Showing posts with label Math Project. Show all posts
Showing posts with label Math Project. Show all posts

Monday, November 5, 2012

Are mathematicians real people?

There's a push in the United States to get more people interested in math and science in order to have leaders in these areas for the 21st-century. So I find it confusing that when I talk to some people about doing project based learning (PBL) in math there is a lot of equivocating. This seems especially true in high school mathematics courses where the content is often disconnected from what people really do on a daily basis. But if we want people to become mathematicians, why can't the project be related to the work that they do?

A Partial PBL Project Outline
(thanks to Mike Kaechele)
  • Topic: Doing Mathematics
  • Standards: CCSS High School: Algebra >> Arithmetic with Polynomials and Rational Expressions (this comes up as being too abstract for projects)
  • Driving Question: What do mathematicians do?
  • Final Product: Presentation demonstrating their ability to engage in doing math (e.g.: making connections, extending ideas, ...)
  • Authentic Audience: Mathematicians

Granted, there is a lot that I don't know about PBL (though it seems a lot like the outcomes-based projects I did in the 1990s) and this particular project is in need of much more detail, but I want to gather more information about the process. Also, I didn't want to set up a bunch of straw-man arguments about PBL in math just to prove a point. I really do want to know whether doing math would be an acceptable PBL project.




Thursday, March 24, 2011

When will they be ready to go on?

from Teaching-Learning Cycle
Assessments play a key role in the Understanding by Design approach to unit planning. They represent the way that I plan to monitor learners’ progress toward a goal. Therefore, I need to think carefully about what I am going to assess (objectives) and how I am going to assess (approaches) before the unit even begins. In other words, effective assessments require planning.

My first attempt at planning with the end in mind was a middle school math project I called the “Dream House.” I was also interested in using alternative forms of assessment and this project seemed a natural place to start. The summative assessment was a class presentation where each middle schooler shared a scale model of his or her dream house along with specific details like perimeter, area, and cost. This was a 9-week project that covered many of the Michigan state standards in geometry, measurement, and number & operation. And the grade on the presentation was their grade for the marking period. I made this video to model what the final product and presentation might look like:


In order to increase the likelihood of learner success, I set up assessments (I called them benchmarks) along the way. Again, I worked backwards in selecting and designing these assessments. I just kept taking a mental step back and asking myself, “What should they be able to demonstrate in order to do the next task?” and “How will I assess/gather data on their level of understanding?”

As you can see in the example to the right, my plan included some traditional forms of assessments (highlighted in yellow). Learners needed to demonstrate proficiency on the skills assessed by these quizzes before they were ready to move on to the next benchmark. Our school determined that 80% or better was required, but you will remember this did not figure into their final grade; it was merely to monitor progress and ensure success.

This video represents a sample of the eighth graders' efforts on the Name Plaque benchmark:


The planning and preparing for this unit took a great deal of work. Fortunately it was the first marking period in the fall, and I had all summer to work on it. Still, many of the quizzes I used were not developed from scratch but modified from our school’s math text. There was no reason to reinvent the wheel and slight modifications offered the data I needed to analyze understanding and make instructional decisions. After all, these were formative assessments.

I point out my use of textbook quizzes because I had a teacher assistant ask me if using existing curricular resources is “cheating.” Another education class had suggested that using such resources is shameful because teachers should and can create better materials for their learners. Maybe with more time and experience we could make better tests and quizzes from scratch. But why would we if what’s available requires minor, meaningful modifications in order to accomplish our goal? It just depends whether or not it fits within our plan.

TEDxGrandValley