Explain at least three ways that technological tools have affected the mathematics curriculum and how it is taught. Give examples to support your explanation.
In classrooms that I have been in technology plays an important role. Jings have been used as an teacher demonstration for students to access a reteaching or in support of homework. Graphing calculators and excel spreadsheets to graphing have been great tools to help students visualize the results of their math data. Also the interactive white board or the simplicity of the elmo projection have allowed students to use technology to see other students work, discuss work, and develop strategies together as a class. The list of technology uses in the class from programs that reinforce or assess students math abilities such as MobyMax, IXL, or a million others is common practice possibly over used and under utilized. Teachers using technology as meaningless fillers is common place in my opinion. The teacher that reviews the feedback results of the program and adjust their teaching or alters the next assigned section is few that I have worked with in math classes. The new generation of programs that adapt or alter the progress to be "just right" for the students progress of skills I hope will not be just set free without review and human interaction/altering based on a teachers knowledge of sequence and student skills. Think about how formative assessment drives instruction...and we might hope that a teacher is not allowing the technology driven curriculum to totally drive the instruction as all students are different and learn in different manners. Sorry about the digression as a special educator that has seen both the misuse of technology and the success of technology being used in the classroom. Technology can be a great asset in aiding students in developing new knowledge, to be a resource to access from anywhere when a teacher is not present, to be a formative assessor, to be a practice/skill reinforcement, to be discussion driver for a class, a presentation of student work or leading thinking for discussion, and as a final assessment tool(I do not see much of this but think that having teachers at times not have to correct papers..time! but to use the saved time to review the errors in order to move forward with instruction. I have observed teachers learning how to use technology, it is an ongoing development that needs more attention and help from colleagues to understand how technology fits in to the ever changing classroom should be a monthly after school session as technology is changing so fast.
There does seem to be “a million” different types of online programs and technologies to utilize for mathematical purposes! I had no idea… I am very appreciative that this chapter highlighted some of the tried and true ones, as I could see that it would take too long to weed through them all myself. I have little experience with online math programs, except for what I’ve done with my son from his school and what I’ve explored in this class (like Conceptua Math and another great one I guess I didn’t bookmark that I played around with to practice decimals and fractions). I have to admit, I immediately searched for the Desmos graphing calculator as soon as I read about it! I have always loved playing with calculators. Maybe it’s pressing the buttons or playing with numbers, whatever it is, my son loves it too. I was happy to read that this is a good sign in terms of future mathematical skill! I think that using technology in some aspects of math class, along with actual teaching of course, is very useful and fun. What a great way to get students interested in math if they are not; most kids like video games and screen time, right? It is a slippery slope, however, and like most of you have said, I do not think that it should supplant good old fashioned teaching any day. Yet, it clearly has its uses in the classroom. I think it is reasonable to allow limited mathematical extensions through technology, as long as students are getting the methods and have an understanding of the processes they are using online. We can’t avoid technological advances, no matter how much I’d like to. In today’s world, it would be harmful to students if we did not allow them such uses and it would place them behind other students who knew the technology and how to use it. There is a lot to learn about it, especially all the things that these programs can do now. Wow, the possibilities really are endless!
Technology has advanced the way teachers teach mathematics by providing tools, games and interactive opportunities to enhance understanding. I really appreciated the way the authors used Fey's quote to describe how best to use technology. "Teachers need to carefully select and design learning opportunities for students where technology is an essential component in developing students' understanding, not where it is simply an appealing alternative to traditional instructional routines." A well thought out approach, I believe is essential when using technology anytime with children. I've been lucky to observe teachers using technology-supported learning in well thought out lessons. Specifically,I have seen how students and teachers use document cameras to share their written work with the entire class. I've seen teachers use YouTube videos to explain concepts like PI to students. As a parent, I have experienced both positive and negative uses of Strategy based drill and practice technology such as FASTT Math. Both my children love using the computer to practice their facts on FASTT Math, but many times I see them choosing to find the easiest level in order to get a 100% instead of challenging themselves with more difficult levels. It's all about the score and not about the learning. Of course,we have talked about it and I realize I need to learn more about the technology before judging. We all have our biases, I guess. One activity I read about in this chapter that seems interesting is the digital white boards. Currently, my daughter uses traditional individual white boards in math class in 4th grade. Students sit in a circle and work problems the teacher puts on the smart board or the main white board. They then turn and talk with partners and finally use their white board to share work with the class. Seems fun and easy. The digital white board offers teachers a way to capture that work and audio explanation and archive or share electronically. This data could be used as a wonderful assessment tool.
I agree with Rachel that the digital white boards sound like a useful tool. Up until this reading I have never heard of a digital white borad. I imagine that with the growing use of technology in schools that they will become a more commonplace tool. I wonder if there is an app that could be used in a similar way on ipads, which are a tool that many students and teachers are already familiar with. Ipads are also more versatile and can be used for more than one application, whereas the digital white boards might be more limited.
I fear mernickg's comment, "Teachers using technology as meaningless fillers is common" is too often the case. Furthermore, I have heard often that a technology brought into the classroom should add value to the instruction, not simply allow students to do something digitally that they could do just as well with pencil and paper.
Table 7.1 identifies seven 'genres' of mathematical activities that combine the strategic use of technology with effective pedagogy. I see effective pedagogy as essential, and often times is the missing element when technology enters the classroom. Regardless, in my limited classroom experience I've seen a number of these genres used effectively. The use of elmos has supported Genre 1. Consider and Make Sense of New Information; specifically, to engage in discourse with peers, teachers, or experts. Although it was a science class, the use of Skype to connect with an expert in the field was a great way to hook students' interest. I would really have to think hard about the professionals I'd connect with in this way to share their use of mathematics - maybe I could find a baker that uses percentages.
All three schools I have worked in during the past 18 months use MobyMax as a skills-building tool. Such a use of technology falls under Genre 2. Practice Various Techniques.
Until I read this chapter I was strongly opposed to students using calculators. While they could be used to calculate an answer, a student must first represent their mathematical reasoning and mathematical expression sufficiently to get full credit. After reading this chapter, I was convinced that there is a place for calculators, assuming there is effective pedagogy associated with their use. For example, "if the primary purpose of the instructional strategy is to practice computational skills, students should not be using a calculator. On the other hand, students should have full access to calculators when they are exploring patters, conducting investigations, testing conjectures, solving problems, and visualizing solutions."
I think for me the challenge will be assuring all students have a solid grasp of the computational skills before shifting to/allowing calculators for the exploration of patters, etc.
I agree with Dean and mernickg that technology can easily be incorporated into the classroom as a filler and take away the value of mathematics. Teachers must make sure that when technology is brought into the classroom it is being used in a way that enhances the lesson being taught. I also agree with Dean that the section of the chapter that discussed calculator use was very interesting. Prior to this reading I was on the fence about students using calculators during math. The book did a great job describing when calculators benefit students learning and when students should rely on pencil and paper math to work through a problem.
“Technology should be seen as an integral part of your instructional arsenal of tools for deepening student understanding” (Page 128) One tool that plays a critical role in mathematics curriculum is the calculator. When used effectively calculators provide students with the opportunity to engage in challenging mathematics that would otherwise be unavailable to them. Situations involving computations that are beyond a student’s ability without the aid of a calculator are not necessarily beyond their ability to think meaningfully. After all, the calculators can only calculate what information is entered by people. By exposing students to calculators and teaching when it to use them they will have more confidence when solving challenging math problems. There are many ways to incorporate calculators into math curriculum in order to support and expand students thinking. For instance, students can practice their basic facts and explore math concepts such as skip counting or decimals. I also think that the calculator provides students with a tool to check their work quickly. As a commonly used tool, I think it should definitely be used in schools as a supplemental tool to the curriculum being taught. Another tool that I have seen widely used in math curriculum are programs used to practice skills they have been taught. Programs such as Xtra Math develop fact fluency and automaticity through systematic sessions. These programs can be easily incorporated into the math curriculum in short bursts of time and are an exciting game for students to practice various techniques they have learned. Of course, it is important to provide students with the opportunity to apply the mathematics they are learning to the real world. An exciting way to do this is to use tools like spreadsheets, graphing calculators, virtual manipulatives, and data collection devices in order to to create mathematical representations of a real-world situation. Students could work on projects in groups or individually to explore a topic they are interested in or related to another area they are studying in school. The use of technology is an integral aspect of math and needs to be incorporated in math curriculum.
In classrooms that I have been in technology plays an important role. Jings have been used as an teacher demonstration for students to access a reteaching or in support of homework. Graphing calculators and excel spreadsheets to graphing have been great tools to help students visualize the results of their math data. Also the interactive white board or the simplicity of the elmo projection have allowed students to use technology to see other students work, discuss work, and develop strategies together as a class. The list of technology uses in the class from programs that reinforce or assess students math abilities such as MobyMax, IXL, or a million others is common practice possibly over used and under utilized. Teachers using technology as meaningless fillers is common place in my opinion. The teacher that reviews the feedback results of the program and adjust their teaching or alters the next assigned section is few that I have worked with in math classes. The new generation of programs that adapt or alter the progress to be "just right" for the students progress of skills I hope will not be just set free without review and human interaction/altering based on a teachers knowledge of sequence and student skills. Think about how formative assessment drives instruction...and we might hope that a teacher is not allowing the technology driven curriculum to totally drive the instruction as all students are different and learn in different manners. Sorry about the digression as a special educator that has seen both the misuse of technology and the success of technology being used in the classroom. Technology can be a great asset in aiding students in developing new knowledge, to be a resource to access from anywhere when a teacher is not present, to be a formative assessor, to be a practice/skill reinforcement, to be discussion driver for a class, a presentation of student work or leading thinking for discussion, and as a final assessment tool(I do not see much of this but think that having teachers at times not have to correct papers..time! but to use the saved time to review the errors in order to move forward with instruction. I have observed teachers learning how to use technology, it is an ongoing development that needs more attention and help from colleagues to understand how technology fits in to the ever changing classroom should be a monthly after school session as technology is changing so fast.
ReplyDeleteThere does seem to be “a million” different types of online programs and technologies to utilize for mathematical purposes! I had no idea… I am very appreciative that this chapter highlighted some of the tried and true ones, as I could see that it would take too long to weed through them all myself. I have little experience with online math programs, except for what I’ve done with my son from his school and what I’ve explored in this class (like Conceptua Math and another great one I guess I didn’t bookmark that I played around with to practice decimals and fractions). I have to admit, I immediately searched for the Desmos graphing calculator as soon as I read about it! I have always loved playing with calculators. Maybe it’s pressing the buttons or playing with numbers, whatever it is, my son loves it too. I was happy to read that this is a good sign in terms of future mathematical skill!
DeleteI think that using technology in some aspects of math class, along with actual teaching of course, is very useful and fun. What a great way to get students interested in math if they are not; most kids like video games and screen time, right? It is a slippery slope, however, and like most of you have said, I do not think that it should supplant good old fashioned teaching any day. Yet, it clearly has its uses in the classroom. I think it is reasonable to allow limited mathematical extensions through technology, as long as students are getting the methods and have an understanding of the processes they are using online. We can’t avoid technological advances, no matter how much I’d like to. In today’s world, it would be harmful to students if we did not allow them such uses and it would place them behind other students who knew the technology and how to use it. There is a lot to learn about it, especially all the things that these programs can do now. Wow, the possibilities really are endless!
Technology has advanced the way teachers teach mathematics by providing tools, games and interactive opportunities to enhance understanding. I really appreciated the way the authors used Fey's quote to describe how best to use technology.
ReplyDelete"Teachers need to carefully select and design learning opportunities for students where technology is an essential component in developing students' understanding, not where it is simply an appealing alternative to traditional instructional routines." A well thought out approach, I believe is essential when using technology anytime with children. I've been lucky to observe teachers using technology-supported learning in well thought out lessons. Specifically,I have seen how students and teachers use document cameras to share their written work with the entire class. I've seen teachers use YouTube videos to explain concepts like PI to students. As a parent, I have experienced both positive and negative uses of Strategy based drill and practice technology such as FASTT Math. Both my children love using the computer to practice their facts on FASTT Math, but many times I see them choosing to find the easiest level in order to get a 100% instead of challenging themselves with more difficult levels. It's all about the score and not about the learning. Of course,we have talked about it and I realize I need to learn more about the technology before judging. We all have our biases, I guess. One activity I read about in this chapter that seems interesting is the digital white boards. Currently, my daughter uses traditional individual white boards in math class in 4th grade. Students sit in a circle and work problems the teacher puts on the smart board or the main white board. They then turn and talk with partners and finally use their white board to share work with the class. Seems fun and easy. The digital white board offers teachers a way to capture that work and audio explanation and archive or share electronically. This data could be used as a wonderful assessment tool.
I agree with Rachel that the digital white boards sound like a useful tool. Up until this reading I have never heard of a digital white borad. I imagine that with the growing use of technology in schools that they will become a more commonplace tool. I wonder if there is an app that could be used in a similar way on ipads, which are a tool that many students and teachers are already familiar with. Ipads are also more versatile and can be used for more than one application, whereas the digital white boards might be more limited.
DeleteI fear mernickg's comment, "Teachers using technology as meaningless fillers is common" is too often the case. Furthermore, I have heard often that a technology brought into the classroom should add value to the instruction, not simply allow students to do something digitally that they could do just as well with pencil and paper.
ReplyDeleteTable 7.1 identifies seven 'genres' of mathematical activities that combine the strategic use of technology with effective pedagogy. I see effective pedagogy as essential, and often times is the missing element when technology enters the classroom. Regardless, in my limited classroom experience I've seen a number of these genres used effectively. The use of elmos has supported Genre 1. Consider and Make Sense of New Information; specifically, to engage in discourse with peers, teachers, or experts. Although it was a science class, the use of Skype to connect with an expert in the field was a great way to hook students' interest. I would really have to think hard about the professionals I'd connect with in this way to share their use of mathematics - maybe I could find a baker that uses percentages.
All three schools I have worked in during the past 18 months use MobyMax as a skills-building tool. Such a use of technology falls under Genre 2. Practice Various Techniques.
Until I read this chapter I was strongly opposed to students using calculators. While they could be used to calculate an answer, a student must first represent their mathematical reasoning and mathematical expression sufficiently to get full credit. After reading this chapter, I was convinced that there is a place for calculators, assuming there is effective pedagogy associated with their use. For example, "if the primary purpose of the instructional strategy is to practice computational skills, students should not be using a calculator. On the other hand, students should have full access to calculators when they are exploring patters, conducting investigations, testing conjectures, solving problems, and visualizing solutions."
I think for me the challenge will be assuring all students have a solid grasp of the computational skills before shifting to/allowing calculators for the exploration of patters, etc.
I agree with Dean and mernickg that technology can easily be incorporated into the classroom as a filler and take away the value of mathematics. Teachers must make sure that when technology is brought into the classroom it is being used in a way that enhances the lesson being taught.
ReplyDeleteI also agree with Dean that the section of the chapter that discussed calculator use was very interesting. Prior to this reading I was on the fence about students using calculators during math. The book did a great job describing when calculators benefit students learning and when students should rely on pencil and paper math to work through a problem.
“Technology should be seen as an integral part of your instructional arsenal of tools for deepening student understanding” (Page 128) One tool that plays a critical role in mathematics curriculum is the calculator. When used effectively calculators provide students with the opportunity to engage in challenging mathematics that would otherwise be unavailable to them. Situations involving computations that are beyond a student’s ability without the aid of a calculator are not necessarily beyond their ability to think meaningfully. After all, the calculators can only calculate what information is entered by people. By exposing students to calculators and teaching when it to use them they will have more confidence when solving challenging math problems. There are many ways to incorporate calculators into math curriculum in order to support and expand students thinking. For instance, students can practice their basic facts and explore math concepts such as skip counting or decimals. I also think that the calculator provides students with a tool to check their work quickly. As a commonly used tool, I think it should definitely be used in schools as a supplemental tool to the curriculum being taught.
ReplyDeleteAnother tool that I have seen widely used in math curriculum are programs used to practice skills they have been taught. Programs such as Xtra Math develop fact fluency and automaticity through systematic sessions. These programs can be easily incorporated into the math curriculum in short bursts of time and are an exciting game for students to practice various techniques they have learned.
Of course, it is important to provide students with the opportunity to apply the mathematics they are learning to the real world. An exciting way to do this is to use tools like spreadsheets, graphing calculators, virtual manipulatives, and data collection devices in order to to create mathematical representations of a real-world situation. Students could work on projects in groups or individually to explore a topic they are interested in or related to another area they are studying in school.
The use of technology is an integral aspect of math and needs to be incorporated in math curriculum.