I'm currently teaching common core geometry, which assumes that a student has algebraic knowledge coming in. Clearly, we shouldn't expect students to retain everything from their algebra class before they take geometry. I've found myself reteaching the entirety of the class what slope is and how to calculate it. Ok, I can understand if about 80% of the students forgot entirely how to create a triangle on a graph and count how long its sides are. That's fine. But there are other concerning observations about some students in my classes, some of whom apparently failed algebra 1 but are being passed along into my class anyway...
- Forgetting which axis is x and which is y, and had difficulty plotting (x,y) coordinates at the beginning of the year.
- Not being able to determine the length of an unknown line segment -- (2) and (?) next to each other, with a total length of (11). She guessed 5.5. Even after I told her the smaller segments add up to 11.
- Not being able to solve the equation x * 1.2 = 24 with any amount of prompting until I literally rewrote the equation as 1.2 x = 24 (I had suggested that she do so herself, but she didn't and we had been talking about this equation together for several minutes).
- Not being able to determine whether a shape looks like it has been rotated or reflected, even though they demonstrate knowledge of what the words "rotate" and "reflect" mean (spatial skills).
- Could not graph an equation in the form y=mx+b at the beginning of the year, and still require prompting and guidance to do so.
I guarantee that some of the students mentioned above will have extreme difficulty in geometry class. Not only do we use algebra in most sections now that it is "common core," but some of them are missing the arithmetic reasoning that they need for geometry. Several failed algebra 1, but passed the "EOC" exam, so they got placed in my classes anyway. They will struggle to pass my class as much or more than they struggled to pass algebra.
- At what point is it a disservice to pass a student into a class they are not ready for?
- How does someone determine the prerequisite knowledge for a math class while recognizing that the knowledge that would be best for students to have is not necessarily the knowledge they will enter with?
- Is having students repeat low-level math classes like algebra before moving on to geometry beneficial, or should students be able to succeed at common core geometry without algebraic background?