Summary of article:
The article starts off by stating that technology is an essential part of learning. Because students need it to learn, teachers then need to be taught how to teach with it. When teachers learn to use technology it will be more beneficial to them if they are taught with the technology, meaning that to learn about it they actually use it, as opposed to just learning about the technology and how it can be useful. Because this is an article about spreadsheets it makes sense that that is the technology that is focused on. The author says that "one unique use of spreadsheets is the ability to interactively model and simulate mathematical situations." Also, using spreadsheets to create tasks can create open- ended teaching and learning situations. The author compares the use of spreadsheets to working in a laboratory. You have the freedom to explore different possibilities. But again, before students can learn from spreadsheets, teachers must be able to use them themselves. The author goes on to talk about some of the things that spreadsheets can do, like the randbetween and countif functions. Also, spreadsheets can help teach probability in different ways than dice and coins, help students see larger numbers in a simulation (flipping coins) than they can do by hand, links between cells create interactive formulas and functions, graph functions, generate sequences, do repetitive calculations without having to type them over and over again, create interactive fractions where students can change the numerator and denominator with a scroll bar, and provide extension for the popular problem of having a fixed amount of fencing and wanting to find the most area. For each of these capabilities the author went into some detail about the commands used to accomplish these tasks. A great thing about spreadsheets is that they allow us to change the parameters of the problems easily, and they can help us search for patterns. A quote that I really liked from the 7th page was, "with careful planning a teacher can design a spreadsheet and use the scroll bars to encourage students to explore 'what if' questions." Teachers should plan lessons with technology, but those lessons don't always have to be elaborate, or even be just lecture or just tasks. They can be whole group, small group or individual activities. The article then provided a couple of examples where teachers have used spreadsheets in lessons. They were the experimental probabilities lesson, distance, rate, time lesson, and the projectile motion lesson. The author concluded by saying, "interactive spreadsheets can promote open- ended exploration of mathematical concepts, take advantage of spreadsheet capabilities that allow the learner to extend beyond, or significantly enhance what could be done using paper and pencil, and give teachers and students an opportunity to discover mathematical concepts in a laboratory like setting."
Summary of class discussion:
Our class discussion started with the same thing that the article started with: as future teachers we need to learn about technology by using technology, not just learning about technology. Dr. Leatham pointed out that the way we learn about the technology is important. We bring in pedagogy by exploring the technology not by creating lesson plans. We will have plenty of practice later with writing lesson plans. We then looked at how excel is like a laboratory or a play group. Excel is a good way to explore data. One of my classmates pointed out that GSP seems like a better play ground because it seems like we can do more with it. This got us talking about GSP vs. Excel. It seems like excel is more of a teacher tool than a student tool, because it can help teachers in discourse, but maybe not help students in their exploration or learning. We mentioned how great GSP is, but it's kind of unfair because we have had a month of experience with GSP, where as we have had hardly any experience with excel, so we really havn't had the chance to see what it can do. But because of our lack of experience some classmates thought that it wasn't user friendly because it's hard for us to figure out simple things. Dr. Leatham just pointed out that once you're familiar with excel it's easy to use. There are hundreds of functions that excel can do.
We turned our class discussion then to how the students could use excel. Excel is nice because it can generate data much faster than paper and pencil, or other programs. But it seems like there is such a big learning curve that it would be hard for students to really do much with it. One of my classmates pointed out that learning about excel can be a basis for computer programing (she often makes the connection to computer programing because she is studying it along with math). She said excel is like a half step. Yes there is a learning curve, but it's better to take a half step in high school then another half step in college, rather than a whole step in college. Dr. Leatham described two ways to use excel with students: create the spreadsheets ahead of time or find them already made, then students don't have to create it themselves and can just explore the math; have students actually create tasks in excel, for this, students need to know more about the math and about excel.
Some other benefits of excel that we explored were that if you can't find the manipulative you want online, then excel is one of the easier programs to use to create your own. Excel is not internet based, so if the internet crashed, you can still go on with the lesson. You can adapt what you need to in excel to fit the task you are working on, where as other java manipulatives can't be changed. The slider feature seemed beneficial for the fractions. Excel can collect and generate specific or random data. We had a little side note about how "random: excel really is. But really, it's hard to convince students of randomness when they are for example flipping coins. As teachers we will have to do more than let them flip coins, or have excel generate numbers to teach our students about randomness. Also, calculators can do some of this random stuff.
Critique:
On the second page of the article it says "by giving pre- service and in- service experiences with such powerful spreadsheets, they can in turn, use their knowledge of mathematics and spreadsheets to design interactive environments for use in their own teaching." To me this sentence pretty much meant once teachers have been taught to use spreadsheets, then they can use them. How profound. I felt like this idea was already established on the first page of the article. Throughout a lot of the article there seemed to be a lot of instruction for how to do the commands for different functions of the spreadsheet, and without having excel open in front of me, that seemed like just a lot of confusing symbols. It would have been more effective to have an interactive article where we could watch movies or something that showed us how to do each thing. Although there were some flaws in the articles write up, i felt like the material was really good. Before reading the article I could honestly think of no reason to use excel in the class room other than to total up grades. This article provided a lot of good examples and motivation to explore possibilities with excel.
Regarding the class discussion, when we were talking about GSP vs. Excel I wanted to point out that I think that the two programs are used for different things. Yes, there are obviously times when GSP will be a better choice than Excel, but there may also be times when we realize that excel can get across the point better than GSP. GSP is more geometry related (hence the name) but of course because of the animation it can be great for other things. But excel is great for making calculations, tables, charts, things that are repetitive, or things that relate to probability. It was good that Dr. Leatham pointed out the two different uses for excel, because our students need to know about excel because they will probably use it at some point in our future, so it'd be good to show our students the basics, then let them use a pre- made task and just explore the math while familiarizing themselves with the technology.
Connections:
I appreciated this article because before reading it I tried to think of reasons to use excel, and the only one I could think of was to do grades. I knew that excel could produce tables and charts, but I didn't see why it was any better than something else. I understand now that some of the features like the ability to repeatedly fill in cells based on some equation and different inputs is really convenient. Also, I never realized that it could generate a set of random numbers, including just two numbers which can represent a coin toss, or 6 numbers, which could represent rolling a dice. Reading the different cases of lessons where spreadsheets were used was helpful for me because the three lessons were of different topics, but they were able to use excel. Because so much focus was initially put on probability problems, while I was reading it was hard for me to think of other times to use excel other than generating random numbers, until the article showed these lesson plans. I really like the fact that it's an off line manipulative. I remember plenty of times in high school where my teacher had to change the plans because the internet was down. It would have been nice if we'd been working with programs that didn't rely on the internet. With regard to GSP vs. excel. I stand by what I said in the critique section. I think that they can be useful for different things.