1. Give a quick thought about what you think is "appropriate" policy on calculator use in secondary mathematics.
2. List any other technology platforms that you have used, are aware of, or would like to become more knowledgeable about - specific to mathematics teaching, or teaching in general.
Calculators should be used for practicing operations/procedures which students already understand. They should also be used to explore abstract graphical representations.
ReplyDeleteI have used:
Matlab, autocad, mathematica...
calculators should be used to further student's understanding on math. what they shouldn't be used on is +-*/ of single digit integers, like they currently are used for by many middle school and high school students.
ReplyDeletei have not used much technology past graphing calculators. i would LOVE to become knowledgeable in programs that come with smartboard, as well as other programs such as geometer's sketchpad
1. Students should know how to use a calculator, particularly in advanced classes (trigonometry, calculus) where their specialized functions come in handy for e.g. answer-checking and graph-based exploration. Unfortunately, most of the calculator use I have seen has also been high school students who use calculators to solve -5-3. While that may be acceptable for the Regents, it's nevertheless disturbing to behold. Surely a middle ground (with greater emphasis on estimation skills) can be reached?
ReplyDelete2. I have used some "fancy" TI calculators, and I have some experience with Mathematica and Java. While I've seen Geometer's Sketchpad, I haven't really gotten to play around with it but would definitely like to. Luckily, my placement school has a few SmartBoards, so I have been able to play with those. I'd still like to see what other software is available for them, though-- as they're completely awesome.
1. I agree that calculator usage for "-5-3" is ridiculous. I have had some teachers argue though that if this frees up some cognitive space for those students to be able to do higher level problems, bring it on. I perhaps take a middle ground.
ReplyDeleteHowever, I do think that calculators need not only function as arithmetic tools. In a class I took over the summer on computers and mathematics education, we spent a lot of time thinking about how me might use technology to help students gain deeper "structural" understanding. Developing an algorithm for a procedure takes a ton of understanding beyond simple procedure. This kind of activity can be done on excel sheets and on graphing calculators. Also, most mathematics done outside of traditional, pure mathematics is done using computing now. Engineers, architects, scientists, etc... all use computers to help carry out mathematical tasks. It would be great to help students gain these skills.
2. In terms of tech we would use in the classroom, I have used a couple of online resources for Java applets. Here are a few links:
http://nlvm.usu.edu/en/nav/vlibrary.html
http://www.fi.uu.nl/thinklets/
I've started getting really into Geogebra/Geometers Sketch pad and I would love to learn more about using it in the classroom.
I feel that, in terms of student learning, balance is the best way to go. Calculators really allow students to see some of the "cool" thins about math that we might be limited in showing them due to resources available. However, when we think about conceptual processes to achieve understanding there is nothing like a pencil and paper to really make you feel like, "Eureka!" or "Now I get it!" Calculators can really almost stunt a student's knowledge if not used sporadically.
ReplyDeleteI took a class almost completely on Geometer's Sketchpad and LOVE it!! My CT is opening all kinds of doors in the Smartboard world this semester too. I have used MatLab, Maple, Latex, and Mathematica in the past
I believe calculators are an important tool for students in high school - WHEN used appropriately. If too much freedom is given to students when using calculators, there is a dependence that develops, especially with students who struggle with operations. It is important for the skill to be taught before the students learn how to do the work on the calculator. For example, in Algebra 2 students need to be taught FIRST how to graph parabolas and how the graph moves when its say y=x^2 +5 before using graphing calculators for the example. I believe calculators are something teachers allow students to use for specific lessons, not something students can choose to use. I have seen way too many students multiply 1*-1 on the calculator, especially in Boston Public Schools or really any urban public school...
ReplyDeleteAs far as technology I have used, I took a course on technology in secondary math education and have worked a little with Geometers Sketchpad, the smart board, Mathematica, and designing websites.
I am very surprised how reliant students have become of graphing calculators. I was not allowed to use a graphing calculator for most of the tests I sat for in high school. Even in calculus, much of the work was completed without the help of a calculator. So when I see teachers tell students to just plug things into the calculator if they don't know how to do it with pencil and paper (such as fractions and simple arithmetic), it really bothers me. The calculator should be a tool in the student's arsenal, not a replacement for thinking and understanding.
ReplyDeleteAlso, many students learn tricks on the calculator or how to do certain things on the calculator but they do not understand the mathematics behind it. To them, it's like a black box. You input some numbers, press the magical buttons in a specific order, and BAM, here's your answer. I definitely feel that it's important to incorporate technology in your lessons but students should not solely rely on the calculator to do most of the work.
I don't really have much experience using technology in math education. I've mostly worked with graphing calculators and did some Matlab and Mathematica. I would love to learn more about Geometers Sketchpad and the smart board.
I agree with most of the above comments that it's surprising how reliant students are nowadays on calculators, and that I am not necessarily sure if this is a help for their learning and understanding. I'm working in a middle school right now, and to be honest, I don't see that any of the math that they do should require a calculator. I think that in general, at this point in their learning they should be doing any calculations by hand, and the math in the middle school does not really lend itself well to be supplemented by some of the cool stuff that you can do on the graphing calculator. I do think that in HS there are some interesting functions for calculators in statistics or modeling classes, but I pretty much think that that is the limit.
ReplyDeleteI'd really love to learn more about Geometer's Sketchpad (I've heard such great things!). Apart from that, I'm interested in exploring the SmartBoard a bit.
I think that calculators can be a great tool for students in mathematics, but, when students become too reliant on them for simple calculations (-5-3) calculators can actually slow students down. When students become dependent on their calculators, I worry that they also lose some of their number sense and ability to ask themselves the question "does this answer make sense?" If calculators are going to be used for more advanced mathematics, I think it is very important that students also have a sense of what it is that they are asking the calculator to do - otherwise it becomes, as Emily said, a black box. That said, graphing calculators can be a tremendous learning tool for generating graphs quickly, modeling different situations, and for use in statistics classes.
ReplyDeleteIn the past, I have used Mathematica, LaTeX, SPSS, S+ extensively. I'd like to learn more about Geometer's Sketchpad and using the SmartBoard.
The only time I think calculators are appropriate is when the students are doing extensive calculations with long strands of numbers and lots of decimal points. 3 digit multiplication and division does not eat up so much time that they need a calculator. It's good practice.
ReplyDeleteI've used 3-4 different stat programs, such as stata, eviews, and sas. I have also used mathematical and matlab a bit. I don't care too much about technology in the classroom, and any programs would be novel to learn but I'm not too concerned with them.
I really don't have much to add, I think everyone else hit the nail on the head. It is ridiculous and counterproductive to use calculators for basic math operations, especially ones that a student should already know how to do. The calculator should never be a crutch, but a learning aide.
ReplyDeleteAnd a calculator (especially a graphing one) can be very handy in acting as said aide in pretty much every high school math field. A teacher who can aptly incorporate some of the less known but important features into the content area is a good one. How that can be done, however, isn't so clear to me.
I agree that students should not use calculators for simple calculations and should probably not use them as much as they do in most secondary schools. However, I do think that calculators are important in high school classes for studying functions and their behaviors as well as as an aid in quick calculations in statistics.
ReplyDeleteI have not really used any math software aside from SPSS and excel. I would like to learn about any software that is good for generating graphs (I used excel for my unit plan, which was particularly annoying) and I would like to get practice using the smart board.
I also agree with everyone that calculators can be a useful tool in class. Unfortunately, I have yet to see it used "properly" in high school. The students almost always rely on the calculator more than they are suppose to. This dependency may come from middle school, which is why I think calculators should be banned altogether in middle school. In high school, calculators should be used only with the approval of the teacher; that means can not be used any other time.
ReplyDeleteI would like to know more about the smart board as I will probably be using one in the future. I also would like to learn more about programs that allow me to create 3-D graphs and shapes. It would come in handy in geometry and calculus.
I think I'll be the last person to agree with everyone else...Calculators are really good when you already know the math and are just using them to save time. I would definitely like to learn more about smartboard use, and possibly see someone who is an 'expert' go through some lessons and examples similar to what Rubenstein did for the classroom management session.
ReplyDeleteI don't think calculators should be allowed / encouraged to be used at the elementary school and the secondary school level, except for some very special tasks (i.e., statistic tasks for science or social study). The students need more practices in calculating by hands in order to gain "number sense". This "number sense" is critical for the students when they learn more advanced Math such as Number Theory, Algebra, and Calculus.
ReplyDeleteIn my student teaching, I have been using Smartboard to teach pre-algebra and probabilities. It's a great tool, easy to use, and the kids love it! I also used the Flash technology and created some animations by myself for one of the lessons. Also I'm exploring the possibilities of using database to track students' performance and auto-generate review worksheets that are tailored based on individual student's previous performance on weekly quiz. The school's computer network doesn't allow Oracle that really add tons of extra work.
ReplyDelete