in which I relearn some things about function notation March 17, 2013
Posted by Ashli in General, Mathematics.add a comment
I can get lazy with my language around mathematics. I try not to, but I know it slips through.
My personal biggest challenge in this regard is statistics. Stats demands precision, and I’m just not there with it yet. It’s a work in progress. If I am every talking about you with stats and I say something ridiculous, please feel free to correct me. I will appreciate it.
Beyond stats, function notation is one of those things that I know a lot of people are very casual about. I see teachers and students (and I know I’ve done it when talking) swapping between f and f(x) as though they are the same thing. To help with clarity, and the seed that made this post happen, here is a nice discussion about function notation that I am blogging about so I have it easily in reach and I thought some of you would also find interesting.
Oh, and there’s that Podcast thing that is now up. There will be a new one up this Thursday, 3/21 that’s a shorter format focused on a prompt, what to do about GReader, and other news of the online math world.
in which I cross-post about the podcast March 8, 2013
Posted by Ashli in Teaching Thoughts.add a comment
For all interested parties, I am starting a podcast called Infinite Tangents. The focus of the podcast will be teachers stories, specifically those around the mathematics classroom.
To listen to Episode 0: An Introduction and learn more about the podcast, click here. Thanks, and please share!
In which I read research articles with interesting contrasts January 14, 2013
Posted by Ashli in Teaching Thoughts, VAM.1 comment so far
Since acronyms seem to be a part of any profession, we have the delight of two MET’s in math education. One is the Mathematical Education of Teachers, which just came out with their second version that I am working my way through. The other is the Measures of Effective Teaching project that the Gates Foundation has been putting on the past three years. Today is about the latter.
You can go and read the whole thing here. If you skip to page 20 you can read their “What We Know” conclusions from the 3 year study. I like a lot of what the report has to say about how to use classroom observation, rigorously training observers, taking a balanced approach, etc. I have a hard time with a standardized test being the end-all measurement and I don’t trust student surveys for an accurate portrayal of a teacher’s abilities.
Interestingly, right after finishing the Gates report I was given a link to this abstract from a paper issued in December of 2012 by C. Kirabo Jackson:
I present a model where students have cognitive and non-cognitive ability and a teacher’s effect on long-run outcomes is a combination of her effect on both ability types. Conditional on cognitive scores, an underlying noncognitive factor associated with student absences, suspensions, grades, and grade progression, is strongly correlated with long-run educational attainment, arrests, and earnings in survey data. In administrative data teachers have meaningful causal effects on both test-scores and this non-cognitive factor. Calculations indicate that teacher effects based on test scores alone fail to identify many excellent teachers, and may greatly understate the importance of teachers on adult outcomes.
I am interested in the idea of a teacher’s outcome on “non-cognitive ability”. How do you measure a teacher’s ability to help kids throw off the fear they all seem to exist in during adolescence as they work to figure out who they are and who they want to be? I don’t think a standardized test measures that well and there is something powerful about realizing you have the respect of an adult who is not your relative and who shows passion for life.
[UPDATE 01/17/2013]
Two new articles have come out that chime in about the statistics (or lack thereof) in the Gates Foundation article. Good reads. And if you teach stats they are rather applicable.
The 50 Million Dollar Lie, by Gary Rubinstein
Gates Foundation Wastes More Money Pushing VAM, by Gene V. Glass
in which I hear from a former student December 10, 2012
Posted by Ashli in Reflection, Teaching Philosophy, Teaching Thoughts.add a comment
Like many teachers, I occasionally get notes or drop-ins from former students. And I don’t care how old they are; they will always be my kids. With the advent of the Facebooks, I have several that I occasionally hear from after they’ve graduated. I especially like the ones that apologize to me for not taking more math in college. Kinda adorable.
Last night I got a missive from one of my darlings worried about her math final. If she doesn’t pass it, she’ll fail the class. This is her first semester in college. The note was short, and she ended it with
Why am I so bad at the maths?! D:
I wrote back the following:
For me, maths was more about accepting a different way of thinking than anything else and that can be the hard part. We’re not brought up in a logic-based society. So much of high school math is focused on procedural thinking–if A, then do B & C, and ta-da! And that’s not really math. That’s more like advanced baking. Useful, to be sure, but not a way of thinking. Since I don’t use those types of problems as my main push in classes it’s also why the typical A-maths kids don’t like me for a few months–they’ve never really had to think for understanding before.
And that right there is the key. Maths makes sense. It’s the Queen of Science for a reason. If you think what you are doing in math does not make sense or is magical, than we need to figure out a different way for you to think about it. Luckily, there are a lot of ways to think about maths that are successful. Unluckily, finding the way that works for your brain can be grueling.
I got through high school using procedural skill (the If A, then do B stuff). I hit a brick wall in my first maths class in college because it didn’t work with that professor. I had to show him how I was making sense of the maths and since I wasn’t really making any sense I didn’t have anything to give him. There were a lot of nights spent in the math study room and I didn’t really get the thinking needed to understand, but I was moving that way. Slowly.
Sophomore year was when it was finally clicking that I needed to build my own understanding so I could stop playing the memorization game (it wasn’t possible to pass some of my classes via pure-memorization as no ones memory is that good. And I was taking Latin at the time so my memory banks were full up with vocabulary).
So yeah, maths is hard if you’re taking the memorize ever permutation of a problem and how to solve it route. Figuring out the patterns behind the maths is a challenge, but it pays a lot of dividends. If you ever want to chat about your stuff, just let me know. I have skype and I use google hangouts quite a bit for my work. Just remember: I am 3 hours ahead of you
What I did in class wasn’t enough to get her to where she needed to be to be successful in college maths. I still focus too much on the procedural at times, but every year I moved more and more away from that as I built up skills toward a teaching style I never saw in high school maths. I’m curious to see how much my classroom skills will atrophe while I am out of one or if the level of ed-research, blogs, and consulting work I do will help me hold steady. One can only hope.
I miss my kids.
in which I send you to a research survey October 29, 2012
Posted by Ashli in Uncategorized.add a comment
If you follow me on the twitters, they you have already seen this link. At NCTM Hartford (which I’ll be blogging about, just not when my power may fail at any moment), I got to meet a delightful Math Ed doctoral student who is taking a look at Math modeling. If you have some time and could fill out her survey, it would be much appreciated. Support the community!
To take this survey, you need to be in the US and a 7-12th grade math teacher.
click here to go to the survey.
Thanks for your support in this. As a consumer of math ed research, I feel I should try to give back to it whenever I can.
in which i give a talk on the profession of teaching October 19, 2012
Posted by Ashli in Prof. Development, Teaching Philosophy.7 comments
IM&E hosted a thing at Berkeley October 12-14. I was working with middle grades folks and asked to give the final plenary talk entitled ‘Call to Action’. I chose to talk about the profession of teaching and how I think we get more teachers engaging with teaching as professionals. I’ve tried to type up what I said in the talk based on my copious notes, powerpoint, and memory below the cut. I know it’s not exact and I suspect my memory is editing to make me sound better, but I don’t have a video recording (thank Gauss) so it will have to do. I’ll warn you it’s longish, but I would love to hear your thoughts on professionalize and education in the comments.
Oh, and this is the tweet that spurred much of my ideas for the talk. Or rather, had me re-writing much of my ideas for the talk.
in which 3d graphing is explored September 28, 2012
Posted by Ashli in Math Art, Precalculus.2 comments
in which the unit circle gets its due and movement is noted September 12, 2012
Posted by Ashli in Uncategorized.1 comment so far
A colleague of mine who is teaching Precalculus this year asked about a Unit Circle Project that is mentioned in my outline from when I taught the course. I realized that it’s something I’d never written down as I learned it at a T3 conference in Seattle (from Rhonda Davis) but I didn’t get the handout due to the over-full session and the presenter does not exist online from what I can tell. Over the years I’ve done it my way and like to put it right near the start of Precalculus.
Students in the district see a pinch of trig in Geometry and maybe a small bit in Algebra 2 if they took honors, but Precalc is the real beginning for them. I’ve scribd a teacher’s guide for the Unit Circle Project and a student worksheet that goes with it for anyone interested.
In other news, I am now living on the East Coast in Maine and working as a mathematics consultant for a few groups (teaching jobs are not to be had here due the remote nature of my new location). Hopefully this will mean I’ll get to clear out and post several half-done blog entries over the next while. Unpacking comes first, though. And if anyone is going to NCTM Hartford, let me know as I also plan on attending.
in which i adore Peg Cagle July 2, 2012
Posted by Ashli in Teaching Philosophy.1 comment so far
My interpretation of her words regarding teachers as professionals:
Don’t let anyone call you a ‘natural’. They may mean it as a compliment, but it diminishes the intellectual work that we do as professionals to become as good as we have to be to educate our children.
in which i employ a plant May 11, 2012
Posted by Ashli in Lesson Disclosure, Teaching Thoughts.1 comment so far
One of the fun parts about participating in the online community is meeting members of the online community in person. I had a chance to meet Daniel Schneider, aka Mathy McMatherson, and break some bread while enjoying one of my favorite things: edu-math-chat. And if you are not reading his stuff, you should be. I will be utilizing his Wall of Remediation idea for my Support class kiddos to study for the final in Algebra 1 which covers distinct skills from our SBG setup.
During our chat I was reminded of something I used to do that for some reason I have not been doing the past few years. I thought I would write it out here to help me remember to use it again in the future. I think best when I get a chance to write things down, so this may be a bit free-flowing.
So picture this: you have a lesson planned that will hopefully lead kids through some mathy ideas to a big conclusion. You are concerned, however, that they will not ask the questions you are hoping for and are unsure of your abilities to steer the conversation without obviously grabbing the wheel. This was my state of being for several years (and still is sometimes). On the spur of the moment in class during my 2nd year of teaching I decided to ask I kid I trusted to keep a straight face to ask a specific question if I gave a signal. It wasn’t critical to the question, but it was a nuance I didn’t think the kids were picking up on. I ended up giving the student the signal and they asked the question. This caused a pause in the class and then more back and forth conversations in the group about this point. My plant jumped into the discussion and none of the students thought anything out of the ordinary had happened.
Was I covering for weak group-discussion-leading skills? Maybe. Did the kids see something they wouldn’t have seen otherwise had the question not been asked? Yup. Was it better coming from a student than it was from me? I think so. I believe that students often respond better to the questions/responses of their peers than they do to myself. Peanuts effect and whatnot.
Fast forward a bit. I ended up using plants on occasion. Sometimes for questions, sometimes to say wrong answers I wanted to make sure got covered. I totally got caught in some classes, which I was able to play up enough that the kids found it amusing and the plant was giving off smug ‘chosen one’ vibes. I realized that getting caught could be great. I chose to sometimes give a kid a written question/comment with vocabulary they would never use, but I totally would. Authentic learning environment? Nope. Did kids pay attention, get a laugh, and build not only mathematical understanding but also classroom community? yup.
I once used it freak out students. Used to be my 1st period support kids would see me twice: once for support and once for regular algebra 1. I had a kid ask in support about other math symbols (we were doing inequalities if I remember right). This was a student who expressed dislike of math, but was well-liked by his peers and rather good at math he ‘got’. I wrote out some abstract form of “for all x contained within the reals ….” in symbolic notation. he thought the ‘code’ was pretty cool, so I asked if he could remember what it meant. He repeated it back. Fast-forward to period 2. Regular algebra 1. Same symbols question comes up. I get my plant a quick glance and he is playing it cool. I write up the symbols again, tell the class it’s an advanced math sentence and ask if any of them know what it says. They are, of course, stuck on the upside-down A. My plant raises his hand and TOTALLY plays this up. Squints his eyes a bit, rubs his chin, “well, I think it says …” Beautiful performance. I wanted to applaud. Every other kid in the class is staring at him, his friends are whispering demands for how he knew that. I congratulated him and repeated what he said while pointing at the sentence and then continued with the lesson.
I’m pretty sure he admitted to them later about being a plant, but it definitely got the attention of the class and I started seeing the upside-down A and the triple dots for ‘therefore’ on some papers.
Some notes on the details. I never used the same kid twice. I never made it a regular thing lest they get paranoid about one another. I’ve not done it in years. I think in the National Board year-of-crazy it got lost and I hadn’t even thought about it (which tells you how infrequently I did use it).
I’m much better at helping to direct conversations and making sure that kids are set up properly to make the connections I want these days. That does not, however, mean I am not thinking about how to use the ‘plant’ idea in some of my upcoming lessons.
