Teaching and Learning Resources by Peter Pappas

## Why Study Algebra?

Today I listened to NPR's Scott Simon and Keith Devlin of Stanford University, answer the question: Why Do We Need to Learn Algebra? (NPR Weekend Edition Saturday~February 28, 2009). Devlin described how spreadsheets have become essential to managing everything from your finances to your fantasy football team. And of course, spreadsheet are basically collections of algebraic formulas. You can follow this link to the NPR story, comments and audio file. Teachers might use Devlin's comments as a springboard for getting students to think and discuss the application of algebraic thinking in their lives.

This is essential, since algebra is emerging as an academic gate keeper. I'm not a math teacher, but I suspect it stems in part from the fact that many students lack basic computation skills. But more importantly,  students have to be able to transition from concrete lower order thinking skills (arithmetic) to higher-level and more abstract thinking (algebra and beyond).

As Doug Reeves has noted, "The single highest failure rate in high school is Algebra I. After pregnancy, it’s the leading indicator of high school dropout. The leading indicator of success in Algebra I is English 8. The Algebra 1 test is a reading test with numbers.”  District Administrator, April ‘05

If Reeves is correct, then this is as much a literacy problem as a math problem. Teachers of all content areas can pitch in to support the higher order skills (analysis, evaluation and creating) that will help students with more advance mathematical thinking.

## Teaching Innovation

Innovation – an idea put to work – stands at the pinnacle of higher-order thinking. It begins with a firm grasp of the basics. Then the innovator must continue up through Bloom's taxonomy of thinking skills to analyze patterns and needs, evaluate alternatives and finally create something to resolve to the problem. Creating is nothing more than a new combination of existing components.

The New York Times has devoted much of this week's "Education Life" (1/3/09) to showcase 23 innovative ideas generated by students. The same issues details a number of college course on entrepreneurship – "Dreamers and Doers."

<<< The Elizabowl’s shape shifts to hold more or fewer fruits. The idea is to separate fruits into individual compartments to retard spoilage. Photo by by Sarah O'Brien (it's inventor)

Let's hope this focus on innovation and sustainability can extend down to K-12 education. Kids are getting plenty of time with the basics – when do they get to create something original with them?  Seems more valuable and engaging than test prep.

## Start Your New School Year with Rigor and Relevance

##### start the school year

As a social studies high school teacher, I faced over 25 years of the first day of school. When I first began teaching, I did usual thing – working through the class list (“do you prefer Patrick, or Pat?), a dry recitation of the class rules,  passing out the textbooks. Blah, blah, blah – think of the message it sent to my students.

As my teaching style evolved from the lecture / work sheet model into a more engaged learning environment, I redefined how I wanted to introduce my students to my course. I also came to understand that it was imperative that I get all my students to contribute a few comments to the class during those first few days. Very quickly classes learn which students are the talkers and non-talkers. Once those roles are locked in – it’s very difficult for student for break out of them.

So I did not waste the opening week of school introducing the course – my students solved murder mysteries. I took simplified mysteries and split them into 25-30 clues, each on a single strip of paper. (You can download one of the mysteries and rules from my website.)  I used a random count off to get the kids away from their buddies and into groups of 5-6 students. Each group got a complete set of clues for the mystery. Each student in the group got 4-5 clues that they could not pass around to the other students. They had to share the clues verbally in the group and that guaranteed that every student is a talker on day one.

While the students worked to solve the mystery – I concentrated on learning the student names. After I introduced the mystery, I bet them that by the end of the first class, I could go around the room and recite their names. While they worked on the mystery, I circulated getting to know students and their names. Another message – in this class, we’re all learners.

Over the next few days we would process their problem solving skills, group dynamics, differences between relevant and irrelevant information and introduce the idea of higher-order thinking like analysis, evaluation and creating. We might even have time to try another mystery to see if they got better.

By week two, I got around to passing out the textbooks. But by then I had already introduced them to what was most important about my class.

Image credit: flickr/pobre.ch

## Bloom’s Taxonomy: Creativity and 21st Century Literacy

Innovation requires both a strong foundation in content knowledge and the ability to apply that knowledge in new ways – usually across a variety of disciplines. And it requires using all of Bloom’s skills from remembering through creating. Creating is not a skill limited to the gifted. It’s something that all students can do – think of it as a new combination of old elements.

Digital technology gives students access to information and creative tools that enable them to be creators as well as consumers of content. New technologies have put students in charge of the information they access, store, analyze and share. You can’t broadcast (lecture) at students.  They won’t be a passive audience. They expect information control and functionality.

For more, I recommend a site from Andrew Churches, a New Zealand educator who matches Bloom’s Taxonomy with instructional technology to move students from lower to higher order thinking skills.

## Students Can Become Proficient Writers – Try a QuickWrite

The recently released NAEP report suggests that only about one-third of our eighth graders and about one-quarter of the nation’s high school seniors are proficient writers. The results are not much better than the results of the NAEP’s last report in 2002. More

If we want to bring these numbers up, students should be writing on a daily basis in all of their classes. So how do we give students more opportunities to hone their writing skills without overburdening our secondary teachers with loads of papers to grade?

Why not use the QuickWrite strategy.

• As students enter class, they see a prompt on the front board that requires them to revisit a previously lesson. This makes more productive use of the opening minutes of class where teachers are usually tied up in “housekeeping” tasks.
• Students are trained to write briefly, but in complete sentences.
• After five minutes, selected students read their answers aloud to the class. Students are instructed to read exactly what they have written. This requires quick organization of thoughts and prevents rambling oral replies.

The QuickWrite is followed by short discussion. Teachers call on volunteers, drawing out divergent viewpoint:

• “Does anyone have a different idea?”
• “How did those two students’ QuickWrites differ?”
• “What do these QuickWrites tell us we should study today?”

This strategy stimulates students’ higher-order thinking about a concept from the previous day. Teachers can easily check for understanding before beginning a new lesson. The class is now ready to link this newly anchored understanding to the content of the upcoming class.

Most importantly, a QuickWrite gives students a chance to evaluate what they think is significant and share what they’ve learned with their peers. It restructures the typical teacher-led discussion that too often finds the teacher playing “guess what I’m thinking?”

For more ideas and resources, visit my literacy posts on this blog.