Geometric Rotations and Angles: How are they Connected?

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Dawn Teuscher recently had a paper titled “Geometric Rotations and Angles: How are they Connected?” published in the conference proceedings for the Psychology of Mathematics Education – North American conference. Dawn has answer a few questions about this paper below:

Who were your co-authors on this paper?

Navy Dixon and Sariah Stevenson

Who would you say is the target audience for this paper?

Curriculum developers and mathematics education researchers

What is the big problem you hoped to address with this paper?

Geometric rotations is a transformation that is difficult for both teachers and students. Teachers understand and emphasis with their students the need to identify a center of rotation as well as an angle of rotation. Therefore, we wanted to explore what are students meanings of rotations and what unintended meanings might teachers convey to students when they teach geometric rotations. 

What are some of the key ideas in the article?

(1) Students who understand what an angle measures are more successful with geometric rotation questions.

(2) Students seem to understand that rotations preserve the size, shape and orientation of a figure.

(3) Students seem to relate an objects position to a clock or a compass rather than to an amount of turn.

(4) Using the coordinate plane may actually limit students understanding of rotations and angle measure.

What are some of the main ideas you hope your audience will take from the article?

Teachers need to address the meaning of angle measure with students starting at grade 4.  Students need to be pushed to not rely on visual placement of an image, but to understand what an angle is measuring.  Teachers need to move away from the prototypical right angle (parallel to the bottom of the board or ground.


With the adoption of the Common Core State Standards for Mathematics 12 years ago, the content of geometric transformations was shifted from high school to grade 8. In our research with middle grades teachers, they often discussed their difficulty in teaching geometric rotations. Therefore, we analyzed 444 middle grade students’ responses, across four states, to eight rotation questions from the SMART assessment. The results corroborate teachers’ challenges with teaching and student learning of rotations. Results indicate that students have a rigid understanding of angle measure that may impact their understanding of geometric rotations. Although angle measure is introduced in grade 4, we hypothesize that teachers need to provide additional opportunities for students to expand their meaning of angle measure.