Including Curriculum Focus in Mathematics Professional Developmentfor Middle-School Mathematics Teachers
Nimisha PatelWright State University
Suzanne FrancoWright State University
Yoko MiuraWright State University
Brian BoydDayton Regional STEM SchoolWright State University
This paper examines professional development workshops focused on Connected Math, a particular curriculumutilized or being considered by the middle-school mathematics teachers involved in the study. The hope was that asteachers better understood the curriculum used in their classrooms, i.e., Connected Math, they would simultaneouslydeepen their own understanding of the corresponding mathematics content. By focusing on the curriculum materialsand the student thought process, teachers would be better able to recognize and examine common student misunder-standings of mathematical content and develop pedagogically sound practices, thus improving their own pedagogicalcontent knowledge. Pre- and post-mathematics content knowledge assessments indicated that engaging middle-schoolteachers in the curriculum materials using pedagogy that can be used with their middle-school students not onlysolidified teachers familiarity with such strategies, but also contributed to their understanding of the mathematicscontent.
No Child Left Behind (NCLB) mandates regarding thenecessity of highly qualified teachers for all students haveincreased the professional development opportunitiesavailable to K-12 teachers (Desimone, Smith, & Ueno,2006). While it is logical that professional development ofteachers contributes to higher student gains, it is difficultto quantify its effect size. Research indicates that the mosteffective models require teachers to spend a minimum of49 hours engaged in professional development annually(Yoon, Duncan, Lee, Scarloss, & Shapley, 2007). The mostfrequently offered opportunities often focus on math andreading; this is not surprising given that NCLB focuses onstudent achievement in these two areas.The Mathematics and Science Partnerships (MSP)
program funded by the Ohio Department of Education is aspecific initiative focused on teacher professional devel-opment. The goal of the MSP is to increase academicachievement of elementary and secondary students inmathematics and science by improving instructionalquality (Mathematics and Science Partnership Programs,n.d.). A collaborative unit funded by the MSP is a specialcenter at a large Midwestern urban university. This col-laborative unit represents seven universities and educa-tional resource centers in the local area. Through thiscollaborative unit, a professional development program isoffered to regional math and science K-12 teachers; itinvolves weeklong sessions during the summer monthswith follow-up meetings occurring throughout the subse-quent school year. To date, most pre- and posttests of
participants mathematics and science content knowledgehave shown gains (Cole, Ryan, & Tomlin, 2005). More-over, pre- and post-attitudinal surveys indicate significantgains in teachers perceptions of their own mathematicaland science content knowledge, pedagogical prepared-ness, and attitudes about teaching mathematics andscience.While positive correlations between students math-
ematics achievement and the mathematical knowledge/training levels of mathematics teachers have beenevidenced (Yoon et al., 2007), the latter tend to reflectmeasures of teachers general computational abilities.Hill, Rowan, and Balls (2005) research, however, exam-ined the relationship between teachers mathematicalknowledge utilized in their pedagogy and students math-ematics achievement, rather than the teachers generalcomputational abilities. Thus, teachers pedagogicalcontent knowledge (PCK), as well as their contentknowledge, has been explored in relation to studentachievement. Mathematical PCK includes content knowl-edge that is specific for teaching, including an under-standing of students common misconceptions of specificmathematics content. The results from Hill et al. indi-cated that student achievement was greater when math-ematics teachers have both content knowledge and PCK.In other words, there is a difference between strict math-ematical content knowledge and ones PCK with respectto mathematics; having both positively impacts studentachievement.
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With this in mind, three weeklong workshops focusedon the mathematics curriculum teachers would use in theirclassrooms. The hope was that as teachers better under-stood the curriculum used in their classrooms, they wouldsimultaneously deepen their own understanding of themathematics content being taught using those curriculummaterials. By focusing their learning on the materials andthe student thought process, teachers would be better ableto recognize and examine common student misunder-standings of mathematical content and develop pedagogi-cally sound practices, thus improving their PCK.
Literature ReviewEffective Professional DevelopmentProfessional development opportunities for K-12 teach-
ers typically reflect a patchwork of opportunitiesformal and informal, mandatory and voluntary,serendipitous and planned (Wilson & Berne, 1999, p.174), often because there has been a lack of generallyadopted infrastructure for professional development. TheNational Partnership for Excellence and Accountability inTeaching published guidelines for effective teacher profes-sional development (ERIC Development Team, 1999) thatincluded the importance of extending professional devel-opment beyond the one-day workshop, promoted opportu-nities for teachers to learn as they are expected to teach,focused on reflection and collaboration, and recommendedmore content-focused teacher learning (Ball & Cohen,1999; Hawley &Valli, 1999; Krajcik, Blumenfeld, Marx,& Soloway, 1994).No Child Left Behind Act of 2001 has also attempted to
provide guidelines for professional development, estab-lishing five criteria that reflect those that are high inquality:1. It is sustained, intensive, and content-focusedhas a
positive and lasting impact on classroom instruction andteacher performance.2. It is aligned with and directly related to state aca-
demic content standards, student achievement standards,and assessments.3. It improves and increases teachers knowledge of the
subjects they teach.4. It advances teachers understanding of effective
instructional strategies founded on scientifically basedresearch.5. It is regularly evaluated for effects on teacher effec-
tiveness and student achievement.In a study about the effectiveness of professional devel-
opment for teachers, Yoon et al. (2007) streamlined thesefive criteria into three components:
1. It should be focused, coherent, well defined, andstrongly implemented (Garet, Porter, Desimone, Birman,& Yoon, 2001; Guskey & Sparks, 2004; Loucks-Horsley,Hewson, Love, & Stiles, 1998; Supovitz, 2001; Wilson &Berne, 1999) (p. 4).2. It should be based on a carefully constructed and
empirically validated theory of teacher learning andchange (Ball & Cohen, 1999; Richardson & Placier, 2001;Sprinthall, Reiman, & Thies-Sprinthall, 1996) (p. 4).3. It should promote and extend effective curricula and
instructional modelsor materials based on a well-defined and valid theory of action (Cohen, Raudenbush, &Ball, 2002; Hiebert & Grouws, 2007; Rossi, Lipsey, &Freeman, 2004) (p. 4).Yoon et al. (2007) posited that:
Professional development affects student achievementthrough three steps. First, professional developmentenhances teacher knowledge and skills. Second, betterknowledge and skills improve classroom teaching.Third, improved teaching raises student achievement.If one link is weak or missing, better student learningcannot be expected. If a teacher fails to apply newideas from professional development to classroominstruction, for example, students will not benefit fromthe teachers professional development. (p. 4)
Mathematics Curriculum UnderstandingIt is a natural conclusion from the studies on effective
professional development, then, that effective professionaldevelopment for mathematics teachers should includetime on mathematics content knowledge as well as onmathematics curriculum. Fuerborn, Chinn, and Morlan(2009) demonstrated that professional development usingcurriculum increased the middle-school mathematicsteachers understanding of the content. For example, adeeper knowledge of number sense or geometry may beenhanced by developing more familiarity with the curricu-lum materials that will be used in the delivery of thisparticular content. The way teachers read, interpret, anduse materials is shaped by their content knowledge of andviews about mathematics (Remillard & Bryans, 2004).Curriculum materials are a strong determinant of whattakes place in the classroom; content knowledge and cur-riculum familiarity are intertwined in the development ofeffective lessons, and consequently student achievement.The connection between content knowledge and curricu-lum makes it essential to provide mathematics profes-sional development when new curriculum materials areintroduced.
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Regarding preservice teachers, Frykholm (2005)described a study about curriculum study and teacherpreparation over a four-year period. Qualitative data con-sisting of interviews, discussions, classroom observations,and student work were triangulated to support the findingthat curriculum is an effective resource for preserviceteacher training. More specifically, the use of the curricu-lum not only contributed to shifts in understanding howstudents learn, but the curriculum-based training also con-tributed to preservice teachers content knowledge andPCK.The following study investigated the influences related
to a curriculum-based professional development workshopfor licensed teachers.
Research QuestionsThis study focused on three key questions:1. Does participation in professional development
focused on Connected Math significantly influence teach-ers mathematical content knowledge?2. Does participation in professional development
focused on Connected Math significantly influence teach-ers perceptions of their own pedagogical preparedness?3. Does participation in professional development
focused on Connected Math significantly influence teach-ers attitudes toward teaching mathematics?Given prior research, it was expected that participation
in the weeklong curriculum-focused workshop wouldpositively influence teachers mathematical contentknowledge, their perceptions of their mathematical peda-gogical preparedness, and their attitude toward teachingmathematics.
MethodologyThis study focused on the summer 2008 professional
development opportunities centered on middle-schoolmathematics teachers use of the Connected MathematicsProject (CMP) materials. The CMP is a grade 6 through 8curriculum that was developed at Michigan State Univer-sity (Connected Mathematics Project, 2006) throughfunding from the National Science Foundation (NSF). It isone of five middle-school NSF-funded programs origi-nally developed in the mid-1990s. The summer 2008workshops utilized the most recent revision of these mate-rials, the CMP2.The CMP2 materials are student- and inquiry-centered
materials.A context or problem is posed at the start of eachlesson,with some time for students to investigate, usually ingroups. This is followed by summary time led by studentsand the teacher to highlight explicitly the mathematics
concepts learned. For example, when learning about mul-tiplying fractions, students using the CMP2 materials con-sider the context of sharing a tray of brownies. Throughin-class activities and discussion, students learn about analgorithm formultiplying fractions that makes sense withinthe context of sharing brownies. This instructional practiceis a divergence from more traditional approaches that typi-cally focus on teaching a skill, and then requiring studentsto apply that skill. As such, this technique is new for manyexperienced in-service teachers. Moving from a traditionaltext to the inquiry-based CMP2 materials is not a naturalprogression for most middle-school mathematics teachers.The intent of each of the workshops was to help teachersunderstand the mathematics content in-depth enough tofeel comfortable using a student-centered and inquiry-based method of teaching. The format of the workshopsprovided teachers insight into how the CMP2 materials arestructured and what mathematics content is developedthrough each lesson. By focusing on the mathematicscontent in these middle-school curriculum materials andthe order of lesson presentations, we believed that teacherswould learn more mathematics content themselves whileincreasing their positive attitudes about teaching math-ematics and strengthening their pedagogical preparedness.The rationale for offering a professional development
workshop focused on the CMP2 was twofold. First, manydistricts in the area had adopted the CMP2 materials, butteachers had not received sufficient support to implementadequately such materials into their own classrooms.Second, for districts that had not adopted the CMP2 mate-rials, there was a need to familiarize teachers with thematerials as they considered adopting the CMP2 materialsfor their district.ParticipantsParticipants represented two major groups: One group
of teachers was from districts that had adopted the CMP2materials, but the teachers had not received sufficientsupport to implement the materials into their own class-rooms; the second group of teachers was from districtsthat were considering adopting the CMP2 materials.Fifty-seven licensed teachers of sixth-, seventh-, andeighth-grade mathematics in a Midwestern state chose toenroll in one of the three weeklong workshops. The par-ticipants represented 18 school districts, which variedacross student population, socioeconomic status, andgeographic location. Three separate workshops wereoffered: one for sixth-grade teachers, one for seventh-grade teachers, and one for eighth-grade teachers. Threeparticipants did not complete their respective workshop.For final analyses, there were 26 teachers of sixth grade,
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16 of seventh grade, and 12 of eighth grade. Descriptivedata of the participants are presented in Table 1.MeasuresTwo instruments were used to measure participants
mathematical content knowledge and attitudes: the Diag-nostic Mathematics Assessments for Middle SchoolTeachers (DTAMS) (2008) and the Mathematics GradeK-8 Local Systemic Change Through Teacher Enhance-ment: 2006 Teacher Questionnaire (2008).DTAMS. The DTAMS (2008), which includes a pretest
and posttest, were developed at the University of Louis-ville to measure specifically the mathematics contentknowledge of middle-school mathematics teachers. Thecontent tests for teachers of grades 6, 7, and 8 focused onnumber and computation, geometry and measure, andalgebraic ideas, respectively. The level of difficulty, as wellas th...