I read the article Pre-service Secondary Mathematics Teachers' Beliefs about the Nature of Technology in the Classroom
Summary of Article:
This article was written by our very own Dr. Leatham about the beliefs Pre- service teachers (PSTs) have about using technology in the classroom. Teachers do not agree on when technology would be most beneficial for students, some think it should be used after students understand the concepts they are learning about, and others think it should be used before the learning takes place in order to help students understand material. This debate has frequently been described in terms of a before-versus-after dimension. Hanzsek-Brill describes three different places along the BVAD (before- versus- after dimension): exploratory, post-mastery, and pre-mastery. Exploratory is when teachers are exploring the technology to see how it can be beneficial, post mastery is when teachers have mastered the technology and believe it should be used, and pre- mastery is when teachers have used technology, but haven't really been able to get to its full potential.
Dr. Leatham then points out that in order to study what PSTs belief about teaching with technology we have to study what it means to believe something. He then gives three different descriptions of belief. First he says that "beliefs can be described in terms of their psychological strength, varying from central to peripheral", "a second dimension of belief organization considers the quasi-logical relationships that may exist among an individual's beliefs", "a third dimension of belief structure is the extent to which beliefs are clustered in isolation from other beliefs."
Dr. Leatham studied 4 students to find out what their beliefs about teaching with technology were. One student, Ben, believed that technology should be used to enhance student learning, but that doesn't mean that it is always the best way to do it. A second student, Jeremy, believed that technology should always be used in teaching. A third student, Katie, believed that the use of technology should not be something that is forced on the students, but that they can use it when they want to, she said it should be a natural part of classroom instruction. The final student, Lucy, believed that technology could be very beneficial when used correctly, and that it is just a part of a bigger set of tools, or manipulatives, that she can use to teach.
There were three dimensions of teaching that came out of this study: availability, purposeful use, and teacher knowledge. Under these categories were also before- versus- after dimension, constant- versus- periodic dimension and alignment. One of my favorite lines from this article (I put it in bold in my notes) is that "students associate the appropriate use of technology with when it is made available. By contrast, when technology is constantly available, students choose when to use it." We can't just think of how we want to use it to teach, but also how the students will use it to learn; they need to see its advantages. Finally, it is always important to have a purpose for using the technology. Don't use it just to use it, this could actually end up not being helpful or useful to your students or yourself.
Summary of Class Discussion:
Our class discussion started by someone asking Dr. Leatham how he found the 4 students for his study. He said that it was really a volunteer basis, and it was pretty much luck that they all had different views. There was actually a 5th student who Dr. Leatham studied, but he didn't include her in the paper because she didn't add any new insights. Our class discussion then turned away from the logistics of the paper, to its content. A student asked for clarification about the terms pre- mastery, exploratory and mastery. They are all pretty much ways of thinking about how to look at a piece of material and how the students will look at it. With regard to technology the explore phase is when teachers are testing out the technology the pre- mastery phase is when teachers aren't really comfortable with technology, or don't really like to use it, and the mastery phase is when people are able to use the technology well.
We then spent a lot of time talking about the use of calculators. Ben, one of the students in the article, said that he believed that if you're going to let students use calculators on homework then you should let them use it on the test, but if you're not going to let them use in on the test then they should not use it on homework. If you're teaching someone to do mathematics with a tool, then assess them without the tool it doesn't seem fair. There are some good reasons that calculators shouldn't be allowed on tests. The example came up is that in calculus if we were allowed to use our calculators on the test, then we could just use the integrate buttons and not have to do any work. This lead to a discussion about what is mathematics. Is is calculations? is it problem solving? is it finding patterns? is it something else? If you think that it is all about the calculations, then you won't want your students to use calculators on the test. If you think its about the principles behind the calculations then it shouldn't matter if students use a calculator or not. To get around some of the problems of using calculators teachers can ask conceptual questions about the math, not just computational ones. The question then is how important is the actual ability to add vs knowing the concepts behind adding to the teacher?
Although we might not have formed our opinion about teaching with technology yet, it is always important to keep up with technology. You owe it to your students to know all of the new technology, also, it's going to be part of your students lives, so it helps you to relate to them in some way. Something that is often said against teaching with technology is that it's unfair to the students who don't have computers at home to go home and practice. One of my classmates pointed out that on the other hand when else are those students going to have the chance to be exposed to the technology? Only in school. When people value technology they will find a way to get access to it.
One of my classmates asked that although we might think that teaching with technology is good, when are we supposed to find the time to use it? We already have to make lesson plans, find the technology, learn how to use the technology, create worth while mathematical tasks, improve our teaching strategies, find real world applications and more. Dr. Leatham's advice to us was to do our best. You have to do the best you can every day as a teacher. When you start out teaching there will be a lot of things that you wont be able to do you. It takes years of teaching to turn you into a master teacher. Don't expect to get it right the first time. Bite off a slightly smaller goal first. Remember to engage students in some meaningful mathematical discussion every day. Even if the lesson plan might be boring, you can still engage the students and ask meaningful questions. If you have evidence that the students are thinking about mathematics, that's what important. Then build in the other stuff when ever you can. Your lessons don't always have to be a three day long exploratory tasks.
Critique:
From this article we have seen different view points of technology, which have been educational for sure, but I feel like it's intuitive to say that some teachers will love to use technology, some wont love it, and some will sometimes love it. I liked that the article went into more depth about each perspective, so as a teacher I can be a little more prepared. Meaning, if I realize that I do like using technology, having read the other perspectives can help me be sure that I am doing the right thing for my students, and help me understand that there can be other ways to teach. I enjoyed being able to hear Dr. Leatham talk about his process for selecting and evaluating the students. I wonder, if the students hadn't been from the same school, would the results have been different, or are these opinions typical of PSTs? I think I was able to learn from the article because it helped me see other points of views, and understand their validity. I also wonder if there are more perspectives than the four given here? I can't think of any that would be too different than these, so they'd probably be sub categories of these. But when I read an article I appreciate the author mentioning that there could be other possibilities than the ones listed. With regard to the class discussion, I didn't feel like we talked about the article specifically a lot, but more so the beliefs about using technology. Of course that was the point of the article, but that wasn't the whole thing.
Connections:
This article is pretty much 100% connected to me as a PST, because it is about PSTs. Dr. Leatham mentioned that during part of the time that he studied the PSTs, they were doing their student teaching, so actually these students were one step ahead of where I am now. Because I am coming to the end (one month left) of the teaching with technology class, seeing examples of beliefs about technology is valuable to me because it reminds me that I need to figure out what I believe about using technology, and it helps me see different perspectives. As I mentioned in the critique section, it can help me evaluate if what methods I am using are correct for my students because I can look at other perspectives and see if different methods would benefit them more. Although I have learned a lot about the benefits of technology, I feel like I won't really beable to have an opinion about teaching with it until I actually have that experience. It's like judging a chocolate shake before tasting it... you really shouldn't. I feel the same way about technology. Once I have started using it in my classrooms I will really be able to understand it's benefit. I hope that I will be able to keep up with the technology, and be able to understand how to use it when I teach. This class is helping me gain the desire to learn about it, next I need to actually do it.