Note: Thank you Matt Jones, CSU Dominguez Hills for the heads up.
Emily Hanford of NPR has a nice article about physicists, who are lecturing less and getting better results. Be sure to also click on the link "Listen to the Story"for the radio broadcast.
http://www.npr.org/2012/01/01/144550920/physicists-seek-to-lose-the-lecture-as-teaching-tool
Physicists have collected data providing evidence that learning gains are better when students are deeply engaged in the subject and allowed to collaborate with peers. Sandra Laursen, University of Colorado Boulder, also has data collected at the college level from mathematics courses. Laursen's results are in alignment with this article. Laursen's group has a number of findings. Among the long list of findings, there is statistically significant evidence suggesting the more an instructor talks the less their students learn. (Link to Colorado Study).
As Ed Parker says, "See What They Can Do."
Tuesday, January 24, 2012
Sunday, January 22, 2012
A Peek into the (Near) Future
Apple Inc. introduced iTunes 10.5.3, which includes interactive textbooks. This is almost surely the wave of the future, no matter what teachers and instructors might think of technology. Just as the CCSS represents a great opportunity, so does advancing technology. The Math community should experiment and investigate the options.
For those who say, "Run what brung ya," see Kodak. Kodak, once a giant, the inventor of the digital camera sensor is now headed for bankruptcy. The point isn't just about our individual preferences as instructors. We also have to consider what our students need to compete in the 21st century.
For those who say, "Run what brung ya," see Kodak. Kodak, once a giant, the inventor of the digital camera sensor is now headed for bankruptcy. The point isn't just about our individual preferences as instructors. We also have to consider what our students need to compete in the 21st century.
Do we have to have answers today? No.
Should we explore and study this? Absolutely yes!
Are/will international competitors be exploring technology and education? Absolutely yes.
Thursday, January 19, 2012
Teaching a Course for the Second Time (or Third...)
Winter term has started here at Cal Poly. In fact we are in week 3. This winter quarter I am teaching two sections of Math 330 Algebraic Thinking with Technology for future elementary school teachers. The course title isn't the point of this post, though I may talk about this course in the future. What I want to get to is that I taught this course last term for the first time. This quarter I am at an advantage as an IBL instructor, since I have laid out the course materials once. For the second time around I can now review my notes, look for problems that did well and try to fine tune problems to get students into the learning zone, where the problems are not obvious and not out of reach.
A hidden "side" advantage of IBL is that we become much more efficient as we repeatedly teach a course. So prep time declines with each iteration until it reaches a steady state. Moreover, we gain valuable insights into the learning issues. This is part of Math Knowledge for Teaching that helps instructors help students.
Example 1: Let's say students really struggled with Problem N last term. They tried it, but no one got it and things stalled big time. Some extra time and special cases were needed to get students going. This time around I can put into the problem sequence an exploration, where students investigate some given special cases and are asked to build several more examples. Then using what they learned from this experience, they hopefully are better prepared for Problem N. I don't want to make Problem N too easy or give away too much, but want to get the core ideas out into play through investigating related examples.
Example 2: Problem K was way easy for nearly all of the students. This time I'll leave Problem K as is, but add in a few more challenging problems after Problem K to ramp up the level. (Note: In math finding really hard problems isn't the issue. The issue is finding appropriate challenges for the developmental level of your students. This changes with each class, so one is always getting things "in the ballpark" and adapting to each situations.)
It's Jazz. You have Rhythm Changes in mind, but it's not the same every time.
A hidden "side" advantage of IBL is that we become much more efficient as we repeatedly teach a course. So prep time declines with each iteration until it reaches a steady state. Moreover, we gain valuable insights into the learning issues. This is part of Math Knowledge for Teaching that helps instructors help students.
Example 1: Let's say students really struggled with Problem N last term. They tried it, but no one got it and things stalled big time. Some extra time and special cases were needed to get students going. This time around I can put into the problem sequence an exploration, where students investigate some given special cases and are asked to build several more examples. Then using what they learned from this experience, they hopefully are better prepared for Problem N. I don't want to make Problem N too easy or give away too much, but want to get the core ideas out into play through investigating related examples.
Example 2: Problem K was way easy for nearly all of the students. This time I'll leave Problem K as is, but add in a few more challenging problems after Problem K to ramp up the level. (Note: In math finding really hard problems isn't the issue. The issue is finding appropriate challenges for the developmental level of your students. This changes with each class, so one is always getting things "in the ballpark" and adapting to each situations.)
It's Jazz. You have Rhythm Changes in mind, but it's not the same every time.
Friday, January 13, 2012
Architecture and Education Part 1
Last week I was in Boston, MA for the Joint Mathematics Meetings. I have never been to Boston before, and I was excited about the trip. After a long travel day and a couple of days of meetings, I needed to get outside, feel the sun, breath fresh air. I needed to see a bit of Boston before getting back on a plane headed to the west coast.
Before I left for Boston, my wife told me to go and visit the Boston Public Library. She said it's a special place. This then leads to the point of this post -- the influence of architecture on education. I'll do this through photos and captioning. Part 1 is about a big idea. Part 2 will be about our little 'ol classrooms and how they can be set up in simple ways to encourage students to interact.
Entering the building reveals old-world architectural themes. The patterns above you as you walk in lead your eyes up.
The stairs for you to walk slowly, and make several 90 degree turns. These 90 degree turns force you physically to change directions as well as encourage you to prepare the mind for what is to come.
When you reach the top of the stairs, you arrive at a hallway. The black iron doors on the right side are the entrance to the great hall. Two more 90 degree turns to go.
Finally one arrives in the great hall. Arriving in this special place is truly inspiring. You are encouraged to learn in a space like this. Great minds have studied here in the past, are studying here now, and will study here in the future.
Before I left for Boston, my wife told me to go and visit the Boston Public Library. She said it's a special place. This then leads to the point of this post -- the influence of architecture on education. I'll do this through photos and captioning. Part 1 is about a big idea. Part 2 will be about our little 'ol classrooms and how they can be set up in simple ways to encourage students to interact.
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| Outside on the steps |
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| A statue gazing at a sphere deep in thought |
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| Inscriptions of the names of the giants, upon whose shoulders we stand |
Entering the building reveals old-world architectural themes. The patterns above you as you walk in lead your eyes up.
Then as you walk past the entrance, stairs lead you slowly up to a new chamber with art up high, lions honoring the fallen, and arches that again lead the eye upwards.
The stairs for you to walk slowly, and make several 90 degree turns. These 90 degree turns force you physically to change directions as well as encourage you to prepare the mind for what is to come.
When you reach the top of the stairs, you arrive at a hallway. The black iron doors on the right side are the entrance to the great hall. Two more 90 degree turns to go.
Finally one arrives in the great hall. Arriving in this special place is truly inspiring. You are encouraged to learn in a space like this. Great minds have studied here in the past, are studying here now, and will study here in the future.
Some takeaways (at least for me). Environment matters. Indeed, if architecture and decorations didn't matter, we would all live and work in boxes with no paint, no art, no human influence. But that's not the case. Building designs affect how we interact with people and how we go about our work. Living and working in well-designed spaces matters.
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| See you next time! |
Sunday, January 8, 2012
The CCSS is a "Great Opportunity"
I just returned yesterday from the JMM, and it was a great conference as usual. This post is not going to be a conference report. That will come from the MAA and AMS newsletters. Instead I want to share a little gem. The CCSS is short for Common Core State Standards.
After the IBL Centers meeting on Friday, I had a front row seat to an amazing interaction between John Worrell, a student of R. L. Moore, and Paul Sally. John approaches Paul, as Paul is leaving the meeting room, to say hello. Paul asks John, "How old are you?" John replies that he is 77. Paul admits that he is in his 80th year.
Then with all the fire and passion of a 21 year old basketball player that just hit a game-winning shot, Paul proclaims that the CCSS, with the process and practice standards, is a unique opportunity to revive American mathematics education to the highest levels. IBL is a critical component of this as is the preparing and training of K-12 teachers. Paul shouted out that he is going to live 20 more years and see that achieve this goal. It was a special moment indeed!
The adoption of the CCSS presents to the mathematics community a unique opportunity. It is a once in a generation opportunity. Reform efforts over decades have brought us to position where we have the potential to not just reform, but more importantly transform American mathematics education.
The CCSS have at the heart the kinds of things we want from students such as problem solving, critical thinking, justification, making conjectures. To implement this adequately can only be done through active learning pedagogy. I do not know of a system that can accomplish these things through passive, solitary work on rote skills.
Some challenges:
After the IBL Centers meeting on Friday, I had a front row seat to an amazing interaction between John Worrell, a student of R. L. Moore, and Paul Sally. John approaches Paul, as Paul is leaving the meeting room, to say hello. Paul asks John, "How old are you?" John replies that he is 77. Paul admits that he is in his 80th year.
Then with all the fire and passion of a 21 year old basketball player that just hit a game-winning shot, Paul proclaims that the CCSS, with the process and practice standards, is a unique opportunity to revive American mathematics education to the highest levels. IBL is a critical component of this as is the preparing and training of K-12 teachers. Paul shouted out that he is going to live 20 more years and see that achieve this goal. It was a special moment indeed!
The adoption of the CCSS presents to the mathematics community a unique opportunity. It is a once in a generation opportunity. Reform efforts over decades have brought us to position where we have the potential to not just reform, but more importantly transform American mathematics education.
The CCSS have at the heart the kinds of things we want from students such as problem solving, critical thinking, justification, making conjectures. To implement this adequately can only be done through active learning pedagogy. I do not know of a system that can accomplish these things through passive, solitary work on rote skills.
Some challenges:
- Professional develop of K-12 and college instructors
- Appropriate curricula
- Educating and supporting administrators and parents about how they can support IBL classrooms
- Mentoring and coaching students in a new (perhaps foreign to them) active learning paradigm
Tuesday, January 3, 2012
Announcement: IBL Workshop June 19-22, 2012 in Santa Barbara
First, let me wish all of you a Happy new year!
This workshop is an MAA PREP sponsored workshop for instructors who teach 2nd year Calculus courses and courses for prospective K-12 teachers. More information is available at MAA PREP Workshop at UC Santa Barbara in June 2012.
This workshop is an MAA PREP sponsored workshop for instructors who teach 2nd year Calculus courses and courses for prospective K-12 teachers. More information is available at MAA PREP Workshop at UC Santa Barbara in June 2012.