Problems in Mathematics Education

I believe there are several problems in mathematics education today including the emphasis on standardized tests and the way we push students onto the next mathematics course.

In the article, “How Mathematics Counts,” the author states, “So long as procedures predominate high-stakes tests, procedures will preoccupy both teachers and students.” I agree with the author that our education system’s focus on high-stakes testing leads to some negative consequences with regards to mathematics education. I see the effects of this at the high school where I’m student teaching. Approximately 200 out of 900 students fail the HSPA exam each year at this high school. I teach two sections of the SRA class for those seniors who failed the exam during their junior year. Even now that all the students have passed either the make-up HSPA or passed the SRA process, the students still think of themselves as failures in math and many of them think they need to continue to learn math through the drill and memorize method. A couple weeks ago, I taught a new unit on Strategy and Logic games to help them improve their analytical/critical thinking skills. This was a topic that they told me they were interested in, earlier in the marking period, however, I was met with a great deal of resistance throughout the unit. When I asked the students about their resistance, they said that they think they need more traditional math practice since that’s what they failed. Our education system has brainwashed students into thinking that there is only one way to learn math (which is the high-stakes test way) and that if you don’t succeed in learning that way, then you’re a math failure and always will be.

At times, our education system seems more intent on pushing students through to the next math class and graduation rather than ensuring that the students understand what they are learning. In “How Mathematics Counts,” the author noted that the increase in the number of students taking Algebra II is not being met with a decrease in the number of students taking remedial math courses at the collegiate level. This means that while we are pushing more students to take Algebra II in high school, we are not necessarily seeing the benefits of this push at the collegiate level. I see the affects of this everyday. One of the Algebra II classes I teach has 10 students. 8 out of the 10 students are failing (or nearly failing) the course and have been all year. When my cooperating teaching and I looked into their previous math grades, they all barely passed and some of them failed during the regular school year and then passed the course during summer school. While I think that some student’s failure is partially due to a lack of effort, I think that many of them don’t have the foundational Algebra skills to succeed in more advance Algebra courses because they never understood the basic concepts to begin with. But our system just pushes them along because teachers are pushed to get through the entire curriculum. I think the students are the ones who lose with all this pushing because we’re setting them up for failure in future, more advanced math courses. Perhaps if we could slow down a bit and allow students more time to interpret and understand the calculations that we teach them (as stated in the “How Mathematics Counts” article), students could gain more mathematical and critical thinking skills than they could if they just barely get through the procedures of Algebra II.

I feel like one potential underlying driver of some of these problems is the ambiguity regarding the overall purpose of education in general. After reflecting on issues such as those discussed above, I’m often left wondering if the point of education is to prepare young people for the workforce or if education should be a purely academic experience. Perhaps it’s a combination of both, but I’m not sure that many problems in mathematics education can be addressed if we’re trying to work in both directions.

NSF Project Reflections

One common theme from the NSF curriculum reviews was about learning several math topics through problem solving and applications rather than focusing on one math topic at a time. I think approaching math in this way could address one of the issues that I see in mathematics education, which is students being unable to transfer the math skills they learn to solve problems. So far in my student teaching role this semester, I have been teaching math in a more traditional way. I had every intention of teaching problem solving and using guided discovery, but now that I'm in the classroom, I find it much more difficult than I anticipated. Now that I've become aware of how the NSF curriculums use problem solving as a base, I'm starting to develop a more realistic idea about how I might be to implement similar kinds of lessons within my school's traditional math curriculum.

As a future teacher, one of the main concerns I have about these curriculums is whether or not they will adequately prepare students for college level courses that are typically taught in a more traditional way. Few (in fact MATH 579 is the only exception) of my college level courses have been based on problem solving and applications. So I'm left wondering if we're setting students up for failure in the future without exposing them to more traditional methods of learning. On the other hand, if students learn to solve problems and apply math, perhaps they will easily adjust to college courses because of the way they learned math....

Discovering The Distance Formula

Here's an activity that might help students appreciate the usefulness of the distance formula. I think this would be considered an application, but tell me if it's not:)

Students can work in pairs or small groups. Each group is given a coordinate plan with a line drawn on it and is asked to find the length of the line. They should be able to determine the coordinates of the endpoints and the line should not be vertical or horizontal (because that'd be too easy!). As the students are working, the teacher can observe the various methods that students use. If no one has thought of it after awhile, the teacher could suggest that the students create a right triangle with the original line as the hypotenuse. Ask them, "how might this drawing allow them to find the length of the line?" Hopefully some students will use the Pythagorean theorem, but if not, the teacher can introduce this idea.

Then the teacher can lead the class in deriving the distance formula by generalizing the process that they just used with the Pythagorean theorem.

Students can go back to the original problem and apply the distance formula directly to see that it works.

Why Is Learning Math Important?

While I think there are practical math skills (e.g. adding/subtracting, making change for a $20, balancing a checkbook, etc.) that help students in their everyday lives, I don't think these are the most important reasons to learn math. I think one of the overarching goals of education should be to help students develop a toolbox of skills for making effective decisions and thinking critically. Each of the subjects that are taught in schools (math, art, English, music, social studies, science, etc.) provide students with a different set of tools for their toolbox. The process of learning math (and not necessarily the mathematical concepts themselves) helps students develop analytical skills and and a way to logically process data and information, thus providing students with a unique set of tools that they may not learn in other subjects.

About Me

Like many people in Montclair's MAT program, becoming a high school math teacher is my second career. Growing up, I always wanted to be a math teacher, but I ended up graduating from Penn State University with a degree in Management/Human Resources instead of a teaching degree. For the 5 years between undergrad and grad school I worked for two healthcare companies. Most recently, I worked at Johnson & Johnson recruiting students to work for my company. It was a great job, but I wanted to be passionate about my job/career and I wasn't.

So one day I was sitting by the pool and had one of "those moments" that I'll never forget when I decided to change my life and become a high school math teacher. I packed up my pool gear and started to research how to become a teacher. Less than a year later, I quit my job and started grad school at MSU.

Even though it's been almost 2 years since I've earned a real income (that's been tough), I'm confident that I made the right decision to change careers. I observed a high school classroom last semester and felt excitement for a job that I never experienced before. Every day, I left the school feeling completely energized. My hope is that this passion will continue once teaching is my full-time job!

Are there seasoned teachers out there who haven't lost their passion? I hope so!