## Sunday, February 28, 2016

### Exploring the #MTBoS

My elementary preservice teachers (PST) are exploring professional development this week. The first assignment was to do a webinar or our local conference, Math in Action. Global Math was Problem Strings with Pam Harris (awesome) and Christopher Danielson is keynoting Math in Action, so fortuitous timing, say no more. The second assignment is to find a blogpost to recommend to teachers, so I thought I would pass these along. The list of leads I gave them is:

Apologies for any exclusions. These are all people who's work has come up so far in class. What elementary blogs would you add?

Their recommendations:
Dana -  https://mathmindsblog.wordpress.com/2016/02/11/rhombus-vs-diamond/
Summary: This blog post is about a class of students looking at four different shapes, and trying to find the odd one out.
Review: I thought this blog was great because instead of simply telling the students the names of the different shapes, the teacher let them think and reason for themselves; she allowed them to come up with and defend their answer by themselves.

Dayna - This is a great lesson to combine English and math and get students excited to learn. My response to the lesson is that I love that as a teacher you get to see the students thought process when they are working on this problem. http://marilynburnsmathblog.com/wordpress/chrysanthemum-an-oldie-but-goodie/

Kalyn - https://tjzager.wordpress.com/2015/06/06/comparisons-a-little-bit-more-older/
This post talked about how comparison problem are everywhere, even outside of school. Although they can be difficult at first, the lightbulb goes off and the problem makes sense! I really enjoyed this post and the person example that it gives of her daughter and the conversation that they had about math, but also about life. A lot of good stuff here!

Ally - http://exit10a.blogspot.com/2015/12/22-30-50-100.html
This is a great blog. It's about how is he works with "Alex", going through counting. It was a great read.

Amber - For my blog post, I chose to look at some more of Graham Fletcher's stuff. And although we aren't learning about volume right now, I thought this post was a great representation, which shows real life problem solving. It offers that children are robbed when force fed uninteresting story problems from a text book, and Graham offers an interesting 3 ACT problem as a substitute. My reaction to this concise, yet powerful read is that I would like to try a problem like the one he brings up. I bet students would be very interested in it. http://gfletchy.com/2016/02/14/im-placing-a-hit-on-the-pseudo-context/

Sarah - https://mathmindsblog.wordpress.com/2016/02/05/obsessed-with-counting-collections/ Summary: Second graders explore sorting by counting by 2's, 5's, and 10's. A similar activity is conducted with first grade students. One students has difficulty counting when there is a leftover present. Review: This post really made me think deeply and question the use of ten frames. Kristin Gray does an excellent job of questioning the thinking of students and that is something that I, personally, need some work on.

Chris - http://followinglearning.blogspot.com/2016/02/art-for-maths-sake.html
Summary: This blogpost is about an "artsy-mathy" activity he did with students involving creating trees out of factor trees.
Review: I absolutely loved this post because it addressed an issue with "artsy-mathy" activities, which is that they tend to be less artsy than an art lesson and less math than a math lesson. I enjoyed how he addressed the issue by making more out of the project and creating an exhibit where the students could teach to younger students.

Orina - http://marilynburnsmathblog.com/wordpress/four-strikes-and-youre-out/ I thought this game was really interesting and fun because students have to use number sense to try to win. A lot of students are familiar with hangman and it's a math way to play a fun game.She comments at the end about how this game is competitive and can be cooperative also. Playing games can bring more fun to the classrooms, but she comments that we must make sure there are some competitive and some that are about cooperation.

this teacher was trying to get her students to understand grouping and have then work together to see what made the shapes different and what the noticed in general. a lot of then saw that there are many triangles in the rectangles.

Heather - http://gfletchy.com/2016/02/14/im-placing-a-hit-on-the-pseudo-context/ I really enjoyed this blog post because it addressed the question we all ask ourselves, when will I ever use this? I like the way he addresses practical examples and being able to take those practical examples and use those for practice problems not "mind numbing" problems. (John says: "be sure to see Joe's follow up.")

Summary: Counting circles can serve as more than one purpose of just counting; it helps you practice standards, recognize patterns, etc.
Review: I never knew you could do a counting circle in some many different ways; the more questions you ask your students about it, the more they will think about it, and deeply understand the material better.

I admire their taste in posts!

The other thing is how much I want to thank these bloggers. By sharing your classroom you are having a profound effect on other teachers - and on the future. It takes time and vulnerability for you to write, and I want to thank you for it.

## Saturday, February 20, 2016

### Teacher's Block

I am struggling with my college algebra class.

There is the classic misalignment of what they think math is and what I want them to be able to do. The makeup of the class is almost entirely people who are done with math after this course. In our department, we're trying to separate this from precalc, making a new course for people moving on in math and this course will be for people finishing their math. The goal is to make this course more conceptual, and prepare students for use of mathematics in other subjects. Previously this course had so many skill objectives that teachers were put into coverage mode. Tenure track faculty teach it occasionally, full time affiliate instructors sometimes and most frequently adjuncts.

The course started off on the wrong foot. Two problems that have been a smash in the past went awry. On the house painter problem they were unable to convince themselves of the answer. And on the fair pay problem a misconception was shared and caught on so that it became insoluble. When they came back, one student had a nice intuitive solution that he could not convince the class - even with my help - that it was correct. Finally someone asked me point blank if his answer was right. "Yes, but one of our goals is that you are able to decide for yourself."

Ay ay ay.

By nature, they are reticent to talk to each other. Despite my urging repeatedly, and sharing how math is best learned through discussion. Many don't engage in activities, they're waiting for me to tell them how, many are not doing the homework, and absenteeism is about 20%. Standards based grading has been a tougher sell than usual because this class, as a group, wants the math that was.

I've removed a lot of choice, I've been doing more demonstrations and spending time on the teacher half of gradual release of responsibility, and I'm super explicit about what problems show which standards on assessments. They still won't talk, and many won't engage in in-class inquiry. They will make up something rather than ask about a question they don't understand on an assessment.

Ay ay ay.

The other day I saw this image on Twitter, but stupidly didn't catch the source. Simon Gregg remembered - it was David Wees!)
Our College Algebra picks up with quadratics, but a lot of the work I do with students visualizing patterns is for linear content. (We did do the growth problems, though.) Doing some other work I realized that the students were not understanding symbolic representations as generalizing number patterns. (There are even such quadratic examples on my own blog!) They had been getting by on regression rather than representation. I though this problem would be a great introduction to this kind of generalizing.  It did seems to be helping connections form. I wanted to extend this to cubic or higher, so I built this pattern.

First we discussed what was going on, what they noticed and what they wondered about. Very few students wondered about how many cubes for the next building. More assumed that the next building was to be built with exactly that many orange blocks.  That's very different than my thinking, and emblematic of how difficult it is for me to anticipate how this class will respond to prompts.

I built a very scaffolded worksheet. I used to make stuff like this all the time, but have been moving away from it. But sometimes students need supports.

Another adjustment I'm trying to make is, instead of roaming the room to eavesdrop and do formative assessment,  to roam and ask questions, try to encourage table conversation, and hover over students doing work for other classes or just sitting. I feel a little awkward promoting engagement by (what feels like) intimidation, but students need supports sometimes.

One of the more successful areas of class so far has been the math writing. They have six assignments over the course of the semester, they can count towards SBARs, they can revise for their final exemplars. Several people are writing about this problem for their current writing. That tells me this was at a good place for them, and I'm happy to see some of the sense making.

Meg writes:

Michelle:
The strength of the temptation to give in, to teach them how they think they'd like to be taught is way stronger than I would have guessed. But so is my stubbornness to not give in. What I am trying to be wary of is to keep my stubbornness from stopping me giving the support that students need and teaching the students in front of me, rather than some fantasy class.