Regarding the free and freemium ideas, you should also understand the fact that many learning software programs that are not free are very inexpensive, only dollars per child per year. In many schools, this means that you can buy them with the leftover budget dollars that would otherwise not be spent or would be spent on something the school may not ever use.

The tools listed in this article are not learning tools. Rather, they support your curricular goals in other ways. When it comes to learning software, free usually means poor quality or supported by grants that will eventually disappear and change the software from free to fee. For very popular software, it could mean supported by advertising.

You should wish to support really good learning software with a modest fee so that it can be maintained and enhanced to continue to deliver great learning experiences to your students.

http://bit.ly/21MmbbI

I work with Dr. Mike on an algebra project. He made me re-read your posts several times. I have to say I missed quite a few things in your posts. You are right in many aspects… What you said was actually very helpful to our project. Hopefully we can talk more in the future.

What you said is true, but the issue is that algebra does accomplish much, much more than your list. Parts of algebra can be replaced by other subjects, but then we are missing some unique features that can be provided only by algebra.

Many, many students don’t like ELA and they do fail ELA tests. Should we find something else to replace English?

“In Hacker’s defense, I have no doubt that some high school algebra teachers, maybe even a majority of them, spend their time emphasizing arcane definitions and complicated formulas instead of the problem-solving skills, copious applications, and intrinsic beauty that should be at the core of an algebra class.”

I also believe that for those who will be continuing with math beyond algebra, they *must* learn the ‘grammar’ of math that is learned in an algebra class and for those who will not, a separate class focused on problem solving using algebraic concepts (without the grammar) would be beneficial.

I was pretty bad at math, but I’m pretty good with informal logic, simple programming and spreadsheets.

Although you have made a false equivalence, allow me to use your metaphor in my response.

Algebra is indeed an edifying subject – I feel as though I made that quite clear. I also made it clear that there are other profitable and noble things for kids to learn. To use your analogy, algebra isn’t all vegetables, but a single type of vegetable. And if kids don’t like, say, broccoli, but readily eat cauliflower, spinach, or cucumbers, why force them to eat the broccoli? In other words, there are many other valuable and profound subjects that accomplish the same purpose of Algebra (namely, critical thinking, reasoning, logic, memorization, challenge, communication, language, etc.). For some, taking Algebra makes sense. For others, it doesn’t – and they ought to pursue those other subjects which suit them better.

As I hinted, food and education are not equivalent (and with the most popular worldview being one of naturalism, that should be relatively easy to see). Food is necessary for life, and, in fact, one can scarcely go without it for even a two weeks. Education is not so, and there is ample evidence that many peoples, tribes, cultures, etc., do not educate and yet they survive.

Do not misunderstand me. I do not discourage the notion of everyone taking Algebra simply for children’s happiness. This is not about making things easier or more fun. It’s about doing what’s right. Algebra is indeed a fulfilling subject, but if that’s the reason we force kids into taking it, then why don’t we also force them to take swimming, dancing, debate, theology, architecture, and all of the other myriads of profitable subjects? And more to the point of the original post, kids don’t “need” this useful subject. That is false. As I mentioned in my previous post, yes, it is a worthwhile subject that would be helpful to them, but in no way is it “needful” for them. Unless you would like to redefine what the word “need” means.

It is wrong to force kids to eat vegetables. They all love fries, so parents should feed their children with fries all day long to make them happy…

Let us assume that the purpose of an education is pragmatism – that is, that teachers are teaching students things that they will need and will use in their life. If this is true, then it is not absurd to think that we should be spending the majority of our time giving them useful skills and knowledge to that end.

This, however, is not the case in any Algebra 1 classroom. The vast majority of time is spent on developing skills that culminate in solving equations, graphing equations, and simplifying expressions. These skills are developed by rote and recipe, which is to say, they are not developed at all, but merely memorized. Almost none of this – the content of the class or the procedure in which it is presented – is at all pragmatic.

And thus, if pragmatism is the goal, then Algebra does not meet the standard. Not even close.

Algebra is class similar to grammar – it serves to teach the student the language of math. And while grammar is necessary – since poor writing and communication can be detrimental not only to one’s professional life, but also their personal life – Algebra is not, since only mathematicians speak in Algebra. Perhaps that point will be disputed. If this is the case, I challenge you to determine the statistics of those who solve, graph, or even read equations in their everyday life.

I was very disappointed with your examples. Your list does not in any way provide a convincing argument for why students “need” Algebra. They might “want” it. But they might also want theology, or art, or athletics. To assert that students “need” algebra because they might use it here and there is simply an irresponsible argument. I can see the “need” to add numbers together. I can see the “need” to be able to write. I do not, however, see the “need” to see what the winning percentage of a team will be if they win a certain amount of games.

Does this mean we should abolish Algebra entirely? By no means! However, we need to seriously reconsider how we do it and to whom we teach it to. In many ways, math is like art or music. With some guidance from someone experienced, you must learn yourself through your own work. You have to fail. You have to try again. You have to explore. There’s practice and rote involved along the way, to be sure, but there’s also plenty of adventure along the way. And like art and music, not everyone can (or should) be bothered to go through this process (which, let’s face it, is time-consuming, difficult, and sometimes fruitless). Those that do will be immensely rewarded – not with esoteric skills, but with knowledge, love of learning, curiosity, logic, reasoning, and intuition, just to name a few.

The fact is, if the goal of education is pragmatism (which is the facade that modern education paints – but that’s a debate for another day) then algebra is nearly worthless.

Of course, I would hold that education is not – and frankly, shouldn’t be at all – about pragmatism. It’s about developing and training the mind on how to think, learn, and communicate. It’s about building a foundation with logic and reasoning, and teaching kids truth and virtue. If that’s the case, then Algebra stands as a desirable pillar to explore. But it also means that it needs to be actively explored, and not memorized. And if the student doesn’t desire to explore it? That’s OK too – there are many other noble fields that a student can grow and develop his or her mind on.

Thanks for taking the time to read my thoughts. Looking forward to your response.
Joe

Unfortunately in traditional education their use is simply to transfer incumbent, ineffective, inefficient, one size fits all teaching which does nothing to advance deep student learning.

Over and over again the research reflects this and its ignored time and time again

The educationally innovative pedagogy, seamless integrated into software, delivered to individual students over common devices, in an individually facilitated, belended and flipped envirnment is what work

Lets get past the device and focus on the rearch reflecting what advances student success outcomes