Tuesday, August 28, 2012

Guess and Check

I used this as a warm-up activity for 8th grade today. I got this off of 101qs.com from someone named Adam Bevan. (Whoever you are, thanks!)


Here's what I loved about it:
A. Some kids noticed right away that you could use the 9 as a 6.
B. Some noticed that 1's and 2's had to be on both cubes to make 11 and 22.

And that's as far as many got. Many were paralyzed by the fact that there was no certain way to know where the rest of the numbers went. They thought that there had to be one right answer, and could not decide on how to fill the rest of the blanks.

I had to keep pushing kids. Guess. Take a guess. Do you need a 3? Of course you need a 3. You don't know where to put it? Try putting it here. Will that work? I don't know either. Keep guessing and see what happens.

So my kids learned two valuable lessons today. 1. Sometimes you solve things by guessing. 2. Sometimes there's more than one right answer.

Looking back: It would have been better for me to have a physical representation of this. Some students never saw these blocks before and couldn't really grasp the concept.

Nathan Kraft

Sunday, August 26, 2012

Working for the Man: A Cautionary Tale


This is another post for the mathtwitterblogosphere people. The topic for this one could be anything I want with the catch that I can't reveal its oddity to the reader.


As often as possible, I try to make sure that none of my posts are too vainglorious, but I was honored to have Dan Meyer pass my name on to a company as someone who could write math tasks for their new curriculum. I was hesitant at first since my writing is not very Hemmingway-esque, but was excited to do something different. I love writing lessons for my class and analyzing what works. And now I was getting paid a decent amount of money to do it! Awesomeness.

Turns out, not so much.

I started by working on something I already felt comfortable with: rates and speed limits. I used this video as the introduction for the activity and quickly started working on conforming a lesson to the company's format. But it wasn't as easy as I thought it would be. The format itself felt restricting and I continuously asked myself, "Is this really what they want?" I slowly started to think that this would be a huge time-sucker and it would definitely take away from what I was trying to plan for my regular teaching job. 

Once I was getting paid to write math lessons and had restrictions placed on how that should be done, what used to be fun became work. My school doesn't pay me extra for investing all of my time into my own lessons. And I love the freedom of creating my own work in the format that I choose. Eventually I had to resign the task-writing job.

Since then, I've been reading a book called "Drive" by Dan Pink which was suggested by a former colleague (and about fifty other people). The whole point of the book seems to be that extrinsic rewards stifle creativity. That people do their best when the task itself is rewarding and actually underperform once a reward is offered. There seems to be a huge parallel between the ideas in the book and my experiences this summer. And I've begun to think about how this can also be applied to my classroom. How can I offer similar kinds of freedom when my students are exploring math and problem-solving? How can I limit the use of extrinsic rewards (grades) as a motivator? Will students see my use of standards-based grading as a way for them to control their own learning, or will they see it as another carrot-and-stick routine?

The avuncular, Nathan O Kraft

(Secret message to you know who (not Voldemort): You might be thinking, hey, he didn't use okra. Look at my name again. Snap.)

Sunday, August 19, 2012

I Still Suck at Teaching (and how I'm going to fix that)

Disclaimer: I'm writing this post in response to Sam Shah's and the mathtwitterblogosphere's initiative to get more teachers blogging. If you're a new math blogger like myself, you should check them out.

I once heard someone say that when you enter your sixth year of teaching, you'd feel confident with your ability to teach. That you would "know what you're doing". Well I'd like to thank Dan Meyer, Steve Leinwand, Fawn Nguyen, and Andrew Stadel who, through their expertise and great ideas, have proven to me that I still suck at teaching.

There are two big ways that I will be improving my teaching this year. The first is the use of standards-based grading. I was first introduced to SBG through Shawn Cornally at ThinkThankThunk. I've also been influenced by Robert Marzano's Classroom Assessment and Grading That Works, a presentation by Grant Wiggins (Understanding by Design), some blog posts by Dan Meyer, and a bunch of emails back and forth with Fawn Nguyen and Andrew Stadel (two great teachers who are also trying to unravel this beast).

Everything about SBG makes perfect sense. It helps students retain what they've learned by allowing them to self-monitor, re-learn, and re-assess. It also helps me, the teacher, focus on what is essential. The biggest issue will be acceptance (from administration, students, and parents) of the grading process (how do I assess, how do I assign a letter grade). I think everyone is so entrenched in the tradition of point systems and letter grades, that this will meet some resistance at first. The trick will be properly explaining it (which I'm attempting to do here).

The other big change for this year will be the use of more problem-solving sessions, especially in the three act format as explained by Dan Meyer. I found out about Dan through his TED talk and I was immediately blown away. I then found his blog and 101qs website and started using his format with great success. It's amazing to me how student motivation can be intensified through the use of proper media and real real-world problems. (I say real real-world because I've found that many textbook examples of "real-world" are made up. How do they get away with that?) I've made my own three act lessons here, but my favorite is Andrew Stadel's File Cabinet. To me, this is the standard to which all other three acts should be judged.

As the year progresses, I will be sure to use my blog to report on these changes. It seems like these are very new concepts for many people and we're all trying to figure them out at the same time. Sharing this learning is the best way for all of us to become better teachers (and maybe not suck so much).

Nathan Kraft

Two things:

1. I briefly met Dan Meyer in Philadelphia at the NCTM conference in April. He suggested I start blogging. I thought he was crazy.
2. I've also been very influenced by Steve Leinwand. Even if you're not interested in SBG or Three Act Lessons, you should watch this very short video and think about your own practices. He also has a great book called Accessible Mathematics which expands on what he says in this video.

Wednesday, August 8, 2012

More Integer Operations


I was writing this in another person's blog entry about rules for integers. Figured I might as well put it on my blog.

For subtracting, I like to talk about owing money. If you’re at the restaurant, and you have a bill for $45 (-45), and I come along and say, “Hey, let me pay that for you.”, I would take away that negative: -45 – (-45) = 0. You now owe nothing.

You can do similar things for multiplying.
3(5) means I give you three 5 dollar bills: net result, add 15 (+15)
3(-5) means I give you three IOU slips (each owing $5): net result, lose 15 (-15)
-3(5) means I take away three of your 5 dollar bills: net result, lose 15 (-15)
-3(-5) means I take away three IOU slips: net result, gain 15 (+15)
OR
getting something good is good
getting something bad is bad
losing something good is bad
losing something bad is good
I learned that last one from a student, and who knows where he picked it up.
Nathan Kraft