Using Field-Based Assignments to Develop Visions and Skills with Best Practices in Teaching Mathematics
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Using field-based assignments in math methods courses can help address the disconnect teacher candidates often experience between their prior math learning, developing understanding of learning theories, and clinical experiences. The document discusses how assignments like observations, interviews, and teaching help unify these experiences when supported by coursework. However, research shows methods courses may not be long enough to affect lasting change. Therefore, it is important to understand how field-based assignments specifically support teacher candidate learning and practice. The presentation aims to provide a rationale for these assignments, examples used, and their impact on developing teacher candidates' visions and skills in teaching mathematics.
![“Classroom discussion based on students’ own
ideas and solutions to problems is absolutely
‘foundational to children’s learning’” (p. 21). I
believe that students need to be guided, but also
need to have time to explore concepts on their own.
This allows for independent learning and can result
in more confident students. When students are
given opportunities to work out problems on their
own, they are more likely to remember.
[I] noticed that as I am teaching I like to
guide students to the correct answer,
which is a bad trait. I need to help students
justify their answer, so that they become
confident in their mathematical skills.](https://image.slidesharecdn.com/amtefieldbasedassgn2012-140111192636-phpapp01/85/Using-Field-Based-Assignments-to-Develop-Visions-and-Skills-with-Best-Practices-in-Teaching-Mathematics-9-320.jpg)
![In the video, I noticed myself helping too
much. It’s so hard not to! I realized that I
have to back off and give the student
some space to see what they are doing.
Some things may take a while to sink in, I
can’t keep pushing. I also tried to
encourage her too much.
Overall I learned a lot from [the Inquiring to
Understand] project and also learned that I have a lot
more to learn about this teaching technique. I saw a
lot of connections from our readings and classroom
discussions to this project. I would like to get to learn
more about how to introduce and “teach” a new
operation or skill using this technique because I’m still
really confused about how that would work.](https://image.slidesharecdn.com/amtefieldbasedassgn2012-140111192636-phpapp01/85/Using-Field-Based-Assignments-to-Develop-Visions-and-Skills-with-Best-Practices-in-Teaching-Mathematics-11-320.jpg)
Using Field-Based Assignments to Develop Visions and Skills with Best Practices in Teaching Mathematics
- 1. Using Field-Based Assignments to Develop Visions and Skills with Best Practices in Teaching Mathematics Nicole Rigelman, Portland State University Gina Post, Wittenberg University Association of Mathematics Teacher Educators Annual Conference February 10, 2012
- 2. SessionOverview Provide you with a rationale for using field-based assignments in math methods courses, a framework for gradual increase of student interaction, data regarding the impacting such assignments have on teacher candidates vision and skills with research-based practices, and an opportunity to discuss ideas for implementation with colleagues.
- 3. The Problem Teacher candidates often wrestle with the disconnect between their personal prior mathematics learning experiences, their developing understanding of learning theories, and their clinical experience. - Zeichner, 2010; Allsopp, DeMarie, Alvarez-McHatton, and Doone, 2006
- 4. A Response To unify these experiences many teacher educators incorporate guided observation, interview, and teaching assignments that are supported by course-based reading, discussion, and reflection.
- 5. However… research suggests that methods courses are of too short duration to affect any lasting change in teacher candidate attitudes and beliefs about teaching. - Ball, 1996; Borko& Putnam, 1996
- 6. Therefore, it is imperative that teacher educators determine in what ways and to what extent field-based assignments support teacher candidate learning and practice.
- 7. So… What are some of examples of field-based assignments you currently use in your setting? Why?
- 8. Research Question In what ways and to what extent do field-based assignments support teacher candidate learning and practice? Common Field-Based Assignments Inquiring to Understand Math Mini-Lessons/Routines Problem-Based Lesson
- 9. “Classroom discussion based on students’ own ideas and solutions to problems is absolutely ‘foundational to children’s learning’” (p. 21). I believe that students need to be guided, but also need to have time to explore concepts on their own. This allows for independent learning and can result in more confident students. When students are given opportunities to work out problems on their own, they are more likely to remember. [I] noticed that as I am teaching I like to guide students to the correct answer, which is a bad trait. I need to help students justify their answer, so that they become confident in their mathematical skills.
- 10. I love letting the students share their thoughts with a partner, not only so I can ensure everyone has a chance to speak, but also so I can hear the mathematical discourse that can occur between peers. I find it so interesting when students who are seemingly best friends can argue about which number is a divisor and which is a quotient, fight over who is right, and then go back to being best friends after class. I also enjoy when I hear a student talking about math after class is over, I then know math has permeated their thinking and the lesson must have intrigued at least that student.
- 11. In the video, I noticed myself helping too much. It’s so hard not to! I realized that I have to back off and give the student some space to see what they are doing. Some things may take a while to sink in, I can’t keep pushing. I also tried to encourage her too much. Overall I learned a lot from [the Inquiring to Understand] project and also learned that I have a lot more to learn about this teaching technique. I saw a lot of connections from our readings and classroom discussions to this project. I would like to get to learn more about how to introduce and “teach” a new operation or skill using this technique because I’m still really confused about how that would work.
- 12. After reviewing all of my results from the student and peer interviews, I realized that I really enjoyed using this protocol... I believe that I now have a better sense of the way that I can impact student’s mathematical thinking on a daily basis in the classroom. By using the inquiring questions I found out a great deal about students strengths, difficulties, and misconceptions about the math that they were doing. By using this protocol formally or informally in the classroom I think that I could get students to really think about math rather than simply “doing” math. I believe that the understanding of mathematical concepts gets even deeper when students are asked to justify and contemplate their reasoning behind doing math the ways in which they do.
- 13. I realize today was my first day attempting this method, so I think tomorrow can only be better. I need to remember for tomorrow to pay closer attention while the students are exploring and utilize some “talk moves” during this time as well and not just during the explaining time... Today, I found it a little easier to keep track of the students and the strategies they used along with posing individual questions to understand their thinking during the explore period. This helped me better sequence the students for the explaining period...To be honest, I do not know if I ordered in a meaningful way, and I do not know how to tell...I chose strategies that were suitable to the word problem. I would have liked students to catch on that they could have added by counting by 10, but that strategy was never presented.
- 14. We have been learning about an inquiry-based curriculum and how to really allow students to own their thinking. Through completing assignments such as Inquiring to Understand and the PBL, I have been able to incorporate some of this in the classroom. This not only has shown me what an inquiry-based classroom might look like, but has given me the chance to understand how my students think in math, which will only help in future instruction…. These Connecting to the Field Assignments really taught me that the more you know about your students, the more effective you will be when teaching lessons
- 15. What influence have your field-based assignments had on teacher candidates’ visions of and skills with mathematics teaching? How do you know?
- 16. References Allsopp, D. H., DeMarie, D., Alvarez-McHatten, P., & Doone, E. (2006). Bridging the gap between theory and practice: Connecting courses with field experiences. Teacher Education Quarterly, 33(1), 9-35. Ball, D. L., (1996). Teacher learning and the mathematics reforms: What we think we know and what we need to learn. Phi Delta Kappan, 77(7), 500-508. Borko, H., & Putnam, R. T. (1996). Learning to teach. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 673708).New York: Macmillan. Zeichner, K. (2010). Rethinking the connections between campus courses and field experiences in college and university-based teacher education. Journal of Teacher Education, 61(1-2), 89-99.