Misconceptions assignment by katie grace olmsted

kgolmsted22 — 2024-10-25 18:29:21 UTC

When students begin learning transformations in geometry, they typically start by doing one at a time. Once they start advancing in the topic, they begin to experiment with multiple transitions to get one pre-image to an image. One misconception I've noticed students having is that the order of these transformations do not matter. For example, if a student was given a pre-image then the following transformation:

1) rotation by 90 degrees

2) (x+5, y)

3) dilation by 3

many students will start with step 2 because it is considered the "easiest" and then continue with steps 3 and 2. Going through the steps in any different order then 1, 2, 3 will give you a different ending image.

kgolmsted22 — 2024-10-25 19:02:01 UTC

I will give students each a worksheet with 6 different transformation problems on them. It will be the same three transformations given in the "target misconception" section of this padlet.

1) rotation by 90 degrees

2) (x+5, y)

3) dilation by 3

The 6 different problems will be all the different orders of these three transformations possible. Students will compelte each problem independently before comparing answers. I will give the students ten-fifteen minutes to finish each problem. I will also stress before the students start working that they must do each translation in the order they are given.

kgolmsted22 — 2024-10-25 19:07:47 UTC

Next, I will have students get into groups of 3 or 4. They will go over each of the 6 problems and compare their findings. Hopefully, it will be obvious that they do not always get the same image depending on order. If some students did not get different images for each, students can discuss how their processes differed and why there should be different final products.

kgolmsted22 — 2024-10-25 19:13:53 UTC

After comparing answers, I will prompt students to discuss why different orders of transformations cause pre-images to turn into different images. While students are having these discussions, I will walk around and listen to everyone's reasoning. I'll be making mental notes on which group has an explanation that is easy to understand and accurate for them to share in the next step of the discussion.

kgolmsted22 — 2024-10-25 19:23:11 UTC

After discussing in smaller groups, I will call the entire class together for a big discussion. I'll call on groups to share their findings on the transformation order of pre-images. We will also bring up the question if transformation order always matters or if there are times when it doesn't.

kgolmsted22 — 2024-10-25 19:27:26 UTC

A conceptual conflict will occur when students begin to realize that order does not always matter. For example, the list below shows two transitions where it does not matter the order you perform each transformation.

1) (x+5,y)

2) (x, y-2)

While it is true that order does not always matter, it is important to emphasize to students that there are scenarios where they do, and for that reason, students should always complete their transformations in order to ensure accuracy.

kgolmsted22 — 2024-10-25 19:29:16 UTC

After the discussion once students understand the importance of order, I will have each student create a two-step transformation where order is important. Students will show how the images from the two different orders are different. This will be their exit ticket and they will turn it in on their way out of class.

kgolmsted22 — 2024-10-28 19:54:07 UTC

After the discussion I will present this photo to the class. While I think a mathematical discussion and their own work will be very helpful to understanding the misconception, it will also be helpful to visualize it in a more organized manner.

Website: https://mathbitsnotebook.com/Algebra2/FunctionGraphs/FGCompositeTransformations.html