Friday, April 26, 2013

Pre-Algebra Math Curriculum

Yes, I occasionally get to exchange some email with Harold Jacobs, my all-time favorite math text author.  Publisher WH Freeman forwards email to him from their website from people with questions about his texts.  He received an inquiry from Michelle, who asked about a good homeschool curriculum leading up to the algebra book by Harold Jacobs, and since Mr. Jacobs hasn't taught math at that level and doesn't have experience homeschooling, he forwarded the question to me.  Michelle was wondering about Math-U-See and Saxon.  She was also asking about some fun things to do in math.  Here is my reply:

I have not used Math-U-See.  I'm aware that the author has worked hard to develop a good course.  Folks generally stay with it through algebra and geometry.  I don't get many kids with a Math-U-See background.

Saxon is fine for kids who like hard work for the sake of hard work.  It's ok up through the Algebra 1/2 book, but the algebra book takes the idea of cycling back to review one step too far.  It strikes me as somewhat helter-skelter, and I refuse to teach from it or to tutor kids from it.  The subsequent high school books are just as frustrating.  Still, I know some kids who had a good guide (parent who was good with math) to get them through algebra with Saxon, and were fine.

Here's what I DO use for pre-algebra:

1.  The homeschool group I administrate uses the reproducible worksheets from Steve and Janis Marcy, http://www.marcymathworks.com.  These include everything that might be taught in general math and pre-algebra, but don't include instructions. They are thorough and complete, however, covering all of the needed topics.  A savvy parent will enjoy these. If they need directions I have kids write directions on the back of a sheet.

2.  The Mental Math series on Amazon:
These are also reproducible.  They are a nice balance to developing proficiency with a calculator.  Kids DO need to develop proficiency with a calculator!

3.  There are a lot of $6 workbooks that can be found at Barnes and Noble, sometimes Toys R Us for keeping things fresh over the summer, and these are JUST FINE for regular use.  Each book focuses on a topic, like fractions, decimals, graphing, etc.  Use them up, throw them away, buy them again for the next kid.  There also are some very good supplemental books by the Critical Thinking publishers.  Here's one:

4.  I have recommended ALEKS.com as an online website for use by adults needing to refresh and re-learn concepts from pre-algebra forward.  The ALEKS folks have been diligent at filling in the gaps and developing coursework, and the system is VERY good at diagnosing gaps in learning and understanding and drilling to fill those in.  At $20 per month, it is the cheapest math tutoring I know.  I've sent some folks out to ALEKS to polish some skills before they enter classes at the community college, and I've learned that if ALEKS says they know the material, then they know the material.  The ALEKS folks have developed their online materials for kids as soon as they can read.  I haven't reviewed that level, but I wouldn't park a kid in front of a computer for a long period of time, anyway.  Some will eat it up, however.

The most important part of pre-algebra is showing where it is used all of the time.  That's where homeschooling is excellent, if parents aren't stuck in the classroom paradigm, thinking that math education has to be done at a table with a book.  Going to the grocery store, shopping online for a good deal, measuring and weighing and cutting in the kitchen and Dad's shop, comparing cellular contracts, talking about the good deal vs. the right fit, on and on.  If parents know how to use the math in everyday life, the kids will be just fine.

When to start Algebra?  Whenever the student is ready.  The big rush is to put it into the 8th grade for everyone.  Huge mistake.  It just means I'll be teaching at the community college until I die, if I like, cleaning up the mess made by pushing it too soon.  I would say that if a young student has competence in all of the topics in anyone's pre-algebra text and is hungry for more, then let him or her begin, but without the necessity of finishing in a year.  I've had students as young as 6th grade in the Jacobs book (I have one now that age), but I find that as bright as they may be, they need more time to digest and complete homework.  For that reason, I have designed a Decompressed Algebra series, which takes two years to complete the book, and provides lots of opportunities for data gathering and analysis, along the lines suggested by exercises in the book.  

Good, solid, math fun?  Play games!  The card game War is how my kids learned to sequence and count.  I've developed matching cards for fractions-decimals-percents, and my pre-algebra class has been playing Go Fish with these for two weeks.  Yahtzee, Sequence, Rack-O, Flinch.  Checkers, Chess, Go, Oware.  These are every bit as important as drill and practice.

But you knew all this!

Monday, September 10, 2012

Why learn anything?

It's a delight when the denominational magazine I receive (because I'm a member of a particular denomination) produces an article so appropriate for education.

Roger Wiens, a senior scientist at Los Alamos National Laboratory is also a member of this denomination.  The article linked to below gives a bit of his personal history and why he has no problem working in a pretty secular field for a pretty secular goal.

We need to keep our brains OPEN, and PLAN to keep on learning. Education isn't just a means to an end as in "I want to be a _______ so I can make lots of money".  Exploration and seeking new knowledge is a kind of worship of God.  God's fingerprints are all over the universe.  We don't worship the fingerprints, we worship the Creator.  The twists, turns, surprises, variety, and magnitude are all meant to get us to open our mouths and say "Oh, my God!  That's AWESOME!"  Seeking new knowledge always opens our brains to think creatively.  It's hard work!

The creativity we learn from the Creator Himself is meant to be turned around to our everyday situation.  How can we make our life better right here?  How can we make the life of our neighbor better?  How can we bring Christ to our world?

http://www.usmb.org/roger-wiens-why-i-explore-space

Friday, June 1, 2012

How postponing college can pay - BIG!

I ran into a former ZLO parent today who showers me with gratefulness every time I see him for advice I gave concerning his son some years back.  He had a very interesting update, and I asked if he'd write a paragraph or two on the outcome.  Here it is.


Dear Molly
Thanks so much for your encouragement to start our son in tech school instead of college.  He was only 15 when we had that discussion.  Now at 19 I thought I'd give you an update. 
He graduated last year from Bellingham Tech's welding program utilizing the Running Start program.  There he made friends with older men with clear career goals. 
He is currently working at Central Welding Supply.  He was hired in spite of the fact that he was too young to get a HAZMAT commercial drivers license.  They love his work ethic and enthusiasm.  His employer has offered to pay for tuition and books for anything related he wants to take.  How interesting that our son has received basically a full ride scholarship from his current employer.  He would never have been ready for this if we had pushed academics right away.  Your advice was crucial,  to push the hands on experience first.   He will still probably wait to pursue a business college degree.  However he plans to take an evening class this fall at BTC.  
As his friends struggle to get through Whatcom or Skagit, he is making a living wage with full benefits, no college debts and free college later.  Thanks again for encouraging us to wait on college for him.  This has helped develop self confidence and sped up his emotional and spiritual maturity.   
Thankful for you and ZLO.
Jeff Hodgin
For those of you who aren't sure your child has academic capabilities yet, please understand that tech college and/or work is a safe, viable, cheaper option.  Tossing a student into a highly academic atmosphere where they fail a class causes them to carry a track record that will NOT open doors for them down the road and may well increase the overall cost of college.  There are NO 18-year olds who MUST go to college.  Allowing them more time to mature is good, no matter what their capabilities are.  And you just might find someone willing to pay for their college later.

Thursday, March 29, 2012

Why we homeschool

I've written this in an earlier entry but I seem to be using it often these days.

Homeschooling families (most of them) do NOT want their kids sheltered in a greenhouse.  They want the sun to shine on their heads, the rain on their faces, the wind in their hair.  They just want to be able to choose what grows up next to them.

The world would weigh us with knowledge of things for which we have no strength to bear at such an early age.  The ability to carry that knowledge will come in due time, but there isn't any need to burden a child with adult ideas and actions too early.  The world's purpose in burdening a child is to break that child, and form the child to the whims of the world.  A set of loving parents can choose a more appropriate time for a child to take on the world.

Thursday, January 26, 2012

Why we keep on trying when it's hopeless

View this:


Carly is an autistic child on the far end of the autistic spectrum, who has learned to communicate.  It turns out that a normal intelligence was locked behind an autistic interface.  It was with persistence and luck that a hole was opened for her to squirt a message to the outside world:  "There's a healthy intelligence in here!"

For me the message is that it's when things look hopeless is when it's time to try to learn the most.  Too often we give up, throw in the towel, and walk away.

There is also a time to take the work off of the loom, discard it, and start again.

I don't have the wisdom to always tell which is which.  Sometimes we CHOOSE to take on a project or person to try to fix up that person.  This might be a bad idea.

But sometimes life hands us a helpless or hopeless situation.  I think that the lesson of Carly is that unless we try, sometimes try a lot, we will miss opportunities to learn.

That's education!

Saturday, September 17, 2011

Computers in education, or a stick in the sand?

I'm a big fan of Paul Akers and his Saturday show, the American Innovator, on KGMI. The show is leaving the radio station in a few weeks, but continuing in an internet format.

Today's show, with former educator Dr. Charles Schwahn, made me just cringe. The topic was about increasing kids' eagerness and willingness to learn. Dr. Schwahn's new book is "Inevitable: Mass Customized Learning". His premise is that we have the technology to customize learning for students of all ages, and that by using this technology, we should be able to increase our success rates in education.

I'm here to tell ya, 'Tain't necessarily so!

Dr. Schwahn DOES make the point that we need to meet the student at their point of expertise. Of course! We don't teach calculus to kindergarteners, and for that matter, we don't teach algebra to very many 6th graders. Experience, fluency with the pre-requisite material, and cognitive maturity are all necessary to learning. So is interest in the subject matter on the part of the student, which means there sometimes has to be an expert in front of the student who is passionate about the subject matter.

I'm sorry. That is NOT a computer. Drilling with a computer can kill interest. We HAVE some technology that can be used to diagnose a student's gap in understanding. It does not make learning more enjoyable for everyone, nor does it increase student success rates.

Disclaimer: I'm not going to dig out research and statistics. I'm going to tell you about my experience. Let's see if it corresponds to yours.

I LOVE technology. I wish this stuff worked better than it does. I have an iBook, an iPad, and an iPhone. I own my own video-projector for teaching. I have books on ebook, audio, and text books that can be highlighted and annotated. I'm excited about the possibilities. We bought our first computer in 1984. My husband has diverged into being a PC, out of sheer rebelliousness, I think. I am a Mac.

I've also taught students from pre-K to the graduate level, in a range of settings from public to private, university and community college. I was a substitute teacher in all kinds of classrooms for about 180 days. I currently work at the community college level and with homeschoolers. Their ability to innovate and individualize WILL CHANGE THE FACE OF EDUCATION if the educational community will permit themselves to look at it.

The problem is that we have an industrial manufacturing, conveyor-belt model of doing education. As Dr. Schwahn pointed out on the American Innovator show this morning, this method of doing things is exactly geared to getting the results they have always been getting.

What we need is a customer-service model of doing education. "What do you need? How can I help you?"

After all of the innovation, technology, learning styles theory, Bloom's Taxonomy, and training and re-training educators in crowd control and mass learning, education comes down to this: It the ability of one teacher to get in the face of one learner and ask "Which part didn't you understand?"

Students can cycle and recycle through computerized learning and never be asked this question. That is why mass individualized instruction via technology won't, WILL NOT work. Dr. Schwahn acknowledges that an expert teacher is an expert in the use of computer-aided education, that intervention at some point will be necessary, but I'm pretty sure that schools will buy technology with the hope that they will have to depend less on the warm-body instructor. Warm-body instructors are much more expensive than mechanical boxes, and require bennies and pensions.

Why do I think that technology is such an educational dead-end, when I'm so in love with technology?

In 1992 I finished my MA-Ed in instructional resources, or how to use technology in education. Granted, that was using 1990's technology. The color Mac hit the market about 1991. But I love technology, and have voluntarily stayed current with it, as I was when I went into the program.

I went into it hoping to learn how to write great instructional software. I came out thinking it can't be done. (What an expensive lesson that was!)

I spent many hours watching kids using a wide variety of technology. I did learn some things about what interested kids. It most definitely is NOT instructional technology.

I wrote some little programs to test my skills and my theory. One helped kids match the uppercase letter with the lower case letter. One helped them sound out or guess 3-letter words like 'run' or 'cat'. I also gathered up a few pieces of software that were already in publication and put them all in front of kids. They would get about eight screens (or pages) into the software, turn and look at me and ask, "What else do you have?" They. just. weren't. interested. Not any of them. Some of the kids saw my disappointment and humored me and went a little farther. None, not any of them completed any of the instructional packages, however short they were.

The software that DID catch their attention was the software that let them explore. Kid Pix is (a version still exists) to Adobe Illustrator what a tricycle is to a Porsche. You don't need instruction. You can't fall off. Kids would play with that for HOURS on end, but sometimes it was 15 or more hours of playing before they had a picture they wanted to print. In a school computer lab at that time, at a half-hour of lab time per week, that could be 30 weeks, or most of the school year, before something was produced. Not very efficient use of educational time.

Another piece I designed made use of a laser disc, which functioned like a CD but was the size of the old vinyl records. It had hundreds of digital photos and some video clips of animals. I created a piece of software that sorted these alphabetically, and titled the piece "Alphabet Animals". A page would be presented with a list of animals that started with a particular letter of the alphabet, for which there were photos or video on the laser disc. The student would click on the thumbnail, hear a pronunciation of the name of the animal, and the disc (hooked up to a separate TV monitor) would show the photo or play the clip. Kids went through EVERY ONE of those animals from A to Z. There wasn't any way to measure what they'd learned, however.

Research and reading I went through showed a similar experience with older students. Instructional technology worked best with adults, and when the subject matter was VERY narrow. But everyone liked to explore. A very few games were somewhat successful, like Number Munchers, which had a Pac-Man format. But nearly every year in the '90's there would be a new piece of software to help students learn Algebra. These would last a year and then disappear. Friends who were homeschooling tried them, and discarded them, and came to me for math help.

I got myself evicted from the computer lab at the school my kids attended. There was a very expensive and very awful program by the Josten's company, designed to teach lessons in math and English to kids from K to grade 8. I observed about 90 minutes over my kids' and their classmates shoulders, and wrote a lengthy critique of the software. The district decided I should not be in the computer lab because I might sabotage the software. I didn't have to do anything. It was really, really awful! And taxpayers in the district had spent a lot of money on the software. This is how instructional software is implemented in conveyor-belt education.

Not much has improved since then. Learning software packages have uniformly come and gone. But what has survived and grown is the software that lets people explore. Google. And you can't measure what is learned! (Do you have to, to create a life-long learner?)

On the adult level, completion rates for distance learning courses are typically about 50%. Not all who complete a course pass the course. That's much worse than our current educational conveyor belt. Typically about one-third of students fall off that conveyor belt and fail to finish high school in a K-12 setting.

Distance-learning courses are often no more than a syllabus online, where students slog through lectures posted online, complete exercises from a book, and perform as individuals much the way they would in a large college lecture hall scenario. Not much online learning is student-interactive. Getting students to interact is a challenge, even to interact with each other in an online course. Many choose online learning because they prefer anonymity. We find, however, that they do better in online courses when they can collaborate, and we design tasks to get them to collaborate. Many students balk at that, preferring their Facebook page for that activity. Hmm.

I teach a distance-learning pre-calculus course, using an online software delivery system called ALEKS. It is absolutely as good as it gets. ALEKS is VERY good at diagnosing what a student doesn't know and making a student learn it. Students must perform a task three times in a row, perfectly. The company is doing an excellent job of diversifying the delivery of their product, filling in gaps, making the product as complete as possible. It really is a great way to refresh and polish math you may have taken years ago.

However, after four terms of teaching a course with ALEKS I find that my completion rates are no better than for any other distance learning course, and not all who complete pass the course. Students who collaborate online and offline do better. I have learned to make students go do the free, 3-hour trial that the company offers to see if they can learn this way. About half turn away. Still, only about half of the students who begin the course finish, and not all pass. I think this is as good as it gets for computerized instructional technology. If you absolutely must take one more math course, then ALEKS might be a good way to get that course out of the way. That's the best recommendation I can give the best instructional delivery system I have found.

This raises all kinds of questions about the best way to use instructional technology. I can sit back and listen to all of the arguments, all of the ways that the institutionalized conveyor-belt educators are trying to implement instructional strategies, and it still comes down to this:

Education happens when one teacher gets in the face of one learner and asks "Which part didn't you understand?"

That's a very low student-teacher ratio. It can happen in class sizes of less than a dozen students. I find my personal limit is about eight.

At ZLO, where I meet with homeschoolers for classes, we find we can actually deliver a year's worth of curriculum in two, 75-minute meetings per week, for 36 weeks. We use warm-body instructors, and we've learned that technology must be what instructors know how to use. It's up to the instructor to discover, learn, purchase and use devices and software they think can improve their educational delivery. Most K-12, well, probably K - university instructors would feel like they've died and gone to heaven in this setting. It really does work.

Summary: Don't dictate technology to education. It's not the technology that's important at all. What makes education soar for a student is an instructor who is passionate about what s/he knows, is eager to make it accessible to students, with the freedom to teach the best way s/he knows how, whether it's a stick in the sand or a projected image.

Monday, May 9, 2011

Nope, college may not pay, AT ALL!

Here's a pretty dismal article about how much college is really worth:

Is a Bachelor's degree worth it?

Bottom line:
College is expensive.
Consider working for a few years BEFORE you go, to help clarify WHY you want to go.
Don't go to find out what you want to do with your life.
Go when you have a clear idea of what college will get you, as in "I need to have a ___ degree in order to be a ___"
Don't go unless you have it paid for.
Don't pay for college with student loans.