kitchen table math, the sequel: Computer-Based Math Instruction

Thursday, March 25, 2010

Computer-Based Math Instruction

What are current products (local computer or web-based) for individual teaching (learning) of math. I came across one called ILEARN, but it seems to be positioned as a remedial product, not as a curriculum replacement. I also found the web site (www.ilearn.com) very annoying because there are no detailed examples.

Are there any that are what we would call rigorous? If schools are really not going to have teachers teach (just guide), then I'm not sure why a 21st century (!) computer-based approach would not be really big. All kids could progress at their own speed and mastery could be done on an individual basis. One of the issues of the Everyday Math crowd is the requirement to achieve mastery "for all" before moving on to new material, but this is not a problem because everyone is moving at his/her own pace. Nobody is being pushed or slowed down. If kids get A's on the computerized test, they can move on. Otherwise, a report can be generated which gives the teacher a good idea of how to help the student.

Like a lot of modern teaching (even without computers), this assumes that the role of the teacher is only for support. It could be that their goal is not full inclusion or differentiated instruction, but mixed-ability group learning.

Does anyone know of a rigorous computer-based math curriculum?

29 comments:

RMD said...

I like ALEKS. The material is broken into small units, and you can't do units where you haven't mastered the prerequisites.

I still, however, have to teach the material as my son doesn't always want to read the explanation, nor is the explanation enough sometimes.

But, if you master ALEKS, I can say that your probably know the material since it does period testing and reteaches material that isn't mastered.

Anonymous said...

ALEKS (as mentioned)

EPGY

MathScore (actually no teaching, but lots of practice in specific skills)

Thinkwell (video teaching and canned computer exercises, tests) (I'm not sure how rigorous it is.)

Catherine Johnson said...

I like ALEKS, too. I've completed the geometry course & have done, I think, 2/3 of Algebra 1 (which is a HUGE course... I've done all of Saxon Algebra 1 & nearly all of Saxon Algebra 2 & I'm nowhere near finished with ALEKS Algebra 1.)

I find the explanations a little hard to follow sometimes - I'm with RMD; most students are going to need a teacher or parent explaining things.

What's funky about ALEKS is that the organization is entirely hyperlinked. You never study a coherent, complete lesson & then practice; instead you are given a problem to solve and you have to click on the links inside the problem to get explanations of how to do it. Typically there are several such links inside each problem - which means you have different windows open with different explanations....

So, although I'm using ALEKS, and I recommend it....I'm not sure it's the most effective way to teach math online.

RMD is right about the review and practice. The software keeps track of what you've learned - and whether you still know it.

SteveH said...

Are all ALEKS courses $19.95/month? That's cheap compared to the cost of a teacher who is a guide on the side and spending most of the class with the kids who need the most help.

"I still, however, have to teach the material as my son doesn't always want to read the explanation, nor is the explanation enough sometimes."

I'm teaching my son Geometry at home because he is a year ahead, but it doesn't work well when he just reads the book. It's much better and faster for me to introduce the material. The school offered to pay for an online course. It was with the www.k12.com people. I didn't like it, so now we are using a regular textbook at home.

Are there any reasons why a computer-based approach would be better than a book explanation? The only thing I can think of is that the student wouldn't be allowed to move on unless he/she was paying attention and answered some questions.

SteveH said...

"...most students are going to need a teacher or parent explaining things."

Doesn't that defeat the purpose of computer-based learning? The way I do things now is to explain things to my son, and then give him some problems to do (on paper). I suppose that the computer would be better at automating the testing and analysis of weak spots, but that's not revolutionary.

But, to make the transition to a school-based system where everyone is at his/her own level, then the teacher can't introduce the material - although there is not much of that going on right now.

Anonymous said...

I don't have any experience with it, but there is one called Reasoning Minds being used in some schools in Texas. It covers the arithmetic levels and does not continue into algebra.

Anonymous said...

"Are there any reasons why a computer-based approach would be better than a book explanation?"

In *theory* a computer based approach could do the following:

(1) Provide explanation to student. Hopefully, this explanation had been tested on a wide range of students and had been experimentally verified to be the one most likely to work.

(2) Show some examples.

NOTE: At this point, we could still be doing everything in a textbook.

(3) Provide the student with a problem to solve.

Now ... if the student gets it correct, we move to the next, slightly different problem in the sequence. BUT ... if the student gets it wrong ...

my guess is that there are only a manageable number of standard mistakes. For each one we could have the computer bring up a *new* example, showing the kid how the mistake was a mistake, and why the correct approach got the right answer.

As an example: Adding fractions. ½ + ½ often leads to ¼. At least initially. If the computer knows to look for this mistake, it can then be ready with a nice followup explanation, and they some more problems of this sort before proceeding.

One could imagine a sequence of problems like this:

1/2 + 1/2 = _____

1/2 + 1/4 = _____

1/2 + 1/3 = _____

(with more steps in between, probably).

Each of these kinda builds on the earlier one(s) and has its own set of "common mistakes".

A book can't do this very well.

Is there any software that does this? Not that I know of.

-Mark Roulo

lgm said...

Accelerated Math by Renaissance Learning is another computer math program. It's meant to be skills practice to complement a teacher.

Try artofproblemsolving.com for rigorous courses at a better price than the talent search offerings. They aren't computer; they're distance learning on-line with an instructor that knows math.

>>Are there any reasons why a computer-based approach would be better than a book explanation?

1. student is not adept at reading and learning from the textbook
2. student benefits from visuals in sequence (for ex. showing slope-rise/run, student would be shown in two steps where he would have to figure out the steps in the text's graphic).

palisadesk said...

I heard good things about a computer-based math program (on CD I think; I knoiw it's not web-based) entitled Teach Your Children Math Well. It's for home use or tutoring, not school use as it can't be installed on a network. That's why I have no personal experience of it. The author has a background in DI, precision teaching and ABA so it is doubtless well-designed instructionally, and I have had positive reports from people I respect.

You can check it out hereand I think somewhere on the site is an 800 number; you can call and get specifics from the author. It looks like it goes up to a Grade 8 level.

palisadesk said...

I heard good things about a computer-based math program (on CD I think; I knoiw it's not web-based) entitled Teach Your Children Math Well. It's for home use or tutoring, not school use as it can't be installed on a network. That's why I have no personal experience of it. The author has a background in DI, precision teaching and ABA so it is doubtless well-designed instructionally, and I have had positive reports from people I respect.

You can check it out hereand I think somewhere on the site is an 800 number; you can call and get specifics from the author. It looks like it goes up to a Grade 8 level.

OrangeMath said...

I specialize in this area. I've used everything, but MathScore (soon). While it seems counter-intuitive, rigor isn't among the first issues at looking at software - at least in a classroom environment. For example, a major concern is the number of questions in the database! If there aren't enough questions, then students cheat like crazy. Furthermore, the main value of online instruction - isn't the instruction - but the "continuous formative assessment."

Actually, good instruction is a problem. Several software vendors, such as ALEKS, intentionally keep the instruction brief, because it forces the students to think more in solving problems. The programs that really instruct well - they sell WELL to curriculum consultants, etc. - but students don't learn more. They do less work. This sounds bad, but consider textbooks. Students don't read them. They start on problems and flip to examples.

Much more can be said, but before developing opinions; use ALEKS first. It is by far the most robust product - with a solid AI engine - and it uses constructive responses. It may not cover enough for an independent active learner, if so; try Cognitive Tutor. If price is an issue and you work with primary SmartMath.eb.com and ixl.com are fruitful. However, for pre-K, start with Symphony Math.

If your focus is pre-Algebra, iPass from iLearn is actually a great product - a bit costly for me, and you need to buy into its 2x2, proportion approach.

With experience, you will develop bias that has nothing to do with Instruction. For example, StudyIsland has great questions and it allows users to submit corrections to questions (ALEKS has no wrong questions) but it's just multiple choice. APEX has great instructions and some constructive responses, but unlike ALEKS, the response must be exact in spelling, etc - a dumb system and APEX has numerous wrong/bad questions.

I haven't toyed with expensive solutions like Apangea. They include instruction with real person help. This is the big deal that many of you want. While Apangea uses US Math majors, the future is low cost help from India when a student gets stuck.

This was written quickly. Contact me if you have questions: orangemath@gmail.com

SteveH said...

"Is there any software that does this? Not that I know of."

The programming doesn't seem difficult, but defining the content, analysis, and sequencing would be difficult.


My son's Glencoe Algebra and Geometry texts are good about pointing back to explanations for each problem in the back of each section. If the student has trouble with the problem, that pointer put him/her at the right explanation really fast.

The program would also have to break down the introduction of each section into very small chunks with questions and answers. When my son starts a new section on his own, he does not read things carefully. I still struggled with that in college until I forced myself to read every word (in a technical textbook) and understand exactly what it meant. There could be only 3 pages of explanation, but they are usually packed with a lot of information. My son just wants to breeze over the explanations and dive into the problems.

It seems like the advantage of a computer-based sysem would be in the ability to force kids to stick with small chunks of information at a time. They can't skip or gloss over important information and skills. If each chunk is small enough, then it would be easier to diagnose problems and to provide alternate explanations.

I'll bet that this would annoy my son - taking time to prove that he knows some simple idea, but I've found that I'm much happier when he is annoyed. That means that he is having no problems. Frustration is much worse. I don't think (even one-on-one) that I can ever hit it just right; neither frustrated or annoyed.

OrangeMath said...

OK, for those that want rigor, you should try Raffles from Heymath: http://heymath.com/main/productPrime.jsp. Heymath has excellent flash demonstrations combined with Raffles Singapore Curriculum. Spend some time on this site and see what is making Asia tick. Also, SmartMath is sold through Encyclopedia Brittanica, but it is Hong Kong's Planetii.

Math software is a worldwide competition with ALEKS and ST Math technology leaders, but there are many others. Remember, price matters when comparing.

RMD said...

OrangeMath .. .

Great reviews .. . thanks!

One thing about developing computer instruction . . . it's very, very expensive. And if you adopt a software model that doesn't end up being effective, it's a very expensive mistake.

I guess ALEKS could develop more systematic explanations for each concept. But just the Math 3 unit is over 120 pieces of pie .. . that's a lot of development and testing. And it's usually not too much of a problem working with the given explanation .. . they're pretty good .. . often better than my explanations.

SteveH said...

Thanks OrangeMath. Now I have a reference frame to start doing my homework.

Catherine Johnson said...

Are all ALEKS courses $19.95/month?

iirc it's cheaper if you buy 6 months or a year...

Catherine Johnson said...

the main value of online instruction - isn't the instruction - but the "continuous formative assessment."

absolutely --- a huge help

Stuart Yeh's book is about this - big effect sizes in the classroom using the Renaissance software (is it Accelerated Reading & Accelerated Math? not sure --)

Catherine Johnson said...

yup - this is it

same folks who are now selling AlphaSmarts

Renaissance learning

OrangeMath said...

Another key aspect of math software is "coverage:" not all students respond to a software program well. Every classroom needs at least two programs to reach everybody (time on task, number of problems). ALEKS has great coverage - somewhere between 60-70 % with my reluctant students, adding IXL or Smartmath gives me close to 100%.

Note: I laugh when people simply compare programs. As a teacher I play to find a fit. I need at least 2 programs. If you use just one, like "I Can Learn," which has nice embedded videos for instruction, I doubt if all students succeed. Don't be confused by averages in score growth, when every student must learn.

If I don't use ALEKS, I need 3 programs. For example, I respect Cognitive Tutor a great deal, but not many of my students respond to it. They quit.

Catherine Johnson said...

What Works Clearinghouse finds no evidence that Accelerated Math works... but the Yeh book raves about it.

OrangeMath said...

For a school, ALEKS costs $42.50 per license per year. Home users cost more because home teachers require tech support.

I've tried to be positive in my comments, but it should be said that Accelerated Math is getting pretty old. It has good value and I use it still, but I wouldn't start with it. The non-linear, adaptive model of ALEKS works better.

Catherine Johnson said...

What is Cognitive Tutor like?

Catherine Johnson said...

Several software vendors, such as ALEKS, intentionally keep the instruction brief,

good description -- it's been too brief for me

I frequently Google other explanations. That's worked out OK, but it's annoying.

It's true that I could probably power my way through the problem using the bare bones explanation ALEKS provides but I don't want to.

OrangeMath said...

What Works Clearinghouse is correct on math software. It doesn't work as well as you think it should. I believe that the reason is that NUMBER SENSE - Singapore Maths great strength - is hard to teach online. Certainly, this is ALEKS's weakness. For younger students ST Math, Symphony Math work well at a high price. I've been successful with SmartMath also under this concern. This is why I push SmartMath. It is multiple-choice, but the large number of multiple-choice questions and their rapid delivery seem to help develop Number and Measurement Sense well. Heymath! also helps in this area.

Please note that I'm not a PhD, but I reflect a great deal. This is "anecdotal research" over 6 years working with problem students.

Catherine Johnson said...

Interesting.

Why do you think Yeh found such great results in the Texas school?

(Of course, Accelerated Math was being used entirely for daily, rapid formative assessment - not for teaching.)

SteveH said...

How do schools feel about these programs and their use by individuals. It seems that schools would have to completely break the habit of mixed ability group work. Does it make some teachers feel like they are too much the guide on the side?

Catherine Johnson said...

Actually, Steve, Yeh's book is well worth taking a look at. (I think I have a paper by him around somewhere - I'll email.)

In the book the system was somewhat like the Keller Plan. The classes were mixed-ability (this is elementary school) and each student did practice problems or practice reading at his or her level.

The very little kids didn't even know that their level was behind other kids' levels (though obviously that would change by 3rd grade at least).

The system sounds great to me & they had very large effect sizes.

So I'm perplexed by the What Works findings.

I think the kids in Yeh's book used the software **only** for taking assessments every day. The computer scored their tests immediately & the kids wrote down their scores on their own charts -- and the teacher got reports, too.

It's a system of "rapid formative assessment."

Very rapid, as in same classroom hour rapid.

Catherine Johnson said...

The other extremely cool thing is that the software apparently **produced** "professional learning communities" naturally inside the school. Because the teachers all had an identical set of assessments and scores to analyze, they naturally talked to each other about how their kids were doing - and how they could move the scores up.

If that's true (I have no reason to think it isn't), it's a minor miracle. One of the big issues with professional learning communities, as I understand it, is simply getting teachers to commit to them -- getting them set up and getting them working.

The near-daily use of Accelerated Math & Accelerated Reader software supposedly produced a natural 'learning organization.'

SteveH said...

"What Works Clearinghouse finds no evidence that Accelerated Math works... but the Yeh book raves about it."

I went to the Accelerated Math web site and found it very poor. I watched their video and know only that a computer prints out individual worksheets and that the kids fill out a scantron answer sheet. They feed it through the scanner back to the computer to get their results. Obviously, this doesn't require a computer for each student which could provide immediate feedback and teaching support.

I can't say anything about their content or problem selection because they didn't say a word about it! However, they seem to expect schools to buy into the concept. All I can say is that it's probably much better than what many schools are doing now, but that isn't saying much. At least it takes mastery seriously, unlike Everyday Math. I suppose you could rave just about that one aspect.