Abstract
In this study, teachers’ narrative descriptions of themselves as learners and teachers of mathematics were used to understand teachers’ interpretations and implementations of a reform-oriented mathematics curriculum. Twenty elementary school teachers’ mathematics life stories were categorized into six types, based on teachers’ descriptions of both their early experiences with mathematics and their current perceptions of themselves as mathematics learners and teachers. The focus in this article is on the sense-making practices (noticing, interpreting, implementing) of teachers who told turning-point stories – those stories in which the teachers initially experienced significant failures in mathematics, but, as the result of a turning-point experience, now view themselves positively as both learners and teachers of mathematics. The importance of both the turning-point story and the particular meanings teachers attribute to this story for understanding teachers’ specific practices in the context of reform are detailed here, followed by implications for curriculum design.
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Appendices
Appendix A – Mathematics Story Interview for Teachers (Based on version by Dan P. McAdams, Northwestern University (1993)
Introductory Comments
This is an interview about the story of your life experiences with math. Teachers’ lives vary tremendously, and they make sense of their own math experiences in a variety of ways. Our goal is to begin the process of making sense of how teachers interpret their own math experiences. Therefore, we are collecting and analyzing the stories of teachers’ experiences with math and looking for significant commonalties and significant differences in those stories that people tell us.
Critical Events
We would like you to concentrate on a few key events that may stand out in bold print in your story. A key event should be a specific happening, a critical incident, a significant episode in your past set in a particular time and place. It is helpful to think of such an event as constituting a specific moment which stands out for some reason in your experiences with math. A very difficult year in high school would not qualify as a key event because it took place over an extended period of time.
I am going to ask you about several specific events. For each event, describe in as much detail as you can what happened, where you were, who was involved, what you did, and what you were thinking and feeling in the event. Also, try to convey what impact this key event has had in the story of your life experiences with math and what this event says about who you are or were as a person and as a teacher.
Event #1 Peak Experience
A peak experience would be a high point in your story about math in your life – perhaps the high point. It would be a moment or episode in the story in which you experienced extremely positive emotions; like joy, excitement, great happiness, uplifting, or even deep inner peace after some math experience. Tell me exactly what happened, where it happened, who was involved, what you did, what you were thinking and feeling, what impact this experience may have had upon you, and what this experience says about who you were or who you are now as a teacher.
Event #2 Nadir Experience
A “nadir” is a low point. A nadir experience, therefore, is the opposite of a peak experience. It is a low point in your experiences with math. Thinking back over your life, try to remember a specific experience in which you felt extremely negative emotions about math. You should consider this experience to represent one of the “low points” in your math story. What happened? When? Who was involved? What did you do? What were you thinking and feeling? What impact has the event had on you? What does the event say about who you are or who you were as a teacher?
Event #3 Turning Point
In looking back on one’s life, it is often possible to identify certain key “turning points” – episodes through which a person undergoes substantial change. I am especially interested in a turning point in your understanding of math. Please identify a particular episode in your life story that you now see as a turning point. If you feel that your math story contains no turning points, then describe a particular episode in your life that comes closer than any other to qualifying as a turning point.
Event #4 Important Childhood Scene
Now describe a memory about math from your childhood that stands out in your mind as especially important or significant. It may be a positive or negative memory. What happened? Who was involved? What did you do? What were you thinking and feeling? What impact has the event had on you? What does it say about who you were? Why is it important?
Event #5 Important Adolescent Scene
Describe a specific event from your adolescent years that stands out as being especially important or significant with respect to math.
Event #6 Important Adult Scene
Describe a specific event from your adult years (age 21 and beyond) that stands out as being especially important or significant with respect to math.
Event #7 One Other Important Scene
Describe one more event, from any point in your life, that stands out in your memory as being especially important or significant with respect to math.
Life Challenge
Looking back over your life and interactions with math, please describe the single greatest challenge that you have faced. How have you faced, handled, or dealt with this challenge? Have other people assisted you in dealing with this challenge? How has this challenge had an impact on your experiences with math?
Influences on the Life Story Positive and Negative
Positive
Looking back over your life story, please identify the single person, group of persons, or organization/institution that has or have had the greatest positive influence on your perspective of math. Please describe this person, group, or organization and the way in which he, she, it or they have had a positive impact on your story.
Negative
Looking back over your life story, please identify the single person, group of persons, or organization/institution that has or have had the greatest negative influence on your perspective of math. Please describe this person, group, or organization and the way in which he, she, it or they have had a negative impact on your story.
Alternative Futures for the Life Story
Now that you have told me a little bit about your past, I would like you to consider the future. I would like you to imagine two different futures for your story.
Positive Future
First, please describe a positive future. That is, please describe what you would like to happen in the future with regards to your interactions with math, including what goals and dreams you might accomplish or realize in the future.
Negative Future
Now, please describe a negative future. That is, please describe a highly undesirable future for yourself with regards to your interactions with math, one that you fear could happen to you but that you hope does not happen.
Additional Questions
What do you think it takes for a student to be good in math?
What are your goals for your students in math?
What are your strengths and weaknesses as a math teacher?
Appendix B – Levels of Practice Framework
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Drake, C. Turning Points: Using Teachers’ Mathematics Life Stories to Understand the Implementation of Mathematics Education Reform. J Math Teacher Educ 9, 579–608 (2006). https://doi.org/10.1007/s10857-006-9021-9
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DOI: https://doi.org/10.1007/s10857-006-9021-9