Presentations

MSTP 6—8 grade algebra

CAMBRIDGE, MN 8/20—21/2012

Here is a set of links for videos and other resources pertaining to day 1 of our work (equality).

And here is a set of links for videos and other resources pertaining to day 2 of our work (ratio and proportion).

Connected Mathematics

Minneapolis Public Schools with Leif Carlson 8/13-15/2012

I have written about teacher explorations of sums of measures of the interior angles of a polygon before. In addition, my future elementary teachers had to write on the topic of angle sums in non-convex polygons. Here is a particularly strong example.

There are some really useful videos of CMP classrooms at the CMP website, including the ones we viewed in our session. And there are some older, more highly produced ones at the Modeling Middle School Mathematics website.

The TIMSS video we saw is online, together with a large collection of videos of 8th grade math teaching around the world. The book length version of “Teaching is a Cultural Activity (pdf)” is titled The Teaching Gap. It’s a great and quick read, available super-cheap used on Amazon.

Somebody mentioned Mathalicious this week. Great stuff, super smart people working on it. They have some free sample lessons on the website.

Finally, someone mentioned the book Zen and the Art of Public School Teaching. I have not read this book but it’s on my list now.

Our powerpoints were nothing great, but in case they’re useful to you, here they are as pdf’s. day.1. day.2. day.3.

@ LAURA JEFFREY ACADEMY, ST PAUL, MN 1/5/2012

Links relevant to our work:

Jason Buell is a middle school science teacher who has written extensively on standards-based grading.

Shawn Cornally is a high school math and science teacher who has done so also.

The Minnesota Math and Science Frameworks online database is the best organized resource for the MN math standards, and it includes substantial discussion of each, as well as sample assessment items.

@ Laura Jeffrey Academy, St Paul, MN 7/25-28/2011

We produced several documents during the week. The titles of these below are links to the .pdf files.

• Analysis of what everyone needs to know and how we might structure a summary for Covering and Surrounding Problem 1.2
• Table for collecting data in Frogs, Fleas and Painted Cubes Problem 2.1
• Rough alignment of Minnesota 2008 mathematics standards (grades 5-8) to CMP
• Units for grades 5-8

Interactive whiteboards

@ Getting to Know CMP 6/21/2011 (repeated 6/23)

NOTE: I have begun a Resources page where useful files such as these will be stored henceforth. See that page for fraction strips, individual Tupelo Township maps, etc.

Here are the Smart Notebook files we used: Wumps, Tupelo Township, Shape Set.

Here is the handout from the session (pdf).

Links to the articles cited:

• Education week article on Smart Boards
• Fraction Photo Frenzy
• Integrating Technology

Here’s a blog post I wrote about uses of technology in math classrooms. You may find it to be provocative reading.

And here are some resources for getting started with GeoGebra:

• Beginner’s guide (geometry)
• Beginner’s guide (algebra)
• Constructing equilateral figures
• Constructing angle sum diagrams

“MATH 2.0” or
What can you do with this?

@ NCC 3/24/2011

Here is more information about the orange juice pH problem.

Dan Meyer’s blog is a treasure trove of ideas for the sort of applications of technology we discussed. I owe him greatly for teaching me new stuff. I have done a multipart analysis of his work on the escalators problem; much of it recaps ideas from our session at Normandale.

Would you like an answer to the salt problem?

How smart is that board, anyway?

@ CMP Users’ Conf., MSU 2/25/2011

Here are the Smart Notebook files we used: Wumps, Tupelo Township, Shape Set, Pouches and Coins.

Here are the Wumps as .gif files-right click on each to download, then insert in your document to use.

We looked at a couple of GeoGebra files at the end of the session. After March 7, 2011, the following links will take you directly to some GeoGebra tutorials that you may find useful in learning the software: (1) Downloading GeoGebra and making your first sketch, and (2) Using GeoGebra to make a dynamic construction.

My GeoGebra sketches are available as interactive web pages (very bare bones and you do not need to have GeoGebra to run them). (1) A simplified version of the Japanese triangle diagram, and (2) A dynamic hexagon.

The TIMSS videos are available online (free registration required).

Five practices for improving mathematical conversations in the classroom

@ CMP Users’ Conf., MSU 2/25/2011

I neglected to distribute the handout (pdf).

The article on which the session was based is available through NCTM’s website. Here is the full citation, with embedded link: Smith, M.S., Hughes, E.K., Engle, R.A. & Stein, M.K. (2009). Orchestrating discussions. Mathematics teaching in the middle school, 14, (9), 548—556.

In the session, we worked a revised version of the licorice laces problem (pdf) from Bits and Pieces I.

Connected Mathematics

@ Kodiak, AK 1/5/2011

Research

The following question arose in our work, “What is the research base on problem-based mathematics curriculum?” Here are a couple of resources to get started understanding this:

(1) A summary of some of the major studies and perspectives on the website “Mathematically Sane”.

(2) A literature review specifically on CMP, including abstracts of the articles. Of particular interest here will be the “Research Articles and Reports” list.

In both cases, the summaries are helpful but so much more can be learned by reading a few articles in some depth.

technology

A CMP teacher in Maine, Shawn Towle, has compiled a collection of technology links matched to CMP units and investigations.

Below are links to a few other resources we discussed:

GeoGebra

Illuminations

And here are the Smart Notebook files we used: Wumps, Tupelo Township, Shape Set, Pouches and Coins.

How does video restructure a content course for elementary teachers?

@ AMATYC annual conference, Boston, MA, November 11, 2010

The two main projects from which I have found useful videos for my number course are CGI (Cognitively Guided Instruction-at UW, Madison) and IMAP (Integrating Mathematics and Pedagogy-at SDSU).

I have written about CGI in a few blog posts; the IMAP website has a couple of sample videos. If you teach content or methods courses, you should have no trouble obtaining a desk copy of the CD-ROM from your Pearson representative.

Several people asked about the technology I used to display the videos. I imported them into iTunes. Also, you can open them directly from the CD-ROM using QuickTime Player, but if you import into iTunes you don’t have to have the CD with you. Either way, you also get around the issue of the small image that the CD-ROM’s software displays (but you lose the transcripts). As long as you own the CD-ROM’s in question, this falls within the fair use provision of copyright law.

There are two articles I cited in my talk that did not make the handout. The full citations are below:

Fuson, K.C., Wearne, D., Hiebert, J.C., Murray, H., Human, P. G., Olivier, A.I., Carpenter, T. P., Fennema, E. (1997). Children’s conceptual structures for multidigit numbers and methods of multidigit addition and subtraction. Journal for Research in Mathematics Education, 28, (2), 130–162.

Philipp, R. A.  (2008).  Motivating prospective elementary school teachers to learn mathematics by focusing upon children’s mathematical thinking.  Issues in Teacher Education, 17, (2), 7-26.

Connected Mathematics

@ Kodiak, AK, August 2010

Monday

Technology. I mentioned GeoGebra, a free open-source software project that has both algebraic and geometric features. I also mentioned in passing Geometer’s Sketchpad. I showed a graphing calculator for the iPod Touch/iPhone. It turns out that this app is now also available for the iPad, and that it supports video output (so you can hook your iPad up to your projector and display your graphs that way).

Standards. We discussed Alaska state standards and resources related to aligning CMP with these standards. Pearson has produced such documents; links below. Be aware that these are produced with an eye to demonstrating coverage rather than to helping teachers understand the flow of curriculum or to make assessment decisions.

• Sixth grade AK standards aligned to sixth grade units
• Seventh grade AK standards aligned to seventh grade units
• Eighth grade AK standards aligned to eighth grade units

Research. We spoke at length about research on mathematics teaching and learning. The best resource for summaries of current research right now the final report of the National Mathematics Advisory Panel.

Professional Development. I mentioned an article that reviewed research on elementary mathematics professional development programs. Those programs that focused on changing daily instructional practices were found to be more effective than those that focused on curriculum or on technology.

Connected Mathematics

@ Grand Junction, CO, August 2010

Articles. Here are links to some articles I mentioned during our work together…

The article “Orchestrating Discussions” was in the journal Mathematics Teaching in the Middle School. The article describes five practices for effectively using student ideas in whole-class discussions (i.e. during the summary).

The “Orchestrating Discussions” article came out of the Quasar project at University of Pittsburgh, which looked at instructional practices in urban middle mathematics classrooms. In particular, the project was interested in studying classrooms that maintained high levels of cognitive challenge. There are many research-oriented papers produced by the project. Here is a starting place.

I mentioned an article on questioning and “press”. That article is titled “Discourse that promotes mathematical understanding”. The article predates NCTM’s electronic database. The full citation is below. I will hunt down a copy to share with Nicole.

• Kazemi, E. (1998). Discourse that promotes conceptual understanding. Teaching children mathematics, 4, (9), 410-414.

Planning. I put together a model for planning (more elaborate than most of us can carry out most days, but a goal to strive for and a useful reminder of the resources available in the curriculum). I will type this model up and post it here soon.

Technology. I mentioned GeoGebra, a free open-source software project that has both algebraic and geometric features. I also mentioned in passing Geometer’s Sketchpad. I showed a graphing calculator for the iPod Touch/iPhone. It turns out that this app is now also available for the iPad, and that it supports video output (so you can hook your iPad up to your projector and display your graphs that way).

Connected Mathematics

@ Appalachian State, June 2010

Thursday

We discussed a NAEP (National Assessment of Education Progress) item about fraction estimation. Here is a link to the history of NAEP. And here is a link to a press release about the most recent North Carolina NAEP scores.

Wednesday

We did a partner quiz and I discussed, but did not provide copies of, an improved partner clock (pdf). Download, adapt and use if it’s useful in your classroom.

We discussed elevation graphs from the Tour de France. The New York Times has a lovely multimedia site for each year’s Tour, and it was the source of the graphs we used.

Tuesday

I discussed the article “Orchestrating Discussions” from the journal Mathematics Teaching in the Middle School. The article describes five practices for effectively using student ideas in whole-class discussions.

In a brief discussion of various ways to share student work with our classes, I mentioned an article from Teaching Children Mathematics titled “Fraction Photo Frenzy”. The article describes an activity in which the author and her students used digital cameras and a Smart Board to annotate and share their work with manipulatives.

Monday

Tinkerplots link

M&M data (pre-2004)

M&M data (post-2004)

Roller coaster data

Getting to Know Connected Mathematics

@ MSU, June 2010

Thursday

We talked about beliefs about teaching and learning in light of this country’s persistent achievement gap. A place to get started in thinking about these ideas and what they mean for our classrooms is a book titled, White Teachers/ Diverse Classrooms. The specific materials we used to think about beliefs came from a professional development workshop at the Science Museum of Minnesota.

Management session

Anne Marie Nicoll-Turner posted handouts and resources from the management session on her school website. Look in the class links/files for today section. These resources will be available for a limited time due to limited server space.

Technology session

Shawn Towle, seventh grade presenter from Falmouth, ME, shared his Moodle site for technology resources related to CMP.

Tuesday

Kathy mentioned a resource in the National Library of Virtual Manipulatives for the Pythagoras puzzles in Problem 3.2.

We used these carefully constructed squares in the summary of Problem 3.1 after finding Pythagoras.

We watched the Lisa Brown video from the Modeling Middle School Mathematics project. The project’s website has clips from this video, as well as from another CMP classroom and classrooms from other middle school curriculum projects available for free viewing.

Monday

The very important topic of the relationship between learning and high-stakes testing came up on Monday. Here are links to two recent articles about researchers taking this relationship seriously and asking the question, What are the characteristics of an effective teacher in the era of high-stakes testing? One article was in the New York Times in March; the other was in The Atlantic magazine in January.

The software I used for the changing rectangle is Geogebra. It is a free open-source dynamic algebra and geometry software. Send me an email if you would like the file to play around with.

Partner Quiz Session

@ Connected Mathematics Users’ Conference, February 2010

A few years ago, together with my colleague Michele Luke, I wrote an article about our use of partner quizzes in middle school mathematics classrooms. At the Connected Mathematics Users’ Conference, I expanded on that article in a one-hour session.

Click here to download images of my slides from the session (pdf). Send me an email if you would like the original Keynote file containing the slides (WordPress only allows certain file types to be posted.)

In the second half of the session, I had participants create a rubric for grading some problems from the partner quiz. In particular, I assigned pairs of participants a problem from the quiz and asked them to consider (in this order) what “good”, “poor”, “weak” and “excellent” work would look like from students. I asked them to aim for the big picture mathematically. Teachers have lots of experience talking about whether to take off 1 point or 1/2 a point for a missing negative sign. We have much less experience describing what quality work looks like. This was a chance to practice.

Click here to download these descriptions (pdf).

The final part of this task, which I posed but left open for participants to consider, is What grade do you want to assign to each category: amazing, good, weak and poor? In my classroom, it goes like this: amazing: A, good: B, weak: C, and poor D or F. I do not advocate that anyone else adopt my stance. But I do think it is important to be clear with ourselves about the connection between the overall quality of a student’s work and the grade that is earned.

Opening Talk

@ Connected Mathematics Users’ Conference, February 2010

On Friday, February 19, I gave the opening talk for the Connected Mathematics Users’ Conference in East Lansing, MI. The title was Why things are as they are in CMP: Tales from the Revision. Below are some resources related to the talk.

Betty Phillips and Glenda Lappan wrote an article for the journal Educational Designer about the development of the curriculum.

Click this link to download my slides (pdf).