics content courses taught in the math-ematics department, but with MKT as an emphasis. In thispaper, we will call these courses IMPACT (Impact ofMathematics Pedagogy and Content on Teaching) courses.Along with reporting our results, we outline related rec-ommendations for teacher education programs to helpfoster and strengthen PSTs predispositions to ensure thatthey acquire the knowledge and skills necessary to suc-cessfully teach elementary school mathematics.</p><p>Theoretical FrameworkCurrent research suggests the importance of MKT to</p><p>enable elementary school teachers to teach mathematicseffectively (Ball, 2003; Ball et al., 2001; Fennema &Franke, 1992; National Council of Teachers ofMathematics, 2003). Additionally, Hill, Rowan, and Ball(2005) found that this knowledge is significantly related tostudent achievement supporting the efforts to improvemathematics education in schools by improving the math-ematics education of teachers. However, there is noconsensus on how best to prepare elementary PSTs inorder to achieve the important combination of M-CK and</p><p>School Science and Mathematics 1</p></li><li><p>M-PCK that make up MKT and, in turn, support studentlearning (Kirtman, 2008). For example, Ball (2003) notesthat increasing the quantity of teachers mathematicscoursework will only improve the quality of mathematicsteaching if teachers learn mathematics in ways that make adifference for the skill with which they are able to do theirwork. The goal is not to produce teachers who know moremathematics. The goal is to improve students learning(p. 1). Shulmans (1986) seminal work on pedagogicalcontent knowledge (PCK) is relevant as it recognizes thatPCK is at the intersection of content and pedagogy.M-PCK therefore requires that teachers not only under-stand mathematics content, but also can transform it tosupport student learning (McDonnough & Matkins, 2010).For elementary PSTs, taking more mathematics contentcourses may support increased M-CK, but it may notsupport development of M-PCK.</p><p>Moreover, in Balls (2003) remarks to the SecretarysSummit on Mathematics, she noted that few mathematicscourses offer opportunities to produce knowledge that isappropriate for elementary school teachers. Further, sheurged that ongoing research in this area is crucial (p. 9).It follows that identifying courses that have been designedto provide elementary PSTs with the specialized contentknowledge called for by these scholars (Ball, 2000; Ball,Thames, & Phelps, 2008; Shulman, 1986) is necessary forimproving elementary school mathematics instruction.Mathematics methods courses have been investigated withrespect to content knowledge, attitudes, and self-efficacy(e.g., Evans, 2011), but there is little in the literature touncover the types of mathematics content courses that mayprovide a foundation for building not only M-CK, but alsoM-PCK. Therefore, an investigation of mathematicscontent courses for elementary education PSTs seems tobe a logical next step for research.</p><p>Because MKT is well researched by the Learning Math-ematics for Teaching Project (http://sitemaker.umich.edu/lmt/home), providing an alternate lens for viewing contentcourses would seem useful. In particular, researchers havepointed out the importance of investigating PSTs atti-tudes toward mathematics and mathematics teaching forimproving teacher preparation (Pajares, 1992; Philipp,2007). Indeed, Pajares (1992) argued for more research inthe beliefs of PSTs as they play a pivotal role in theiracquisition and interpretation of knowledge with repercus-sions in practice. More recently, the National Council ofTeachers of Mathematics (NCTM, 2003) noted, Candi-dates comfort with, and confidence in, their knowledge ofmathematics affects both what they teach and how theyteach it (p. 4). This is aligned with research on teacher</p><p>efficacy that indicates a link between positive teacherbehavior and student performance (Henson, 2001;Tschannen-Moran, Woolfolk Hoy, & Hoy, 1998).</p><p>The concept of teacher efficacy (Tschannen-Moranet al., 1998) rises from the work of Bandura (1986) relatedto self-efficacy. Bandura defined self-efficacy as peoplesjudgments of their capabilities to arrange and executecourses of action required to attain designated types ofperformances (p. xii). It impacts the things we do, ourefforts toward them, and how long we persist in workingout solutions to problems. Researchers, such as Gable andWolf (1993), have proposed that self-efficacy is the basisfor a causal model, analyzing human motivation, thoughtprocesses, and behavior (p. 12); additionally, they suggestthat confidence is an appropriate indicator of self-efficacy.This implies that PSTs who report high confidence levelswith respect to M-CK and M-PCK are likely to haverelated high self-efficacy.</p><p>Measuring attitudes (i.e., confidence or efficacy) towardM-CK and M-PCK could provide indicators of possibleimpact on future mathematics teaching practices. Forexample, Palardy and Rumberger (2008) investigatedteacher attitudes, along with investigating relationships toteacher background and instructional practices, withrespect to teacher effectiveness (i.e., student learninggains). In their study, although teacher background did notshow relationships to math achievement, one teacher atti-tude, specifically teacher efficacy, was associated withmath achievement gains. This suggests that using atti-tudes, especially ones associated with efficacy, may beuseful in uncovering links to M-CK, M-PCK, and, indi-rectly, student learning. It is noteworthy that Palardy andRumberger specifically pointed to coursework in the dis-cussion of their findings, saying:</p><p>Consequently, based on the findings of this study, itwould be wrong to dismiss the importance of teachertraining and background qualifications for effectiveteaching. It may be, for example, that specific course-work or specific aspects of the directed teaching expe-rience are critical preparation for effective teaching. . . (p. 129)</p><p>Thus, it seems important to consider possible improve-ments in mathematics teacher preparation that can beguided by the identification of course experiences thataffect PSTs attitudes toward M-CK and M-PCK that inturn may impact future learning and teaching. While someresearch has been conducted on the influence of math-ematics methods courses and student teaching on PSTs</p><p>Toward Improving Math Teacher Preparation</p><p>2 Volume 114 (1)</p></li><li><p>attitudes (e.g., Evans, 2011; White, Way, Perry, &Southwell, 2006; Wilkins & Brand, 2004), less has beendone to explore the influences of mathematics contentcourses on PSTs attitudes toward learning and teaching.For example, Evans (2011) used survey methods tomeasure gains in PSTs increase in positive attitudes andself-efficacy with respect to mathematics teaching andlearning as a result of participation in a reform-basedmethods course. Studies such as Evans provide a begin-ning, but it would be useful to unpack the questionsfurther. A natural follow-up question could be: Whenexamining PSTs participation in a reform-based methodsclass, does specific prior mathematics content courseworkinfluence their attitudes related to M-CK or M-PCK?</p><p>In considering attitude as a measure, a reasonableapproach is to tap into attitude instruments related tomathematics that have stood the test of time and have beenfound to be reliable. For example, the FennemaShermanMathematics Attitude Scales (FSMAS) and modificationsof these scales have been used consistently and reliablysince their introduction in the 1970s (e.g., Fennema &Sherman, 1976, 1977, 2004; Mulhern & Rae, 1998). Atestament to the credibility of these attitude scales is thatthe 1977 article that introduced the FSMAS was includedamong the NCTM classics publication (2004) and wassaid to be among most frequently cited articles in main-stream journals of educational psychology (Carpenter,Dossey, & Koehler, 2004, p. 26). The FSMAS thereforeprovide a credible foundation for investigating mathemat-ics attitudes. This instrument will be discussed in greaterdetail in the methods section of this paper.Research Questions</p><p>As a mathematician and a mathematics educator whowork with elementary PSTs, we sought to investigateinfluences of specific mathematics content courses onelementary PSTs attitudes toward M-CK and M-PCK. Inparticular, we were interested in the impact of mathemat-ics courses that were designed with elementary PSTs inmind and offered prior to taking the mathematics methodscourse (i.e., IMPACT courses). As we moved forward, weasked: Do the IMPACT courses influence PSTs attitudes,and in turn their learning experiences? To address thisquestion, we decided to conduct a quantitative study in acontext where both, PSTs who participated in one specificIMPACT course and those who did not, would be found.The natural place was the mathematics methods courses.At our institution, all elementary education PSTs arerequired to take a mathematics methods course within theSchool of Education, along with at least three quantitative(i.e., mathematics or statistics) courses outside the School</p><p>of Education. One may assume that PSTs attitudes wouldchange before and after completion of the mathematicsmethods course (e.g., Evans, 2011); what is not so clear ishow this change differs between those who have takenIMPACT courses (C group) and those who have not (NCgroup). In this study, we asked the following researchquestions:</p><p>1. How do the attitudes of the NC group and the Cgroup compare before and after taking the mathematicsmethods course with respect to M-CK and M-PCK?</p><p>2. Is there a change in attitudes with respect to M-CKand M-PCK before and after completion of the mathemat-ics methods course for each group?</p><p>MethodsIn order to measure elementary PSTs attitudes toward</p><p>mathematics and the teaching of mathematics, we investi-gated instruments that have been used extensively andfound to be trustworthy. In particular, the FSMAS havebeen used for more than 20 years to investigate attitudestoward mathematics (Mulhern & Rae, 1998), providing asolid base from which to build an instrument for this study.</p><p>The original FSMAS were developed in 1976 andconsist of the following nine subscales: Attitude TowardSuccess in Mathematics scale; Mathematics as a MaleDomain scale; Mother, Father, and Teacher scales; Confi-dence in Learning Mathematics scale; MathematicsAnxiety scale; Effectance Motivation in Mathematicsscale; and Mathematics Usefulness scale. Studies on thepsychometric properties of the FSMAS have generallyprovided support for the reliability and validity of thescales (Melancon, Thompson, & Becnel, 1994). Addition-ally, Mulhern and Rae (1998) reported that it is possible touse each subscale separately on its own. Some researchershave developed abbreviated versions of the scales(Mulhern & Rae, 1998) because the original scales consistof 108 items and take an average of 45 minutes to com-plete. In addition, researchers have rewritten the items toadjust to different participants age, or language, or tomeasure attitudes in other subject areas (Elliot, 1990;Mulhern & Rae, 1998; Stricker, Rock, & Burton, 1993). Inall cases, the modified versions of the scales were found tohave factor structures comparable with the original scales,as well as strong internal consistency estimates.</p><p>To construct our instrument, we strategically selecteditems from the FSMAS Confidence subscale and theEffectance Motivation subscale. The Confidence subscalemeasures confidence in ones ability to perform well on atask, while the Effectance Motivation subsca...</p></li></ul>