<p> Throughout the history of teacher education, the final fieldwork experience has often been called the single most influential experience in teacher preparation programs (Burns, Jacobs, &amp; Yendol-Hoppey, 2016; Feiman-Nemser &amp; Buchmann, 1986; Parker-Katz &amp; Bay, 2008). Though this experience has been expanded to include fieldwork experiences throughout many teacher education programs (Guyton &amp; McIntyre, 1990), the final fieldwork experience remains the closing activity and the lasting image of teacher preparation (Feiman-Nemser &amp; Buchmann, 1986; Rosaen &amp; Florio-Ruane, 2008). Given its importance, though, researchers know relatively little about it. &ldquo;The knowledge thus produced is akin to the quantum theory of physics; we know what goes in . . . and what comes out . . . but not what occurs in the interim&rdquo; (Guyton &amp; McIntyre, 1990, p. 524). Given the current reforms in mathematics education and mathematics teacher education (National Council for the Accreditation of Teacher Education, 2010; National Governors Association Center for Best Practices &amp; Council of Chief State School Officers, 2010), Guyton and McIntyre&rsquo;s observation is still relevant today.</p><p> During the final fieldwork experience, university-based and school-based mathematics educators must work together on behalf of the novice to marry university-promoted theory (especially reform-oriented theory) with the practical classroom expectations of day-to-day teaching life. Though there is much research on how this kind of work should be done and the dilemmas that have arisen during fieldwork (e.g., Knight, 2009; Loughran, 2006; Nolan &amp; Hoover, 2004; Sergiovanni &amp; Starratt, 2006; Sullivan &amp; Glanz, 2013), we have little information about the experiences of the mathematics educators who collaborate during final fieldwork. Furthermore, we have very little information on how these educators navigate mathematics reforms to prepare teachers of mathematics. </p><p> This multi-case study was designed to investigate three novices, their school-based mentors, and their university-based mentor (me) who collaborated during a year-long final fieldwork experience at the close of a middle school mathematics teacher preparation program. To write single case reports that illuminated our collaborative experiences, I wrote the &ldquo;stories&rdquo; of each triad. To collect these stories, I used individual and group interviews, paired conversations, asynchronous text interviews, conference observations, collaborative fieldwork artifacts, my own practitioner-researcher journal, and three cycles of participant member checks. After verifying the veracity of the stories of each triad, I engaged in cross-case analysis to make assertions about the commonalities and unique circumstances that defined these fieldwork cases. This study adds to teacher preparation fieldwork literature by evoking a response from educators working in the field and providing them with examples of open dialogue that created more empathetic collaborative experiences. The study also provides evidence that the empathy generated by sharing stories can create more productive and effective learning experiences for the novices involved. In particular, open dialogue provided the collaborators in these cases with a platform for acknowledging pedagogical differences, negotiating fieldwork expectations, and setting and meeting novices&rsquo; professional goals. For future investigations of teacher preparation fieldwork collaboration, this study provides evidence that a practitioner approach to research affords the researcher exceptional access to the stories of novices and mentors and establishes empathetic bonds that can make the telling of those stories both illuminating and respectful of the voices they represent.</p>

<p> This design research study examined how professional development in the context of a research practice partnership developed Algebra 1 teachers&rsquo; collective understanding of the eight Standards for Mathematical Practice (SMPs), part of the Common Core State Standards. Over two years, 15 teachers participated in a task analysis routine that included the alignment of mathematical tasks to the SMPs. Group consensus of these task ratings were analyzed quantitatively using Randolph&rsquo;s kappa, along with a measure of individual contributions to consensus that was based on calculations of pairwise agreement. Task rating discussions, which targeted disagreement in the task ratings, were analyzed qualitatively using a grounded theory approach. The analyses revealed that consensus for SMP alignment decisions increased over time. Practice 4, <i> model with mathematics</i>, was the only practice for which there was a strong consensus that tasks were aligned to a practice. When alignment to SMPs was correlated with task ratings for cognitive demand, a positive correlation existed between demand and practices one through four, but no correlation existed between demand and practices five through eight. Examination of individual raters&rsquo; contributions to SMP alignments showed differences in the use of content knowledge, use of standards definitions, and attention to alignment criteria. Teachers who attended most to the alignment criteria scored highest in their individual contributions to consensus. These findings add to Brown&rsquo;s theories of <i>design capacity for enactment</i> and <i>pedagogical design capacity</i> (2002, 2009) by arguing that curriculum alignment to academic standards is a process of perceiving affordances in curricular materials, and that the process necessarily relies on consensus interpretations of standards and socially developed criteria for alignment. The implications of this study suggest that task analysis is useful, but not sufficient for developing teachers&rsquo; understanding of the SMPs, and that the quantitative methods employed in the analysis of this study could have utility as a formative measure in other professional development and research. </p><p>

This study explores the process of planning, implementing, and following-up teacher professional development programs (TPDPs) in Palestine focusing on the programs that are directed to mathematics teachers. It also describes teachers’, supervisors, principals’, and policy makers’ beliefs about mathematics and mathematics teaching and learning, and the beliefs that TPDPs have about mathematics teaching and learning. The study used qualitative methods, including interviews and document analysis, to collect data. The participants were chosen from two district areas in West Bank and included five policy makers, eight supervisors and training developers, four principals, and six teachers. In addition to interviews, training materials and policy documents related to teacher training and supervision were studied for the purpose of this study. The data obtained from these documents integrated and validated the data which were collected through the interviews. The findings of the study suggest the necessity to improve the methods used in teacher training in a way that activates the role of the trainee teachers and reflects the content of the training in the process of teacher training. In addition, there is a need to provide teachers with better follow-up methods through and after their participation in TPDPs. Most importantly, TPDPs should be based on a clear vision of their objectives that is based on understanding the problems in student learning and current teaching practices as well as the desired behaviors and actions that help to mitigate problems. The findings also indicated that most of the participants hold the instrumental view of mathematics where mathematics is viewed as a body of facts and procedures. Furthermore, their views about mathematics teaching and learning and the curriculum correspond with the instrumental view or with the content-focused approach in teaching mathematics. The researcher concluded that there should be more emphasis on TPDPs that are planned on the district and schools level or what is called job-embedded professional programs. In parallel, trainers’ competences should be upgraded so that they are more able to respond to teachers’ needs in their contexts. Improving the way in which TPDPs is planned and implemented will have a greater influence on teachers’ beliefs and practices.

<p> This study investigated the relationship between attention to student thinking during lesson planning and the level of cognitive demand at which tasks are implemented for six pre-service teachers enrolled in a teacher education program that focuses on attention to student thinking during planning and instruction. Lesson plans were examined for attention to student thinking using two coding schemes, and samples of student work were examined to assess the level of cognitive demand at which tasks (associated with the enacted lesson plans) were implemented during instruction. Other planning related data sources were qualitatively drawn upon to support the extent to which pre-service teachers focused on student thinking with regard to planning. </p><p> One of the lesson planning coding schemes provides numerical scores indicating different degrees of attention to six elements of student thinking. The level of cognitive demand of task implementation for each lesson was able to be coded as high or low. In particular, the quantitative analysis suggested a trend that as overall attention to student thinking during lesson planning increases the odds of high level task implementation become greater compared to the odds of low level task implementation. Given a small sample size the quantitative results need to be considered within their limitations.</p><p> Qualitative analysis examining attention to student thinking during planning and task implementation supports the quantitative trend. In particular, the qualitative analysis suggests three findings. The first finding is that the two pre-service teachers who demonstrated the most attention to student thinking with regard to planning were the only pre-service teachers who implemented all of their tasks at a high level of cognitive demand. The second finding is that when receiving specific planning based support for a lesson as part of a university assignment, all the pre-service teachers were able to implement the task at high level of cognitive demand. The third finding is that a large majority of lessons using tasks accompanied by detailed planning support sources were implemented at high levels of cognitive demand.</p>

<p> En la actualidad existen estudiantes que manifiestan tener actitudes negativas hacia la matem&aacute;tica e indican que el hecho de tener que tomar un curso de matem&aacute;tica les provoca ansiedad. El prop&oacute;sito de esta investigaci&oacute;n fue determinar cu&aacute;l es la actitud hacia la matem&aacute;tica de estudiantes universitarios que tomaron alg&uacute;n curso b&aacute;sico de matem&aacute;tica e identificar si muestran tener ansiedad hacia la clase de matem&aacute;tica. De la misma forma, se determin&oacute; como se relacionan esas actitudes y la ansiedad hacia la matem&aacute;tica con diferentes caracter&iacute;sticas demogr&aacute;ficas y acad&eacute;micas, incluso con el &eacute;xito acad&eacute;mico en estos cursos b&aacute;sicos. </p><p> En esta investigaci&oacute;n se determinaron las actitudes y la ansiedad hacia la matem&aacute;tica de 182 estudiantes de un recinto en particular de una instituci&oacute;n privada, localizada al sur de Puerto Rico los cuales tomaron un curso b&aacute;sico de matem&aacute;tica. Para ello se utilizaron dos cuestionarios, el de Actitud Hacia la Matem&aacute;tica de Elena Auzmendi y la traducci&oacute;n en espa&ntilde;ol de sMARS por Isabel N&uacute;&ntilde;ez y colaboradoras. Los estudiantes mostraron actitudes m&aacute;s positivas en los factores actitudinales ansiedad, agrado, utilidad y motivaci&oacute;n; en los niveles de ansiedad se reflejaron datos positivos en los factores examen y tarea. Al comparar las actitudes y la ansiedad con las caracter&iacute;sticas demogr&aacute;ficas y acad&eacute;micas se encontraron diferencias estad&iacute;sticamente significativas para el g&eacute;nero, la primera generaci&oacute;n, el promedio general, la nota final, el uso materiales y lecturas, el uso de la calculadora cient&iacute;fica y graficadora, el uso de manipulativos y el uso de libros electr&oacute;nicos. El mejor modelo de regresi&oacute;n log&iacute;stica para explicar el &eacute;xito acad&eacute;mico en el curso b&aacute;sico de matem&aacute;tica se determin&oacute; que el mismo estuvo compuesto por las variables demogr&aacute;ficas del g&eacute;nero; las variables acad&eacute;micas del promedio general, la modalidad del curso, uso de la calculadora cient&iacute;fica, adem&aacute;s de las variables de actitud y ansiedad. La variable con mayor cambio y m&aacute;s determinante para alcanzar el &eacute;xito acad&eacute;mico en el curso de matem&aacute;tica es el promedio general.</p>

This research study was motivated by a hypothesis, generated on the basis of formal and informal observations, personal and professional experiences, discussions with prospective teachers and a pilot study conducted by this author; that pre-service teachers have a high level of mathematics anxiety and negative attitudes about mathematics. The primary purpose of this research was to examine the relationship between mathematics anxiety and pre-service teachers. The secondary purposes of this study were to examine the relationship between anxiety and performance and to examine the relationship between math anxiety, test anxiety, and stereotype threat. A quantitative experimental research design was used to investigate the research questions. The population consisted of prospective teachers at colleges and universities in Louisiana. The sets of data are mathematics anxiety of prospective teachers, a test anxiety inventory and a mathematics performance task. A personal data questionnaire was used to gather demographic information and attitudinal information about the participants. The implications of this study for elementary teacher education programs point to increased attention on the mathematics anxiety of pre-service teachers. This process is two-fold. One, it is recommended that pre-service teachers be made aware of their mathematics anxiety level and their attitudes about mathematics and two, it is recommended that teacher education programs acknowledge and address the importance of these affective variables and their role in pedagogy.

This study was purposed to understand the experiences of a group of undergraduate teaching assistants (UTA) working in a college remedial mathematics program which emphasized constructivist problem solving. Data were collected from four sources: in-depth and post interviews with the UTAs, interviews with the co-working instructors, interviews with two students from each of the UTA's class, and classroom observations. Results were presented in two ways: (a) UTAs' stories were told in individual profiles, detailing their experiences learning math from early school years and their teaching math in the current context; and (b) from the perspective of their four tasks (asking constructivist questions, classroom circulation, homework grading, and working in the Study Center), describing their successes and difficulties. Three important results were surmised from the data. First, UTAs' past experiences with math had a large effect on how they perceived their own math abilities and the way they thought that math should be taught. Second, the use of constructivist approach to teaching and learning was effective in changing UTAs' perceptions of what math was and how it could be learned; however, it also added pressure to these UTAs in their work with their students. Third, because of the contructivist emphasis, UTAs experienced early on impact and task concerns as well as personal concerns. Suggestions for preparing training program's for similar populations were advanced.

<p> This study investigated secondary mathematics pre-service teachers&rsquo; (PSTs) knowledge of resources in terms of digital technologies, and explored the processes of both selection and integration of technology into their lesson plans. This study employed a case study design. Participants were six secondary mathematics PSTs who enrolled in a methods course. Data sources included technology portfolios submitted as a requirement in the methods course and semi-structured interviews. The types of digital technologies were classified either conveyance technologies which are used to convey information or cognitive technologies which enable users to perform mathematical actions and receive immediate feedback (Dick &amp; Hollebrand, 2011). Each task in these lesson plans was evaluated by using the Task Analysis Guide (Stein, Smith, Henningsen, &amp; Silver, 2009). Finally, the intended way of technology use was identified whether as amplifier which enables students to accomplish a task more efficiently and accurately or as recognizer which transforms students&rsquo; actions and enables them to reorganize their thinking (Pea, 1985). </p><p> The findings indicated that the PSTs&rsquo; technology knowledge was limited in terms of the content. It was clear that these PSTs&rsquo; technology knowledge, the capability of technology, ease of use, availability of technology in the context, students&rsquo; familiarity with technology, and appropriateness of technology to meet the learning objectives were the most important factors influencing their technology selection and integration. Furthermore, the findings exhibited that the PSTs preferred to build their lesson around with a high cognitive level tasks which were either doing mathematics or procedures with connections and their intended way of technology use in these tasks was identified as either an amplifier or a reorganizer. In general, the findings also revealed that when the level of cognitive demand of the selected task was doing mathematics, the intended way of the technology use in these tasks were as reorganizer. </p><p>

This study focused on preservice teachers at early childhood and elementary levels to identify prior beliefs they bring to their mathematics methods classes, how these beliefs affect their understandings about mathematics teaching and learning, and how these beliefs are reconstructed while engaged in a contructivist designed mathematics methods course. Data collected included in-depth student journal entries, personal histories of preservice teachers' prior mathematics experiences, and small group interviews. An interpretive analysis of the data identified emergent themes related to preservice teachers' beliefs about themselves as learners and teachers of mathematics and how these beliefs were reconstructed during the course. Five major themes were identified: preservice teachers prior beliefs and experiences; increased understandings about themselves as learners of mathematics; new learning about mathematical pedagogy; new or different ways of learning mathematics; and anger about their previous mathematics experiences.

This longitudinal study explored the extent to which mathematics education lecturers' constructivist beliefs and aligned practices were communicated to students in a New Zealand primary pre-service teacher education degree programme. An integral part of this exploration was the identification of particular aspects of lecturers' practice that had a significant impact in enhancing the adoption of constructivist ideas on learning and constructivist-aligned teaching practices by student teachers. This goal had a practical focus on more effective course teaching within the chosen philosophical framework of constructivism. At a more theoretical level, there was a focus on the development of a constructivist approach to teacher education for teacher educators through the medium of mathematics education. A potential outcome of the development and widespread adoption of such a constructivist-aligned pedagogy within teacher education could be the significant furthering of a "reform" (or transformative) agenda in school education with its potential for enhanced learning by children. The methodology comprised both quantitative (survey) and qualitative (interview) techniques to collect information which allowed the capture of different but complementary data, so building a "rich" data set. The surveys were conducted using two leaming environment instruments underpinned by particular constructivist perspectives: one focusing on the overall nature of the learning environment at an individual level from a critical constructivist perspective, and the other focusing on the nature of interactions between teacher and student teachers at a classroom level from a socio-cultural constructivist perspective. / Surveys were conducted with the lecturers at the beginning and toward the end of the study, while the student teachers in these lecturers' classes were surveyed over a three year period. The interviews were semi-structured following an interpretative (evolving) research approach, with the "results" of ongoing data analysis being fed into later interviews. The interview data were analysed for personal perceptions and understandings rather than for generalisation and prediction with the intention of focusing on the identification of emergent themes. Interviews were conducted with lecturers at the beginning of the study and again toward its conclusion while student teachers were interviewed at the end of the study. The lecturers claimed constructivism as their underlying philosophical belief system and the initial surveys established baseline data on the actual nature of the lecturers' beliefs and how these were perceived by the student teachers. Similarly, the initial interviews explored the espoused beliefs and congruent practices of lecturers and student teachers. These two sets of data were compared to establish their congruence or otherwise. Further interviews with the lecturers focused on the survey data and my reconstruction of what the lecturers had said previously when interviewed. Later survey and interview data were also examined against the baseline data for evidence of change over the four years of the study. The data demonstrated that the student teachers perceived the existence of moderate to strong socio-cultural constructivist-aligned classroom environments when considered at a class (group) level, and a moderate alignment with critical perspectives at the individual (personal) level. / There was a high degree of consistency between staff and student teacher views, and the student teachers' views were consistent across the year groups (first, second and third years) and throughout the four years of the study. Lecturer practice(s) congruent with constructivism were the basis for student teacher change toward understanding and their adoption of constructivist ideas and aligned practices. Specific lecturer practices were identified as particularly effective in achieving such change. These effective lecturer practices may assist in establishing the foundations of a constructivist-aligned pedagogy for teacher education. The lecturers' modeling of the practices they were promoting for student teachers' practice was identified as a key element in promoting change. Indeed, the tension between traditional and transfornative approaches was exacerbated in situations where lecturers' promotion of a preferred practice was different from that which they enacted. The continuing existence of such situations and associated tensions has the potential to limit the extent of any change.