Cognition and understanding are abundant, not absent, within the Saxon practice. In fact, mixed practice requires a greater cognitive demand as students have to connect mathematical procedures with constantly changing real-world and mathematical contexts. Many opponents of the Saxon approach falsely label the practice within the program as a mindless and rote activity. I highly recommend an open-minded review of the practice within the newest editions of the textbooks.
Complex problems certainly play an important role in mathematical understanding. When those problems develop rigor incrementally, much is to be gained. However, I believe a balance should be struck. Educational psychologists point to the limited ability of complex, open-ended activities to move understanding into the long-term memory of students. One such article, Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teachingby Kirschner, Sweller, and Clark does a good job of summarizing and clarifying this understanding.
John Anderson Lowell, IN
________________________________ From: John Clement <email@example.com> To: firstname.lastname@example.org Sent: Thursday, May 5, 2011 10:02 AM Subject: Re: [math-learn] Other Comments On High School Algebra 2
But what about the role of cognition and understanding? When you improve the metacognition of students and get them to understand they do much better than with drill and practice. For example we have found that fewer more complex problems work better than many practice problems. And part of the success of Modeling is the coherent design of the instruction. Also the concepts are revisited, and a new model based on the old one is developed. This also is a spiraling back.
John M. Clement Houston, TX
> > The Saxon texts strategically distribute the content > typically found in chapters and units within more traditional > texts. This allows more time and practice for skills and > concepts to be mastered before the next increment of rigor is > added. The daily, cumulative practice is the glue that holds > the approach together. Doug Rohrer from the University of > South Florida has done some interesting research regarding > the advantages of mixed and spaced practice, the method used > in the Saxon approach. >
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