Publication Type: Conference Paper/Unpublished Manuscript
Abstract: Math-by-mail is an extracurricular math enrichment program that gives students in school the opportunity to correspond with mathematicians and discuss topics in recreational math. The program is run by the Davidson Institute of Science Education at the Weizmann Institute of Science.
The correspondence is done through a series of math booklets dedicated to topics in recreational math. The booklets are available either in hardcopy or online via a special purpose website dedicated to the program. The correspondence with the mathematicians is conducted via an online forum available at the website. The completed booklets are sent to the mathematicians by mail or submitted electronically for review.
Math-by-Mail provides the talented student with enrichment that stimulates creative thinking and expands the student's knowledge way beyond the limits imposed by the curriculum and their peer environment.
Teachers who run the program in their schools have found Math-by-Mail useful for talented students, providing them with mathematical challenges and broadening their math horizons beyond the scope of the regular class curriculum.
The program is currently run in five countries and four different languages (Hebrew, English, Spanish, Arabic) with over 2000 participants.
Feedback from the program, both from teachers and students is very positive.

Publication Type: Conference Paper/Unpublished Manuscript
Review Method: Peer Reviewed
Abstract: "You are the first math teacher who ever cared whether I understood or not." I have heard these words again and again out of the mouths of students who work hard in my classes. As math teachers, we have the unfortunate reputation of loving our content first, and our students a far second, if at all. So, my first key to motivating students is to convince them, in both words and actions, that I care about them and their success in math.

My second key to motivating students is to spend a good part of the first day doing math with them and introducing them to my teaching style. I choose material which is relevant to them, challenges them to think, but does not completely intimidate them. More importantly, I create an environment in which participation is not only "safe," but is also crucial in the learning process.

Because I have found that students "will not care how much I know until they know how much I care," I carefully weave this theme throughout everything I do on the first day - from necessary administrative tasks, to my choice of content, to the way in which I teach that content. For me, designing such a lesson on the first day reaps huge rewards for the rest of the semester: it encourages students who "hate math" to persevere, and it inspires many others to achieve success in math that they did not think was possible.

Publication Type: Conference Paper/Unpublished Manuscript
Abstract: Because science and mathematics content are usually taught as discrete courses, students often fail to make connections between disciplines. To resolve this “mismatch”, we have implemented a freshman and sophomore integrated science curriculum for all math, science, secondary mathematics education and science education majors. The curriculum is primarily composed of up to 6 mathematics courses (a review of algebra and trigonometry, along with calculus, units on statistics, and differential equations) and a 5-course “backbone” laboratory/research series (introductory labs in biology, chemistry and physics). Students take those portions of the curriculum that are required by their major.

The curriculum puts students in cooperative, technology supported learning environments where content is integrated among courses. The goals of the curriculum include improved teaming and communication skills; improved laboratory and research skills; improved mathematical thinking and problem-solving skills; early awareness of innovative teaching techniques in education majors; and development of learning communities of students. Existing courses were revised to incorporate examples and demonstrate relationships among concepts from multiple disciplines; relate student learning to real world examples and experiences; integrate teaming, critical thinking, problem solving and communication skills; and integrate effective use of technology for instruction.

Here, we will provide an overview of the curriculum as it relates to education majors, outline the opportunities and challenges of the integrated curriculum, and discuss assessment results to date. We will also present strategies we have used to model innovative instructional strategies in science and mathematics within the curriculum.

Publication Type: Conference Paper/Unpublished Manuscript
Abstract: This study examines the desire and willingness of girls to enroll in a single-sex math class for one year (9th grade) of their public school math education. Individuals create and develop self-efficacy beliefs as a result of the verbal persuasions they receive from others. Negative peer messages about the single-sex math class discouraged girls from choosing to enroll. Messages about femininity and heteronormativity reinforced girls’ actions with threats of negative labeling for non-compliance. In labeling the single-sex math class as lesbian math, boys reinforced the heteronormativity of the adolescent peer culture and threatened girls with the ultimate gender stigma of sexual deviance. The desire to present a self-meaning consistent with the presented self caused many girls to give up choices that reflected their interest, to instead fit in with the designations of cultural popularity.

Publication Type: Conference Paper/Unpublished Manuscript
Review Method: Peer Reviewed
Abstract: Math-Anxious Elementary Teachers' Change Process in a Graduate Course Aimed at Building Math Confidence and Reducing Anxiety


Overview and Objectives


This presentation will report some findings from a second phase of an ongoing study on math-anxious, elementary teachers, focusing on the following questions:

(i) How does elementary teachers' math anxiety affect their teaching practice?
(ii) How can math-anxious teachers be empowered in building math confidence and overcoming their anxieties?

The first phase of the study involved data collection from a group of math-anxious elementary teachers who participated in a series of eight Math Empowerment workshops (Cohen & Green, 2002).

Data collection for the current study took place in a new graduate course, specifically designed for helping math-anxious elementary teachers gain confidence in math and deal with their anxiety. The one-term course utilized a holistic approach in supporting participants' math learning and confidence building. The approach combined group problem solving and math explorations with reflection, relaxation and guided visualization activities, utilizing approaches developed by the course instructor (the first author) as well as those reported in the literature (Hembries, 1990; Tobias, 1978/1994).

This paper provides an overview of the course and focuses on the affective responses and attitudinal change of nine of the highly math-anxious course participants as they advanced through the course. The findings are based on these teachers' journal entries, open-ended questionnaire responses, final reflection papers and researcher notes.


Background and Theoretical Framework

Research on attitudes toward math and math anxiety has been prevalent since the seventies (e.g. Tobias, 1978/94; Hembries, 1990; Ho & al., 2000; Ashcraft, 2002).While most of the research in this area focused on students rather than teachers, numerous studies have focused on teachers, and on adults in general (e.g. Evans, 2000, Bush, 1989). Some studies investigated the relationship between teachers' teaching styles and their students' attitudes toward math (Bush, 1991; Karp, 1991; Norwood, 1994; Newstead, 1998; Jackson & Leffingwell, 1999).

It has been well documented that pre-service and in-service elementary school teachers often exhibit math dislike and/or anxiety (e.g. Bush, 1989; McCulloch Vinson, 2001). Recent math reforms have added new dimensions in teachers' math-related fears: the need to teach a reform-based curriculum, including not only unfamiliar content but also educational philosophies and instructional approaches that teachers may have never been exposed to (Battista, 1992; Loewenberg Ball, 1996).

Researchers have extended early work on math-related anxiety and attitudes to include the broader perspective of the 'affective domain' (or 'affect') in math. The latter was defined as consisting of three facets of affect: emotional states, beliefs and attitudes (McLeod, 1989; 1992; 1994;). Values/morals/ethics were later added as a fourth facet of affect (deBellis & Goldin, 1997). Much of this research dealt with student affect during non-routine mathematical problem solving (McLeod, 1992). Teachers' beliefs about math and math education have also been the subject of much research over the years (Thompson, 1992).

Recently the concept of attitude toward math has received considerable attention from researchers who claimed that it is an ambiguous, ill defined and unstable construct (Ruffel, Mason & Allen; 1998, Di Martino and Zan, 2001; Gellert, 2001). A new theoretical framework for analyzing attitudes and changes in attitudes was developed by Hannula (2002). In this framework attitude is defined as the combination of emotions in a situation, emotional reactions based on prior conditioning, expectations, and goals/values. The current study draws upon above theoretical frameworks and specifically that of Hannula.


Methodology and Data Sources

The current study was a qualitative, action research-like study (McKiernan, 1991) in which the first author acted as a teacher-researcher, with the second author as her teaching/research assistant in this new graduate course..

The graduate course, titled: Gaining Confidence In Mathematics: A Holistic Approach to Overcoming Mathematics Anxiety (Elementary), included eleven classes during a six-week summer term, and each class was three to three-and-a-half hours long. The class included eighteen members in total, thirteen of whom were in-service teachers. Four were pre-service teachers in one of the two-year master's programs that include initial elementary teacher training. All but three of the course members had varying levels of math anxiety and/or dislike. The three non-anxious teachers included a college math instructor and two teachers with strong math skills who took the course because of their interest in math anxiety. These three (and the research assistant) acted as "gentle coaches" for their math-anxious classmates during group and individual math work.

Participants in the study included nine of the course members who identified themselves as highly math anxious at the beginning of the course. Two of these were pre-service teachers who had not yet taken their math methods course, and the others were practicing teachers with a range of prior teaching experience.

Course Structure and Activities: The course was taught using reform-based principles. A highly supportive and 'safe' learning environment was created where the math-anxious teachers were more likely to take risks. The course included a math learning component, consisting of group explorations and problem solving, oral and written communication activities, math games and puzzles, along with some class discussions on selected math topics. One of the central math topics covered in this course was rational numbers in their various forms and representations. The confidence building component included two guided visualizations, each immediately followed by journal writing, group reflection activities, various 'affective' journal entry probes and strategies for dealing with anxiety, frustration and inner criticism.

One of the course assignments consisted of keeping a learning journal documenting personal learning experiences, insights and reactions to readings assigned. The instructor responded to each journal entry, offering empathy, suggestions, praise and encouragement as appropriate. A weekly math homework assignment including a few non-standard math problems was also given four times during the course. Students were also required to write a final reflection paper. Students' in-class math work and weekly math assignments were never evaluated in this course. They got credit for their math work based only on their efforts, willingness to ask for help and perseverance.

Data Sources: The data for this study included participants' journal entries written in class or at home; participants' final reflection papers, three questionnaires, including also some open-ended items, as well as researcher field notes. Participants' math work during the course was described in some field notes but was not part of the data.

Findings

The findings reported in this presentation will describe the nine participants' affective responses and change process as they moved through the course. This section will be organized according to specific themes that emerged during the data analysis. Each theme will be discussed and illustrated with excerpts from students' written expression during the course. Here we only include an overview of some of the findings.

Overview of Findings

All of the nine study participants were teaching in the primary (K-3) grades, and all but one had never taught at higher grade levels. This is not surprising since all of them described themselves as highly math anxious and lacking in sufficient math knowledge at the beginning of the course. As it turned out, their self descriptions in the initial questionnaire matched their behavior and math knowledge manifested during the course. Their math knowledge turned out to be mainly procedural (Hiebert & Linquist, 1990) and they lacked a solid math foundation that would be essential for reform-style teaching in the junior grades. Most of them expressed their serious concerns about teaching in the junior grades, regardless of the teaching approach (reform or not). Teaching problem solving and being confronted by students more knowledgeable than themselves who might pose problems they could not solve, was a frightening prospect.


Despite the participants' initial high anxiety level, all of them successfully completed the course and made significant progress in constructing their mathematical knowledge dealing with their fears. Having had negative math experiences in their own schooling, these teachers were highly committed to improving themselves as math learners and teachers. They held a vision of themselves as devoted and knowledgeable math teachers who could help their students learn math "the right way". This vision kept them going despite the moments of frustration, confusion or even panic during the course.

Most of the study participants went through a significant change in their beliefs and attitudes that was clearly described in their journal entries and reflection paper. Their math self-concept improved significantly. While they were still somewhat math anxious at the end of the course, their level of math anxiety was substantially reduced and their anxiety was often related to specific math topics that they had not yet mastered. They reported starting to use math more in their daily life rather than relying on others to do the work for them. Moreover, some of them even started liking math! - As one of the teachers put it: "I feel as though this course marks the beginning of a journey for me - a math journey. I refuse to believe that I can't be good at math. In fact, I've actually begun to like math".

(Bibliography in a separage file to be provided upon request)