Lesson Planning

I head back to work on August 8th.  I have been thinking about integrating some of the wonderful apps I've seen so that students have a good chance to learn the math while utilizing the technology.  I have to remember to put in activities which make the students plan out and finish an activity with open ended questions so they end up explaining how they got to their answer.  Too many of my students do want to make sure they do every problem correctly the first time and are asking for help on every single problem.  I think I may have them create presentations with showme as a way of communicating their work.  I think this will give them a chance to work on vocabulary, explanations and make them more comfortable with public speaking.

computation or mathematics

I started reading a book and I'm only in chapter one but three things popped out at me.
1.  Mathematics is patterns
2.  Mathematicians work in collaboration with each other rather than in isolation.
3.  Computation begins with the question and finds the answer.  Mathematics begins with the answer and finds the question.
This last one I found quite interesting because as part of the warm-up this past year I posed some answers and had the students work towards the question.  My warm-ups are on the smartboard, ready and waiting till the students arrive and class starts.  They do the warm-up while I take roll, etc. 
Often I have said something like you have three different numbers and two operations to get -35.  I let the students write the problem.  The more advanced might do -6 x 5 + -5  while the less advanced might to -40 + 5 x 1.  I find this type of warm-up gets them thinking and helps them practice their order of operations in a fun way.  I've had students tell others they messed up on the order of their math.
Most of my students prefer to work together.  This coming year, I am going to request that they have to ask at least three other people before they ask me for help when they are working together.  They have a culture where you must do it correctly the first time so they don't like working independently.

Equivalence tiles app and Which one does not belong?

I stumbled across this free app the other day and downloaded it to check it out.  Although  it is designed to be used by elementary students , it could be used by middle school students who need some help with fractions, decimals and percents.  It has blocks from 1/2 to 1/12 with the equivalent percents and decimals located below each fraction tile.  The space available is the whole unit so if you want students to see 1/2 + 1/3 they can do it but if you want 3/4 + 1/3, you have a problem.  I like that you can use any of the three representations but again it is designed for younger students so it is not an app I would use in the high school.
During warm-ups, I sometimes use a problem called "Which one does not belong?".  I give a list of 4 choices such as xy, x^2z, x^2y, xy^2.  Students then have to justify their choice.  For instance, they might say x^2z because it is the only one with the variable z or xy because neither of the variables is squared.  This gives them a way to justify why they made the choice they did.  The state tests here often have questions which require students to justify their answers and this gives them a way to practice while developing higher order thinking skills.

Project based vs menu driven learning?

I was looking at a link to project based learning ideas and realized for as long as I've been teaching and as long as I've heard of project based learning, I still am rather unclear about it.  This is even though I worked in a district with levels, end of level tests and the idea of moving towards project based learning.  From my understanding, you assign a project, have the students work through each part of the project and at the end, they turn in the final project and in the process, they have learned several to apply several math standards.  In menu driven learning, students are taught the material, given the menu to create several small projects based on learning styles to turn in for points. 
Where my thoughts are going with this is are they mutually exclusive.  Can you create the over all project and break the parts down into a menu so each student or groups of students will be able to create the final project using different smaller parts that works best for them.  I realize each project will have to broken down into steps so students are not overwhelmed but could each step have three different choices on how to accomplish it?  Since so many of my students are ESL, I have to do a break down so each student knows the steps they have to follow but not necessarily how to do each step.  For instance, when I assign the "Design your dream bedroom" I have them draw 6 scale drawings to show the 4 walls, floor and ceiling so I know where all the windows, doors, lights, and how the room itself looks.  I then have them create an estimate for the finishing cost of the room including flooring, paint, wall paper, ceiling tiles, etc.  I need to look at being able to combine both projects and menus to give students a better choice and increase their learning.

Math DJ into to Algebra app

I down loaded the free version.  Again the free version has only one chapter included with 30 problems to practice.  Each problem is for the most part a single step equation the student has to solve.  These problems are solved the same way as yesterday's app.  The student selects the correct number of bubbles with the letter so as to get the correct answer for the variable.  The problems start out easy but by problem 17 or so, they become much harder.  One example is 5G - 36 = -G which takes a bit more thought to solve.  If a student comes up with the wrong answer, it tells you that your answer is incorrect and to retry so a student must rework the problem till he gets it correct.  This app is one I could easily use in my lower  level algebra I class to help scaffold students who struggle with solving simple one step equations.  I much prefer this over the pre-algebra app for practice.

DJ Pre-Algebra Free

Found this program which is the free version of DJ Pre-Algebra.  It comes with only chapter 1 with 30 problems.  Chapter one only covers the basics of adding and subtracting signed numbers.  The student is given a problem such as E = 1 + 5  and the student chooses the number of bubbles with the letter E that corresponds with the correct answer.  This is not something I would use with my high school students.  I might consider using it for a much younger group of students who are just starting out with signed numbers.  The problems are a bit too easy and there  is no activity as a reward to make them want to strive towards something.  I think that having a number line on the side to help students see how signed numbers work might make it easier for students to really learn the material.  I would guess that this is good for 5th or 6th grade.

Algebra Tutorial app

I found this free app in the itunes store and it sounded quite good.  I opened it up and noted that it has lots of topics such as fractions, linear equations, inequalities, systems of equations, various equations for finding a line, circles, factoring, and quadratic equations.  I looked at a few topics such as systems of equations.  Each topic and subtopic shows examples of working problems with some written steps but the written step takes the place of actually showing the step visually so if you need to see the actual step, you are out of luck.  The app does provide the opportunity to look at more than one example. 
The other problem is that in some topics they only show one way of doing the work.  For instance, in systems of 2 equations, the app only provides examples for the elimination method.  I know that I will often tell students to use substitution if they can because it is a bit easier.  This app does not show substitution.
I am not sure this is an app I would use in class because the examples are not done as well as examples in a book.  I think this app is more for adults who are reviewing their algebra, rather than being used in class.  I have other apps, I can use to take examples out of the book, write questions for them to answer and have them submit the answers electronically. 

General thoughts

I saw an infographics which showed how mobile devices are being used rather than how they should be used.  In other words most uses seem to be more of the throw the app in to be used rather than using the app as a tool to increase understanding.  I admit I often throw the device in because I do not always take time to ask myself the most important question "will this further their understanding."  Sometimes, I put an activity in for expedience rather than for actual learning.  When I integrate any activities on the mobile devices, aim going to have to ask myself how this is going to further their understanding and not just throw something in.  

It always takes time to plan a lesson in depth to create a proper learning environment rather than falling back on worksheets and the same old same old.  This is something I struggle with on a regular basis.

Algebra Card Clutter

I found this app while I was checking free apps on itunes.  It is focused on helping students learn to order numbers of all types.  When you open the app you have a choice of full course (levels 1-14) or the advanced course (levels 8-14).  Each level focuses on specific numbers such as naturals, integers, fractions,  decimals, absolute values, and square roots.  When you play the game, it will automatically start at the lowest level.  It shows 5 cards with 5 numbers which the players has to tap in order from lowest to highest.  If you select the correct card in the correct order, it will fly off the page.  If you are incorrect, it will not move, so you have to make a different choice.  There are only 5 cards in each level so you would not get a chance to really practice with additional cards.
Although I like the idea, I am not sure I would use this in my classroom as it does not provide enough real practice in ordering numbers.  Many of my students would just touch the cards until they get all the cards off the screen before moving on.  There does not seem to be a mechanism in the app to have students practice different numbers until they are proficient at ordering them.
The only way I see using this is to let students practice a level on the app and then do a worksheet asking them to order the same type of number. 

update on subtext

The other day I got an update for my subtext and it states it now does pdf files.  This is a huge jump for me in that it allows me to scan a copy of work into a pdf file to use in the classroom.  I have several books on activities that can be done in a center and this application will allow me to use these activities so I do not use as much paper as I normally do.  I see it as a way of cutting down on students loosing their work and its there if a student is absent.  I can also assign them a worksheet via this program so they work a few problems and turn it in.
I am still working on getting some activities using subtext ready for the next school year.  I have a web page with questions and a video attached to the reading.  I am thinking of having a few problems associated with the reading so students can practice what they just learned.  In the mean time I have a couple programs I am going to test to make a podcast type presentation to go with the material.  I hope to start with those on Monday so I can report back. 
Once school begins, I can let you know who it all works out.  We all know that what we hope happens does not always happen.

Barron's algebra app

This is the second app I found by Barron's but it is for algebra.  The first level is just reviewing the use of positive and negative numbers.  It has three. Quiz levels and you must get 80% in order to unlock the video game and move up to the next level.  Each level has 20 questions and again the program does not tell you which problems you missed.  This maybe due to not having a large base of questions to choose from.  

I think not telling students which problem they missed is not helpful but it does make them check all their work especially if they do not like figuring out where they made the mistake.  I see some positive uses for this app in my classroom.

Barron's Pre-algebra part two

I gave some more thought to the complaint given by reviewers that this app does not identify wrong answers and I realized that most of the time in real life, we do not have answers available to check.  So why not use this app as a way to help students become accustomed to doing the work, checking it and if you are not sure, check your answer with other students.  This is a way of fostering cooperation, checking work, etc.  

this app is primarily for students to work on order of operations and practice using both positive and negative numbers.  It also has problems that use a double negative. Problems start easy and work to the more complex.  I still have to figure out the games you are allowed to play after meeting the 80% mastery level.   

If all else fails have the students show all their work.  Tomorrow, I will get around to reporting on Barron's algebra app.

Barron's Pre-Algebra app

I am back from traveling and now have real access to the Internet.  I was searching the App Store for free apps and found Barron's painless pre-algebra app.  It had a rating of three stars and no reviews newer than 2011.  I figured that in two years they had time to improve the app.

Well, the app has three levels of problems.  Each level has 20 multiple choice questions and you need to get 80% to move on to the next level. There is a game associated with each level but it is only accessible after you get the 80%.  The problems are good and increase in difficulty and complexity.  The bad thing is that the quiz does not provide any feedback to tell you which problems you missed.  This is the same complaint reviewers had two years ago and this has not been resolved.  The idea is good but the implantation leaves a lot to be desired. This is a free app and if you use it for practice with students working out each problem until they reach the 80%, it does give students some good practice.

 Tomorrow, I will take a look at Barron's algebra app.