Matrix Mess

I started with this handout and a warm up problem of multiplying matrices (I had a diagram handy for students who forgot how to multiply matrices).

It didn’t go well at all. Can you help solve my matrix mess?

The problem was, I didn’t want to take the time to properly review matrices, I just wanted to remind students that they’re useful when solving systems. This obviously backfired.

You already know this is going to go badly because the material is split into three places and is dependent on me showing up with a diagram at the right moment. Students were totally baffled why they were multiplying matrices. They didn’t understand that the calculator would be taking the inverse (some tried to multiply the matrix by -1). They didn’t read the instructions all the way through and were calling me over to help with the calculator.

Head on over to the original post to get the whole story and see my attempt at a re-write.  Thoughts on how to salvage this lesson would be greatly appreciated!

Why Set It Equal to Zero?

This post from Growing Exponentially starts with an awesome insight on how students interpret solving equations.  But then the test reveals a stubborn misconception and some procedural understanding (or difficulty with mathematical explanations in general?).  Can you help?

Most of my students correctly selected Kristen; however, I was extremely disappointed in their explanations. I expected their explanations to be more in depth after the many discussions we had about solving for the x-intercepts. They mostly went with the procedural explanation of setting it equal to zero. I wanted them to explain WHY we set it equal to zero. I don’t know how to ask that without directly giving away which student’s work is correct in the first place. There’s also a problem with the many responses claiming Kristen is correct because she found two solutions. This tells me I need to do more examples with only one.

At this point in the year we’re moving onto exponentials, but I’ll be thinking about this problem for a while. Any advice would be greatly appreciated!

Mistakes Mean We’re Getting Better, Right?

Original post from Epsilon-Delta.  Lots of productive, some struggle, but mostly an awesome insight:

My class activities have to start somewhere; they can’t just magically be perfect…isn’t that what we tell our kids:  you have to practice and have patience if you want to become really good at something?  I guess the same goes with becoming good at making the students do the work.  Learning how to scaffold; learning how to ask engaging questions; learning when to step in and when to stay out.  This takes a lot of practice.  No matter how much preparation I put into a lesson or activity, I have to practice delivering it, too…and that can’t be done without kids in the room.

How Could You Solve This?

A challenge: JNewman85 claims there are half a dozen ways to solve this equation in his post.  How many can you find?

$\frac{1}{x} = \frac{3}{2}$

Which would you expect students to gravitate towards?  Which would you like students to gravitate towards?

Note: mentioning bad words and linking the corresponding document doesn’t guarantee a link back from this blog, but it sure doesn’t hurt!

You Have to Breathe

We know stress is in the air. One week until state tests at my school. If you’re struggling, productively or not, take the time to slow down and breathe.

Via Delta Scape

“The only thing you HAVE to do today is breathe in and breathe out. You could survive the day without food or water or sleep. The things you have listed are things you want to do – things you or others find urgent. But at the end of the day, everything that must get done gets done, and that begins and ends with breathing. Anything else you accomplish is just frosting on the cake.”

Happy teacher appreciation week!

Struggling with Diverse Learners?

Last night Kate gave a great Global Math talk about differentiation in math class.  If you weren’t able to watch it last night, it was recorded and you can watch the video (and see our chatter!).

Julie and I are going to encourage our readers to blog about differentiation, and then post them on both of our blogs.  So, if you would like to blog about differentiation, your post will be featured on both Julie’s blog for MS Sunday Funday and the #matheme page.

To Submit your post on differentiation to both blogs:
1)  Comment to this post or tweet your link to me (@crstn85).  Include #matheme in your tweet.
2)  Click here to submit your post to MS Sunday Funday.  (Julie will post them next Sunday, May 12th.)

Can’t wait to read what strategy you tried!

(cross posted on Julie’s blog and Drawing on Math)

Counteracting Springtime Blues

What resources have you found that really kick-start your professional learning? That really sparks your love of teaching and learning? I need to get rejuvenated. That’s what I think was the biggest problem this year – I wasn’t feeling the passion of loving what I do. I need to find my mojo again… my teaching groove….

I’ll be excited to read what people come up with because I’m right there too.  Last week was rough, hoping next week will be better because I still have 2 months to go!

Principal Seeks Self Reflectors

This week’s Infinite Tangents podcast is an interview with Ashli’s former principal, Greg.  In discussing what he looks for when hiring, self reflection comes up repeatedly, along with flexibility in lessons- being willing to change the plan when you see that something isn’t working out.  This blog gets a mention and Greg shares that he’d be suspect of any blog that doesn’t post some things eligible for submission to Productive Struggle because no one is that perfect.

So, just in case you’re planning to apply for a job, you know, ever again, you should submit a post!  Right after you listen to the podcast of course.

A Question on Forced Collaboration

Should you let kids work alone when they request it? I have a lot of students who absolutely do not like to work with other students and often cause a behavioral disruption or down-right refuse to work altogether. Since I teach middle school I usually try and fight them on this because I believe working with others is an important skill; however, should I instead recognize that that student learns better working independently and allow him/her to work alone?

“Whole-class discussions. How hard you are for me to lead!”

Cool post.

Day 1: We started by challenging the students to find a Eulerian path and circuit through the basement (we didn’t use that language). And then took them to the basement.

Good struggle:

What I still need to work on

Ohhhh whole-class discussions. How hard you are for me to lead! How to balance argument/excited participation with listening? How to balance desire to go to lunch with listening? Discussions, I aspire to be best buddies with you one day in the near future. Please be open to our future, awesome relationship. Love, Sarah.

How do you structure a good conversation? 5 Practices, anyone?