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Information Age Education Blog


Information Age Education (IAE) is an Oregon not-for-profit corporation founded by David Moursund (http://iae-pedia.org/David_Moursund) in August 2007. The IAE Blog (http://i-a-e.org/iae-blog.html) was started in August 2010. Other IAE free resources are listed at http://iae-pedia.org/Main_Page.
Apr 06
2011

Higher-order Thinking in Algebra II and in Reading Instruction

Posted by: Dave Moursund

Tagged in: Forecasting

I have struggled with developing an appropriate title for this IAE Blog entry. That is because I am trying to join together ideas from two excellent but quite different articles. 

Whoriskey, P. (4/3/2011). Requiring Algebra II in high school gains momentum nationwide. The Washington Post. Retrieved 4/6 2011 from http://www.washingtonpost.com/business/economy/requiring_algebra_ii_in_high_school_gains_momentum_nationwide/2011/04/01/AF7FBWXC_story.html?wprss=rss_homepage.

Rebora, A. (4/4/2011). Can reading be saved? (An interview with Kelly Gallagher). Education Week. Retrieved 4/6/2011 from http://www.edweek.org/tsb/articles/2011/04/04/02gallagher.h04.html.

Key Ideas in the Whoriskey Article

Here is a very brief summary. Successful completion of high school Algebra II is a good predictor of success in higher education and in a career. In addition, Algebra II and/or College Algebra is required in many college programs of study. These observations are leading many states to require Algebra II for high school graduation.

My belief is that the logic behind this requirement is questionable. I think of a good Algebra II course as a cognitively challenging, rigorous, and demanding course. It is a course that builds on previous knowledge and skills, develops useful habits of mind, and contains a lot of content.

Algebra is often called the "language of mathematics.” Learning Algebra II with understanding requires significant progress in learning to read, write, speak, listen, and think math. Unfortunately, the course is often taught in a manner that allows a student to pass the course—indeed, even get a good grade in the course—and make little progress in the communication and deep thinking aspects of the subject. Many students question the value and possible use of the content being covered. They pass the course but find that not only do they have to take it over again in college (there the course it titled College Algebra) but often they are not able to pass the college version of the course.

As I was reading the Whoriskey article, it occurred to me that one might think of a student’s success in an Algebra II course as a measure of both general IQ and math IQ, and as a measure of both general cognitive development and math cognitive development. Success requires habits of mind, perseverance, dealing with delayed gratification, and other characteristics that serve a student well in future studies.

This type of thinking leads to a fundamental question. Is it the content of an Algebra II course that is so important to future academic and professional success, or is it the other types of things I have discussed above? If the latter is correct, then a requirement of Algebra II could be replaced by a requirement of other challenging, rigorous, demanding coursework. In this latter case, a student might select courses that seem more relevant to their personal interests and goals. Intrinsic motivation might be a driving force in making a decision of what course(s) to take.

Key Ideas in the Kelly Gallagher Interview

In brief summary, Gallagher argues that most students learn to read (at a decoding level) but many do not learn to read with understanding. They do not become careful, critical, deep-thinking readers who can make effective use of reading as an aid to learning.

In addition, many students do not learn to read for pleasure. This means that a great many students view reading only as another academic requirement or hoop to be jumped through. They do not read enough to develop both the automaticity and the various habits of mind that make reading both fun and a fundamental tool in accessing and processing information.

Quoting from the article:

I’ve noticed a very large change, especially in the last 10 years. Students are reading a lot less. And here’s the compounding problem: That lack of reading has created a gaping hole in students’ prior knowledge and background, which is very, very important to bring to the page. A lot of times my kids can read the words on the page, but they can’t comprehend the text because they don’t have requisite prior knowledge and background information.

I think our kids are much more likely nowadays to find other things to do rather than read. They sort of encapsulate themselves in an entertainment bubble when they go home. A lot of Facebook, a lot of texting, instant messaging, and so on. They do a lot of entertaining themselves, but I’m not sure they do a whole lot of informing themselves.

Kids today really struggle with difficult texts. They don’t do a very good job of monitoring their comprehension. They don’t know how to fix their comprehension when it falters. And I’ve found that their ability to really focus in on their reading seems to lessen with each year.

Integrating the Two Articles

Our educational system faces the challenge of a rapidly changing world and students who are adjusting to that changing world. Educational leaders know that it takes years of effort for a student to develop the knowledge and skills that a good education can produce.

Educational leaders see the growing disconnect between students and our educational system. Politicians and many other people believe that a solution is more high-stakes testing, better definition of standards, and increased math requirements for high school graduation.

For me, the two articles reinforce my belief that these approaches are ill-conceived and will not be successful. Many of our efforts to do the best we can for our students are, instead, alienating our students and are not producing better educated students.

Suggested Readings from IAE and Other Publications

You can use Google to search all of the IAE publications. Click here to begin. Then click in the IAE Search box that is provided, insert your search terms, and click on the Search button.

Click here to search the entire collection of IAE Blog entries.

Here are some examples of publications that might interest you.

Brain science and cognitive neuroscience for children and teachers.

Changes in nature, nurture, and tools that help us get better at representing and solving cognitively challenging problems.

Cognitive development.

Creating academic standards that that may be inappropriate and unattainable.

Disrupting class: How disruptive innovation will change the way the world learns.

Education for increasing expertise.

Empowering learners and teachers.

Our Analog Human Brain in an Increasingly Digital World.

Student and adult desires for instant gratification and extrinsic motivation are significant roadblocks to improving education.

Teaching for improved critical thinking.

Twenty-five years of little progress in improving education.

What the future is bringing us.

 

IAE

Comments (2)Add Comment
davem
Students are as gifted as in the past.
written by davem, April 06, 2011
There is a growing schism between the capabilities and interests of young people and the requirements that our society wants to place on them.

In terms of raw brain power ("nature") students are as capable as they have every been. Increasingly, however, there is a growing schism between the "nurture" that students and their peers provide for themselves and the nurture that our school system and others are providing. Our education system does not seem to understand how the communication and other capabilities of the Internet have become such a routine and integral component of students' lives. Schools do not understand the capabilities (and limitations) of ICT as an aid to representing and solving problems.ICT systems can solve or greatly help in solving many of the problems that our schools want students to learn to solve without use of the technology.

To be more specific, authentic education needs to consider the fact that as adults, people function in a world of open computer, open connectivity, and easy access to powerful aids to learning and problem solving.
davem
Reading across the curriculum
written by davem, April 06, 2011
Neither the Algebra II article not the reading article emphasizes the value of students learning to rad within a specific discipline in order to learn the discipline.

Students may well memorize the statement Algebra is the language of mathematics" but most do not learn to communicate in and think in this language. They learn to "decode but they do not develop the fluency needed to be a functional communicator in the language.

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