Math Misconceptions and Considerations HSG-CO.C.10
Look closely at errors in students’ work (formative assessment) to help you reflect and make instructional decisions to suit all students’ needs.
My students can’t do proofs so we don’t spend time on it Classroom teachers and mathematics education researchers agree that students have a hard time learning how to do geometric proofs. Misconception: Since the students in my class struggle too much with proofs it seems like a waste of time. They just get frustrated and quit! My students lack the perseverance to complete a proof on their own.
I only do fill-in-theblank two-column proofs with my students because that’s all they can handle.
What to do: Some of the statements above are true, to an extent. However, some of the responsibility for these student shortcomings lay at the feet of the teacher. Teachers should allow their students to engage in meaningful struggle in class. Not every task should be easy for students. Putting students in situations like these will increase their ability to persevere through a problem and decrease the tendency for students to quit. Many geometric proofs involve higher-level thinking and the use of the standards for mathematical practice. These are skills that need to be developed in the students. Students only need to know how to do two-column proofs In many geometry textbooks, two-column proof is the most prevalent so it becomes the one that teachers rely on most. Misconception: Two-column proofs are the easiest type of proofs for students to do so that’s all they are exposed to. What to do: Proofs in geometry should not be restricted to two-column format. Most proofs at the college level are done in paragraph form, with the write explaining and defending a conjecture. In many cases, the two-column format can hinder the student from making sense of the geometry by paying too much attention to format, rather than mathematical reasoning.