This isn't a particularly useful outline of an activity we presented. However, there are very useful resources attached throughout the paper and the papers we researched and included in the bibliography are incredible! Plus, all the research we did gave me an idea about how to teach negatives in algebra through area explorations, rectangles, and squares! I'm really excited to develop it and will post it when I finish putting it together! I promise it will be awesome!
Right from the start of our presentation we had some pretty big issues with the technology we wanted to use. One of the problems with setting up on the spot is that there is no time to test and make sure everything is going to function properly. Initially, the Notebook software we needed would crash every 15-30 seconds after opening it, so our SmartBoard aspect was almost completely useless. Fortunately we got it to function just as we needed it, but the SmartBoard was out of calibration and it wasn’t calibrating properly. Overall though, once we got past these couple bumps and bruises with the technology, it all worked smoothly for the most part. It definitely would have been helpful to have a backup plan for a scenario such as this, as technology can at times be finicky, and there is not always time to fix it.
Our peers were already well versed in algebra tiles thanks to the previous days activities. The time that they spent exploring squares and their properties was invaluable to our presentation. After some reflection I could not help but think the concepts that we presented were far too vast for a 45 minute presentation. However, if we were to have split the activities that we had into four different presentations then the product of our presentation would have been far more effective in teaching our peers about the properties of algebra tiles. A more focused exporation of positive algebra tiles, a more intense activity involving the properties of negative tiles, and a single activity exploring the properties of lattice multiplication that tied into a factoring activity later on would have created an atmosphere that allowed the students to explore the tiles themselves later on. Concerning the properties of positive tiles, there was a need to allow students to further explore the concept of multiplication as represented by area. Adding further tiles of different shapes and sizes to this activity would have expanded the learning potential. However, having students build squares and rectangles from predetermined sets of trinomials allows them the opportunity to get comfortable and familiar with the materials before getting into the more difficult ideas of negative area and factoring.
In regards to teaching students about trinomials containing negative terms, we found that it would be useful to review the concept of operations involving integers. During our presentation is was somewhat difficult even for our classmates to understand why it is needed to keep all negative algebra tiles together along one side of the trinomial representation and all positive tiles along the other side. Renée brought up a great point which we could have explained. That is, when multiplying a negative integer with a negative integer we get a positive product (same with a positive integer multiplied by a positive integer). But when we multiply a negative integer with a positive integer we get a negative product. If we were to represent our trinomial with negative and positive tiles interspersed, even if the tiled representation generates a square or rectangle, the placement would not satisfy our mathematical rules for integer multiplication. This would have aided in addressing any confusion that our students may have when investigating with algebra tiles.
After using tiles to build squares and rectangles to factor since grade nine I have only one new suggestion. The idea of negative area, as presented by Andrew and expanded upon using tile activities, would allow students the opportunity to explore the concept of algebra tiles even further. Using black negative tiles, colored positive tiles, and a black backdrop could enable us to teach about polynomials using direction. Statements such as “the black negative tiles cover up portions of the grid that we don’t want to find the area of” would be possible and the need for integer multiplication of negatives would not be needed to determine which color tile is needed to complete the rectangle students are building. Instead we could use questions such as “do we want to find this area or is this part of the section we don’t want to find the area of?” However, consistency is important in mathematics and allowing students to use integer multiplication in order to factor is a useful and familiar tool that students can use without too many misconceptions being made.
When working in a group it is hard to have a proper flow. In group work, I think there needs to be more practice on the actual presentation, to ensure timing and flow of thought is clear. This is also true in individual teaching. It may take more then one try to present a lesson properly. This is why it is important to have a detailed lesson plan to follow, or for others to follow. It may also be helpful when presenting a new topic/lesson on the first time it might be helpful to have notes or an outline handy. It is important to remember that a concept may take more/less time then you had originally thought to cover in a period. It is important to remain flexible and allow for some changes. Having problems or an extension activity is a great idea for making up for any shortcomings. Also, keeping an eye on the clock and managing the time properly is very important.
Written by Christine Crowe, Andrew Johnson, Kim Simon, and Darcy Bundy
No comments:
Post a Comment