So, I am a PhD student at an education school. While there are others at the school who study various aspects of mathematics education, I am (as far as I know) the only student who actively studies pure mathematics and is interested in mathematics education from that vantage point.

First, I am frustrated with the way that people in the education world seem to perceive mathematicians. I was, quite honestly, shocked at the degree to which stereotypes seem to govern these perceptions. It is assumed that mathematicians haven't thought enough about pedagogy, are out too of touch, and think too abstractly to be worth consulting on K-12 mathematics. My decision to pursue classes in pure mathematics is generally met with confusion. My hope to work collaboratively with math educators, math education researchers, and practicing mathematicians is seen as naive.

On the flip side, the prevailing attitude among most mathematicians is that people go into math education simply because they don't have the chops to make it in a pure math PhD program. This implies the assumption of weak math skills. Furthermore, they assume that those of us in the math education world are myopically focused on and uncritical of the dominant curriculum.

Now, there is truth to both of these stereotypes. Yes, research mathematicians have a reputation for being poor teachers and explainers. And yes, many in the math education world lack background or interest in any math beyond calculus. However, neither of these is uniformly true and these stereotypes are incredibly damaging to both camps.

On the one hand, mathematicians wonder why so many students fail freshman classes or switch out of math majors. They also lament the quality of K-12 math education and wonder how schools and mathematics teachers can sleep at night when they teach mathematics that is so dry and uninspiring. On both of these counts, they would do well to turn to those who study pedagogy, schools, and history. Our knowledge could help them greatly widen the appeal of their field and dispel many of the negative connotations that students have with college math departments. Math departments especially struggle with recruiting and holding on to students of color. This is another area where the education world has a lot of advice and nuance to offer.

On the other hand, teachers and math education researchers assume that research mathematicians live in a place in the clouds above them, unable to reach down and offer anything useful. The work they do is so far past and detached from the work students do in schools, how could they possibly help? What this misses is the incredible depth of knowledge, enthusiasm for the subject, and intuition that mathematicians possess. While their ideas probably need to be translated and filtered to be age appropriate, they have a lot of important things to say about what math education is missing and what we could do to make it better. People in the US see mathematics as a dry, rote subject. Their memories of it are colored by anxiety and failure. Who better to consult on how to work on this issue than the people in the country who know best the true character and beauty of the subject.

I think that one of the major reasons that math education has flip-flopped, stalled, and been such a battleground is that these two camps have been unable to work together for the most part since the 1970s. The war between pure and applied math departments, too, doesn't help the situation.

As a math education student who also cares deeply about abstract math and thinks it has a place in the K-12 and community college worlds, it is incredibly frustrating to deal with these stereotypes from both sides. On the one hand, I am thought to be out of touch and naive and my insistence that thinking about the epistemological value of certain topics is met with disbelief. On the other hand, I am immediately assumed to be a low skilled oaf who should leave the conversation about curriculum to the real mathematicians.

Rant ended. Post thoughts and/or questions.