In Stage 3, Christy’s progression to attending to student thinking was triggered by the US’ suggestion that Christy use bell-ringers to addressed her students’ difficulties. In subsequent online posts, Christy described several occasions where she used bell-ringers in both her general and advanced classes to address students’ misconceptions or lack of pre-requisite knowledge. Planning bell ringers that addressed student misunderstanding seems to have prompted Christy to describe her students’ misconceptions in more detail than in her earlier online posts. (see Table 4.7)
Figure 4.7 Christy’s plans about using bell-ringers
Date Excerpts from Christy’s online posts March 27, 2013
at 8:31pm • Today we worked on Conics. …My students then worked on a worksheet asking them to identify a conic given it’s standard equation. Then I asked them to find the center or vertex of each conic. …I also found the students struggled when it had a center or vertex at the origin. They didn’t like it when there was no number. They also didn’t like it when the formula had a positive but the vertex was a negative.
I think I will start doing more misconceptions as bell ringers. March 27,
2013 at 8:53pm
• Again today we worked on parabolas… This group had a harder time with the example with the distance formula so I did another example of this type. I noticed that they were struggling with the distance formula in general. Tomorrow I think I will do a bell ringer with one problem that is finding the distance given two points and another that is finding the distance given two points that have numbers and variables. I think this will help them understand the problems we did today.
Figure 4. 7: Christy’s plans about using bell-ringers.
Furthermore, using a “find the error” bell-ringer to address students’ misunderstandings in her advanced classes, actively involved students in thinking and was a shift from
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Christy’s initial efforts to remediate students’ errors by simply “reviewing a lot.”(see Figure4.8)
Figure 4.8 Christy uses a bell-ringer in her advanced class
Christy’s online post excerpt- April 22, 2013 at 3:53pm
Christy: Today I again taught radicals. We started with a bell ringer. The bell ringer was over misconceptions from last class…I then analyzed their answers. I found common mistakes and typed them up as a bell ringer. They had to fix the common mistake. I allowed the students to work in groups for this.… I think this really helped them… I think I will continue doing bell ringers like the one I did today. I really like that and felt it really helped my students
Figure 4. 8: Christy uses a bell-ringer in her advanced class.
In summary, Christy’s progress in attending to students’ mathematical thinking was centered on how Christy’s attended to students’ misconceptions. She progressed from being overwhelmed by student errors and weaknesses to planning and designing bell- ringer activities to remediate and head-off misconceptions.
In conclusion study participants’ online comments revealed their progression through various stages of development in relation to aspects of standards based teaching practices. The implication of this finding will be discussed in Chapter 5.
Study participants’ perception of how online mentoring conversations were related to their development toward standards-based instructional practices
All study participants indicated that online mentoring supported their
development in effectively enacting aspects of standards-based instruction. In her post interview comments Kathy credited online mentoring conversations with encouraging and affirming her efforts to promote student collaboration and mathematical discourse and for providing suggestions about strategies to improve the nature of collaboration and discourse among her students (see Figure 4.9).
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Figure 4.9 Kathy’s post–interview comments relating online conversations to her development
“It was originally my idea to have them pick and [discuss] a method [for solving systems of equations] My US [said] it was a good idea for facilitating the communication about math which was one of things I wanted to work on. It was reassuring to hear someone say that you are working toward the goals that you have set.” (see Kathy’s conversations in Appendix D).
“My US suggested to ask the group members to discuss predictions and then as a group to put forth their predictions to the class instead of them all …working in isolation and then we would, as a class, talk about each prediction, …I feel like that is something I tried to keep with …There was actually a group activity that I created a little bit later where I had the students in groups where they had to reach a consensus as a group before they could presented it. So it ( the group activity)kind of stemmed from that online ]conversations. ( see Kathy’s conversation in Appendix D).
Figure 4. 9: Kathy’s post interview comments.
Jake post-interview comments indicated that in online conversations, the US pushed him to get out of his comfort zone and take some risks about presenting material in ways that engaged his students thinking. In addition Jake found the online conversations to be a venue for positive affirmation from the US about his introduction of a new strategy (completing if - then statements) to elicit students thinking and promote student collaboration
Figure 4.10 Jake’s post-interview comments relating online conversations to his development
My US pushed me to do things outside my comfort zone.…. She voiced her displeasure with some things I was doing. And it was like Ok, it’s time to do something different because I was tired of not doing things sufficiently …just in her comments she had some good things to say …Take some risks, this is your time to take risks …so I appreciated that about this online stuff.
(See Jake’s conversations in Appendix D)
It was good to me that my US affirmed my “ if then” statements. I appreciated that, otherwise, I might have scraped it…. It gave me another tool that I could use, a different
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tool in my back pocket. The positive affirmation was good… I used the “ if then statements a couple of other times.” (See Jake’s conversations in Appendix D) Figure 4. 10: Jake’s post interview comments.
Sam’s post interview comments indicated that he found that the questions that US asked him in online conversation about student collaboration during group work forced him reflect on aspects of group work that he might have thought about by himself.
Figure 4.11 Sam’s post interview comments relating online conversations to his development
The fact that could have this conversation (See Sam’s conversation1 in Appendix D) and not be in the same room was fantastic for me because it helped me to formulate even better ideas about what I was doing in classroom, because US asked questions that I might have thought to ask myself. And, her experience in the classroom came out in in her questions because I think US anticipated some of things that I had blogged, things that I was not able to anticipate. ... For me, US asked questions that I may not ever been able to come up with or formulate on my own, which made me think over those posts even more when I did my response. So, I was getting, not just the benefit of reflecting on the activity on my own, but I was then getting a second opportunity to go back and reflect again with additional questions, with another set of lenses. When US keyed in with some of her questions, it gave me, yet, another perspective that allowed me to re-inspect what I had experienced and then talk about it some more.”
Figure 4. 11: Sam’s post interview comments.
Christy credited online conversations with prompting her to think more about students’ misunderstandings and what she “could do to fix them”.
Figure 4. 12 Christy’s post interview comments relating online conversations to her development
“I had not really thought about the misunderstanding too much before this comment (US’ comment on February 27,2013 See Appendix D)“I thought more about what I could do with misunderstandings and how I can fix them.
Towards the end, I started making bell ringers, that kind of did some of the stuff before; it was mainly for my other classes because they forgot a lot of math like simple things… so it was more for them( general classes) with their misunderstanding and that helped them.” With this class (the advanced Algebra 2 class), I started doing exit slips …, and then I graded them and put them in pile and put in piles based on misunderstandings so like, if 5 of them made the same mistake, I would put them together, and then I made that into a bell ringer and then, they had to fix their mistakes on the next day I saw them. That was kind of cool. They got to figure out what they did wrong and that class did very well with that.
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them very much I told them to work with their friends …. I wanted them to get on their own. I had them really think about it for a while and then we did it together … it really helped them not to make those mistakes again. I think they will not often make those mistakes again.”
“I learned a new way to help them with misconceptions which was really cool I think if they do it themselves they figure it out on their own instead of me just telling them because if I tell them stuff they don’t’ really listen but if they figure it out on their own, it’s like, ‘yes’, I did it !”
Figure 4. 12: Christy’s post-interview comments.
In summary, all participants found online mentoring supported their progress in enacting standards-based instructional practices during their student teaching internship. The implication of this finding will be discussed in Chapter 5.
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