As of recently, I've tried to be the model of the "growth mindset" with my students. Not so much with the material that they may be studying, but rather as a teacher. I try to show them how a positive mental attitude mixed with the idea that I am always doing my best to learn new perspectives and outlooks when it comes to approaching a problem is beneficial to them as a life-long learner, rather than saying "Oh, probability?! I've always been bad at probability, so here are a few things to memorize so that you can at least take the test!" (I'm still not the best at probability though...but I'm getting there!)
So over the next few years, I'm setting a few goals that I would like to meet in order to maintain my own growth mindset as a teacher and also install the idea of a growth mindset into my students.
Goal 1: Nix the Tricks
A couple of months ago, I read Tina Cardone's book Nix the Tricks, It confirmed my belief that I am not alone in the fight of attempting to achieve conceptual understanding for my students. Yes, there are a few "tricks" I may still use (I'm comfortable with students using exponentials and logarithms as inverse operators), but overall, nixing the tricks from my teaching only benefits everybody. Conceptual understanding is hard to achieve when everything that is known is based off a shortcut. And if a concept isn't understood, the harder it is to do well in a class; and the harder the class is, the more likely a fixed mindset of "I will never get this material" will start to sink.
So nix the tricks! Teach the underbelly of what is going on! I've done my best to get students to wrap their collective heads around concepts and it's all worked out well so far.
Goal 2: Omit the word "should" from my vocabulary
I have to admit, I am a huge James Tanton fanboy. His ideas, creativity, and sheer honesty motivate me to become a better teacher. I must've read most of his essays at least twice, which is why I was surprised that I never caught onto this idea until yesterday. In his essay 12 Points About My Teaching, Tanton describes why he believes he has been successful in his teaching endeavors. His eighth point was that he knows there are mathematical ideas that he does not know. There are ideas that students just don't know. And that's okay! It is okay not to know things. But it is not okay to not want to know them. It is also not okay to tell students that a certain topic is something they should know, especially when reviewing.
Every year, I, along with every high school Algebra teacher, struggle teaching rational functions because many students struggle with fractions in general. Students don't remember that common denominators are necessary when adding or subtracting fractions, or that when dividing fractions, all you must do is multiply by the reciprocal of the second fraction. And the struggle is justified.
While working with a student last week on this exact topic, I told them that adding and subtracting fractions is something that they SHOULD know how to do. But really...should they? Many students don't work with these ideas for YEARS until working with rational functions. They rely on their calculator to do the dirty fraction calculations for them. Should we expect them to remember?
I had to catch myself and I rephrased. I told that students that "adding and subtracting fractions is something we can 'expect' you to be able to do." With literal handmade quotation marks. I don't blame students for not being able to remember that. Hell, I haven't seen calculus in years, so I've had to re-learn everything so that I can help students. So I understand the struggle completely. So rather than saying they SHOULD know something, focus more on review! Before exploring how to use operations on rational expressions, take a day to go over addition and multiplication of fractions. And don't just review how to do it, but explain why they work. Younger students are good at following blindly. Refresh their older selves as to why common denominators are needed to add fractions.
I do urge anyone who reads this, especially math educators, to look at both Cardone's book as well as Tanton's essay(s). They are really eye-opening,
Until next time, happy math!