toward improving the mathematics preparation of elementary preservice teachers
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Toward Improving the Mathematics Preparation of ElementaryPreservice Teachers
Fabiana CardettiUniversity of Connecticut
Mary P. TruxawUniversity of Connecticut
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.
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).
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
realm for educational studies (e.g., Evans, 2011; Henson,2001).
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.
Theoretical FrameworkCurrent research suggests the importance of MKT to
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
School Science and Mathematics 1
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.
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.
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
efficacy that indicates a link between positive teacherbehavior and student performance (Henson, 2001;Tschannen-Moran, Woolfolk Hoy, & Hoy, 1998).
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.
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:
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)
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
Toward Improving Math Teacher