Interesting perspective on teaching math.

I was doing research on the internet to find some real world math problems that I could have my students do and I stumbled across this blog http://blog.keycurriculum.com/2012/03/what-do-you-wonder-real-world-math-problems-are-everywhere/
In it, the author has a short video of Annie Fetter from the Math Forum in which she says we should use senarios with questions like What do you notice? and What do you wonder? You are not after the students to actually solve it just look at it and find information.  The class has a discussion on it and then for homework you have the students write about what they talked about in class that day.  Toward the end of the entry are three websites, one of which has some great things to use for that. 
This is a cool way to integrate writing into the classroom while being able to assess student thinking and understanding of certain math ideas. 
I am always looking for new ways to integrate writing and to assess student understanding.  My students due to cultural influences are afraid to make a mistake and want you to check all their problems.  I need to help them be less afraid of making mistakes and being willing to work independently.
If anyone has ideas or scenarios I could use in a High School math class, I would love to hear.

Factoring and Showme or educreation

I was able to use the venn diagram today to show my students to find the LCM of an algebraic fraction.  It worked beautifully and helped several of my students understand finding the LCM of this type of fraction.  They could find LCM's for numbers but had trouble extending their knowledge to an algebraic fraction.
I am thinking of having the students make a presentation showing how to use the venn diagrams for finding the LCM of algebraic fractions.  I am thinking of having them use showme or educreation which is what I'm familiar with.  I am going to research apps tonight to see if there is an app that would make more of a podcast type presentation with video/sound/etc. 
This might help them connect with their prior knowledge.  If anyone has  suggestion on apps that would be good for this type of presentation. I'd love to hear from you.

update on two apps and a new one.

I spent some time going through the Boss T Maths I downloaded the other night.  It appears the one I found are just samplers rather than the full versions. The first one, Expanding and Factoring, shows you how to expand the distributive property or factor it from the expanded form to the original problem.  The examples are for a(b + c),  a(b-c),  (b+c)a and (b-c)a.  The app provides some vocabulary and a geometric representation.  Once you get to the practice problems, you can access the ones for the first examples but the others are locked and  you need to purchase the full priced app.  You can access the first practice problems for factoring ab + ac and evaluating ab + ac.  Again, if you want to any of the other problems you have to upgrade.  I was rather disappointed in that I was unaware of this being a lite version rather than the full version.
The special binomial products is set up in the same manner as the other.  You have to upgrade to access all parts of this app.  I think I could still use this effectively with my students for reteaching or guided practice using the examples.  Although I cannot access all of the practice problems, I can always create problems with the answers contained in a QR code so once my students have finished the problems, they can check their work.
I found a book making app Book Magic.  It allows kids to make their own books.  I can see this being used by elementary students to create books on shapes,  processes,  etc.  The app comes with basic shapes and it also allows the students to draw pictures, import photos or other material.  This is a bit too simple for older students. 

Journaling

I am looking at incorporating journaling in my math classes as it is important to include more writing in my class.  I found a nice program Journalize which I got on the day it was free.  It looks just like a journal but it allows you to import pictures, etc and I am thinking it would be great if I could have students keep journals in some manner so they can write about what they are having trouble with, write a letter to a penpal explaining what they did in class, create a drawing and import it.  Make it more friendly than the usual write it down on a sheet of paper or keep in a book.  Too many of my students loose their pencils, binders, etc.  The less paper I have to have them deal with, the more they turn in.
I found two programs from Boss T Math.  One is on the distributive property and the other is on special binomial products.  It comes with instruction and quizzes and seems to be done in a very mathematical way.  I have downloaded them and will play with them over the weekend.  This company makes 7 more and all but one are free at this point in time.  I'll give you a report on the two apps on Monday

Infographics

I've been reading about infographics and I think it is something worth trying.  Since my college prep is in the middle of a project, I think on Monday I will give them a choice of actually writing the short report or preparing an infographic on logs and natural logs and their use.  I think they might have more fun doing the infographic rather than a report since it is a bit more creative.  From what I've read about infographics, these would be great for the probability unit as students can see the real life applications of probability.  Bingo is a huge business out here and parents will often go play to 3 or 4 in the morning.  Maybe an infographic on the probability of Bingo would be a good place to start the unit. 
I am hoping to discuss a couple math apps I discovered on iTunes that will help students with the distributive property and with the special binomials such as (x^2 - 4).  I even have ideas of how to do a graphical representation on Geoboard but I want to do more research on other apps that might help me with the graphical representations.
If anyone knows of one, let me know.

Three apps

I downloaded three apps I found on a list of apps you should have if you are teaching math.  One seems to have disappeared and I've been unable to find it.  The three I found are Ooops, Virtual Manipulatives, and iSpy-x.
The basic premise of Ooops is that you get several numbers and operations that are equal to something.  You insert parenthesis to make the problem come out right.  It has 5 levels and uses all four operations.  Sometimes it uses one set of parenthesis, sometimes it uses two.  When you think you have the answer, you hit the check button and it shows the work with the answer your problem has and tells you if it is right or wrong.  I like this app in that it gives the students a better conceptual grasp of PEMDAS and how it can effect the results of the problem.
Virtual Manipulatives has actual manipulatives for fractions, decimals and percents.  It uses the bars that start at 1 and then are subdivided for 1/2, 1/3, 1/4, etc.  The 1/3 for fractions, decimals and percents has all the same color and you can move pieces so you can have students explore 1/2 = 1/4 + 1/4 or 50% = 10% + 10% + 10% + 10% + 10%.  Virtual Manipulatives is great for the upper elementary or middle school grades.  I could see using in high school with students who struggle with basic math or in a pre-algebra class.
Finally iSpy-x which is supposed to help students learn to solve simple problems such as 2 + x = 7. You can choose the one of three levels and on each level you can select the operation or used mixed operations.  I downloaded the program 3 different times and each time it had a different bug.  I could never get it to work on more than the easy level for addition.
I know that I am going to load Ooops on my iPads next year to use in the classroom.  I like it and it can provide great differentiated instruction due to the 5 levels it offers.

Virtual manipulatives in the classroom.

Currently I use two different ones in my math classes.  One is Geoboard for the iPad.  It is just like the real life geoboards we have in our classrooms except this app comes with two different boards and lots of colored rubber bands but no chance of loosing either the board or the rubber bands.  I've used it for students to create various types of triangles such as those classified by sides, or angles, finding the number of triangles in a polynomial as a starting point to find the equation telling the interior measurements of the angles, tessellations, transformations, etc.  If you use a geoboard in real life, you can use this app to do the same thing.
The second app I've used in geometry is Geometry pad.  It allows students to use a coordinate plane for geometry.  It allows students to make all sorts of quadrilaterals and polygons, triangles, circles with radius, arcs, chords, etc.  There is an option for points, angles, lines, rays, segments, perpendicular bisectors, medians, altitudes and angle bisectors.  you can draw, type, use a ruler, and do certain functions.  I've used this one when the book has a coordinate plane problem, transformations, midpoints, diagonals, etc.  If I have to resort to worksheets for certain activities, I will have my students use this app to help them complete the worksheet. 
Due to iPads not having java, I am unable to use many of the virtual manipulative websites on the internet.  I found another app that has great ratings and I hope to down load it tonight to play with.  Its virtual manipulatives and focuses on decimals, percents and fractions.  Although it is rated for middle school, many of my lower performing high school students are weak in that area.  I think this could be used in that class to help them learn how decimals, percents and fractions relate to each other.  I hope to give more information on this app on Monday or so.

A first

Today the students in my College Prep math class asked me to stop the video I was showing on the properties of logs so they could take notes.  I show the videos using the smart board because I have limited bandwidth and we don't have the serious stuttering problem that often happens if everyone is trying to watch a video at once.
I am going to explore the showme and Educreation apps over the summer.  I am thinking of using the learning menu idea where I give them the menu at the beginning of the unit and let them choose a couple projects that are due at the end of the unit right before the test.  I hope that I can have the students use either of those apps for one of the projects on the menu.
I have so much to do this summer as I plan my units.  I am going to try to have more integrated technology but it also depends on what changes they make over the summer.

Which is first, the lesson plan or the technology in planning?

I just read an article on edtechreview.in about technology and pedagogy in which they discussed teaching and technology.  Do you choose the technology and then write the lesson plan or do you write the lesson plan and choose the technology?  Personally, I don't think it is either.
From my perspective of teaching math, it is more important to choose the concept first, decide how you want the concept to be understood by the students and then look at where in the process the technology is best used.  Technology is a tool to help students learn the material.
One item taught during transformations is tessellations.  I introduced this section by showing pictures of tesselations on my smartboard. I asked questions about what they saw and how they think these were made.  We reviewed types of transformations and discussed  how they were used to produce certain pictures.  This was followed by a video on tessellations and I asked them to design their own tessellation on the geoboard app on the iPad.  Once they had their tessellation created, they transferred the design onto graph paper and colored it in.  This took about two 55 min periods to complete.  The students stayed engaged and we used technology to further the lesson.

Too much to do and not enough time

With high stakes testing coming up, I've been focusing more on the mathematics they need to pass the tests.  Unfortunately, I know I should be incorporating my technology into this more but due to pressure I end up resorting to standard teaching methods.  I was realizing today, that I could have taken the practice tests in PDF form, sent them to my students one page at a time, had to work on the problems, create explanations and mark up the forms with the information.  They could have sent the forms back so I could look at the responses to monitor their knowledge and understanding. 
I stumbled across a website today where the author of the article discussed having students create the questions for use with the clickers.  It was noted that many of the students created low level questions.  When I say low level, I am referring to Blooms Taxonomy.   Anyway,  this person gave up but I'm wondering if this could be done with my students.  I am wondering if I can have them create the answers and questions for a Jeopardy game using my SmartBoard. 
I have a few other outlets such as Quizlet and Survey Monkey to check out to create quick quizzes my students could take on-line.  I've read of one technique where you set up three or four quizzes for the week.  If the student passes the first time, they are done, if not they can try it a second time to see if they pass.  Its a mastery learning technique.  I know it uses a lot of paper and the kids like to "loose" it so I don't get them back. This might work better.  I plan to try it in two weeks due to testing happening next week.

SAS Flash cards and Read along

I had a chance to download and check out some apps from the SAS institute.  The first is Read Along which is for early elementary.  I showed it to a kindergarten teacher and an elementary reading specialist. They both like that the application allows three levels of reading.  First level, the program reads as the words are highlighted.  Second level the program only reads the words the students asks for and the third level for no help.  They plan to use them as soon as their mini iPads arrive.

Now for the big one.  I checked out the SAS Flash Cards and was suitably impressed with the application.  It offers more than most flash card programs I've used and offers enough choice to be happy.  When you make a new deck you can choose your subject.  For math, they offer two different possible types.  One is math and the other is a text, sound, and picture card.  The second type allows you to actually read the question, import pictures and add clarification. Once you've chosen the type of card, you may then choose the type of question.  You have a choice of multiple choice, fill in the blank, true or false or plain.
You have the choice to keep the deck private on the iPad or upload it to the SAS site to make it public.  Once you start using the flash cards, you have a choice of practice or quiz format.  The application provides scratch paper so you can actually work the problem.
The SAS site has lots of decks that people have made and can be shared if you want to see what is there.  I really enjoyed playing with the program and am going to install it on my classroom set of iPads.

Two math and one language arts apps

I received a note from NTCM and there was an article on two apps created by the SAS mobile education.  Both apps are for elementary, one math for grades K to 5 to help with number sense.  It is Math Stretch and described as a suite of activities.  I sent the info to a coworker and hope to hear from them.  The other elementary one is Read Aloud that reads a story and the child can follow the story as it is read.  The description states that there are 3 mode, read to me, help me read and read by myself.  I plan to download both and check them out.  I'll report back in a few days with my impression.
On the page, there is the SAS flash cards for high school students.  I want to check this one out as it seems to allow you to add pictures, voice, etc.  I don't know if you need the internet to use the cards or if it stands alone.
So this is one I want to check out for use in my classroom.
Enough for the moment.