South Dakota adopted the Common Core State Standards for Mathematics (CCSSM) in 2010. I think that anyone that compared these mathematics standards to the previous standards would say that the CCSSM are more rigorous. In fact, the SD Department of Education (DoE) saw the need for workshops and training on the new mathematics standards and provided this training: several teacher workshop have been funded to provide additional training for teachers on the CCSSM. It isn’t so much that the content is new, but that the way of teaching and emphasis on understanding rather than just following procedures is different than before.
This past year in the state there has been a lot of discussion on the shortage of highly qualified math teachers and a need for an alternative certification. These discussions led to the DoE creating rules for a new Intermediate Mathematics Endorsement. This new endorsement would allow a teacher that holds the endorsement to teach several courses, including Algebra I, Geometry, and Algebra II. One might ask what extra courses need to be taken to earn the new endorsement. Sadly, no extra courses--a teacher simply has to have a valid teaching certificate in some content area and then pass the Middle School Math Praxis.
Since I teach pre-service teachers in a course called Geometry for Teachers, I thought I had an excellent opportunity to ask these future math teachers if they would feel prepared to teach geometry if they passed a test that covered the geometry content from the Middle School Math Praxis. I gave the students the list of geometry topics from the exam as well as the high school geometry CCSSM.
I asked the students’ permission to use some of their comments anonymously in my blog. Below are some of my favorite comments from the students. Each of these comments is from a different student.
Comment from student: “I don't think that passing a test with those things would leave you qualified. You would be missing one of the biggest parts of geometry... proofs! I feel that you need to know why you are doing any of those things and why they are true. This might be the single most important part. Along with that I don't think I would have enough knowledge about circles. I feel like what I'd be able to teach in circles would be limited.”
Response from another student: “I completely agree with you. Proofs are probably the most important factor in geometry, so barely knowing how to do them ourselves would make it nearly impossible to teach young students. We have to be aware of how everything works and why it works that way. “
Comment from student: “I do not feel as though I would be able to teach geometry successfully by merely passing this exam. The topic list is vague, as is its statement that you must "understand" the topics. I believe that the test should require proofs because the ability to achieve the right answer doesn't mean you necessarily "understand" the reasoning/process, which is why proofs are included in the standards. I think that the topics presented are a good start, but that they need to be elaborated on more so that they are more specific. Also, the exam is only one form of assessment and I think I would need to be tested in more ways in order to feel qualified to teach not only geometry but any subject. “
Comment from student: “After taking that exam, I would not be qualified to teach a high school geometry course. One reason is the lack of details. The exam covered fairly overarching and brief details while the standards include more specific ways to do things such as using rigid motions. Another aspect missing from the exam is proofs. Verifying and proving things is a large part of the common core standards and there was no evidence of that kind of assessment on the exam. Besides for the topics themselves, just passing a geometry test does not imply that I would be good at teaching the subject. I would need to have further training to learn how to teach that content knowledge. Altogether, I would not feel qualified.”
Comment from student: “If an exam that covered those topics was used as a basis of evaluating whether or not I should be a teacher then I wouldn't feel qualified to be a teacher. First knowing a subject and being able to teach a subject are two different things. I could know every single detail about something but have no people skills or just not know how to word things so that people that aren't at the same academic level can understand. The other thing I noticed was that proofs were not explicitly mentioned on the list of topics. I remember when I took geometry in high school that my teacher was good at explaining to us how to go about doing proofs, which we spent a lot of time doing so I feel that it is a major component of high school geometry, and she was able to answer or give hints on a majority of the problems that we had concerning the proofs. She possessed content knowledge and people skills.”
These students are enrolled in a Mathematics with Teaching Specialization program. They all agree that passing a test doesn’t make one qualified to be a teacher and that passing the Middle School Math Praxis is not sufficient to teach high school geometry. To me, this Intermediate Math Endorsement is an insult to these students who are going to complete a rigorous mathematics degree. I am very impressed with these students so far this semester and am confident that they are going to be great teachers.