Date

Presentation

Mathematics and Science Teachers and Teaching in Highly Effective Urban Elementary Schools

Room 2121 Benjamin Building
11:00 - 12:00 with discussion and free lunch to follow

By

Walter Secada, Ph.D.
University of Miami

Investigating The Gap Between Naturally Continuous Space and Discretized Space

Room 2121 Benjamin Building
11:00 - 12:00 with discussion and free lunch to follow

By

Whitney Johnson, Ph.D .
Michigan State University

This talk will bring together work involving secondary mathematics preservice teachers and my understandings of the text ‘Where Does Mathematics Come From’ by George Lakoff and Rafael Nunez.  The preservice teachers analyzed a section from Aristotle’s Metaphysics.  In his text Aristotle advances an argument for the theory that a line is not composed of points—a belief that is now considered mathematically incorrect.  This discussion will assist the audience in differentiating between Aristotle’s conception of space and the modern day conception of space in mathematics as described Lakoff and Nunez.

The details to be discussed will be portions of an audiotaped class of the preservice teachers as they discuss the Aristotle reading.  The presentation will consist of some background information, presentation of the framework from Lakoff and Nunez and the presentation of some data.

What Could It Mean to Make and Probe a Hypothesis in reserach on Instruction? the Place of Proof in Geometry as a Case in Point.

Room 2121 Benjamin Building
11:00 - 12:00 with discussion and free lunch to follow

By

Patricio Herbst , Ph.D .
University of Michigan

What is in a task? Understanding the Complexity of Mathematical Activities

Room 2212 Benjamin Building
12:00 - 1:00 with discussion and free lunch to follow

By

Vilma Mesa , Ph.D .
University of Michigan

Investigating Students' Opportunities to Develop Proficiency in Reasoning and Proving: A Curricular Perspective

Room 2121 Benjamin Building
11:00 - 12:00 with discussion and free lunch to follow

By

Gabriel Stylianides, Ph.D .
University of Michigan

There is widespread agreement that reasoning and proving should be a central feature of all students’ mathematical experiences. Yet, research shows that students often have serious difficulties acquiring competency in this domain. To make matters worse, research also shows that mathematics teachers themselves often face difficulties in reasoning and proving. How can we gain leverage for helping students to develop proficiency in reasoning and proving? In this talk, I argue that students are unlikely to develop proficiency in reasoning and proving on a large scale unless attention to this mathematical practice is woven into curriculum materials; research suggests that teachers’ decisions about what to implement in their classrooms, and how to implement it, are mediated through the curriculum materials they use. Despite the central role that curriculum can play in the development of students’ reasoning capabilities, little research has focused on the place of reasoning and proving in curriculum materials and on the development of methodological techniques to investigate this issue. In this talk, I present a methodological approach I developed to examine the curricular opportunities designed for students to acquire competency in reasoning and proving. I also summarize findings I obtained from applying this approach to analyze a popular, NSF-funded, middle school mathematics curriculum.

Semantic and Syntactic Proof Productions

Room 2121 Benjamin Building
11:00 - 12:00 with discussion and free lunch to follow

By

Keith Weber , Ph.D.
Rutgers University

The purpose of this presentation is to distinguish between two qualitatively different ways in which individuals construct formal proofs. Proving can be understood as a purely formal enterprise in which one begins with assumptions and definitions and draws inferences by manipulating symbolic formulae in a logically permissible way until one deduces the statement to be proven. I define a proof that is produced in this way to be a syntactic proof production. Alternatively, mathematical assertions can be understood as meaningful statements about mathematical concepts and objects. Considering representations of these concepts and objects can be instrumental in deciding what might be true and what formal derivations should be made in a proof. I say a semantic proof production occurs when the prover makes use of intuitive representations of relevant mathematical concepts to suggest and guide the formal inferences that he or she draws. In this presentation, I will report the results of a study that I conducted with students and mathematicians in abstract algebra. In this study, I presented eight undergraduates and eight mathematicians with pairs of groups and asked them to prove or disprove that each pair of groups was isomorphic. The results of this study will illustrate syntactic and semantic proof productions in the context of abstract algebra, highlight which type of proof productions are used by undergraduates and which are used by mathematicians, and discuss theoretical limitations to relying solely on syntactic proof productions.

The Impact of Using Representations on Student Achievement:
Fractions, Decimals and Percents

Room 2121 Benjamin Building
11:00 - 12:00 with discussion and free lunch to follow

By

Ye Sun , Ph.D.
Texas A & M University

The This study examined teachers' use of representations in classroom instruction as well as students' written representations by a mixed method, data were collected from 14 middle school teachers in over one year period. Descriptive statistics as well as structural equation modeling were used to analyze the nature and quality of teachers' classroom instructions, students' written representations and the relatioship between the students' written representations and their achievement.

The Success of Students with Learning Disabilities in University-Required Mathematics Courses

Room 2121 Benjamin Building
11:00 - 12:00 with discussion and free lunch to follow

By

Brooke Evans, Ph.D.
Morgan State University

The number of students with learning disabilities attending institutions of higher education has dramatically increased in the last ten years and will continue to do so. Since federal laws in the United States and many other countries require appropriate accommodations for students with learning disabilities, it is important for universities to evaluate the effectiveness of their services. This talk will highlight effectiveness of a class reserved for students with learning disabilities and identify predictors of student success. Success of students enrolled in a section of finite mathematics reserved for students with learning disabilities will be compared to the success of students with learning disabilities who fulfilled their mathematics requirement in other sections. Student documentation, such as high school GPA, SAT scores, and intelligence test scores, will also be discussed as predictors of student success. These predictors serve to help academic advisors place students with learning disabilities in the courses, based on their individual profile, which will allow them more chances for success in their university-required mathematics courses.

Teaching To Perform the Roles of a Teacher

 

Room 2121 Benjamin Building
11:00 - 12:00 with discussion and free lunch to follow

By

Patricio Herbst , Ph.D.
University of Michigan

In this talk I will describe a course on teaching methods for secondary mathematics teachers designed to flesh out the notion that initial teacher education needs to develop proficiency in key activities of teaching that all teachers need to perform. I argue that such approach to teacher preparation capitalizes on the assets that prospective students bring with them and permits to set appropriate, developmental goals for beginning teachers. I describe the curriculum of such methods course as well as some features of the pedagogical approach used with prospective teachers. In particular I show sample performance rubrics, which are used to teach each of the teaching activities and later used by students to critique their own teaching as well as that of their peers. Excerpts from students’ comments in interviews and in their writing for the course demonstrate that these rubrics allow students to examine their own teaching, organize how to reflect on their teaching, and set precise and reachable goals for improvement.

The Instrumediation of Mathematical Activity and Capability

 

Room 2121 Benjamin Building
11:00 - 12:00 with discussion and free lunch to follow

By

Kenneth Ruthven, Ph.D.
University of Cambridge

This talk will examine how the tools used by teachers and students shape the strategies to which mathematical tasks are amenable and the ideas brought into play, and thus the techniques employable by students and the ideas open to development. Illustrations will be provided relating to the educational use of calculators at different educational stages. The first part of the talk will draw on some of my earlier research into the use of arithmetic calculators in the primary school and the idea of a calculator-aware number curriculum. The second part of the talk will draw on recent collaboration involving researchers whose development work on using symbolic calculators in upper secondary schools has been shaped by the ideas and methods of Rabardel’s instrumental approach and French mathematical didactics.

Investigating Transitions For Learning and Teaching with Technology: The Case of Algebra

Room 2212 Benjamin Building
11:00 - 12:00 with discussion and free lunch to follow

By

Michal Yerushalmy, Ph.D.
University of Haifa, Israel

In planning a long term learning or curricular sequences there is an aim to plan a sequence which is as smooth as possible and that helps the teacher to unpack the mathematical ideas in a way that allows students to smoothly construct knowledge. Is it at all a possible mission? Does the nature of growth of mathematical knowledge fit such smooth incremental design?  Does technology offer new ways to design such sequences? Technology, when appropriately designed and used, can help to design learning environments that may change to various degrees the assumption about previous knowledge and the order new concepts are introduced. Research of long term learning and its effects helped teachers by informing and analyzing the expected transitions. How relevant are finding of this research when new reform curricula supported by technology is now designed? Are there stable discontinuities that would require transitions independently from the specific instructional design? How could research contribute to this issue of stability or instability of cognitive discontinuities and epistemological obstacles? My research agenda concentrate on trying to learn where new obstacles appear or old remain and why. To demonstrate it I will describe our experience of developing and implementing long term curricular sequences with the use of technology for algebra. While there are quite a few function's based algebra curricula with technology there is lack of research of long term learning of algebra with technology that inform about discontinuities that would require conceptual transitions in the teaching and in the designed activities.

A Theoretical Framework for Understanding Teachers' Personal and Pedagogical Understanding of Probability and Statistical Inference

Room 2121 Benjamin Building
11:00 - 12:00 with discussion and free lunch to follow

By

Yan Liu, Ph.D.
Vanderbilt University

Probability and statistical inference are among the most important and challenging ideas that we expect students to understand in high school. Research has consistently documented poor understanding or misconceptions of these ideas among different populations across different settings. Contrary to the overwhelming evidence of individuals' diffculties in learning probability and statistical inference, there is a lack of insight into the mechanisms by which transmission of this knowledge in classroom happens. Particularly, research on statistics education has not attended to teachers' understanding of probability and statistics (Garfield & Ben-Zvi, 2003). The purpose of this study is to develop an insight into teachers' understandings of probability and statistical inference and to understand the ways in which teachers' understandings of these subjects support and constrain possible ways in which they might shape instruction. To this end, we undertook a teaching experiment with eight high school mathematics teachers. Using a combination of design experiment and constructivist teaching experiment methodologies, and the results of four prior teaching experiments with high school students on the same subjects as the starting point, we conducted this teaching experiment over the course of two weeks (Liu & Thompson, 2004). The teaching experiment was designed with the purpose of provoking the teachers to express and to reflect upon their instructional goals, objectives, and practices in teaching probability and statistics. Analysis of the data indicated that teachers had a complicated, inconsistent mix of meanings with regard to the ideas of probability, sampling distribution, hypothesis testing, and margin of error. My talk will demonstrate both teachers' understandings of these ideas, as well as the theoretical framework that emerges from the analysis.

Mathematics Knowledge for Teaching
(and Teaching Teachers)

Room 2121 Benjamin Building
11:00 - 12:00 with discussion and free lunch to follow

By

Lew Romagnano, Ph.D.
Metropolitan State College, Denver, Colorado

What mathematics must teachers know, and how must they know it, to teach so their students develop "mathematical proficiency?" In this seminar, we will review some research results, and some of the challenges of addressing these questions empirically. We will discuss elements of a framework for answering these crucial questions with particular attention to middle- and high-school teachers.

Seeing, Believing, Proving in Mathematics

Room 2121 Benjamin Building
11:00 - 12:00 with discussion and free lunch to follow

By

Doris Schattschneider, Ph.D.
Professor Emerita of Mathematics, Moravian College

The proverb "Seeing is believing" applies to mathematics, as an encouragement to use pictures to illustrate, to discover, and to even to prove. Computer software has made it easy to produce accurate pictures (even ones that move) and to generate numerical evidence to aid in this process. But there is also a caution: sometimes our eyes (and belief) can fool us; only mathematical proof can confirm or deny what seems to be true.

Why History of Mathematics Matters

Room 2121 Benjamin Building
11:00 - 12:00 with discussion and free lunch to follow

By

David Henderson , Ph.D.
Cornell University

We have found that students and even mathematicians are often confused about the history of geometry. In addition, many expository descriptions and textbooks of geometry (especially non-Euclidean geometry) contain confusing and sometimes-incorrect statements. This is true even in works written by well-known research mathematicians. These include answers to questions such as: What, when, and why was the first non-Euclidean geometry? Can you trisect any angle? What does "straight" mean in geometry? Why in high school is transformation geometry difficult to integrate with traditional Euclidean geometry? We introduce the notion that the main aspects of geometry today emerged from four strands of early human activity, which seemed to have occurred in most cultures: art/patterns, navigation/stargazing, motion/machines, and building structures. These strands developed more or less independently into varying studies and practices that from the 18-th and 19-th century on were woven into what we now call geometry. We will then discuss how these four strands can help us to clear up common misconceptions and increase people's interest knowledge, both in geometry and its history.

The Role Scaffolding in Facilitating Students' Self-Regulated Learning with Hypermedia

Room 2121 Benjamin Building
11:00 - 12:00 with discussion and free lunch to follow

By

Roger Azevedo , Ph.D.
University of Maryland

Learning with computer-based learning environments (CBLEs) involves intricate and complex interactions among cognitive, motivational, affective, and social processes that occur in specific tasks and learning contexts. Current psychological and educational research on learning with CBLEs provides a wealth of empirical data indicating that learners of all ages have difficulty learning about complex topics in areas such as science and math. Learning with CBLEs requires students to regualte their learning--i.e., analyze the learning situation, set meaningful learning goals, determine which strategies to use, assess whether the strategies are effective in meeting the learning goal, evaluate their emerging understanding of the topic, and determine whether the learning strategy is effective for a given learning goal. Students need to monitor their understanding and modify their plans, goals, strategies, and effort in relation to contextual conditions (e.g., cognitive, motivational, and task conditions). Further, depending on the learning task, students need to reflect on their learning. My research attempts to facilitate students' learning with hypermedia by testing the effectiveness scaffolds, or instructional aids, designed to support and facilitate students' self-regulated learning (SRL). In this presentation, I will present results from our research on SRL with hypermedia that converges product and process data. An examination of the effects of different scaffolding methods on students' shifts in mental models (from pretest to posttest) and how these shifts in conceptual understanding are related to the dynamics of SRL processes used by students while learning with hypermedia. Lastly, I will discuss how the results can be used to inform the design of hypermedia environments as metacognitive tools to foster learners' SRL of complex topics.

Motivating Teacher Practices that Promote Mathematics for All

Room 2121 Benjamin Building
11:00 - 12:00 with discussion and free lunch to follow

By

Shelley Sheats Harkness, Ph.D.
Miami University, Ohio

Picture a university classroom where students who typically dislike mathematics work through breaks and after class ends.  Students are eager to share their strategies and are out of their seats, leaning over tables to talk with one another about tasks they are trying to understand.  They are not satisfied with rules and procedures that they learned in previous mathematics classes but want to understand “why” the divisibility rules work or “why” you can invert and multiply to do the division algorithm for fractions.  What teacher practices promote this kind of behavior? 

Dr. Harkness will share results from studies that addressed this question.  Morrone, Harkness, D’Ambrosio, and Caulfield (2004) used content analysis of teacher statements made during large group instruction to understand why these preservice elementary school teachers were highly motivated in their social constructivist mathematics course.  Harkness, Morrone, and D’Ambrosio (submitted paper) analyzed student mathematical autobiographies and end-of-semester reflections as data that revealed, in the voice of the students, further insight into the context of the course.  And, further analysis of data, Harkness in the form of interviews of the teacher builds upon this work by examining the teachers’ beliefs, practice, and subject matter knowledge.  Dr. Harkness will share insights gained from these studies with a focus on teacher practices that motivate students to engage in, risk, and “do” mathematics.

Math Teachers as General Educators

What are the obligations of math teachers
to contribute to the broader education of students?

Room 2121 Benjamin Building
11:00 - 12:00 pm

By

Nel Noddings, Ph.D.
Stanford University

Closely related to this general theme is a question which has become increasingly interesting to me: How much math can be learned non-sequentially, thematically, or even incidentally? I'll draw on literature, art, philosophy, history, etc.

The Role of the Language of Mathematics in Interpreting and Implementing the Maryland Voluntary Mathematics Curriculum.  A Look at the PreK-3 Geometry Standard

By

Genevieve M. Knight, Ph.D.
Coppin State College

Undergraduate Mathematical Knowledge for High School Teaching

By

Brad Findell, Ph.D.
University of Georgia

Math and Art: The Good, the Bad, and the Pretty

By

Annalisa Crannell , Ph.D.

What's the Case for Cases as a Pedagogical Approach in Mathematics Teacher Education and Professional Development?

By

Katherine K. Merseth, Ed.D.

Students' Participation in Mathematics As A Scientific Research Discipline

By

Karen King, Ph.D.

The Relationship Between Middle School Mathematics Teachers' Understanding of Proportional Reasoning and Their Mathematics Curricula

By

Kim Bethea, Ph.D.

Reclaiming the Classroom in Classroom Assessment

By

Janet Coffey, Ph. D.

Lesson Study in Japanese Schools

By

Clea Fernandez, Ph.D.