As a follower of math dignitaries in the Twitter world, I am aware of various opinions on homework for math class. I am surprised to see some teachers advocating doing away with it. Of the teachers that I've read about, they are mostly elementary teachers and I can live with that. However, as a high school teacher, I am not ready to give up homework yet.
Of course, like any subject there are gray areas. The discussion shouldn't be, homework or no homework. To me, the concern should be, did the student develop an understanding of the material in class. If they did not, then choices must be made. The student can choose to be satisfied with the level of understanding that they gained in class or they can seek to develop a greater understanding outside of class.
And, the math teacher bears responsibility here as well. Math teachers can customize their curriculum to ensure that students get what they need in class. However, I believe that if we limit student activity to math class, compromises must be made. For me, I already feel that it is difficult to cover all the standards in the given number of days with homework. And, aside from standards, there is a certain level of pressure from the teachers of higher level classes to cover a large number of topics. So, in a particular environment, a teacher may have to choose between breadth of material and time constraints for students.
In a world where all teachers were perfectly autonomous, I would be happy to eliminate homework and cover fewer topics. Sometimes, I imagine if I was really smart, I would figure out a way to cover every topic in the given time and all kids would understand. But, I haven't figured out that way and I haven't read any paper or book from a teacher who has. If you are reading this article and you figured out how to cover every topic that Common Core requires in Algebra 2 in high school in the given number of days with no homework, please share your secret recipe. I suspect I am not alone, maybe there are others that could be enlightened as well!
I have another unique consideration and that is I teach in a block schedule. My students and I will complete all of Algebra 2 in about 90 days. We started end of August and we'll be done by end of January. Then, essentially, we start a new school year from Jan to Jun. There is a theory in this environment that you just provide 2 lessons every day, but, from my experience, kids don't learn that way.
Hope you don't mind my rambling, but I have more to say. There is also a difference between homework and other work that needs to be done outside of class. By the way, did I mention that I flipped my class? My homework is watching videos and taking notes and sometimes completing Khan Academy exercises. Classwork is where we solve problems together. So, I feel that homework is less stressful in my class, just watch videos and take notes. But back to my thoughts about other work outside of class. I put pressure on my students to come in outside of class to work on improving their understanding. I offer extra credit and I offer a variety of ways to earn it including finishing their classwork problems, studying for a test, reviewing the results of a test, Khan Academy and even some novel things like playing the game, Dragonbox. So, with me, I am asking my students to do homework and I am asking them to put in some extra time aside from the homework. Of course, not all students need to put in this extra time. Some attend class, do their homework and get the grade they desire. But, for students that are not getting the grade they desire, I feel they need to put in some extra time.
Don't know that I have any specific conclusion. Just wanted to write down and share my thoughts and see what others think.
Saturday, August 27, 2016
Friday, February 12, 2016
My example of Common Core Mathematical Practice 1, "Make sense of problems and persevere in problem solving." A friend of mine posted this on Facebook:
The Problem
A bit of a rant.
Two years after leaving FiOS for Comcast, I'm back in the FiOS family. It wasn't without aches and pains. The new router had to be near a place where they could run Cat-6 to the outside box, which was not near where the router was before. In order to get network jacks near where they were installed with Comcast, FIOS installed a network extender which caused a bunch of setup problems this afternoon after the installer left. I had to go and figure out how to configure the network extender, using a bunch of Google searches and reading of different documents and forum posts.
That wasn't the end of the drama. For my birthday, I bought myself a TiVo Bolt and some TiVo Minis for the bedrooms. The reason you want to do this is to save on equipment rental fees. The TiVo uses a cable card to access all the channels you subscribe to. However, because this isn't the "normal" install using the cable company's set-top box, there are different setup procedures which the installers aren't familiar with. While it appeared the cable card was working, I noticed that not all the channels I subscribed to were showing up. So, fixing that issue took a long call to the special Verizon cable card number and re-explaining multiple times the problem.
It took me about 8 hours to get the installation completed and reconfigured to be fully up and operational. The speed of the wireless network is great and the TiVo works better than it ever did on Comcast.
The end
Thursday, November 29, 2007
Slates and Clickers
Interesting discussion with a former student today. First of all a disclaimer- I take students complaints about other teachers with a grain of salt. Other teachers have come to me with complaints from my previous students, so I know we can't always match students and teachers perfectly.
With that in mind, I shall proceed. So, a former student comes to me to ask for help with an upcoming Algebra 2 test. Last year when he took my class, he failed because of zero effort. Nevertheless, he was not a horrible kid and he felt comfortable coming to me for help this year. It's funny because he's not very happy with his current teacher and now he's regretting that he didn't try harder last year when he had me- in his mind, the more reasonable teacher.
He complained about the pace of the class with the new teacher. Two lessons per day, no review day before tests and sometimes two tests in the same week. Then he started getting into other details. He said the teacher used slates to allow students to try problems and then show their results to the teacher. The teacher would then point to each slate and say whether it was right or wrong. This frustrated my student quite a bit because he would be told that his answer was wrong, but not why it was wrong. It's interesting to me because the slate idea has been kicked around for a few years now and some people think it's a cure all. It's one of those ideas that sounds good, but it's questionable whether it really is beneficial for students. Of course, like many good ideas, the level of success is dependent on implementation as well.
In comparison, I've been having some great luck with my clicker system. It's a technology system that is designed to give instant feedback to students just like the slates do, with several advantages over the slates- and in some people's minds, several disadvantages. With the clicker system, I create quizzes using PowerPoint. Each slide has a question and several multiple choice answers. Every student in the class gets a remote control and I have an infrared receiver attached to my computer. When I display the question, students press a button on the clicker to "vote" on the multiple choice answer they think is right. After all the students have voted on a particular question, a bar graph appears that shows how many students voted for each answer. If I want, I can also show them which answer is correct. So, like the slate system, students get instant feedback. Unlike the slate system, students get multiple choice answers, so they have something to work toward. Of course some teachers would complain that students may reverse engineer the answers or may copy answers from a neighbor and I'll admit there are problems. But like anything, there can be implementation issues and they need to be worked on. So, I'll continue to work.
With that in mind, I shall proceed. So, a former student comes to me to ask for help with an upcoming Algebra 2 test. Last year when he took my class, he failed because of zero effort. Nevertheless, he was not a horrible kid and he felt comfortable coming to me for help this year. It's funny because he's not very happy with his current teacher and now he's regretting that he didn't try harder last year when he had me- in his mind, the more reasonable teacher.
He complained about the pace of the class with the new teacher. Two lessons per day, no review day before tests and sometimes two tests in the same week. Then he started getting into other details. He said the teacher used slates to allow students to try problems and then show their results to the teacher. The teacher would then point to each slate and say whether it was right or wrong. This frustrated my student quite a bit because he would be told that his answer was wrong, but not why it was wrong. It's interesting to me because the slate idea has been kicked around for a few years now and some people think it's a cure all. It's one of those ideas that sounds good, but it's questionable whether it really is beneficial for students. Of course, like many good ideas, the level of success is dependent on implementation as well.
In comparison, I've been having some great luck with my clicker system. It's a technology system that is designed to give instant feedback to students just like the slates do, with several advantages over the slates- and in some people's minds, several disadvantages. With the clicker system, I create quizzes using PowerPoint. Each slide has a question and several multiple choice answers. Every student in the class gets a remote control and I have an infrared receiver attached to my computer. When I display the question, students press a button on the clicker to "vote" on the multiple choice answer they think is right. After all the students have voted on a particular question, a bar graph appears that shows how many students voted for each answer. If I want, I can also show them which answer is correct. So, like the slate system, students get instant feedback. Unlike the slate system, students get multiple choice answers, so they have something to work toward. Of course some teachers would complain that students may reverse engineer the answers or may copy answers from a neighbor and I'll admit there are problems. But like anything, there can be implementation issues and they need to be worked on. So, I'll continue to work.
Friday, November 23, 2007
Re-engineering the Math Classroom (textbook technology)
The textbook vendors are really coming around with technology support. McDougal-Littell writes the textbooks we use for most of the math classes at my high school. I just spent some time with my rep at a recent math conference. I was amazed to hear what they have to offer. They have an online system at their web site that can be used for quizzing students online or for assigning homework online. They also offer such expected things as an online graphing calculator.
I also inquired about newer, better test generators and they had a pleasant surprise. I had recently tried out the new test generator provided with some new textbooks we received, but a found it lacking. It was way too slow on my old dinosaur computer. And it was slow compared to the older test generator that I had been using. The only reason I was interested in a new test generator was because the old one didn't have enough questions to cover all the topics that we covered in the book. Also, I was hoping for more algorithmically generated questions versus static, database questions.
Well, I got lucky. Even though we had only recently received the new test generator, there was an even newer one that the vendor had available. They demonstrated it to me and it was awesome. It was fast and full of nice features. It did seem to lose some of the older features that I liked, but it had some cool new ones.
However, back to the online homework/assessment system. Over the years, I have used diagnostic exams from the Mathematics Diagnostic Test Project (MDTP) from University of California. They offer a nice set of tests that can be used for diagnostics, but also for benchmarking. Where are your students at when you first meet them and how do they improve after you're done with them? Well, the textbook vendor came up with an online assessment system that automatically diagnoses student weaknesses and then allows you, the teacher, to generate a list of remediation assignments and it will even let you pull together the files for the assignments and either print them or email them to the student!
These types of technology are bound to make teaching better and more efficient.
I also inquired about newer, better test generators and they had a pleasant surprise. I had recently tried out the new test generator provided with some new textbooks we received, but a found it lacking. It was way too slow on my old dinosaur computer. And it was slow compared to the older test generator that I had been using. The only reason I was interested in a new test generator was because the old one didn't have enough questions to cover all the topics that we covered in the book. Also, I was hoping for more algorithmically generated questions versus static, database questions.
Well, I got lucky. Even though we had only recently received the new test generator, there was an even newer one that the vendor had available. They demonstrated it to me and it was awesome. It was fast and full of nice features. It did seem to lose some of the older features that I liked, but it had some cool new ones.
However, back to the online homework/assessment system. Over the years, I have used diagnostic exams from the Mathematics Diagnostic Test Project (MDTP) from University of California. They offer a nice set of tests that can be used for diagnostics, but also for benchmarking. Where are your students at when you first meet them and how do they improve after you're done with them? Well, the textbook vendor came up with an online assessment system that automatically diagnoses student weaknesses and then allows you, the teacher, to generate a list of remediation assignments and it will even let you pull together the files for the assignments and either print them or email them to the student!
These types of technology are bound to make teaching better and more efficient.
Wednesday, November 21, 2007
Re-engineering the Math Classroom
Fuzzy logic and Bayesian Networks could be used to evaluate the effectiveness of of multiple choice assessments- especially clicker system assessments.
Textbook test generators can be used to generate questions for clicker system quizzes.
Virtual manipulatives work great for pre-algebra classes especially NLVM with the virtual equation balance. Also there are several nice sites for tangrams. And don't forget Google Earth.
edhelper.com is a nice worksheet generator web site.
Algebra in Motion offers a set of Geometer's SketchPad visuals and animations to demonstrate a variety of algebra topics visually. For this reason alone, Geometer's SketchPad would be very useful.
Mimio has produced a low cost item that allows you to turn any whiteboard into a smartboard. This item used in conjunction with Geometer's SketchPad (a computer and a projector) could really help facilitate graphical drawing on the whiteboard and it's capture capability helps to eliminate redundant lesson delivery.
If you don't attend regular math conventions, conferences and workshops, you are missing out on a lot.
Supplemental materials are great and some textbooks make great supplemental materials. Harold Jacobs has written several textbooks that provide a meld of classic text based problems with modern critical thinking and problem solving challenges.
MathType is great and very useful for PowerPoint presentations, however, there are some other technologies coming along- like the Open Office formula editor- that may make formula entry easier. MathType actually is pretty good for use with SmartBoards or Mimio systems because of the big buttons and all the pointing and clicking. But if you want to type equations- and I believe this is the quickest method to enter formulas (or anything in the computer)- Open Office formula editor allows you to enter formulas like you enter equations into the graphing calculator. For example, x^2 + 3x -2 for a nice quadratic or (-b +/- sqrt(b^2 - 4ac) over (2a) for the good old quadratic formula. Unfortunately, you can't have the best of both worlds. MathType does allow you to type formulas, but you have to learn the syntax of a typesetting system called TeX. Open Office allows you to type the formulas easily, but it does not allow you to migrate the formulas to Power Point easily- and that's a problem if you must use PowerPoint like I must with my Interwrite PRS clicker system.
Textbook test generators can be used to generate questions for clicker system quizzes.
Virtual manipulatives work great for pre-algebra classes especially NLVM with the virtual equation balance. Also there are several nice sites for tangrams. And don't forget Google Earth.
edhelper.com is a nice worksheet generator web site.
Algebra in Motion offers a set of Geometer's SketchPad visuals and animations to demonstrate a variety of algebra topics visually. For this reason alone, Geometer's SketchPad would be very useful.
Mimio has produced a low cost item that allows you to turn any whiteboard into a smartboard. This item used in conjunction with Geometer's SketchPad (a computer and a projector) could really help facilitate graphical drawing on the whiteboard and it's capture capability helps to eliminate redundant lesson delivery.
If you don't attend regular math conventions, conferences and workshops, you are missing out on a lot.
Supplemental materials are great and some textbooks make great supplemental materials. Harold Jacobs has written several textbooks that provide a meld of classic text based problems with modern critical thinking and problem solving challenges.
MathType is great and very useful for PowerPoint presentations, however, there are some other technologies coming along- like the Open Office formula editor- that may make formula entry easier. MathType actually is pretty good for use with SmartBoards or Mimio systems because of the big buttons and all the pointing and clicking. But if you want to type equations- and I believe this is the quickest method to enter formulas (or anything in the computer)- Open Office formula editor allows you to enter formulas like you enter equations into the graphing calculator. For example, x^2 + 3x -2 for a nice quadratic or (-b +/- sqrt(b^2 - 4ac) over (2a) for the good old quadratic formula. Unfortunately, you can't have the best of both worlds. MathType does allow you to type formulas, but you have to learn the syntax of a typesetting system called TeX. Open Office allows you to type the formulas easily, but it does not allow you to migrate the formulas to Power Point easily- and that's a problem if you must use PowerPoint like I must with my Interwrite PRS clicker system.
Sunday, November 11, 2007
Wednesday, October 31, 2007
Great day for being a teacher
What a fantastic day to be a teacher. One of my former students has been nominated by district to be flaunted in the annual report because of her experience at my high school as related to great strides she has made in life. Another student came in today to tell me that she had always loathed math even though she was good in other subjects. She paid me some high compliments and told me that other students were saying good things about me as well. Also, I've begun to use a classroom response system (CRS) in my classes and today I created a monster quiz for my Foundations of Math class. It was a really enjoyable way to spend 45 minutes with my students.
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