Internet Research for TechQuest Project

During my research for this TechQuest Project I have found three sites that have been particularly helpful so far and have learned some things along the way. The first site is a blog (http://continuities.wordpress.com/2008/07/24/geometry-before-algebra/) that started with a woman asking questions about the merits of having geometry before algebra. The 47 quality replies to the post have given me some ideas and a different perspective. Many people advocate taking algebra out of the geometry class all together. While I could still hit all of the standards without algebra mixed in, I would not be doing justice to the ones who can do it. What has changed in my mind is whether I should still demand it out of the students who do not have the skills at the beginning of the class. This would require me (or any teacher in this situation) to provide more differentiation than normal in the class, but may help to push and challenge all the kids while helping them to be successful and meeting the benchmarks.

The second site (http://www.imprint.co.uk/pdf/Thompson_Snow.pdf) was a short paper supporting Peter J. Snow’s “Charting the Domains of Human Thought.” The major idea that I took from this paper was that the development of the brain can have an impact on the ability of a student to learn the concepts of algebra and geometry. It was his opinion that the correct sequence has geometry first.

The third site I found (http://www.nap.edu/openbook.php?record_id=10297&page=50) is Chapter 5 from Technology and Assessment – Proceedings from a Workshop. It discusses its main point which is a cognitive tutor for Algebra, but what I found interesting was its support of technology for learning math. The program adjusts the content based on how the user is doing and is ultimately an individualized experience. My project is not that sophisticated, but it is of the same ilk. It will allow students with different abilities to be successful in different ways.

Finding good sites was not an easy task for me. I used Google and tried a couple of different strategies. First I used the keywords “geometry before algebra” and all the results in the first five pages, except the blog listed above, were not helpful. Next I tried “algebra scaffolding” and came up empty. Finally, I was somewhat more successful with “algebra technology”. I think using Google is not a great approach. Site dedicated to educational research would probably give better results, although I did find the blog to be very interesting and that would not be in a research database.

Problems of Practice Final

Three years ago my school district made a significant change to the math curriculum. Geometry was changed from a 10th grade class to a 9th grade class. The significance of this move is that it means many students will now take geometry without taking a yearlong algebra class first, like before. Many of the materials and assessments that exist require algebra skills that some of the students have not had. On the other hand, some students do take algebra in the 8th grade and have the skills to complete the exercises without extra time spent. So the problem is that the class is geometry, but expecting learners to complete exercises with algebra they are not prepared for is not fair. At the same time, the students who have had algebra should have exercises that include those skills. These latter students should be challenged and pushed and not have their algebra skills lie dormant for a year before going into Algebra 2.

The problem described above especially shows itself during the unit for volume of solid objects. There are many formulas used and in some types of exercises algebra is a much needed skill. The students without those skills tend to struggle not so much with the formulas or the concepts of volume, but with solving for certain variables once values are inserted into the formula. However, some of the best real world type problems do not require a simple calculation of volume. More common is that the volume is already known and what needs to be calculated is the height or the area of the base. These types of problems are difficult for students without the algebra skills, but very worthwhile for all.

A solution to this problem will allow the students without good algrebra skills to be successful with all problems. It will also prevent students who have had algebra before from taking shortcuts and therefore not honing their skills for the following years.

I plan to create a StAIR (Stand Alone Instructional Resource) that has utilizes the website MyAlgebra. This StAIR will instruct the learners to calculate volume given certain dimensions of a solid object as well as solve for an unknown dimension when given the volume. MyAlgebra is a website that solves for an unknown variable in an algebra equation. I will have to familiarize the students to the site before they complete the StAIR, which can be done in my classroom using a projector and the internet. Students who are still struggling with the algebra at this point of the course will not have to be concerned with solving for the unknown variables. No new purchases would be required, just use of a computer lab for one or two days. Once completed, the StAIR will be posted on my teacher webpage so that the students may go back to use it at their convenience. With the use of this StAIR students will be able to focus solely on the geometry and be able to master the expectations without getting bogged down by the algebraic portions of the problems.

Note: Other options investigated included Texas Instruments N-Spire Technology calculators and The Geometer’s Sketchpad. While these technologies are very powerful and can solve the problem described above, their cost would be unjustifiable.

My plan is to complete the design of the StAIR before the class ends and then actually create and implement it after it is over. I anticipate multiple iterations before it becomes a finished product that requires minimal maintenance.
This project addresses the four common places of education as shown below:

• Someone teaching: The end product of this project will allow a teacher to assign any type of geometry problem that requires algebra to solve and then be the guide on the side. The teacher will not have to worry about short changing some students if they “dumb it down” or worry about leaving others behind if they do not have the same skills as the ones who have taken algebra. The teacher will have to help the students using MyAlgebra get comfortable with the site and the format it requires.

• Someone learning: This opens the door to a very rich and interesting set of problems that are authentic and representative of what students see and experience every day. Students can use this in the computer lab and then anytime thereafter by accessing it from my teacher webpage.

• Some subject matter: The issue here is geometry infused with algebra. Research has shown that when mathematics is demonstrated multiple ways1 (i.e. algebraically, graphically, and/or geometrically) students gain a deeper knowledge of the material.

• In some setting: Students will be exposed to this first in my classroom using a projector and the internet. Then they will have an assignment using this in the computer lab. Finally, they will have access to it via my webpage.

Resources:
1. Texas Instruments Research - http://education.ti.com/educationportal/sites/US/nonProductMulti/research_nspire.html?bid=1
2. Texas Instruments N-Spire Technology - http://education.ti.com/educationportal/sites/US/homePage/nspire-family.html
3. MyAlgebra - http://www.myalgebra.com/
4. Geometer’s Sketchpad - http://www.dynamicgeometry.com/

Problems of Practice Preview

Three years ago my school district made a significant change to the math curriculum. Geometry was changed from a 10th grade class to a 9th grade class. The significance of this move is that it means many students will now take the class without taking a yearlong algebra class first. Much of the materials that exist(ed) required algebra skills that some of the students have not had. On the other hand, some students do take algebra in the 8th grade and have the skills to complete the exercises without extra time spent. So the problem is that the class is geometry and expecting learners to complete exercises with algebra they are not prepared for is not fair, but at the same time the students who have had algebra should have exercises that include those skills. These latter students should be challenged and pushed and not have their algebra skills lie dormant for a year before going into Algebra 2.

The problem described above especially shows itself during the unit for volume of solid objects. There are many formulas used and in some types of exercises algebra is a much needed skill. The students without those skills tend to struggle not so much with the formulas or the concepts of volume, but with solving for certain variables once values are inserted into the formula. However, some of the best real world type problems do not require a simple calculation of volume. More common is that the volume is already known and what needs to be calculated is the height or area of the base. These types of problems are difficult for students without the algebra skills, but very worthwhile for all.