Rotation and reflection are two R's that are very simple to mix up for elementary students. The main difference between a rotation and reflection is the fact that rotation has the students essentially turning the shape while the reflection has the students flipping it over. As a daily assignment we were asked to correct/grade an assessment that involved reflections, rotations and translations. A group of elementary students were asked complete Aaron's picture by following the directions asked of them, for example, "To finish drawing Aaron's second design, rotate the gray shape 1/4 of a turn in a clockwise direction about the origin. Then draw the second shape. Rotate the second shape 1/4 of a turn in a clockwise direction about the origin. The draw the third shape. Rotate the third shape 1/4 of a turn in a clockwise direction about the origin. Then draw the fourth shape."

I had noticed after a few different students did, just as the above picture shows, and reflected about the vertical and horizontal lines when asked to rotate 1/4 of a turn clockwise. This is a great example of the confusion that takes over students when trying to decipher between a rotation and a reflection.

Another observation I made when grading these students' work was that all of the students, when asked to reflect the shape, got all 3 reflections correct. This shows me that the students understand what it means to reflect over a vertical and horizontal line. This could be due to the fact that we are used to seeing reflections daily, whether that be in a mirror or in the store of a window, which make the topic obviously relevant. The fact that a good majority of students had trouble when asked to rotate the shape 1/4 of a turn shows that the understanding is not all there. Using this observation I would suggest that we, as teachers, look into this misunderstanding and dig deep to better serve our students.

One way to represent what a rotation is includes using manipulatives to help students visualize what it is they are being asked to do. Using manipulatives on top of an enlarged handout of a grid would be beneficial to students because they are feeling what is happening instead of having to visualize it on their own. This, in-person, visualization allows them to see the relationship between what they have in front of them physically and what they are drawing on the page.

Another way to further help them with both of these confusing R's includes making the topic into an interactive game as we did in class with the game, "Square Match". This game took two non-symmetric objects, which allows for noticeable reflections, and make 6 game pieces (3 of each object). You then get into teams of two people and try to get all of your objects in the exact same position by either rotating to the right or flipping forward, while trying to get all of your opponents objects in different positions. After playing this game myself, I can say that it was fun and challenging at the same time. I could see elementary students enjoying this game, not even noticing how much thinking they are actually partaking in.

Students have the means to learn these topics it just takes a little extra work for us as teachers. By challenging students we challenge ourselves as teachers to work a little harder and think a little deeper. Being timid and working with topics familiar to us is easy and less work but to see real results in our classrooms it is important to not only challenge the students but to challenge ourselves to be the best that we can be!

I had noticed after a few different students did, just as the above picture shows, and reflected about the vertical and horizontal lines when asked to rotate 1/4 of a turn clockwise. This is a great example of the confusion that takes over students when trying to decipher between a rotation and a reflection.

Another observation I made when grading these students' work was that all of the students, when asked to reflect the shape, got all 3 reflections correct. This shows me that the students understand what it means to reflect over a vertical and horizontal line. This could be due to the fact that we are used to seeing reflections daily, whether that be in a mirror or in the store of a window, which make the topic obviously relevant. The fact that a good majority of students had trouble when asked to rotate the shape 1/4 of a turn shows that the understanding is not all there. Using this observation I would suggest that we, as teachers, look into this misunderstanding and dig deep to better serve our students.

One way to represent what a rotation is includes using manipulatives to help students visualize what it is they are being asked to do. Using manipulatives on top of an enlarged handout of a grid would be beneficial to students because they are feeling what is happening instead of having to visualize it on their own. This, in-person, visualization allows them to see the relationship between what they have in front of them physically and what they are drawing on the page.

Another way to further help them with both of these confusing R's includes making the topic into an interactive game as we did in class with the game, "Square Match". This game took two non-symmetric objects, which allows for noticeable reflections, and make 6 game pieces (3 of each object). You then get into teams of two people and try to get all of your objects in the exact same position by either rotating to the right or flipping forward, while trying to get all of your opponents objects in different positions. After playing this game myself, I can say that it was fun and challenging at the same time. I could see elementary students enjoying this game, not even noticing how much thinking they are actually partaking in.

Students have the means to learn these topics it just takes a little extra work for us as teachers. By challenging students we challenge ourselves as teachers to work a little harder and think a little deeper. Being timid and working with topics familiar to us is easy and less work but to see real results in our classrooms it is important to not only challenge the students but to challenge ourselves to be the best that we can be!