#TMC12 and My Irrational Fear

My first steps into the Twitterblogosphere started with finding a few wonderful blogs.  I read and read and read some more.  Then I noticed the bloggers were also on twitter.  I lurked for an obnoxious amount of time and jumped in a few times but not enough for anyone to really get to know me.  At TMC I wasn't at all surprised that people didn't really know me that well.  I just hadn't really put myself out there.

I started my blog a few years ago to help me sort out some of the ideas I had for the class I had to pick up.  For 6 years I was an Instructional Coach for my Middle School.  That position was eventually cut and I found myself back in the classroom.  The problem with the blog is that I have a completely irrational fear of writing.  The thought of a 1 page reflection paper sends me over the edge.  College was a nightmare.  Tears, tears and more tears.  I'm still not sure how I made it through.  Fast forward to Math Bratt.  It died.  I know I have stuff to share.  Stuff I really want to share but the words always escape me.  Those of you who meet me in person know I have stuff to share and you are allowed to tell me to shut up once in a while.

Everyone has already written so much of how I feel about TMC12.  I never could have put all of my emotions in words as well as everyone else.  Thank you for writing what I could not.  But most of all, thank you for believing in me and encouraging me to write.  Even if it is difficult.  I have the strength to do it because of all of you.  How could anyone not be inspired by each and every one of you?

Please forgive me when my posts are less than eloquently written.  I hope you read them anyway.

Subtracting Integers

In one of the middle school sessions at TMC12 we were talking about integers and how students struggle especially with subtraction.  We were brainstorming different strategies (chips, number lines, rules, etc.)  This is the distance strategy I shared with the group.

When working with students it is important for them to understand that subtraction is more than just "take away".  Yes, we can figure 25 - 3 as "You have 25 candies in your hand and you eat 3. What do you have left?" but that limits us when we expand to include integers.

Using a number line students can also recognize that the distance between 25 and 3 is also 22.   Continue building on what students know.

13 - 4 = 13 take away 4  but also the distance between 13 and 4

So what happens when you switch it?

4 - 13

Many students will intuitively notice the result would have to be negative.  What is the distance between 4 and 13?  It is the same as 13 and 4 only it is negative because the smaller number is first.

*Students have to understand the above to be able to move forward.

9 - (-2) = the distance between 9 and -2, notice 9 is larger than -2 = 11
-2 - 9 = the distance between -2 and 9, notice the -2 is smaller than 9 = -11
-3 - (-8) = the distance between -3 and -8, notice the -3 is larger than -8 = 5

If students have trouble determining the distance, provide a number line.  Counting on to determine how far apart numbers are is another strategy that some students might need practice with.

-135 - 124 =
(the distance from -135 to 0 is 135, the distance from 0 to 124 is 124 so the distance from -135 to 124 is 135 + 124)

Sierpinski's Triangle - 8th grade

Here I go brainstorming ideas for next year. One of my goals was to use the blog to more formally reflect on my year. I have been reflecting but I find those reflections morph into new plans very quickly. This is hopefully going to be a place to brainstorm, get feedback and develop a plan for next year. I will be teaching 8th grade pre-algebra and Algebra I.

I wanted to start the year with something that would allow me the flexibility to review previous ideas and introduce some of the big ideas for 8th grade. I'm looking at Sierpinski's Triangle to be that "kick-off" to the year.

This is a rough list but here are the ideas that connect to Sierpinski's Triangle

• Midpoint/midpoint formula
• Similar Figures
• Fraction/Percent Representation and Operation
• Probability
• Rate of Change
• Representation (graph, table, equation)
• Exponents
• Triangular Numbers (other special numbers)
• Area of triangles (other shapes - how related to triangles)
• Parallel lines/Transversal/special angles
• Pythagorean Theorem and Distance Formula
• Other triangle patterns
• Slope triangles (similarity)
• Other recursive relationships/Fractals

The kick off is Sierpinski's Triangle but the focus widens to include multiple triangle connections. I'm still working on the details of what connections students need to make first and a loose timeline but I am interested in your feedback.

Thanks!

NCTM - More day 1

I feel like I should confess that I am a session hopper. I have a very hard time sitting in a session for the entire time. So many times there are multiple sessions at the same time I want to see. So yeah... I left early on this one...

Connecting and Communicating in Math Class Using Graphic Organizers

Carol A. Hynes

Better utilizing graphic organizers is something I'd like to work on next year so I thought this session might give me some ideas. As part of the introduction, Carol talked about the power of using graphic organizers when adopted school-wide or district-wide.

Some of the graphic organizers she shared were

Links (rule of 4)

Webs

Sorts

Splashes

You can find numerous examples here. You can download the zip file at the bottom of the page.

NCTM Day 1 - Do you see what I see?

Do You See What I See?

3-D Reasoning, 2-D Students

Peg Cagle

This session focused on how students today are different. Peg Cagle spent the majority of the session demonstrating the differences in play for students today.

Play was different

mechanical vs. electronic

do-it-yourself vs. pre-made

nature of public playgrounds

She talked about each of these in more detail.

I was hoping to walk away with the so what do I do to help students and toward the end of the session she gave these suggestions:

• encourage physical activity (team sports to tree climbing)
• introduce 2-d and 3-d dissection puzzles
• full, pour, estimate, measure as much as you can (figure it out - which holds more?)
• play with string (make knots, shapes, loops)
• build stuff

At one point she had us look at paper folding and all the questions you could ask students.

She wonders if memory is stored in a geometric construct how students lack of experience with spatial reasoning might influence memory access.

Problem Solving

I started working on the problem solving rubric. I want it to work for any problem I give students and I want to use it every time I assess their problem solving. Problem solving, in my opinion, has to be non-routine and out of context. They are not application problems of current material.

I have a 4 point scale listed for each item in my rubric. I did not include a description because I'm not sure what it would say. Like my learning targets, much of the determination will be my professional opinion backed by evidence. I tried to include what evidence I would be looking for and I'm hoping to better define the levels through class discussion.

Go here to see the rubric.

What do good mathematicians do?

In my role as an instructional coach we (the other coaches and I) spend time reading, discussing for our own professional growth. Each elementary school has a literacy/math coach. At the middle school, each building has a 1/2 time literacy coach and a 1/2 time math coach. I'm the math coach at my building. The first few years we spent a lot of time building the coaches' understanding of how students learn math. Much of the focus was on developing number sense. It was a great time in my personal professional learning. This year the focus shifted to literacy. I'm 7-12 math certified and have no to very little literacy background. I definitely believe that all teachers have to also be reading teachers. I'm just not sure how to do that... Now back to the main point of the blog...

One of the literacy resources we looked at was all about creating a workshop structure. (I can't remember the book or author. I'll have to get back to you on that one.) The chapter I had to read was about a teacher who focused her workshop time on What do good readers do? That got me thinking about the math connection. What do good mathematicians do? How can I use that to create/drive a workshop culture in my math class?

This is what I've come up with...

• Good Mathematicians work on solving problems.
• Good Mathematicians play games and work on puzzles.
• Good Mathematicians ask questions and explore ideas.
• Good mathematicians practice their skills.

*Disclaimer: I did not come up with this all by myself. Some of the other coaches and I have been talking about what this would look like for math. We are great sounding boards for each other. Some of the other coaches have also included vocabulary to connected it to the Daily Cafe. For my first attempt at this I'm sticking with my four listed above.

What it will look like (I hope)

Problem Solving - Students will have a non-routine problem to solve. In the past I've used problems from Mathematics Teaching in the Middle School or Mathematics Teacher. I also love this place. I hope to have a rubric in place where I can give feedback on the students' ability to understand the problem, devise a strategy, and follow it through (adapting when necessary). Required for all students - At least twice a grading period?

Games and Puzzles - I'm hoping to have a collection of games that connect to the content or a specific outcome. The first grading period I'm focusing on these games with the hope to add more as the year progresses. Polygon Capture, Docfish, Number Subset Game

Inquiry and Exploration - I think this is open for students but I'm probably going to provide some ideas to start with. Networks, fractals, history of math, mathematicians, math careers, math in animation, computer programming, etc. I'm not sure how I'll assess but I'd like students to have a product to summarize their learning. I don't think this will be required of all students.

Practice - State testing anyone? This is built in time for practicing the skills for the state test and for Algebra I. My students are required to take the 8th grade state test but they learned most of the material in 6th and 7th grade. This is a way to keep it fresh. For Algebra I this is time for those students who want to/need to practice a particular learning target. This practice will be graded only for feedback purposes not as a part of their grade.

During the workshop time students will need to working on one of the above areas. My hope is to have my students well trained to be self-sufficient during that time so that I can work with small groups of students re-teaching concepts.