I am finishing up teaching polynomials to my Algebra 2 classes. We are discussing the Rational Root Theorem (i.e. p's and q's) right now. When I presented the material on Friday, I went through the whole process - finding the factors of p, finding the factors of q, finding the p/q values and testing using synthetic division. As much as I like doing synthetic division, I had forgotten how frustrating this process is for students - it is tedious and they know by now that they can find the zeros by finding the x-intercepts of the graph.
So, as I reflected over the weekend and into this morning, I decided when I assess them on this learning target, I am only going to ask them to identity the factors of p and q and the p/q values. I am not going to ask them to fully find the zeros of the polynomial from that list. The more I thought about it, the more it became clearer to me that if they were going to have to find zeros from a polynomial students would have access to technology (such as a graphing calculator or Desmos). As I was working with students today and reflecting on this learning target, I kept coming back to this question: How do we determine when it is important to have students do the processes by hand versus using technology instead? Is it really important to have students find all the zeros by hand? I had to (granted, the first easily available graphing calculators came out when I was a senior in high school) - so why shouldn't my students have to? (note - I know that's not a good reason why, just throwing my thoughts out there.)
This question is not new to me. I have wrestled with it on and off throughout my teaching career. When students have graphing calculators that can do things like graph and find zeros and maxima and minima, etc., this question returns often. However, this year, I have a mixed bag as far as who has a graphing calculator and who does not. With having (4) computers in the classroom, Desmos has been a nice addition and is far less clunky in identifying intercepts and extrema. From the bits and pieces I have caught from tweets, Desmos continues to improve and everything I have seen from them shows that they are incredibly responsive to its users (and teachers!) Bob Lochel addressed the TI vs. Desmos issue in his blog post this weekend "An Open Letter to My TI Friends." I have to say that even though I have not received quite the training and benefits that Bob has from TI, I found myself really agreeing with every point that he made in his Dear TI letter. (Go read it if you haven't already - it's worth it!) But once again, not everyone has access to the technology in my classes. We are not a 1-to-1 school, I don't have a class set of iPads or tablets or even graphing calculators. My classes range from about 30% to 50% of my students having a TI graphing calculator. I have students who do have smartphones, but they are not allowed to use them in school. I'm already starting to think about next year and how I'm going to deal with the whole technology issue. Do I have my students all get TI graphing calculators, full well knowing that many of them will not use them after my class? Do I skip the graphing calculators and find a way to work with Desmos, knowing that I have 4 computers in my class and that's it? Do I try to find funding for a class set of graphing calculators? Tablets?
But I digress from my original query. I have taught for 21 years and this is the same question that I had when I first started teaching with TI graphing calculators then. At what point do you push aside the by hand processes and let the technology take over? Are you shorting students mathematical learning by doing this or is it enhancing it? How do you structure lessons so that the technology enhances the mathematics rather than glosses over it? I'm curious to see what you all think. Please share your thoughts in the comments. Thanks!
Showing posts with label technology. Show all posts
Showing posts with label technology. Show all posts
Monday, February 25, 2013
Wednesday, January 25, 2012
New Tech Tools
I have found two new tech tools that I am really happy with. The first is the whole reason I wanted the iPad from school - a great app called Educreations. Educreations is a screencasting app. It lets me import image files (which I can create from my SMART Notebook files) straight from Dropbox very easily and I can create screencasts for my students. It uploads to their website (here's my profile page) and as long as I leave the screencast as viewable to the public, I can link to it from my website at school. Students can go view them at their leisure. About the only down side to it at the moment is there is no eraser, but the support staff has been very responsive and I hope they incorporate it in the next update. I do like this app a lot.
The second is a great, free website called Quizlet. Quizlet lets you create flashcards in many languages (including math!) and students can review them like normal flashcards, be quizzed on them by the computer, create their own quizzes (they can be printed to take offline or can be taken online) , or play a couple of games that are provided. In addition, students can import flashcard sets to one of several mobile apps (more information here). I stumbled on this because A+ Flashcards Pro is free (it went free right after Christmas) and it said you could import flashcards from Quizlet. I have created several sets - mainly centered around factoring because that's where we are right now. Here's my user page.
I also recently learned about linking to pages in SMART Notebook. I was recently at our SMART Bugs (SMART Board Users Group) and the facilitator (Bret Gensburg) showed us a file he had helped someone set up that was a game. I took the ideas he used in the game and created my own factoring game. The link goes to my Dropbox and you are welcome to adapt it as you would like. It is a SMART Notebook file, so if you don't have SMART Notebook, it isn't going to work. **Updated the file on January 26th - there was one bad link and I increased font size on the game pages.**
**Update: I did the factoring game in my Algebra 2 classes today. Two of my three classes it went well in. Students were engaged and enjoyed it. One class I had four students who pretty much ruined it. They weren't taking it seriously and would copy answers when it was their turn. I instituted the rule that I could ask you to explain where your answer came from for your team to get the point. Not quite totally sure how to work with this. On the one hand, I do like that students are talking to each other about the math as they are comparing answers. On the other hand, I don't like that they copy the answer without really understanding it. So at the moment, the best work around I have is to not only give the answer, but they have to explain it. I am thinking of making each question worth two points - one for the correct answer and one for the correct explanation. If the person has the correct answer but cannot explain it, their team will get the point for the answer and the other team can steal the point for the explanation. Thoughts?**
I hope you found something you can use. I'd love to hear of other useful tech stuff you're using.
The second is a great, free website called Quizlet. Quizlet lets you create flashcards in many languages (including math!) and students can review them like normal flashcards, be quizzed on them by the computer, create their own quizzes (they can be printed to take offline or can be taken online) , or play a couple of games that are provided. In addition, students can import flashcard sets to one of several mobile apps (more information here). I stumbled on this because A+ Flashcards Pro is free (it went free right after Christmas) and it said you could import flashcards from Quizlet. I have created several sets - mainly centered around factoring because that's where we are right now. Here's my user page.
I also recently learned about linking to pages in SMART Notebook. I was recently at our SMART Bugs (SMART Board Users Group) and the facilitator (Bret Gensburg) showed us a file he had helped someone set up that was a game. I took the ideas he used in the game and created my own factoring game. The link goes to my Dropbox and you are welcome to adapt it as you would like. It is a SMART Notebook file, so if you don't have SMART Notebook, it isn't going to work. **Updated the file on January 26th - there was one bad link and I increased font size on the game pages.**
**Update: I did the factoring game in my Algebra 2 classes today. Two of my three classes it went well in. Students were engaged and enjoyed it. One class I had four students who pretty much ruined it. They weren't taking it seriously and would copy answers when it was their turn. I instituted the rule that I could ask you to explain where your answer came from for your team to get the point. Not quite totally sure how to work with this. On the one hand, I do like that students are talking to each other about the math as they are comparing answers. On the other hand, I don't like that they copy the answer without really understanding it. So at the moment, the best work around I have is to not only give the answer, but they have to explain it. I am thinking of making each question worth two points - one for the correct answer and one for the correct explanation. If the person has the correct answer but cannot explain it, their team will get the point for the answer and the other team can steal the point for the explanation. Thoughts?**
I hope you found something you can use. I'd love to hear of other useful tech stuff you're using.
Sunday, January 01, 2012
Tech in My Classroom
As I mentioned earlier, I am one of two teachers in my building (and 7 in my district) who received an iPad for classroom use. I have spent most of break downloading apps, some for school and some for fun (especially since I also got an iPod Touch for Christmas - double yay me!), playing said apps, and fighting off trying to regulate my children's use of the iPad, especially my 8 year old daughter.
As I was talking with my friend who is using a class set of iPads in her classroom, she suggested that I should have a usage policy for the iPad in my class. That way, if a student strays from the designated activity, I could take the privilege away from them and it would state that I would do that. Hopefully that will keep students from straying while using the iPad. I added the iPod Touch because I already have an activity in mind that uses an app that works on both. That way I could allow students to use my iPod Touch and I could get twice as many students using it over the course of the period. We do already have an Internet Usage agreement that students signed at the beginning of the year. Here is what I came up with:
Also, I want to have an idea of what my students have access to technology wise. My district now has just over 50% of our students on free or reduced lunch. Given that, we do have some students who have access to quite a bit of things. Since I don't have an honest idea of what they do have, I am giving them a survey on our first day back as a bellringer so I can get a better idea of what they do have. Here's the survey:
Both are on box.net in both pdf form (as shown above) and docx form and you are welcome to download them and adjust as needed.
When we get to factoring binomials, the app I am planning on using with my students is DiaMath. Thanks to @crstn85 for the suggestion. By setting it on hard and the minimum number as -10 (or -12) and the maximum as 10 (or 12), it should help students with the skills they need to be able to factor successfully. When we get to the ax^2 + bx + c forms, I use the x-form that DiaMath has as the beginning of the problem, similar to what MissCalcul8 does in her post here.
Next up for me is some screencasting. I haven't totally decided whether I am going to work with ShowMe (app and internet) or Educreations (app and internet). ShowMe has been around for a while. Educreations just came out before Christmas. I will probably try both and see what I am more comfortable with. I would love to hear from people who have used both and to hear opinions as to which one is better.
2012 will be another year of changes and improvements (I hope!) to my teaching. Watch this space as I continue to learn new tricks.
As I was talking with my friend who is using a class set of iPads in her classroom, she suggested that I should have a usage policy for the iPad in my class. That way, if a student strays from the designated activity, I could take the privilege away from them and it would state that I would do that. Hopefully that will keep students from straying while using the iPad. I added the iPod Touch because I already have an activity in mind that uses an app that works on both. That way I could allow students to use my iPod Touch and I could get twice as many students using it over the course of the period. We do already have an Internet Usage agreement that students signed at the beginning of the year. Here is what I came up with:
Also, I want to have an idea of what my students have access to technology wise. My district now has just over 50% of our students on free or reduced lunch. Given that, we do have some students who have access to quite a bit of things. Since I don't have an honest idea of what they do have, I am giving them a survey on our first day back as a bellringer so I can get a better idea of what they do have. Here's the survey:
Both are on box.net in both pdf form (as shown above) and docx form and you are welcome to download them and adjust as needed.
When we get to factoring binomials, the app I am planning on using with my students is DiaMath. Thanks to @crstn85 for the suggestion. By setting it on hard and the minimum number as -10 (or -12) and the maximum as 10 (or 12), it should help students with the skills they need to be able to factor successfully. When we get to the ax^2 + bx + c forms, I use the x-form that DiaMath has as the beginning of the problem, similar to what MissCalcul8 does in her post here.
Next up for me is some screencasting. I haven't totally decided whether I am going to work with ShowMe (app and internet) or Educreations (app and internet). ShowMe has been around for a while. Educreations just came out before Christmas. I will probably try both and see what I am more comfortable with. I would love to hear from people who have used both and to hear opinions as to which one is better.
2012 will be another year of changes and improvements (I hope!) to my teaching. Watch this space as I continue to learn new tricks.
Monday, June 21, 2010
21st Century Math? Day One
Well, y'all wanted to hear about my class. I had thought about tweeting about it later, but there are so many questions that ir raised with me that I figured I was better off blogging. Please feel free to either comment and/or tweet me (@Mrs_LHenry). I would really like to have discussion on some of these points.
I am not totally sure what I was expecting to get out of this class. I guess I expected to learn some new software/websites/programs to help teach math better. Here's how my day went:
The first two hours were spent between the housekeeping stuff, all of introducing ourselves, an update on the Core Curriculum, and being told that we should have a web presence and having PowPak and Moodle introduced to us. We had also spent time with Pow Pak and Moodle in my 21st Century Tools class last week. Then a second year teacher presented for about an hour and a half about how he uses the SMARTBoard - really the SMART Notebook software - in his instruction. This was one of the two worthwhile things to me from today since I will have one in the fall and it was the first time I had seen anyone really using the software. More about his presentation in a moment.
After lunch, we went to the computer lab. I had high hopes after being lectured to all morning. We registered for the Moodle for this class and the instructor proceeded to lead us through the websites on the Moodle page. We spent about 45 minutes on virtual manipulative websites. I was thoroughly bored. Most of the manipulative stuff was geared towards middle school and although there was stuff marked for high school, I guess I really didn't see the value of that. Then we worked through a tutorial of GeoGebra that the instructor had printed out for us. I had worked briefly with GeoGebra in another class about 2 years ago, so I was glad to have something to work through. There was a cool activity on showing the slope of a tangent line to a function and calculating the derivative that I will use with my Calculus class this year. (Second worthwhile thing today) Then the instructor proceeded to lead us through the OGT Success website and somewhere in there she also took us to the ORC website - which have been at just about every county training I have attended for the last 4 or 5 years. Another waste of time.
Tomorrow we are supposed to hear from 2 year teacher and how he does OGT (Ohio Graduation Test - our 10th grade test students have to pass to graduate) practice in his classroom, a representative from the company that makes the SMARTBoard is supposed to talk to us, and we're in the computer lab in the afternoon again and we're supposed to talk about using videos (You Tube, Teacher Tube, etc.) and who knows what else.
I am sorely disappointed with the course so far. Again, I am not totally sure what I was expected from "Teaching Math in the 21st Century," but I can say that I expected to learn about things that I have not really done before. I guess in my mind, "21st Century" means that we are using technology to help enhance our instruction and I expected to be doing more with the 4 C's (critical thinking and problem solving, communication, collaboration, and creativity and innovation) they keep referring to. I am having a hard time finding "virtual manipulatives" to be something new. We've all used manipulatives in the past and although it's cool to be able to see them on the Internet and use them on the SMART Board, I just can't get excited about it.
Even as I reflected on 2nd year teacher's presentation about how he uses the SMARTBoard in his class, I am really struggling. Pretty much everything he showed us was basically putting up the same old notes that many math teachers do, but it's on the SMARTBoard and sounds or videos or different effects were added to make the presentation different. That's 21st Century? It seems like to me you're taking 20th Century Math and putting it on the computer. How is that different than what I do now? How is that going to better engage my students and get them to take more ownership in their learning? How is that going to make be a better teacher? I just don't get it. I'm not seeing anything radically different. Am I missing something? Please enlighten me if I am. What is Teaching Mathematics in the 21st Century to you?
Please comment or start a discussion on Twitter. I really am struggling with this today. Thanks in advance.
I am not totally sure what I was expecting to get out of this class. I guess I expected to learn some new software/websites/programs to help teach math better. Here's how my day went:
The first two hours were spent between the housekeeping stuff, all of introducing ourselves, an update on the Core Curriculum, and being told that we should have a web presence and having PowPak and Moodle introduced to us. We had also spent time with Pow Pak and Moodle in my 21st Century Tools class last week. Then a second year teacher presented for about an hour and a half about how he uses the SMARTBoard - really the SMART Notebook software - in his instruction. This was one of the two worthwhile things to me from today since I will have one in the fall and it was the first time I had seen anyone really using the software. More about his presentation in a moment.
After lunch, we went to the computer lab. I had high hopes after being lectured to all morning. We registered for the Moodle for this class and the instructor proceeded to lead us through the websites on the Moodle page. We spent about 45 minutes on virtual manipulative websites. I was thoroughly bored. Most of the manipulative stuff was geared towards middle school and although there was stuff marked for high school, I guess I really didn't see the value of that. Then we worked through a tutorial of GeoGebra that the instructor had printed out for us. I had worked briefly with GeoGebra in another class about 2 years ago, so I was glad to have something to work through. There was a cool activity on showing the slope of a tangent line to a function and calculating the derivative that I will use with my Calculus class this year. (Second worthwhile thing today) Then the instructor proceeded to lead us through the OGT Success website and somewhere in there she also took us to the ORC website - which have been at just about every county training I have attended for the last 4 or 5 years. Another waste of time.
Tomorrow we are supposed to hear from 2 year teacher and how he does OGT (Ohio Graduation Test - our 10th grade test students have to pass to graduate) practice in his classroom, a representative from the company that makes the SMARTBoard is supposed to talk to us, and we're in the computer lab in the afternoon again and we're supposed to talk about using videos (You Tube, Teacher Tube, etc.) and who knows what else.
I am sorely disappointed with the course so far. Again, I am not totally sure what I was expected from "Teaching Math in the 21st Century," but I can say that I expected to learn about things that I have not really done before. I guess in my mind, "21st Century" means that we are using technology to help enhance our instruction and I expected to be doing more with the 4 C's (critical thinking and problem solving, communication, collaboration, and creativity and innovation) they keep referring to. I am having a hard time finding "virtual manipulatives" to be something new. We've all used manipulatives in the past and although it's cool to be able to see them on the Internet and use them on the SMART Board, I just can't get excited about it.
Even as I reflected on 2nd year teacher's presentation about how he uses the SMARTBoard in his class, I am really struggling. Pretty much everything he showed us was basically putting up the same old notes that many math teachers do, but it's on the SMARTBoard and sounds or videos or different effects were added to make the presentation different. That's 21st Century? It seems like to me you're taking 20th Century Math and putting it on the computer. How is that different than what I do now? How is that going to better engage my students and get them to take more ownership in their learning? How is that going to make be a better teacher? I just don't get it. I'm not seeing anything radically different. Am I missing something? Please enlighten me if I am. What is Teaching Mathematics in the 21st Century to you?
Please comment or start a discussion on Twitter. I really am struggling with this today. Thanks in advance.
Subscribe to:
Posts (Atom)