I completely agree with you Victoria. In high school mathematics, evaluation is not used nor expected. It happens far too often that students will want to go further in their understanding of math by asking why something works or why it is important and their teacher will tell they don't need to know or that it isn't important only the current application is important. I think you have to make a conscious decision about encouraging higher level thinking in a math classroom because it isn't necessarily built into the subjects taught in high school which is unfortunate. And I agree that it isn't until recently that I've been expected to think in a higher level fashion and in a lot of ways I think that has handicapped me. So I guess as future math teachers we will have to help them think outside the box.

I think both of you make great points and I believe that most math teachers do not push their students to understand why stuff works just as long as they can apply it to pass a test. What I am concerned with is if a high school student can completely understand material that college students are struggling with. In high school, I had a lot of questions about how some things worked and most of the time the answers were so abstract that at that point I really could not completely understand it. That is why I feel that some topics should be left for a post-secondary instructor to expand upon. I will encourage students to ask questions and to be curious about the thoughts behind the mathematics, but there is some stuff that I still do not fully understand and could not give a good explanation. Therefore, can we expect our students to understand it without getting discouraged?

Personally in high school I hated math and still do to this day because of a math teacher I had. She gave us work out of a book and assigned us the questions that had answers in the back of the book while she played games on her computer. While the math work obviously wasn't hard and I liked that, I didn't learn a thing. When I came to college I still hated math and continued to struggle because of someone who had taught me years before. With a good math teacher (one I had 9-11 grade) understanding math in complicated processes is somewhat easier. I learned a lot from her and she did challenge us to think about things and was always willing to help even after hours. The one I had my senior year was obviously awful and I wish I could say it was a rare case but it is becoming more evident that teachers (particularly a subject like math where there is one right answer) depend on the book to do the teaching and require little thought process otherwise. I believe this is where we come in and change the way our students are being taught.

I have had a similar experience to Victoria's where I have only come to use a higher order of thinking in college mathematics. This is most likely do to the fact that teachers in high school and below have to focus on teaching to the test. There are so many students that struggle with just the basic concepts that teachers do not have time to go into more detail for those that can handle it. Victoria, hopefully, at some point in your career you will be able to teach Honors versions of high school math classes. Here you may have the opportunity to teach somewhat more advanced thinking, and it will not be difficult for you. (For example, my honors geometry class took time to learn about 2 column proofs whereas the general classes did not.)
My other suggestion would be to keep yourself fresh with the knowledge you are learning in college, so when the questioning kids in high school approach you, you will have information for them off the top of your head. This can also apply to courses other than math. For example, english teachers always have the opportunity to suggest additional reading for those who want more advanced literature.
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Audrey Fowler

You all make very good points. So, as you pointed out Zach, I can't expect to involve my students in too much of higher level thinking in math because it probably won't make any sense to the students. However, maybe if I myself "think outside the box," then I can help my students to "think outside the box," as Abby suggested. Then I can include some more evaluation without going so deep that my students are completely clueless.
I guess all of us future high school math teachers will have to hope that we are given the opportunity to teach an honors section of a course if we want to teach more than just the basic, required objectives of the curriculum.
Thank you all for giving me some things to consider as I progress closer to my own high school classroom. My hope is that I will be able to take these ideas as well as other ideas to become a successful and passionate teacher.

I understand where you are coming from Victoria. I am planning on teaching Spanish to high schoolers and I wonder how I will be able to use higher order thinking skills when many of my students will be very much on a beginner level. I discussed this with another Spanish Education major and she pointed out to me that the higher order thinking might come into place through the teaching of the hispanic cultures. Maybe there is some area of math that you could apply this to? I remember in one of my high school math classes we had to write a few papers on some interesting math theories, which definitely involved some serious evaluation.

Victoria, I am hoping I get an honors section because there is so much stuff we can expand upon that I feel we would not be able to do that in a regular math class. Concering what Abby said, I am sure there will be times that we can have our students think outside the box, but will there be enough opportunity that we can expand our students to use evaluation to the point they are comfortable with it even in a non-honors section? In our education classes they tell us to be mindful of what situations and levels students are entering our class with, so can we help catch up students who are behind while we make sure that we still test our more advanced students so that they can get to use more abstract thought processes?

I agree that math is not very easy to teach at a higher level thinking but i also feel that as long as they truly understand the content then they are thinking at a higher level. what i mean by that is if you give a formula for a particular problem but leave it out for a similar problem (but different) and they know what problem to use correctly then they are really thinking and understand the content. But yes it will be difficult to teach and assess at a higher level thinking.