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BLOG DISCUSSION #2
Is there a place for both computation and calculators in the math classroom?
Read the following articles.
http://www.nctm.org/uploadedFiles/About_NCTM/Position_Statements/computation.pdf
http://www.education-world.com/a_curr/curr072.shtml
http://www.sedl.org/scimath/quicktakes/qt9803.html
After reading these articles and reading chapter 7 on your book:
* What is your position on this topic?
* Would you start to use calculators regularly in your mathematics classroom?
* Describe some of the benefits of using calculators regularly? Which on seem to you most compelling?
* What are some arguments against using calculators? Answer each argument against calculators as if you were giving a speech at your PTA meeting or arguing for regular use of calculators before your principal.
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I absolutely believe that there is a place for both calculators and computation in the math classroom. After all, I learned both myself when I was going to school. I agree with the NCTM in their view that students need to master calculator skills, as well as mental and written calculations, in order to succeed as mathematicians.
ReplyDeleteIf I were a math teacher, I would use calculators (as well as other technology) in my classroom. In the current economy, I think that it is extremely important that children become comfortable with using technology. Especially a technology as widely used as the calculator. Calculators can help students with problem solving skills and allow them to concentrate on mathematical concepts instead of spending most of their math practice time on computation.
The arguments against using calculators come down to fear that if students use calculators, they will not learn to compute on their own, they will not learn the mathematical reasoning behind computations, and they will have an exaggerated confidence in their math abilities. To me these are all arguments against poor teaching, not against calculators. If teachers are going to introduce calculators (or other technology) into the classroom, they must provide the proper supports and continuously assess student understanding, just as they would with any other teaching method.
Kylah Torre
I agree with Kylah that there is room for both calculators and computation in the classroom. Surely it is a waste of everyone's time to make students consistently do three- and four-digit multiplication problems when completing other higher-order tasks; however, what I have found is that calculators often do not help students because they do not always know HOW to solve the problems in the first place. Many have never mastered the operations, strategies, or procedures necessary to carry out many more demanding conceptual problems. If a student does not understand how to approach a problem, a calculator serves no useful purpose. Furthermore, needing a calculator to figure out something like 8x6 just shows a lack of basic knowledge, not a conceptual gap in understanding. Many (if not most) students understand, I think, the "concept" behind multiplication but they have never, for one reason or another, memorized the multiplication tables. If this is the case, then using a calculator is fine. But if students do continually rely on one for all their computations, they will need a calculator as a crutch, and that should not be its function. They cannot always use calculators on all tests, so not knowing 9x5 is an avoidable pitfall. I think students should be able to use calculators, but I also feel they should be "drilled" or otherwise taught the times tables up to ten at least, before being thrown the "life preserver" of a calculator for all their computational requirements.
ReplyDeleteMichael makes an important point about the role of teachers: teachers are still held accountable to teach the basics and not rely on technology themselves! Technology and calculators definitely have a place in the classroom but it is up to the teacher to guide the student in its application.
ReplyDeleteNCTM believes that "A balanced mathematics program develops students' confidence and understanding of when and how to use these skills and tools. Students need to develop their basic mathematical understandings to solve problems both in and out of school."
I feel as though a lot of teachers do not balance the basic understandings and practice with technology. In many cases, I feel that it is the basic understanding time that looses out to the more engaging technology because it's easier...for everyone.
At what point is it that the teacher being an enabler and masking a student's difficulties rather than addressing them?
I agree with Kytte, Michael, and Nicole who have argued that there is a place for calculators within the classroom; however I do not feel that it is appropriate to use a calculator on a regular basis on the elementary school level. Proponents of using calculators in classrooms argue that calculators “allow students to spend less time on tedious calculations and more time on understanding and solving problems” and that they “help students develop better number sense” (Linda Starr). While I believe that this statement is true when students are in junior high and high school and learning more complicated math such as algebra, trigonometry and calculus, I do no believe that they are helpful in elementary school when students are building mathematical foundations. I believe all students in elementary school need to focus on mastering mental math and performing paper and pencil operations. Relying on a calculator can definitely become a hindrance. Although research has shown that “Children who use calculators on tests have higher scores in both basic computation skills and problem solving” (SEDL), I still refuse to use calculators in my classroom on a regular basis because my students are not allowed to use calculators on state exams. What happens to children who use calculators throughout the year but are not allowed to use calculators on major exams, how do they perform on test? I seriously doubt that they will perform well because an over reliance on calculators can lead to students who “produce students who can't perform basic tasks without a calculator” (Linda Starr). Thus I only allow my students to use calculators when playing math games on Fridays.
ReplyDeleteI agree with most of what everyone else said. There is a place for both computation and calculators. I teach ninth grade algebra and therefore students rely on calculators to do computations while working on understanding the problem. They are taught the number of ways to solve a problem including how to do it on the calculator. But they are allowed to use them on the regents exam. However, at the elementary level I do agree that it is important for students to learn their math facts and mental math. This way when they use a calculator they can then know if the calculator answers is reasonable. The calculator can also be a good tool to check answers. I think that teaching them to use a calculator properly and other technology is an important skill that they will need. I do, though, see why some may fear an over reliance on calculators however, calculators should not be used in every situation and as Kylah said teachers still need to assess student understanding.
ReplyDelete"A skillful teacher knows how to help students develop these abilities in a balanced program that focuses on mathematical understanding, proficiency, and thinking. The teacher should help students learn when to use a calculator and when not to, when to use pencil and paper, and when to do something in their heads."
ReplyDeleteThis is what I have found most compelling in the article. The whole point of what the NCTM has set as a standard is that the calculator is a tool. If students are improperly using the tool, it is our job as educators to take some ownership of how to teach them to effectively use the tool.
There are plenty of technological tools that they are using effectively to communicate. This is because someone took the time and steps necessary to teach them these skills. I can speak from experience in that I see Twitter messages from students who barely read or spell but somehow are managing to try to document every aspect of their life. I recently had to ignore a friend request of a student who was reading on a 1st grade level and looking for facebookd friends. She had uploaded pics and the works. Someone had to have taken alot of time to show her all these details.
The calculator is just one arm of the many bodies of technological tools that can increase understanding. However, we as teachers have to show them how to use it and correct any misconcetions they may have recieved previously from educators who did not take the time to explain.
I believe that there is room in the classroom for calculators and computation, just as in the working world. I think it would be unfair to a student's education to deny them access and instruction on either. We use both, computation and calculators, in are lives, whether in work, school or personal business. Students need to have a well rounded education that includes technology. To deny them this would be doing an injustice to them in the future as future citizens and worker. It is our jobs as teachers, to expose them to this technology to 1) take the excitement out of this new 'gadget' and see that it is a work tool 2) to be fluent and comfortable in using the calculator for various types of problems, in various situations and 3) to give them equal opportunity as other students to succeed. It is one more tool that they can use when they graduate and become productive members of society.
ReplyDeleteI agree with most of the comments that have been posted so far. I think the it is important as an elementary school teacher that the fundamental concepts be taught and reinforced before any technology is introduced. On the elementary school level children must still develop their number sense and mental math skills so that they can have a sound fundamental knowledge of mathematics. I think it is appropriate to use technology to reinforce or help master skills that have already been taught. It would not be appropriate to use technology in the very first lesson of multiplication for example but once the concept has been mastered use technology to help reinforce the skill. The problem that I have is that the funding for technology is often absent in the public school setting. In my classroom last year for example the two computers that were available did not have access to the internet therefore the ability to reinforce or master any skill that was taught in the classroom was limited. I think that the balanced approach of the NCTM position is a logical approach when debating the use of technology in the classroom.
ReplyDeleteCalculators in the classroom is beneficial for students in all grade levels.
ReplyDeleteThe article states that "it allows students to spend less time on tedious calculations and more time on understanding and solving problems "(Starr,2002). Students need to know and understand how to solve problems mentally and with the use of technology. Teachers should incorporate different ways to solve problems and using calculators is one way to solve problems such as geometry,long addition or subtraction problems that might be difficult for some students mentally so it just depends on the student and how the teacher wants to use the calculator in the classroom. Surely it will not be used as a "crutch" but one of the tools the student can use to solve a problem.
Living in a world of technology today, students need to know how to use a calculator in order to get a job and for personal use as some have agreed is true already.
I agree with Kristin that it would be an injustice to students if we did not teach them how to use calculators. In order to compete in the job market they will need to be comfortable with using various types of technology, not least of which is a calculator. A calculator (or an internet-based application and or data processing software) is an option for solving math problems and should be presented to students as such. As I said before, it is our job as teachers to monitor calculator use and to assess students regularly to be sure that they understand the concepts behind the math they are using. We should encourage them to use a wide variety of strategies to solve problems, calculators included.
ReplyDeleteI agree with shelanthia and dfbb3675 that calculators have less of a place in elementary classrooms where the emphasis should be on mastering basic mathematical concepts. I love shelanthia's idea of introducing calculators through math games.
Kylah Torre
I think people have done a fine job of discussing the do-calculators-have-a-place-in-the-classroom issue. It seems, at this point, that Professor Persaud has posed other questions that she would like addressed so I will list them here and get moving on a newer thread...
ReplyDeleteCan you imagine a classroom where the only thing your student will need is a laptop, no textbooks, notebooks or even paper?
Do you see more students completing High School with these type of programs/schools?
What do you think are the advantages and disadvantages of programs/schools like this one?
Would you like to teach in a school like this? Explain.
Yes, I can certainly imagine a classroom with only laptops and no paper. I'd guess they already exist in some places (probably more affluent socio-economic environments than those in which most of us teach).
Do I see more students graduating in an atmosphere like this? Perhaps. I do think many/most students are more comfortable on a computer than with their noses ina textbook, but I'm not sure it would compel more students to be engaged by education--although I hope it would benefit them in this way.
One advantage is that a school like the one described might better prepare students for the current technology-based job market. Another advantage is the obvious immediacy of access to a far greater base of information.
Would I like to teach in a school like this? Yes and no. It might be fun, but it might also require me to stay on top of all the latest computer/educational technology, and I already have my hands full learning to become a competent educator in this relatively new century...
I can imagine a classroom with only labtops. I believe it will exist soon here in the city and other parts of the world as Michael has said.
ReplyDeleteI can also see high school students graduating from this type of program because it can prepare them for the real world. Living in the world today, students need to have knowledge and experience with computers in order to get a job.
I would like to teach in a school that offers this type of setting because it would
1) help students learn through technology 2) teachers can easily adapt the curriculum for each learner 3)students will be less dependent on the teacher 4)it would be fun to see the outcome of this program if it ever comes into existence.
I agree with everyone in terms of how essential technology is in the classroom. Our kids have grown up with the internet and are more connected (wired) now than any other generation. I truly believe that the way to reach them is with technology. More importantly, most careers that require a solid knowledge of math (Engineering, Medicine, Technology Consultants), require employees to work with software and computers.
ReplyDeleteThere are already a few high schools in the city that have labtops for every single student and they've shown that the kids are more successful in this type of environment.
The only downturn is that kids would have to be restricted from using sites such as MySpace and IM checking their email constantly.
Using interactive sites could help with this.
I've used webquests in class and it's worked wonders!
I just read Michael's last comment....
ReplyDeleteI totally see a world where all kids would need is a laptop, internet connectivity and a cell phone perhaps.
Having access to info. is everything these days but doesn't eliminate the place of classrooms and teachers. I still think kids benefit from being in a room with their peers and having some sort of instruction.
But they could look things up quickly and take notes faster and with better accuracy if they were wired 24.7 in the classroom.
What do you guys think?
I read a psych. article recently that talked about internet anxiety disorder and how a lot of students suffer from it. Think: Getting anxious when u haven't checked your email within 24 hours... Or haven't been able to surf the web within 24 hours. That feeling you get, of being un-connected, lost, etc. actually has a name- It's a disorder.
I thought it was interesting but in this day and age you really can't NOT be connected. I know personally it's made my life a lot more easier and as long as you know when too much is too much and can go 'off the grid' once in awhile, then I think you'll be ok...
Thoughts? Can this affect our kids in the classroom?
I see many negative aspects to using only technology in a math classroom. The first being, that many of my fourth grade students do not have computers at home and are therefore not computer literate. So the time that we would be doing math would be spent in teaching them how to use the computer. Our school's class schedule this year will not allow for that. I also love and value the one on one interaction of the students when they are working together on paper, drawing and inventing and "making meaning" together. This would be lost. Another problem is that technology has already replaced valuable individual time at home between moms/dads and students spending time reading and doing homework together. My students are being held hostage by a tv all weekend, and their moms don't even get off their cell phones when they pick them up from school to say hello. I feel that this has made my students very emotionally needy, and they need that intellectual human contact with their their teacher and other students to learn. This also helps them practice face to face group interaction/social responsibility, etc. In that same vein, I think that calculators are appropriate in middle/high school after elementary teachers have gotten them solid on their mental computation skills. I use the Smart Board in my room, which gives gives them a great opportunity to visualize the math concepts, and to have hands-on technology practice. After taking our math class, I really began to appreciate the value of the connection between math and writing. This year I will have my students keep a math journal in which we will be able to have a running dialogue about what they are learning, any insights they've had after a lesson, and any lingering questions. It will help us to keep the math conversation alive (like this blog) and help my kids with their much needed writing practice.
ReplyDeleteI do believe that it is very possible that soon there will be classrooms that completely rely on laptops and that they probably already exist. They would definitely exist in more affluent schools and further widen the educational gap, thus causing the need for even more dedicated and thorough teachers to work in underprivileged schools (Yea Teaching Fellows!). However I would not be interested in teaching in such a school for a few reasons. The first one being that I think it could be even harder to maintain the class’ focus if I have to constantly compete with a computer. I remember taking computer classes throughout my school career, or having a normal class in a computer room, and most kids did not pay much attention to the teacher because they were far more interested in playing games, checking email or chatting with friends. I also have an issue with the logistics of it all; if we expect students to use laptops for the entire day at school, then would the students be provided with laptops to take home as well? What happens if a laptop gets damaged, who is responsible for it? Lastly, as Michael said, working in that type of environment also requires more work for me. I am still adjusting to being a teacher, I do not think I could handle having to learn all the latest technologies as well.
ReplyDeletei agree with Jac O casey and what she had stated about the negative affects of technology (not just on students but society as a whole.) As what jessie pointed out people have grown to have disorder from being addicted to technology and that is unhealthy too. In the classroom we do have to emphasis human interaction. (teachers and students and students and students interaction) The students need to know how to communicate and this is a basic skill just like adding and subtracting that they need to learn and putting them on computers is not a way to learn communication skills. At the same time i do realize that technology is important for advancement, but it should be a separate class on its own. Learning to use technology should not get in the way of learning math skills or learning how to read.
ReplyDeleteI agree with most everybody on the laptop topic. computers in the classroom is becoming more common and it does have its benefits. Students do need to learn how to use technology as it will help them in the real world. I like the idea of using computers to differentiate material with out it being so obvious and that they are able to have a place for assignments and parent contact. also having greater access to information. However, this can be done without all the instruction done on the computer. such as the computer class or only using the computers for certain lessons or activities not all. I think the anxiety issue is a good point to bring up as well as the learning to communicate issue. I also agree that there is something special with the one on one or group work, drawing and creating other pieces of pencil and paper work. I believe that students have a sense of pride in their work when they can develop a piece of writing, that they have written, revised, etc and then typed or even picking up a book to read.
ReplyDeleteI think it’s important for students to use calculators in the later grades, high school. The earlier grades should of course focus on basic math concepts and computations but many students in high school must focus on higher level thinking concepts. At this point in their education students should be able to do basic computation. Also, calculators and other technology are good ways to differentiate for students with learning disabilities.
ReplyDeleteLooking through the slideshow provided by the Reuters article I noticed that every photo is an image of a child directing their attention to their own computer screen. That seems pretty insular. I wonder if all school subjects would follow the computer math model? So many funny, fascinating, revelational things took place in my class this year as a result of our group idea exchange. Ken Robinson has a wonderful new book called "The Element" that is about the huge range of intelligences and ways that people learn. He says that learning is "diverse and dynamic." As a mom and an educator, I have found that the quickest way to engage a child is to help them figure out what they love and move in that direction. That process requires enthusiasm, support, and ATTENTION. I like to visit classrooms a lot, and the most successful classrooms that I have visited are the ones where there is an emotional mobius between teacher and students. This connection would not be fostered by a classroom where each student would be focused on their own personal screen. Another point which was made by the group against calculator use in the Education World article was that one of our goals as teachers is "to train and discipline the mind and to promote logical reasoning." This skill is found in the process of group interaction where students work together to test their thinking and to be able to logically justify their answers. And then there is a lovely paper trail of all of their beautiful thinking. The bottom line for me as a special educator is that our kids need a lot of emotional and intellectual scaffolding to get them to SEE themselves as students so that they will engage in their own educations. Good teachers are the answer, not computers.
ReplyDeleteI absolutely agree with Jac's comment. I believe that the most effective classrooms maintain a strong relationship between teacher and students, and allow for students to explore their interests in math. However, often times it is difficult to find topics of interests for students, especially in math. What sixth grader actually strikes an interest in dividing decimals?
ReplyDeleteAs special educators, it is crucial to engage in direct, explicit teaching. Although explicit teaching does not coincide with NCTM's philosophy, our students need direction instructions when doing math. Calculators and computers are tools that help directly and explicitly teach students mathematics.
In addition, special educators have difficulty teaching basic mathematics (multiplication and addition skills), while keeping up with the curriculum schedule. Calculators allow students who cannot memorize multiplication and division facts, progress through the curriculum. For example, with the use of a calculator they can participate in more complex math such as algebra or geometry- the calculator will help them compute basic algorithms while learning new concepts.
Of course the goal is for all students to know and understand basic math facts. But in a school system that focuses on test scores and performance it is essential to complete curriculum as outlined by state standards. Using calculators will aid both teachers and students to grasp new material despite basic academic deficits.
As with most "teaching methods" I believe there are both pros and cons to a classroom taught entirely via computer. I know from first hand experience as all of my students currently have their own school laptop that technology brings on a new motivation for students. When it comes to my sixth graders I think it makes them feel grown-up and sophisticated, something they do not feel often. I try to incorporate the computer into my lessons as much as possible because having them actually look forward and excited about completing n assignment is half the battle. I am all for anything that will help them learn better.
ReplyDeletea negative side having computer only classrooms is that fact that most of the students lack the skills needed to actually operate the computer. While I agree that teachers may have to put in a little extra work to teach them these skills in addition to academic concepts I believe it is quite worth it. In a time where we are turning more and more towards a technology-run society it will be necessary to have these skills in order to function. It is time that schools start incorporating technology instruction into the curriculum and daily schedule.
Computer's are absolutely a way to engage students in classroom actitivities. They can be an important tool for strong classroom management. Towards the end of the year, my students were given personal laptops and they were silent throughout class time as they played games and blogged online. The addition of the laptops and the online games helped students who lacked basic algorithm skills memorize and learn math facts. In this case computers are a positive and powerful tool in the classroom.
ReplyDeleteBy contrast, I believe that when computers take the place of direct teacher instruction students learn very little. A teacher has the capability of presenting information in differentiated ways, which is so critical for special education. Special education teachers know how to adapt and change curriculum based on student need, interest, and capability. While a computer can provide supplemental help, materials, and tools for presenting information in alternative ways, they cannot replace teacher instruction. I find it very disturbing that many argue for simulated teaching instruction when students are strugling with the current instruction they are given.
I agree with the comments that have been made regarding the use of computers in the classroom whether its the laptop or desktop it can be an important learning tool but it does not and should not take the place of a teacher instruction. The differentiation that needs to take place within any classroom at any grade level is very important that this come from a teacher. A teacher can tell when a class is ready for more advanced work in a subject area or if there is additional review needed this can't be done by a computer. When mathematic tools including the computer are used appropriately they can help to build a student's confidence in the subject area which is an asset to any classroom. Regardless of the subject area as teachers we strive to bring students to a place of mastery and confidence in the subject area of study.
ReplyDeleteAs far as this debate is concerned I would consider myself a moderate. Calculators should be used in the classroom but only as a tool of differentiation. As educators we all have students that struggle with number sense and standard calculations. These students must be allowed to use calculators so that they are exposed to more difficult problems. However, the students that don't struggle with computation must be allowed to compute basic facts to prepare them for instances in life where they may not be able to use a calculator. It is also our job as educators to help students that need calculators to be less dependent on them as the school year progresses. Lastly, calculators are good in the classroom but can be harmful to students if they are over used.
ReplyDeleteI agree with Maya's comments about the important role that special education teachers play in the instruction of students with special needs. At this point in time we do not have any technology that can take the place of the special educator. However, in the future I do see a world where the computer will play a very important role in instruction for all students. Educators and program developers will create technology that can reach all students in the future.
ReplyDelete