Between Me and the Door

Not a whole lot of action on last week’s, but it was admittedly a little time intensive.

This week’s problem:

A basketball court is made up of square parquet tiles, all the same size, laid side by side to form a rectangle 105 tiles wide and 135 tiles long. If a straight line is drawn diagonally from one corner of the floor to the opposite corner, how many tiles will the diagonal intersect?

Part II: Generalize.

See you in the comments or on twitter!

I have a confession to make.  I teach high school math and I have math anxiety.  I HATE doing math in front of other people.

I think this stems from a few places.

1)  I am horrible at mental math.  I didn’t learn any kind of logical reasoning to go with mental calculations until I was in my early 20s.  The day someone told me figuring out 15% tax was easy because you just had to figure out 10%, then halve it and then add the two together BLEW MY MIND.  I think I was 23.  At 23 I had already earned a university degree and was still trying to compute 15% mentally with no shortcut.  It was around this same time when I started attending professional development that highlighted strategies young students could use to add/subtract numbers, and again, I was amazed.  Simple things, like rounding up and then subtracting that number later (98 +47 = 100+47-2) had never even occurred to me.  To this day my reflex is to try and line up numbers in my head and do all that really complicated carrying business.  While I’m trying to do this, people inevitably look at me and say “You’re the math teacher.”  Yes, yes I am.  And I own a calculator.

2)  I excel at school math.  You know, the kind that involves a 5 step process.  The kind that involves no creativity at all, that involves memory recall of what steps apply to a problem that looks similar.  I excel enough that I can likely give you 2 or 3 options for how to solve any given problem and really explain to you why it works.  I even really enjoy “complicated” school math, because arriving at that final answer after the tedious process appeals to me. (Disclaimer, I also really like things like filing paperwork and filling out excel spreadsheets.  Repetition is soothing, victory is assured.)

3)  I am a slow math thinker.  This might be related to #1.  When I do propose a hypothesis, it takes me quite awhile to feel it out to its logical (or illogical) end.  There is nothing wrong with this, but often working in a group setting other members have already taken off.  I need silent processing time – partially to make sure I actually understand what’s going on, partially because I like to make sure I don’t sound ridiculous when I do voice an idea.

The good news?  I’m getting over it.  It’s taken longer than expected given how okay I am with saying ridiculously wrong things in all other aspects of my life (of course, totally convinced that I am right as I say them), but it is better.  It is something I do have to actively manage however.    Luckily for me, managing my anxiety is much like a 5 step process, and I’m quite proficient at that!

Well this was just so much fun last week (though most of the discussion took place on twitter, maybe I should give this a #tag…) I think we should do it every week

I’m sure youve all seen the jug question at some point in time (if you haven’t, stop watching at 2:52 and figure it out for yourself!)  Sorry in advance if the video gets pulled down, Fox doesn’t seem to love sharing their movie for free.

Untitled from Kate Nowak on Vimeo.

This week’s question:

Let us generalize: The jugs are a and b units. We need to measure x units. For what values of a, b and x is it possible? Explore examples and draw conclusions. Partial solutions are appreciated. Suggestion: As a starting point focus on measuring 1 unit. For what values of a and b is it possible?

Hey folks,

So as part of my grad class we have a math question to answer every week.  We can seek outside opinions from anywhere we choose (so I’m not cheating ) so I figured I’d throw it up on here in case anyone wants to geek out with me every week.

This week’s question:

Consider the set of even numbers = {2, 4, 6, 8, 10, 12,…}. If these were the only numbers in our world, which do you think should be the prime numbers?

Hopefully I’ll see you in the comments!

So I thought long and hard about what I could possibly contribute to an assessment carnival, and amongst all my opinions decided maybe I should contribute something concrete for once.  So, what I have to offer is one simple thing you can do if you love all the things you hear, but don’t have time to implement anything in a way you’d be comfortable with.  This is the one thing you can do tomorrow, with a virtually no change to your prep or instruction that will start to change the way your students think.  Or you can add it on to whatever innovative things you’re already trying and it won’t throw a wrench in your plans or require you to change anything.

Stop marking exams. Even better, stop marking everything.  I’m serious.  The only thing I have marked in the last 2.5 years is a few major projects and final exams.  The projects were likely poor planning on my part, and if I could stop marking finals I would.

Why?  Research tells us that even the best descriptive feedback  is ignored if it appears beside a mark.  The vast majority of students just don’t take the time to look into why that number is there, unless they are unhappy with their mark.  Even then, you’re not guaranteed they will look at your feedback carefully, they will likely skim the assignment/test and file it away.

How?  Make your students mark them of course!  This changes virtually nothing you do.  I still correct everything – typically this means circling the first error – but I assign no points.  When the students are given back their tests, it’s their job to mark and correct them.  I’ve always used a 3 point holistic method of grading for 95% of my exam questions (instead of trying to assign points per step) and I have the students do the same.  This forces the students to look and assess each question.  It encourages great conversation in the classroom as I am extremely unhelpful to them as they are trying to decide if they have earned a 2 or a 2.5.  After the students have marked and corrected their exams, I do look over them to see if we are on the same page.  This is the only added work for you, but I can check a class of 35 in an hour so the extra work is minimal.  Typically students are far harder on themselves than I am for their first few exams until they really get a hang of the marking system.

You can stop there.  You’ve just injected some meaning into those points that your students love to collect.  They have to tie them to what the expectations are and understand how they’ve performed compared to those expectations.  If you’d like to take it up yet another notch, after marking and correcting their exam, have your students fill out a reflection sheet that relates every question back to a concept or skill you were targeting.  This will give them a real visual as to where their strengths are and what they need to keep working on.  If you include a space for them to analyze what kind of mistakes they are making, it can also give them insights in how to adjust their studying or writing strategies.

So, don’t mark your next exam.  Let your students surprise you with the thoughtfulness of their discussions and their desire to understand just where those magical points come from.