Is Algebra an Unnecessary Stumbling Block?

Hello colleagues, The Math Standards spell out clear learning goals for algebra. This Associated Press story, Is Algebra an Unnecessary Stumbling Block in US Schools, appeared in newspapers all across the country in the last day or two. It would be great to see a robust discussion of this issue here in our CoP.

Ready? Set! Go!

Cheers, Susan Finn Miller

Moderator, College and Career Standards CoP

Comments

I have long appreciated the logic and flexibility of thinking that mathematics brings. Engineers, innovators, those that work with finances, programmers, and gambling organizations all benefit greatly from the profits of Algebra. Given my respect, I believe there may be other ways we can instill these benefits. Let us keep the structure, pattern manipulation, logic and flexibility of thinking that is fundamental in most Algebra but change the activities adults can engage in to learn these.

Programming has been one of the most powerful ways to engage in Algebraic thinking and with very easy entry programs like MIT's Scratch and other programs, many can learn Algebraic elements in a fun and creative way. 

Board games that require intense social interaction and flexibility of thinking, such as these games for starters, again create the mental flexibility of pattern manipulation and logic that is often a vital component present in those that excel in Algebra. 

More hand-on experimentation and engineering will offer a medium in which failure is simply part of the process of learning how the patterns and the logic of life works, and does not work. Increasing the number of open ended physical activities that require hypothesis, experimentation, reflection and revision while creating a product can accomplish much of what some mathematicians may wish Algebra to provide in terms of application of learning. 

As the article suggests, a focus on statistics and data analysis can offer many useful skills. After all, what is all that Algebra graphing about other than simply being able to see data in a different format. Technology offers so many ways to represent data without a learner needing to know the procedures used in order to still be able to process data analysis, prediction, and processing. Of course, many in our adult society could benefit a great deal from understanding our financial system better and all the intricate patterns, procedures and symbols that currently befuddle many American adults.

I completely understand that we still need some to know the inner workings and the geeky procedures of mathematics. We should never stop offering those options, but we may wish to keep them as options rather than requirements. Perhaps, we might concentrate on the mathematical thinking highlighted in the standards a bit more as we look at what the base requirements might be. Any experiences we can offer that build flexibility of thinking (math/logic), pattern recognition and manipulation, and the means to predict / reflect / revise really offers our adults a good portion of what Algebra aims to do. Based on the constant aversion we see in the field whenever someone mentions Algebra, I would say our standard algorithms are not effective today. Ironic in a way that it is so hard to flexibly deviate from our standard patterns given the evidence we hear reflected in many media and reports today. 

I would support keeping Algebra as an option for all, but not a requirement for all. There are other ways we can approach the underlying foundations of Algebra we wish to impart to all adults. 

To all that have posted, you all have shared some really good points. I must admit I get tired of having to defend the need for algebra but do understand why many people run in the other direction at the mere mention of algebra. I think we can all agree that algebra is important but it is "what algebra" should be emphasized and particularly, the need to teach algebra with understanding. I think if more of us and our students were taught with algebraic thinking, looking at patterns, developing formulae or graphing for a purpose, we might not be hearing these battle cries. It got me thinking about a wonderful publication that came out in July 1996, A framework for Adult Numeracy Standards: The Mathematical Skills and Abilities Adults Need to be Equipped for the Future by Donna Curry, Mary Jane Schmitt and Sally Waldron  http://www.adultnumeracynetwork.org/files/Framework_AdultNumeracyStandards.pdf.  I served on the working group that gathered information for this publication. I remembered one of my students was quoted for her feelings about algebra. I am posting her response here to add to the discussion.  She said: ​"While basic math skills, e.g. adding and subtracting, are obviously important, it is also useful to have  working knowledge of algebraic language. I am surprised by the opportunities I've had to use 'algebra mind', which I was unaware of before I acquired it.  For instance, I now know that God didn't create complex mathematical formulas; the 'Math Wizard' did. Because I have an understanding of how these formulas happen, I am able to apply that knowledge to creating formulas that work for me. 'Algebra mind' has also made a contribution to my daily thought process.  I find myself thinking more critically and analytically, which is a nice side effect of all the problem solving...In my opinion, any person who thinks more systematically and analytically, is bound to be a better citizen...crime rate, parenting, population, welfare and many other social concerns. Better thinkers think ahead. 'Algebra mind' should be taught as part of social reform." (p 55).

 

 

 

 

 

 

An announcement from edX for an introductory course called "Programming in Scratch" (https://prod-edx-mktg-edit.edx.org/course/programming-scratch-harveymuddx-cs002x-1) just appeared in my in-box and reminded me of this thread. I'm posting the link in case anyone is interested in learning more about it. I've used Scratch a little in a course, and it's easy and fun. 

Susan, I found this topic to be very interesting as I am currently teaching Math one afternoon a week at a local adult education program. I remember being on a conference call years ago, and someone asked Lynda Ginsberg if our students were going to have enough time to meet all of the math standards they needed to pass the GED. I mentioned that when I went to high school in Quebec, Canada, we did not learn algebra one year, geometry the next, followed by algebra ll/trigonometry the next. Math was more integrated and not treated as different subjects. In fact all of our courses were "math" as in Math 320, Math 422, and Math 532 - the courses I took. Algebra, geometry and other maths were all woven together based on our skills at that level. If I remember correctly, Lynda told me that math is taught that way in most countries. I think my experience is more similar to what is happening in adult ed. I have observed many adult education programs across Pennsylvania, and I don't recall any of them having a basic math class, an algebra class and a geometry class that were all separate and having a different teacher or time slot. Teachers are more likely to move from one aspect of mathematics to the next rather seamlessly, contextualizing as much as possible so that students see the relevance of what they are learning. I'm assuming that students are capable in basic algebra and geometry since they are passing high school equivalency tests. These may be the same students who struggled so much with algebra in high school. Perhaps it matters more how we teach what we teach? 

We chatted about this yesterday.  There are significant concerns that the "alternative pathways" are still going to limit one's career choices and that people of predictable demographics are going to be guided into them, when they might have the potential to be mathematicians.  

So... to start shutting those doors in middle and high school... don't like that idea.   

Also severely dislike the idea that it doesn't discuss the instruction issues behind the poor student performance.   I work with students who hit "the wall" when confronted with x and y and graphing, as the student interviewed in the article did.   By slowing down and making connections and teaching them that  yes -- we're really changing thinking because we're going into two dimension -- ... most students *can* understand and work with graphs and x's and y's and succeed.   That's not the norm (just ask any stand-up comic who makes everybody groan reminding them of "two trains leave the station... one going x mph...")   

We are using a close cousin to the Statway/Quantway courses they talk about...  well... change is hard... some parts of it work better than others ;)   I like that it is much more based on places where students can really apply the math principles... I like lots of the examples... I tear out my hair days like today when they're doing this convoluted, contrived manipulation of numbers where the directions say "calculate the exact answer" but, actually, they're just supposed to estimate it from the graph.  I wish our people with the money and the power recognized that it's important to invest in designing curriculum and working out the wrinkles before putting it "out there" and basing peoples' academic careers on it... 

 

   I sort of forgot to mention that ... I do think they're right.   Our current math demands slam too many doors on people.  While we're figuring out better ways to teach... we need to pry open those doors... 

Susan, and others,

I have seen some amazing adult numeracy/math teaching, talented and engaging teachers and teacher educators. We are fortunate in adult basic skills teaching and learning to have numeracy and math educators in the Adult Numeracy Network, at the SABES PD Center for Mathematics and Adult Numeracy, as members of the LINCS Math and Numeracy Community of Practice, and elsewhere. However, there are three big stumbling blocks to numeracy and math education. You nailed one, that "our current math demands slam too many doors on people". Another is that we need to dramatically scale up high quality numeracy and math teacher education. The third, and this applies to other adult basic skills teaching areas as well, we need to build career pathways in our field so that there are incentives for talented numeracy and math teachers to enter -- and stay -- in adult basic skills instead of moving to K-12 and higher education where there are full-time jobs, benefits and fairer salaries.

David J. Rosen

djrosen123@gmail.com

As other comments have suggested, algebraic thinking is necessary in any job that involves the manipulation of variables in your head, pattern recognition, or the use more than dumbed-down technological interfaces. In addition, as the Internet evolves into the Internet of Everything, it will become more necessary in our private lives as well. In both lives -- work and private -- we will have to communicate more and more with vendors, technicians, repair people, and so on, who have internalized these kinds of thought processes. It can be difficult for algebraic and non-algebraic thinkers to communicate without at least some level of miscommunication, misunderstanding, frustration, and, sometimes, anger. This can be costly on many levels.

And dumbed-down interfaces may be going away as well. An article from yesterday’s Washington Post (https://www.washingtonpost.com/news/the-switch/wp/2016/03/28/why-apple-and-google-are-struggling-to-design-simple-software/?hpid=hp_hp-cards_hp-card-technology%3Ahomepage%2Fcard) reports that smart phone interfaces are becoming more and more complex as more and more functionality is added to these devices, and the ability to evaluate variables in one’s head will be required to use the software described in an article in today’s issue of the same paper (https://www.washingtonpost.com/lifestyle/food/this-groundbreaking-technology-will-soon-let-us-see-exactly-whats-in-our-food/2016/03/26/763fb9ca-f070-11e5-89c3-a647fcce95e0_story.html?hpid=hp_hp-more-top-stories_unearthed-125am%3Ahomepage%2Fstory).

Stumbled upon this TED talk video this evening and it got me thinking about what subjects and content we deem necessary today. Our assessments, texts and even the structure of our classes seem so focused on the acquisition of content. What if the content, at least some of it is in there? I have seen many a student doodle in my time and probably could make an art gallery from my notes as a student. I had many moments similar to the speaker in which I saw some formal educator flashing "my creation" up on screen with some funky name make up by some guy that has been dead for some time. I know that I had absolutely no clue about the dead guy nor the fact this a particular doodle was mathematically famous already and yet, in my boredom, it just ....came out. 

As I sit here reflecting on all the powerful discussions I get into with students, I am feeling a bit more validated. See, after some intense discussions with great exchanges, I would often feel guilty that my students were not learning what was on the slate or scheduled for the day. Heck, half the time I was not even able to directly tie the conversations to a specific academic content piece. I was convinced that the discussion still had power and brought out thoughts and ideas in my students that were inspiring at the time. 

I share the video above and my reflections in the hopes that it reminds others that learning, real learning can take on so many forms that may not be quantified in our systems. Just in this video for example, was the man's doodle Geometry, Algebra, Algebra II, Pre Calculus or all of the above or none? Sad to think that many of our students just doodling, daydreaming, humming or pacing in a circular patter may at times be experimenting or expressing wondrous learning that we are just not able to "fit in" with objectives laid out for us. 

I wonder if there are any curriculum out there that focus on demonstrated thinking vs content or process. I am thinking of something like a report card that looks like a Habits of Mind checklist or something that concentrates on types of learning a student has engaged in. With so many of our adult learners' life situations, it almost seems that "passing" a Habits of Mind type curriculum may be much more valuable or useful in their life goals than the more traditional curriculum. What do you think?

  1. Is it possible that all humans inherently have some knowledge inside that just leaks out every once in a while through play, meditation or some other stimuli? 
  2. Does a curriculum centered on demonstrated types of thinking more than process/content exist?
  3. Are there any studies that compare the relative value of teaching students to think in multiple different ways vs teaching to finite processes?
  4. Do you feel many adult educators would benefit more from a thinking-based system compared to the current content/process based system?