Concept Based teaching of Algebra

I started doing some research last night about different ways to improve students understanding of Algebra and stumbled across this website "Teaching Math" at learner.org. It is an excellent resource with lots of narrative & video examples of how some teachers have helped students discover math concepts.

The only disadvantage of the videos is that you don't have any control over them. A pause button would be a great addition to the site.

Is there a math facts connection?

Having taught Algebra 1 for over 8 years I have always felt that there is a connection between how well a student understands arithmetic and how well they do in the my Algebra I class. So I decided to do a little bit of research to determine if this could be supported. Here is a graph of the results. The blue line through the graph is a regression line.Details about the study:

• 2 classes
• 11 students: 10 & 11 graders
  
• 14 students: 9 graders and one 12 grader
• Arithmetic test:
  1 minute timed test of multiplying numbers 1 through 10.
• Accuracy of test student responses was mostly 90-100%
  
• 100 multiplication problems were provided
  
• Highest number problems completed 57.
• Highest number of problems completed correctly 56.
  
• Grade came from the previous quarter to determine the level of success in Algebra I because it was available for all students.

Trends and Interpretation:
Except for the two outliers indicated as yellow the trend seems to say that the better you are at arithmetic the better your score will be in Algebra I. The outliers can be explained as a student that is unmotivated and the other as a student that is trying but struggling. Though this isn't enough data to make a case it sure does begin to show a pattern that supports my hypothesis. I'm not sure how good of a predictor it is because as you move along any grid line there is quite a spread between the scores. Also there is the variable of different grading style between 2 teachers for the students grades. It would be great if someone would duplicate this study with the same teacher and a larger student populous.
It should be noted that you don't see any grid points in the upper left and the lower right indicating a good arithmetic score and a bad grade or a good grade and a bad arithmetic score.
Thus I feel that the claim can be supported that the better you are at arithmetic the better you will do in Algebra I. Please feel free to add you data in the comments below. You can find the Math Facts test at worksheetshare.com.

New Worksheets Website

Since it appears that there is an interest in worksheets I've created. I decided to create a new website where you will not only have access to worksheets that I've created but also others. The new website is Worksheet Share.com
Currently there are over 17 math worksheets available, but it is growing. Ranging from addition facts to graph paper, that is problem friendly, to factoring polynomials. Anyone can sign up for a free account and post worksheets that they have created.

Here's how it works. You save your worksheet as a PDF, sign up for a free account, and post your worksheet. Once the worksheet is screened by the users on the system it will be made available for anyone to download.

If you are looking for a particular topic simply search by keyword. If you found someone at worksheetshare where you really like there worksheets simply browse the worksheets created by that author.

You can even make some money from your worksheets. Check it out. Once enough worksheets become available for a particular subject you will be able to order a book on a particular topic or keyword. You can keep track of the plans and improvements at the Worksheet Share blog.

Graph Paper

Is it late and you've run out of graph paper for that assignment that is due tomorrow. Have no fear free graph paper is here. Check out this slick little website printfreegraphpaper.com where you can select your grid size and make your own graph paper.

Are smartboards and tablet PC's the only option?

Many teachers today are looking at getting a smart board or tablet PC for their classroom so that they can "teach more effectively." We are coming back around again in the learning cycles. First there was the black board, then the overhead, then the white board, now the smart board, what next.

I have used a chalk board, white board, overhead transparencies, computer projector, smart board, and a wireless tablet for teaching and would like to share my view of the advantages and disadvantages of each.

• Chalk board:
• Advantages:
  
• Cheap
• Large writing area.
• Students can participate at the board.
  
• Disadvantages:
• Messy, back to the students when writing on it.
• Once information is off the board it is gone.
• Chalk breaks.
  
• White Board
• Advantages
• Cheap
• Large writing area
• Easy to clean
• Students can participate at the board.
• Disadvantages
• Messy but not as messy as chalk
• Markers run out
• Back to students/audience
  
• Overhead transparencies:
  
• Advantages:
  
• You can face the students while lecturing.
  
• Material can be prepared before hand.
• Information can be shown again if using separate transparencies.
  
• Disadvantages:
  
• Can be messy.
  
• You need to make sure you have spare transparencies.
• Limited visual area.
  
• Computer Projector:
• Advantages:
  
• Can prepare material before hand.
• Demonstrate ideas interactively
  
• Can manipulate material while lecturing.
  
• Wide variety of media types: PowerPoint, web pages, video, etc....
  
• Disadvantages:
  
• Difficult to annotate with a mouse.
  
• Technical issues such as computer crashes, bulbs burning out,
• Price
  
• Irrelevant information can distract students from learning.
  
• Limited visual area.
• Provide notes to students when class is finished.
• Smart Board & a projector:
• Advantages:
  
• Can prepare material before hand.
  
• Easily annotate & manipulate material while lecturing.
• Students can participate at the board.
  
• Wide variety of media types: PowerPoint, web pages, video, etc....
• Provide notes to students when class is finished.
• Disadvantages:
  
• Back to the students/audience.
  
• Unless you use a rear projector what you are doing is in the shadow of the projector making it difficult to execute precision movements.
• Expensive
• Irrelevant information can distract students from learning.
• Limited visual area.
• Alignment issues if it gets moved or drifts over time.
  
• Price
  
• Wireless tablet & a projector (not tablet PC):
• Advantages:
  
• Students can draw on the board from their desk.
  
• Can prepare material before hand.
  
• Easily annotate & manipulate material while lecturing.
• Wide variety of media types: PowerPoint, web pages, video, etc....
• Write on the board from anywhere in the classroom
• Price
• Provide notes to students when class is finished.
• Battery life versus laptop or tablet PC.
  
• Disadvantages:
  
• Battery life versus pen.
  
• Learning curve.
• Irrelevant information can distract students from learning.
• Limited visual area.
• Tablet PC & Projector
• Advantages
• Easier to learn how to use than a tablet
• See tablets advantags
• Disadvantages
• Battery life
• No mobility around the classroom unless you purchase an expensive wireless connection.
  

It seems like the current trend today is to move away from white boards towards smart boards. The question though is that really what is best for the students? The white boards is typically a larger area which can allow the student more time to write down information, process all of what they see, and encourage them to write it down because they know it will soon be erased. While white boards also have the disadvantage for those that are slower and unable to keep up. This is the band wagon that the electronic notes group are advocating for, but what about the rest of the students that can keep up and will be come lazy? Research shows that the most learning happens when notes are taken and the lecturer's notes are then studied for the test.

In my math class I have found that teaching with a tablet and a white board is the affordable best option. The projector points toward a side wall in the front of the classroom and the white board is in the front of the classroom. The students are looking to the side of the classroom and I'm looking at the students while lecturing. If there are technical issues I can simply transition to the white board. If I run out of white board space or the markers run out I can transition to the tablet. If I want the information to be available to the students later or I believe that I will receive multiple questions of the same problem then I will use the tablet. I can pass the tablet around the classroom and let the students participate. I've found that it takes less time for the tablet to move than the students, plus the tablet is still a novelty at this point in time. If I need multiple students to write at once I'll use the white board. The tablet also has the advantage that you can copy and paste information, move it around, and insert new information between old information. The projector has the advantage of beign is simply more interactive. Take graphing for example. I've created a slick little flash application that I use to quickly graph lines and inequalities.

So heres what I'm advocating. Use a white board, projector, and wireless tablet. The advantages of a smart board over a wireless tablet are minimal if any and can be limiting depending on how you teach. Any digital solution is going to need a projector so the price difference is going to be the biggest factor and the software that comes with your choice.

• Tablet PC: more expensive than an a laptop with equivalent performance. You can't roam around the classroom, less you purchase an expensive wireless projector connection. Usually no educational software comes with it.
  
• Smart Board: expensive. Sometimes only prepare information on that computer due to licensing. Usually comes with educational software.
  
• Wireless tablet: Least expensive interactive option. Educational versions are available but more expensive because of the software.
  

Those are my views and I would love to hear yours. Please share your views on the topic and what effective ways you have found to use a tablet, tablet PC, or smart board in your classroom.

More Impressed

Being a fan of OpenSource software I really like OpenOffice (OO). I do have to admit that thus far MS PowerPoint has had the upper hand on OO Impress. One of the reasons was that OO didn't have templates that are available in PowerPoint. We'll that has changed. I stumbled upon the OO extensions website: extensions.services.openoffice.org today and found the Professional Template Pack by Sun Microsystems, Inc. It is available in several different languages. It is a must have if you are not into creating your own templates and want something that looks different than the two that come with OO. This is one step closer to Impress being a solid alternative to PowerPoint.

Thanks to Sun.

Math Facts Question Generator

Here it is I finally finished the the Math Facts Question Worksheet generator. With a few adjustments I was able to adapt most of the features of the Moodle Math Question generator to be able to create a printable version with an answer key. This program will create a set of math fact questions based on the users input parameters. At this point this version is limited to addition, subtraction, multiplication, and division.

Highlights:

• Vertical or horizontal problem formatting.
  
• Each time that the page is requested the order of the questions is changed.
• The answer key prints on a separate page.
• Customizable directions
• Custom key/worksheet identifier.
• Integer only answers for division problems.
• Positive answers for subtraction problems.
  

Check it out