Sunday, March 29, 2009

Algebra For All - Another Report...

A recent article in Education Week, entitled Algebra-for-All Policy Found to Raise Rates Of Failure in Chicago, is generating some provocative online comments. Although access is usually restricted to subscribers to Education Week, there may be limited access to this article.

Meanwhile, California currently is mired in legal action regarding implementation of Algebra for all eighth graders.

What does all of this mean? IMO, mandating that all students take Algebra at the same point in time, ready or not, reflects a lack of understanding of the prerequisites for student success in learning algebra.

I've been advocating for some time that the content of an algebra course be standardized. As long as the course contains a common body of knowledge, I would argue that the name of the text, the approach, the instructional strategies, and the extent of integration of technology are of less importance.

Teachers should also be provided with samples of the kinds of assessment questions students should be able to handle. If these exemplars reflect a variety of question-types, balancing skill, conceptual understanding and problem-solving we can be reasonably certain that students are getting an authentic algebra course.

After reading some of the excellent comments on this article, I decided to share my own thoughts. Click on Read more if you would like to see these comments...


First Comment
Considering that this debate has been ongoing for years, one would hope that our current administration will listen to the voices of reason, many of whom have already submitted excellent comments to this article. If you bring together 100 parents and educators and sit them down in a room to discuss this issue, a consensus could be reached that would probably be far more reasonable and helpful to our children than all the research studies and commission reports that have been published.

Here's my best guess of what this group would recommend (much of which was stated above by some of the commenters:

(1) Algebra for All makes sense only if we have Arithmetic for All, i.e., a STANDARDIZED body of content/core knowledge of skills AND concepts, K-7 or K-8. Yes, it is possible to balance UNDERSTANDING AND SKILL and, yes, the preparation of our K-8 teachers must similarly be upgraded to deliver this!

(2) Students must be expected to demonstrate conceptual understanding of and proficiency in basic arithmetic skills including fractions, decimals, percents and ratios. Does this sound impossible given the current levels of student performance? What seems far more absurd to me is expecting proficiency in algebraic reasoning and skill UNLESS this foundation is in place.

(3) We also know that mandating ALL children to demonstrate proficiency AT THE SAME TIME time is unreasonable, however, there must still be strong EXPECTATIONS THAT ALL WILL GET THERE if we provide enough support and demand the needed effort and commitment from each child. Why should parents (and most do not have the means) have to pay thousands of dollars to private after-school companies to supplement their children's learning? This administration should provide whatever funds are needed to provide extra tutorial time in mathematics DURING THE SCHOOL DAY or before or afterwards or on Saturdays or during the summer or whatever is needed to bring children up to level. In return, students must be expected to work hard - NO EXCUSES. Coming for this extra help should not be optional! IMO, that would truly be a 'stimulus' for success.

Other countries have shown that most children can be ready for more algebra at an earlier age provided the necessary foundation is laid.

Prof. Escalante demonstrated that, through superhuman effort, it may even be possible to have CALCULUS FOR ALL! I'm not advocating this nor am I convinced that this is feasible unless one can clone this remarkable educator, however, the main lesson to take from him is the POWER OF HIGH EXPECTATIONS.

Until our society believes that EDUCATION OF OUR CHILDREN IS AN INVESTMENT NOT AN EXPENSE, all the recommendations from all the experts will fail. Listen to the voices of reason, please, before another generation is lost...
Dave Marain

Second Comment


How about some real specifics of what it means to develop algebra sense...

Here is one of many possible ways of developing the distributive property (the basis of 'combining like terms').

Visual:
[{&&&&}{&&&&}{&&&&}] combined with [{&&&&}{&&&&}] =
[{&&&&}{&&&&}{&&&&}{&&&&}{&&&&}]

Verbal:
Three groups of 4 added to two groups of 4 equals how many groups of 4?

Numerical:
(3x4) + (2x4) = 5x4

Symbolic:
3a + 2a = 5a

The language of algebra is the generalization of the language of numbers and arithmetic.

Other countries introduce the symbolic form early on as children are learning their arithmetic facts. Do we? In fact, children can develop both number sense and symbol sense if these are presented in a systematic organized manner. BTW, the use of multiple representations I've shown above is not just to get at different learning styles; it also deepens the child's understanding of numbers and relationships.

BUT, in the end, children also need to KNOW that 3x4 = 12 without hesitation. Knowledge of fact and skills can only be achieved through repetition and practice. Educators know this self-evident truth and they also know that one can accomplish this while students are gaining insight from solving problems and communicating their thoughts. Until we all make a commitment to this BALANCED VIEW of learning, it won't make any difference what curriculum a district purchases.
Dave Marain
MathNotations


Your thoughts...

2 comments:

jd2718 said...

Dave,

I like your puzzles and SAT-type activities and investigations, but it is here:

"IMO, mandating that all students take Algebra at the same point in time, ready or not, reflects a lack of understanding of the prerequisites for student success in learning algebra."

that I am most reminded that we have a common starting point. Excellent post, excellent comments.

Jonathan

Dave Marain said...

Thank you, Jonathan, for those kind words.

I think you know that I've been reiterating this same basic position from Day One of this blog. The decision-makers out there don't even know I exist, but my validation comes from seeing some of my recommendations being realized -- better late than never.

A perfect example comes from one of the staunchest supporters of NCTM's original positions. Recently,he's been preaching NATIONAL STANDARDS and BALANCE and, would ya' believe it, "LESS IS MORE!" (which happens to be the essence of the Curriculum Focal Points document.

He and others are expressing all of this as if it is a radical new discovery! I'm beginning to feel more and more as if I came along at the wrong time or I'm trapped in a time warp.

A century from now, how would you guess this period of time in math education will be viewed?