15 research outputs found
Connecting mathematical knowledge with engagement in mathematics teaching practices
No full textInternational audienceResearch suggests that mathematical knowledge is likely to influence how mathematics is taught. In turn, how mathematics is taught impacts students’ opportunities to learn mathematics. We report on a study examining the connection between preservice teachers’ mathematical knowledge and the nature of their eliciting and interpreting of student thinking. Our findings suggest that preservice teachers elicit and interpret student thinking with more emphasis on student understanding in situations in which they have strong mathematical knowledge of an algorithm used by the student compared to situations in which they have weaker mathematical knowledge about the algorithm used
Designing Simulations to Learn About Pre-service Teachers’ Capabilities with Eliciting and Interpreting Student Thinking
No full textConnecting mathematical knowledge with engagement in mathematics teaching practices
No full textInternational audienceResearch suggests that mathematical knowledge is likely to influence how mathematics is taught. In turn, how mathematics is taught impacts students’ opportunities to learn mathematics. We report on a study examining the connection between preservice teachers’ mathematical knowledge and the nature of their eliciting and interpreting of student thinking. Our findings suggest that preservice teachers elicit and interpret student thinking with more emphasis on student understanding in situations in which they have strong mathematical knowledge of an algorithm used by the student compared to situations in which they have weaker mathematical knowledge about the algorithm used
Deliberative professional development communities as sites for teacher learning.
No full textNew visions of the educated student are leading to new and greater demands upon teachers' knowledge, skill and perception. At the same time research that has examined opportunities for teacher learning has roundly criticized prevailing approaches to professional development and is just beginning to understand more contemporary approaches. The purpose of this study is to develop theoretical and practical insights into contemporary approaches to the professional development of teachers. The study begins with the development of a theoretical construct termed Deliberative Professional Development Communities (DPDC) crafted from learning theory and research on teacher learning in order to understand the content and processes at work in settings of teacher learning. Underpinned by this framework, the study utilizes tools from conversation analysis to examine the social dimensions of learning in a deliberative community of teachers known as the Teacher Reflection Group. Next, the tools of interactional ethnography are applied to understand the role of professional knowledge and the interplay of experience in multiple contexts in the development of an individual teacher within the Teacher Reflection Group. The findings of this study center on a three-part conception of professional knowledge---personal, local, and public knowledge of teaching---that is drawn upon in deliberative communities of teacher learning. The depth, balance and scrutiny that characterize uses of personal, local, and public sources of knowledge in teacher learning approaches are found to impact opportunities of both individual teachers and communities of teachers to develop as true members of a profession. Furthermore, contemporary approaches to professional learning can be characterized as facilitating teacher development by supporting the lamination of ideas garnered through participation in personal, local, and public contexts of learning.PhDEducationTeacher educationUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/123349/2/3079412.pd
Uncovering the Skills That Preservice Teachers Bring to Teacher Education: The Practice of Eliciting a Student’s Thinking
No full textAlthough teacher education is the formal means by which novices are prepared for teaching, they come having already had significant experience in schools. Preservice teachers have formed habits of “teaching” which influence their learning to teach. This article reports a study of the specific knowledge of and skills with teaching practice that novices bring to teacher education with respect to one teaching practice, eliciting student thinking in elementary mathematics, and describes the use of a standardized teaching simulation to learn about novices’ skills. The findings reveal details about preservice teachers’ skills and habits of practice at the point that they enter formal teacher preparation. Preservice teachers’ ways of carrying out this particular practice are categorized into three distinct categories: (a) skills that need to be learned, (b) skills that can be built on, and (c) approaches that need to be unlearned.</jats:p
Edgar Rice Burroughs creator of Tarzan
No full textA concise biography of the prolific author who created Tarzan & was a pioneer of the science fiction genre. Annotation. One of the most successful writers of the twentieth century, Edgar Rice Burroughs's novels of adventure and imagination include Tarzan and the Apes
Pre-Service Teachers' Understandings and Interpretations of the Common Core State Standards for Mathematical Practice
No full textFor at least the past 40 years, the mathematics education community has attempted to characterize important learning goals for students that are not captured completely in specifications of mathematical content objectives. Mathematical processes such as problem solving, reasoning and representation have been prominent in these attempts. The most recent characterization of these learning goals is the Common Core Standards for Mathematical Practice (SMPs). If these important learning goals for students are to be accomplished, it is imperative that teachers understand what is intended to be learned and how their instruction might be tuned to promoting these outcomes.
In this dissertation study, I investigated how pre-service teachers (PSTs) interpret and understand the SMPs. In particular, 17 PSTs, enrolled or recently graduated from an undergraduate or postgraduate elementary teacher education program, completed three tasks that were intended to be approximations of key phases of actual teaching practice: planning for instruction, enacting a lesson, and assessing students. Within each task the PSTs were asked to identify (a) instances during lesson planning where students would be likely to have the opportunity to use or learn to use specific SMPs, (b) instances in a video of a lesson where students engaged in using or learning to use specific SMPs, and (c) instances in assessment items where students had an opportunity to demonstrate their proficiency in using specific SMPs. The PSTs’ designations were compared to those of the authors of the curriculum materials. PSTs were also assessed on measures of their mathematical knowledge for teaching and mathematical beliefs.
Overall, PSTs and the curriculum authors had low levels of agreement in their assignment of SMPs. A close examination of PST responses suggests that they tended to use different criteria to decide when to assign some of the SMPs to mathematical tasks or lessons. For instance, PSTs tended to assign the SMP, “make sense of problems and persevere in solving them,” whenever an instructional element involved a mathematics problem. On the other hand, curriculum authors tended to assign this SMP less frequently and appeared to demand more evidence of both sense making and perseverance. There were also features of the materials that prompted PSTs to assign particular SMPs. For instance, PSTs tended to assign the SMP “construct arguments and critique the reasoning of others” whenever an assessment item asked for students to write or show their work regardless of what was actually being asked of the students. This finding suggests that the SMPs may be underspecified as learning goals that can be enacted by teachers and students at this time. The sample of PSTs in this study had high levels of mathematical knowledge for teaching and similar mathematical beliefs, and the lack of variance across the sample did not allow detection of the influence these factors might have had on PSTs’ interpretations of SMPs.
Results from this dissertation study help to inform the mathematics teacher educator community of patterns in PSTs’ understandings and interpretations of mathematical practices that could help to inform the way beginning teachers are prepared. More broadly, this study suggests that the mathematics education community needs to address the lack of clarity in the SMPs as they are outlined in the Common Core State Standards so that teachers, especially beginning teachers, can consistently implement the SMPs in the everyday work of teaching.PhDEducational StudiesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144042/1/jbpet_1.pd
Preservice Elementary Teachers’ Early Practice of Eliciting and Responding to Students’ Mathematical Thinking.
No full textLearning to teach involves making a shift from layperson to teaching professional over the course of formal preparation. This shift requires putting aside naïve perceptions of self and teaching in favor of an informed conception of the professional teacher focused on others’ –– that is, students’ –– thinking and understanding.
Although many practices are central to the work of teaching, the practice of eliciting and responding to student thinking is crucial for teachers to gain insight into their students’ ideas and ways of thinking. This dissertation investigated novice teachers’ practice of eliciting and responding to student thinking at the beginning of their formal teacher preparation. Based on analysis of 27 preservice teachers’ mathematics discussions during their first four weeks of preparation, the study analyzed the kinds of initial eliciting questions that the preservice teachers posed, and the kinds of responses they gave to students’ contributions. The analyses showed that although preservice teachers had some skill in eliciting student thinking they were inconsistent in the methods of eliciting they used across teaching episodes. When responding to students, preservice teachers in this study often used guiding prompts even after students provided correct answers.
Results from this study offer insights into specific aspects of eliciting and interpreting student thinking with which beginning teachers might need support in order to attend to student thinking. Some of the findings also signaled that there may be tendencies that preservice teachers need to unlearn as part of their preparation in order to become skilled at eliciting and responding to student thinking. The analysis of early eliciting and responding to student thinking practice can inform how teacher educators look at, talk about, and evaluate preservice teachers’ practice.PhDEducational StudiesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133455/1/shdiana_1.pd
Researching a Practice of Teaching Elementary Mathematics Aimed at Disrupting Inequity and Promoting Justice
No full textWhat is the work of an elementary teacher attempting to teach mathematics in ways that disrupt pervasive patterns of inequity and promote justice and success for children from historically marginalized groups? What problems or tensions arise at the beginning of the school year in pursuing these goals and seeking to build community in a heterogeneous classroom? This study examines one teacher’s work in starting the year as she sets out to disrupt normalized patterns of practice and teach in ways that advance justice. Using the tools of first-person research, this study focuses on how the teacher thinks about these aims and examines the tensions that arise for the teacher as she pursues them. Analysis was conducted through a close examination of the teacher’s daily journal, which was supplemented with examination of videos of all mathematics lessons and student work from the first trimester of the school year.
The findings suggest that the work for this teacher coalesced around centering children. What I name centering children refers to the teacher’s intentional moves to understand children’s multiple identities, children’s thinking, and children’s interactions, as she aimed to disrupt historical patterns of inequity, make instructional decisions, and position children from marginalized groups as capable learners and doers of mathematics. This study also takes up the tensions and dilemmas that accompanied this work for the teacher at the beginning of the school year in a diverse elementary classroom.
The findings of this study provide insight into the nuanced complexities of the decisions that one teacher made, as well as the tensions that the teacher faced when intentionally striving to disrupt systemic patterns of inequity to center children. The findings have implications for teachers, teacher educators, mathematics educators, and those who provide professional support for teachers. Through detailed examination of a single case, this study seeks to make explicit how some of the most pressing issues that occur at the beginning of the school year are thought about and approached by a capable, experienced, justice-focused teacher. The findings highlight implications surrounding the dilemmas that other justice-focused teachers are likely to face and suggest supports that are likely to help such teachers.PhDEducational StudiesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/167922/1/ekimmey_1.pd
Preparing Teachers to Formatively Assess
No full textTo engage in formative assessment, preservice teachers (PSTs) need to develop skill with the practice of interpretation. The initial preparation of teachers would benefit from having a sense of the interpretation skills brought by PSTs to teacher preparation. We articulate the nature of interpreting as a teaching practice including: articulating inferences, sampling evidence, developing and applying guiding criteria, and monitoring and redressing bias and distortion. We use a teaching simulation to identify the assets of PSTs' initial interpretive skills and areas in which PSTs might need to reconsider and change. An investigation with a group of PSTs from one teacher education program suggests that many PSTs bring skills with making evidence-based interpretations about a student's process for solving a mathematics problem. However, their skills are much more limited for making interpretations about a student's understanding and have potential for bias and distortion. Implications for teacher education are discussed
