ethanporcaro/eric-fulltext-meta huggingface dataset:
Opportunities to Conceptualize Linear Relationships in United States Mathematics Textbooks: Beyond Y=MX+B
Author: Arnold, Linda
Date: 2011-10-00
Type: Reports - Research
Subjects: Mathematics Instruction,Textbooks,Mathematics Curriculum,Textbook Content,Mathematical Concepts,Content Analysis,Secondary School Mathematics,Grade 8,Grade 9

This study examined opportunities provided for students to conceptualize linear relationships, as reflected in five United States mathematics textbooks. Texts represented a broad spectrum of types: commercial, so-called &quot;back to basics&quot;, and NSF funded. Analysis of allocation, topic choice, presentation, context, and cognitive level was completed. Analysis results revealed that students are being asked to grapple with linear relationships at increasingly younger ages, limits in the models they are asked to use, limits on discussion of concepts and connections, lack a real world context for most problems, and lower levels of cognitive expectation. The results indicate a significant gap between learning goals from intended curricula, and the potentially implemented curricula contained in many current U.S. textbooks. Conclusions suggest ways in which the present curriculum may be transformed. [For the complete proceedings, see ED585874.]
True or False? Pre-Service Secondary Mathematics Teachers&apos; Strategies for Evaluating Statements
Author: Ko, Yi-Yin
Date: 2011-10-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teachers,Secondary School Teachers,Mathematics Teachers,Pedagogical Content Knowledge,Algebra,Evaluation Methods,Geometry,Number Concepts,Accuracy,Validity,Mathematical Logic

To implement current reforms regarding proof and reasoning in secondary school mathematics successfully, pre-service secondary mathematics teachers must have adequate understandings of concepts across mathematical domains for their future teaching. This paper examined the strategies that pre-service secondary mathematics teachers had for evaluating statements in the domains of algebra, analysis, geometry, and number theory. The results suggest that most preservice teachers rely on examples and their (partially) correct understandings of mathematical facts when determining the statement's veracity. The results also suggest that the majority of pre-service teachers accurately evaluate the validity of statements. [For the complete proceedings, see ED585874.]
Growth in Secondary Teachers&apos; Content Knowledge and Practice in Discrete Mathematics
Author: Middleton, James A.
Date: 2011-10-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Teaching Methods,Faculty Development,Pedagogical Content Knowledge,Control Groups,Knowledge Base for Teaching,Mathematics Teachers,Mathematics Achievement,College School Cooperation,Partnerships in Education,Secondary School Teachers,High School Students

Thirty-five teachers teaching advanced topics in high school mathematics were engaged in a year-long intensive professional development project intended to increase their Mathematical Knowledge for Teaching in the area of discrete mathematics. Project activities embodied a models and modeling perspective on pedagogy and learning. Results showed that participating teachers' content knowledge improved significantly in discrete mathematics, their classroom practice improved significantly. Additionally, participating teachers' students outperformed their counterparts in a matched-control group in achievement. Results provide evidence of the effectiveness of mathematical modeling for developing teachers' mathematical knowledge for teaching, and on improving secondary mathematics teachers' practice. [For the complete proceedings, see ED585874.]
Using Conceptual Blending to Analyze Student Proving
Author: Zandieh, Michelle
Date: 2011-10-00
Type: Speeches/Meeting Papers
Subjects: College Students,Mathematical Logic,Validity,College Mathematics,Concept Formation,Logical Thinking,Geometry

We explore ways that university students handle proving statements that have the overall structure of a conditional implies a conditional, i.e., (p [right arrow] q) [implies] (r [right arrow] s). We structure our analysis using the theory of conceptual blending. We find conceptual blending useful for describing the creation of powerful new ideas necessary for proof construction as well as for describing the creation of blends that slow or hinder student efforts at proof construction. [For the complete proceedings, see ED585874.]
The Effects of Teachers&apos; Understanding of Addition and Subtraction Word Problems on Student Understanding
Author: Lunt, Jana
Date: 2011-10-00
Type: Speeches/Meeting Papers
Subjects: Teacher Influence,Pedagogical Content Knowledge,Addition,Subtraction,Word Problems (Mathematics),Elementary School Teachers,Mathematics Instruction,Elementary School Students,Outcomes of Education

This study investigates the influence of teacher understanding on student understanding through teacher practice. Three elementary school teachers participated in a university course that discussed mathematical and pedagogical knowledge regarding addition and subtraction word problems. The data from this study were analyzed qualitatively to describe the nature of the teachers' understandings, the ways teachers used their understandings in their practice, and the nature of their students' understandings. I hypothesize that teachers used their understanding to create and implement tasks at a high level of cognitive demand, maintaining that demand over time, which affected student understanding. [For the complete proceedings, see ED585874.]
Mathematical Knowledge for Teaching Proof: Evidence from and Implications for Professional Development
Author: Lesseig, Kristin
Date: 2011-10-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Mathematical Logic,Teaching Methods,Faculty Development,Pedagogical Content Knowledge,Guidelines,Standards,Educational Change,Educational Policy,Knowledge Base for Teaching

Research suggests that the enhanced role of proof in mathematics classrooms presented in current standards and reform policy poses great challenges for teachers and will require substantial teacher learning. However, to date there is little research detailing what mathematical knowledge might be useful for teaching proof or how professional development might afford such learning. This paper presents a framework for Mathematical Knowledge for Teaching Proof that couples research on justification and proof in mathematics and mathematics education with Ball and colleagues' (2008) conceptualization of Mathematical Knowledge for Teaching (MKT). An empirical study of teachers' proof-related activity in professional development demonstrates the utility of this framework and provides further insights into mathematical knowledge for teaching proof. [For the complete proceedings, see ED585874.]
An Analytic Frame for Examining Teachers&apos; Collaborative Mathematics Work to Develop Specialized Content Knowledge
Author: Campbell, Matthew P.
Date: 2011-10-00
Type: Speeches/Meeting Papers
Subjects: Teacher Collaboration,Mathematics Instruction,Faculty Development,Pedagogical Content Knowledge,Verbal Communication,Writing (Composition),Persuasive Discourse

A common practice in mathematics professional development to enhance teachers' content knowledge is to engage them in solving and discussing mathematics tasks. Yet, what is entailed in these experiences and how teacher discussions afford or constrain opportunities to develop teachers' knowledge of mathematics is not fully understood. In this paper, the authors provide a research-based framework to analyze teachers' mathematical productions (verbal reasoning and written inscriptions) used in collaborative mathematical work that illustrates the complexity of considering teachers' opportunities to learn and how discussion of mathematics may or may not be resources for learning. [For the complete proceedings, see ED585874.]
Reasoning-and-Proving in Geometry Textbooks: What Is Being Proved?
Author: Otten, Samuel
Date: 2011-10-00
Type: Speeches/Meeting Papers
Subjects: Geometry,Textbooks,Mathematical Logic,Validity,Mathematics Instruction,Reflection,High School Students,Secondary School Mathematics

As calls are made for reasoning-and-proving to permeate school mathematics, several textbook analyses have been conducted to identify reasoning-and-proving opportunities outside of high school geometry. This study looked within geometry, examining six geometry textbooks and characterizing not only the justifications given and the reasoning-and-proving activities expected of students but also the nature of the mathematical statements around which reasoning-and-proving takes place. The majority of reasoning-and-proving exercises focused on particular mathematical statements, whereas the majority of expository mathematical statements were general in nature. Although reasoning-and-proving opportunities were numerous, it remained rare for reasoning-and-proving to be made an explicit object of reflection. [For the complete proceedings, see ED585874.]
Instructor and Student Perceptions of Mathematics for Teachers Courses
Author: Hart, Lynn C.
Date: 2011-10-00
Type: Speeches/Meeting Papers
Subjects: Foreign Countries,Preservice Teachers,Student Attitudes,Elementary School Teachers,Teacher Education,Educational Attitudes,Mathematics Education,Education Majors,Case Studies,Knowledge Base for Teaching

This cross case analysis synthesizes results from two qualitative studies on mathematics content courses for prospective elementary teachers: one from the U.S. interviewed instructors, one from Canada interviewed students. Results were examined for common themes. Salient commonalities were found. Two will be discussed here: the role of affect in student learning and the role of connections to the elementary classroom. [For the complete proceedings, see ED585874.]
Preservice Elementary Teachers&apos; Uses of Mathematics Curriculum Materials: The Role of Disequilibrium and Human Resources
Author: Cross, Stephanie Behm
Date: 2011-10-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teachers,Elementary School Teachers,Preservice Teacher Education,Mathematics Instruction,Textbooks,Mathematics Curriculum,Student Teaching,Human Resources,Higher Education,Familiarity,Standards,Geometry,Educational Change,Student Attitudes,Role

Over the course of two years, data was collected focused on preservice elementary teachers' engagement with mathematics textbooks and curriculum materials in two contexts: (1) a university mathematics education course, and (2) student teaching. To frame the results and suggest opportunities for learning, Feiman-Nemser and Buchmann's (1985) critical analysis of experience in teacher education is utilized. These &quot;pitfalls&quot; of teacher education, or particular types of &quot;inappropriate learning&quot; are used as frames to help highlight important ideas from this research. Results indicate high levels of disequilibrium surrounding preservice teachers opportunities for learning, and also point to the importance of human resources during university coursework and fieldwork. Implications for teacher education are shared. [For the complete proceedings, see ED585874.]
Prospective Elementary Teachers&apos; Suspension of Sense-Making When Solving Problematic Word Problems
Author: Contreras, José N.
Date: 2011-10-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teachers,Elementary School Teachers,Word Problems (Mathematics),Problem Solving,Mathematical Models,Arithmetic,Elementary School Students,Mathematical Concepts,Mathematics Instruction

This study investigates the extent to which pre-service elementary teachers (PETs) use their realworld knowledge to solve problems for which the result of the arithmetic operation is problematic, if one takes into consideration the reality of the context. A paper-and-pencil test was administered to 566 PETs enrolled in mathematics content courses. The test included 8 experimental items and 4 buffer items. The findings for a sample of 68 PETs are not very encouraging. The total number of realistic responses varied from 5 to 58 (out of 68 possible for each problem). [For the complete proceedings, see ED585874.]
Learning Trajectories and Key Instructional Practices
Author: Sztajn, Paola
Date: 2011-10-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Instruction,Teaching Methods,Elementary School Teachers,Learning Processes,Mathematical Logic,Faculty Development,Elementary School Mathematics,Sequential Learning,Cognitive Processes

As learning trajectories gain traction in mathematics education, we seek to understand the ways in which teachers may use them in interactions with students. This paper reports on one group of elementary teachers' use of their emerging knowledge of a learning trajectory to examine key pedagogical practices. Findings suggest that a learning trajectory helps teacher place student thinking at the center of these practices. [For the complete proceedings, see ED585874.]
Studying Online Participation and Its Impact on the Development of Mathematical Content Knowledge for Teaching
Author: Silverman, Jason
Date: 2011-10-00
Type: Speeches/Meeting Papers
Subjects: Knowledge Base for Teaching,Mathematics Instruction,Faculty Development,Online Courses,Pedagogical Content Knowledge,Educational Technology,Technology Uses in Education,Interaction,Mathematical Logic,Computer Mediated Communication,Network Analysis,Social Networks,Algebra,Mathematical Concepts

We report on our efforts to support teachers' development of mathematical knowledge for teaching through online professional development. In particular, we report on our investigation into the relationship between online interaction and teachers' development of mathematics content for teaching. Through the integration of content analysis and social network analysis, we identify underlying relationships between aspects of online interaction and teacher learning. Results indicate that while interaction, broadly speaking, was not correlated with teacher learning, particular combinations of content and the centrality of an individual in the interaction were. Implications of these significant correlations for mathematics teacher education are discussed. [For the complete proceedings, see ED585874.]
Preservice Elementary Teachers&apos; Learning from Videocases: Results from the VPEM Project
Author: Castro Superfine, Alison
Date: 2011-10-00
Type: Speeches/Meeting Papers
Subjects: Mathematical Logic,Mathematics Instruction,Preservice Teacher Education,Video Technology,Case Studies,Elementary School Teachers,Knowledge Level,Beliefs,Curriculum,Program Effectiveness,Cognitive Processes,Elementary School Mathematics,Pedagogical Content Knowledge

While understanding children's mathematical thinking is an important part of what teachers need to know in order to be effective in the classroom, preservice coursework often fails to provide learning opportunities focused on this aspect of teaching. Using a videocase curriculum focused on children's mathematical thinking, the authors examined changes in preservice elementary teachers' knowledge of, beliefs about, and ability to analyze children's thinking. Results from a quasi-experimental study indicate that the videocase curriculum had little effect on participants' knowledge and ability to analyze children's thinking, yet a moderate effect on participants' beliefs about mathematics teaching and learning. [For the complete proceedings, see ED585874.]
Mathematical Knowledge for Teaching of Student Teachers and Its Enhancement through a Special Final Course
Author: Mochón, Simón
Date: 2011-10-00
Type: Speeches/Meeting Papers
Subjects: Foreign Countries,Student Teaching,Preservice Teacher Education,Knowledge Base for Teaching,Questionnaires,Secondary School Teachers,Mathematics Instruction,Mathematical Logic,Computation,Program Effectiveness,Knowledge Level

In this article we describe the results of a special final course, at the main teachers' college in Mexico, which had two related main objectives: one was to find out the Mathematical Knowledge for Teaching (MKT) held by student teachers (ST) at the end of their instructional preparation. The other was to discern ways to improve this knowledge and to document the changes observed. In teachers' colleges in Mexico, math contents and pedagogical ideas are taught separately, so we aimed to help student teachers to integrate these. The analysis showed that their knowledge is mainly instrumental but that through discussions and reflection about the main issues, they were able fairly quickly to attain a significant improvement in all the contents included. Moreover, they also showed changes on some of their views about math and its teaching. [For the complete proceedings, see ED585874.]
A Multiple-Case Study of Elementary Prospective Teachers&apos; Experiences in Distinct Mathematics Content Courses
Author: Swars, Susan L.
Date: 2011-10-00
Type: Speeches/Meeting Papers
Subjects: Elementary Education,Preservice Teachers,Student Experience,Elementary School Mathematics,Beliefs,Student Attitudes,Mathematics Instruction,Teacher Characteristics,Preservice Teacher Education,Learning

This multiple-case study explored the experiences of two groups of elementary prospective teachers (n=12) completing distinct mathematics content courses. Individual interviews revealed perspectives on knowing, learning, and teaching mathematics as experienced by the two groups; the quantitative findings indicated differences in mathematical beliefs. One group characterized mathematics as a record of knowledge, difficult to understand and lacking in relevance; learning occurred through rote memorization and via external expertise, with teaching typified as explaining. The other group portrayed mathematics as process-focused, internally constructed, and relevant; learning took place through a focus on children's thinking, with teaching characterized as guiding and questioning. [For the complete proceedings, see ED585874.]
Preservice Elementary Teachers Developing Understandings of Self as Mathematics Teacher and Teaching in Context
Author: DePiper, Jill Neumayer
Date: 2011-10-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teachers,Elementary School Teachers,Mathematics Teachers,Self Concept,Self Efficacy,Seminars,Teacher Competencies,Context Effect

As preservice elementary teachers (PSTs) examine their personal readiness, instructional practices, and their agency in enacting those practices, a ubiquitous question is &quot;What can I do?&quot; to support all students in learning mathematics amidst social, political and institutional dynamics present in today's classrooms. This paper explores how PSTs are developing understandings of self as mathematics teacher and of teaching through participation in a seminar designed to support critical examination of themselves as mathematics teachers, and if and how this self-examination is consequential for their understandings of teaching, particularly as within complex realities of schooling and attention to equity and access. [For the complete proceedings, see ED585874.]
Maintaining Cognitive Demands of Tasks through Small Group Discussions in Preservice Elementary Mathematics Classrooms
Author: Cheng, Diana
Date: 2011-10-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teachers,Preservice Teacher Education,Mathematics Instruction,Teaching Methods,Small Group Instruction,Group Discussion,Elementary School Teachers,Discussion (Teaching Technique),Mathematical Concepts,Cooperative Learning,Difficulty Level

Enacting tasks at high levels of cognitive demand helps preservice teachers make sense of mathematical ideas and serves as a model for instruction. Small group discussions can be useful pedagogical tools for maintaining a task's cognitive demands. In this article, we contrast two small group discussions within a preservice elementary classroom to illustrate characteristics of productive small group discussions. [For the complete proceedings, see ED585874.]
Designed and Emergent Pedagogical Supports for Coordinating Quantitative and Agent-Based Descriptions of Complex Dynamic Systems
Author: Wilkerson-Jerde, Michelle Hoda
Date: 2011-10-00
Type: Speeches/Meeting Papers
Subjects: Mathematical Logic,Measurement,Behavior,High School Students,Learning Activities,Probability,Population Trends,Educational Technology,Technology Uses in Education,Video Technology,Graphs

Often, quantitative and mathematical models are used to study complex dynamic systems--where collections of individual components interact to produce an emergent pattern of behavior. To interpret such models involves 'unpacking' the collective behaviors and interactions that underlie a given pattern. We investigate what representational supports in a technology-mediated agent-based modeling environment led secondary students to question and investigate the relationship between individual behaviors and collective patterns in a population dynamics unit. Our goals are to inform 1) our own design of educational tools and 2) the theoretical elaboration of general &quot;conceptual leverage points&quot; for mathematics and complex systems education. [For the complete proceedings, see ED585874.]
Statistical Preparation of Teachers: Preservice Elementary Teachers (PSTS) Conceptions of Distributions of Data - Thinking about Measure of Center and Variability
Author: Thanheiser, Eva
Date: 2011-10-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teachers,Elementary School Teachers,Knowledge Level,Statistical Distributions,Measurement,Knowledge Base for Teaching,Comparative Analysis,Statistics

Prior research investigating PSTs' statistical thinking is sparse, yet teacher educators need to know how best to prepare future teachers for their work and given the increasing importance of STEM education we need teachers who are capable of preparing students at an early age to think about data. In this paper we share the results from a study investigating pre-service teachers' (PSTs') initial thinking about distributions of data in four different contexts. In particular we investigated how PSTs reasoned about different distributions of data - including how they consider measures of center and measures of variability. Data was collected through surveys and interviews conducted prior to their beginning a statistical unit in their elementary teachers mathematics content course. [For the complete proceedings, see ED585874.]
Project CRAFTeD: An Adapted Lesson Study Partnering Preservice Mathematics Teachers with a Master Teacher
Author: Meagher, Michael
Date: 2011-10-00
Type: Speeches/Meeting Papers
Subjects: Partnerships in Education,Preservice Teachers,Mathematics Teachers,Master Teachers,Lesson Plans,Learner Engagement,Inservice Teacher Education,Classroom Techniques

Reports on a research project designed to implement an adapted Lesson Study cycle whereby preservice mathematics teachers co-create a lesson with a Master Teacher and observe the Master Teacher teach the lesson. Results show the preservice teachers' shift, when designing a lesson, from a 'teacher presenting the task' perspective to a 'student engaging in the task' perspective and the importance of seeing their own lesson taught. [For the complete proceedings, see ED585874.]