Teaching and Learning Resources by Peter Pappas

Don’t Teach Them Facts – Let Student Discover Patterns

4794114114_dd895561bf Develop a classification system – analyze patterns, create a schema, evaluate where specific elements belong. Sounds like a very sophisticated exercise. Not really, young toddlers do it all the time – sorting out their toys and household stuff into groups of their own design. They may not be able to explain their thinking, but hand them another item and watch them purposely place it into one of their groups. They have designed a system.

Humans experience the world in patterns, continually trying to answer the question – what is this? Remembering where we’ve encountered things before and assessing new items for their similarities and differences. Someone once asked Picasso if it was difficult to draw a face. His reply, “it’s difficult not to draw one.” We see “faces” everywhere.

Filling out a Venn diagram isn’t analysis – it’s information filing.

It’s unfortunate that student don’t get to use their innate perceptual skills more often in the classroom. Instead of discovering patterns on their own, students are “taught” to memorize patterns developed by someone else. Rather than do the messy work of having to figure out what’s going on and how to group what they see – students are saddled with graphic organizers which take all the thinking out of the exercise. Filling out a Venn diagram isn’t analysis – it’s information filing. Instead of being given a variety of math problems to solve that require different problem-solving strategies, students are taught a specific  process then given ten versions of the same problem to solve for homework. No pattern recognition required here – all they have to do is simply keep applying the same procedures to new data sets. Isn’t that what spreadsheets are for?

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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. 

 

Excel 

 

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. 
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