Tuesday, June 29, 2010

Exeter - Part 2

The Exeter math conference continued to be exceptional. It is a unique combination of smart, driven people and has the feel of my other favorite conference (Educon).

Carly Ziniuk from The Bishop Strachan School.
We did an activity that compared the relative population by continent between 1994 and 2025. It was a follow-up activity to a tactile project she did with her eighth grade class based on global inequity. The project was well-suited for mathematics because students needed to figure out how to create a stacked bar graph for both years. This involved accurately partitioning the graph into proportional rectangles based on the data. There is decimal arithmetic involved as we needed to know the running total to accurately draw the graph. We worked in pairs and each group member took one of the two years. I am a huge fan of this approach. It uses authentic data and allow students to collaborate without one student doing all of the work. In fact, I would like each student to have their own data. This sets up opportunities for them to compare and contrast their results with peers. Data for each student puts a larger burden on the teacher, but I am confident that a spreadsheet can be created with the individualized answers.

We used Google Earth for several projects. We traced Greg Mortenson's route in Three Cups of Tea, from where he tried to ascend the K2 to where he built his first school. His path has lots of opportunity for mathematical analysis (e.g., rate, climate, etc.). Carly discussed a similar use of Google Earth, where each student tracked a persons' route on the Underground Railroad. I need to do more work with Google Earth and learn how to create realistic 3D buildings using Google SketchUp.

Bishop Strachan School grades it's students on knowledge, application, thinking, and communications. The relative contribution may vary by assignment and the overall subject grades is equally weighted. This is smart. Students are driven by grades and they will adapt their study habits to the system. On a side note, the Chris Lehman's Science Leadership Academy uses a similar set of core values for grading and curriculum design: inquiry, research, collaboration, presentation and reflection. This is very helpful for creating teacher accountability at the assignment level. In addition, these common skills facilitate curriculum mapping and interdisciplinary projects. It is clear from Carly's activities that real-world data can be woven into any math context. Moreover, data can used to raise social issues. Maybe during the course of solving the math problems, they will develop a sense of empathy and start to raise legitimate questions.

Ron Lancaster (see part 1) had more excellent examples of math in the read world. Today's marque problem involved distance and time graphs. We worked on understanding the distance between two people on escalators. One person stars at the top (and goes down) and the other person starts at the bottom (and goes up). The distance between them is a quadratic, which we used Sketchpad to simulate.

In closing, I shared with the class a few links of my Delicious links:

Monday, June 28, 2010

Exeter Part 1

I am attending on of the best math conferences. It is hosted by Philips Exeter Academy. It is a conference that combines week-long classes and shorter 75-minute classes. Here are some thoughts from the first few days.

Project-Based Learning (Carmel Schettino)
There is lots of research showing that Project-Based Learning (PBL) is a better teaching technique than traditional pedagogy. It is more complicated that being a "sage on a stage" and takes practice. Moreover, students not used to being pushed will find it uncomfortable. Some of the characteristics of project-based learning:
  • teachers step back; teachers physically reposition themselves and there is an alternate generation of directions
  • when they teach, they generally model, rather than how a specific process
  • it relies on discourse and discovery; there is often physical activity
  • it is student-directed, which increases ownership; teachers allow, encourage and validate discomfort
  • teachers need to understand the cognitive apprenticeship model of model, coach, scaffold, and fade
  • it is very important for teachers need to keep the learning goal in mind; otherwise the students may feel lost and complain that they are not learning (which in turn will generate complaints from parents)
  • Cindy Hmelo-Silver has done a lot of research on the effectiveness of PBL
  • Several schools use PBL exclusively - Phillips Exeter Academy and the Illinois Math & Science Academy.
  • Other resources include: New Tech Foundation, Buck Institute, and Montana's SIMMS initiative.
In practice, teachers using PBL should be aware of the following:
  • there is always a balancing act between the time spent and letting them explore tangents that may have nothing to do with the learning goal
  • "revoicing" is a form of repeating information back to students and is an effective scaffolding strategy; it lends credence; causes reflection; validates their authority
  • "revoicing" can also be effective in explicitly mapping cause in effect from their discourse and questions; it can also encourage construction of visuals ("please show me")
  • encourage student to use patient problem solving
  • encourage them to try multiple approaches
  • the teacher should present compelling questions
  • scaffolding can be done with images and videos
  • keep in mind that students must take ownership, which means responsibility
One potential pitfall of PBL is to use it for every aspect of a lesson. Discovery is not necessary in all cases. It is fair to "tell" students:
  • when introducing conventional terminology
  • remind students of conclusions they have already reached
  • rephrase students comments and questions (as in "revoicing")
  • alert students than their ideas are unclear
Ron Lancaster of the Ontario Institute for Studies in Education at the University of Toronto
He is the master of authentic learning. He travels around the world and snaps pictures and videos of anything that can be analyzed mathematically. He has a huge collection of images/videos from his travels. We reviewed several and discussed what questions we could ask about them. He is a big fan of having students import images into Geometer Sketchpad and draw analyze them by adding geometric constructs. He also mentioned an interesting math field trip that he does to a local shopping center. He visits the stores ahead of time and finds interesting data. He contacts the stores ahead of time and students visits in small groups. Each group starts at a different store to alleviate crowds (similar to a shotgun stat in golf). I marvel at his ability to literally see math data everywhere in the world - from store signs, to interesting buildings, to sculptures, to a sin wave as part of a company logo.

Summer Work

I am embarking on a summer project to organize my thousands of Delicious links I collected over the past two years. I am not completely sold on how I am going to organize them, but I need to make them more user-friendly for students. This means identifying and grouping content, activities, drills, and games. I would like to have text and video content for each concept from pre-algebra to algebra. I am hopeful that I will return from a few conferences with a clear head to tackle the issues below. If you want to help in this endeavor, just leave a comment or shoot me a message using one of my other online aliases.
  1. identify curricular units and structure
    1. big ideas and key concepts
    2. introductory content/video
    3. real world connections
    4. math connections (concept map)
    5. unit tour of text if textbook used
    6. projects
  2. review each math link
    1. directions for students
    2. what is the goal (score, time, or completion of the activity)
    3. proof of score - screen shot and drop box or does website track it?
  3. how to organize links?
    1. should I use a tool like only2clicks.com or weblist.me? (I like the graphic representation of the website for kids)
    2. should I list them in this wiki?
    3. should I use a social bookmarking service?
  4. find video, simulation, or easy-to-read explanation for each curricular unit
  5. how should I design activities?
    1. collections of Word documents with instructions and/or handouts
    2. should we use a lightweight platform like Udutu or trackstar (link)
    3. do we need a content platform like sclipo.com or udemy.com
  6. Should I to a fee-based math course to save time?
    1. which one?
Image used under Creative Commons license (link)