Thursday, September 21, 2006

Morphing Educational Philosophy

(I found this in my draft folder)

I was rambling earlier:

My philosophy of education has changed since I first started teaching my own children. I started out teaching the way that I had been taught and our style here at home was very much like a public school. Playing school was very comfortable to me and I've had plenty of practice. I went to public school for 13 years of my life and was raised by two public school teachers. I would often help my mom grade tests. Not only that, but I used to line up my plush animals and teach to them, create tests for them, and then take those tests for them so that I could grade them. Yes, I even kept report cards for each of my plush students and sent them to the principal's office when they misbehaved. Guess who their principal was. You got it. I find myself constantly rediscovering our family learning style and reevaluating my philosophy of education. The definitions of the words "learn" and "teach" have dramatically changed over the years, for me, and I can see a difference between "education" and "schooling."

I decided to homeschool my child while obtaining my degree in education. I didn't have anything against public schools, I wanted to be a teacher, and my parents were teachers, but I really wanted to teach my child myself. I was really excited about the concept of home-education. I had all these wonderful fantasies playing out in my mind of me, the teacher/mom, teaching to my very interested and attentive student/child.

HA! (Shouted like the 'basket case' when she interrupts Molly Ringwald's pity party in THE BREAKFAST CLUB)

When I first started homeschooling my now 13 year old, we ordered the K5 Abeka, but he was already reading when it came in the mail, UPS was on strike that year. Needless to say, much of my purchase was a waste of money! We had been playing around with refrigerator magnets and reading many books together. I think that THAT interaction or life-style was enough to make him a reader.

He quickly learned Math in pretty much the same way. He could count, so with a Math Blaster computer game and an abacus, he learned quickly how to solve basic math problems so that he could save the world. (He had to work about 10 Math problems before he was allowed to fire at invaders..) He learned basic math skills so that he could save the world. What motivation! His kindergarten Math book was completed before Christmas, "for the fun of it."

I liked Abeka because it was what my brothers and my sister were using at their private school and I was very comfortable with it. I had helped them study for tests by quizzing them. I guess I tried really hard to play classroom here in my home but it just wasn't working out that way! I lacked the 20 other students to help encourage my son to sit still? That was hard for me!

I can remember reading out loud to my son as his body would move very much like the minute hand of a clock: his head would start out pointing to the 12:00 position, like in my fantasies, but would end up at 6:00, 9:00, and 3:00.. feet in the air. He always knew what I had just read, but his body couldn't be still! In fact, if I forced him to be still, he couldn't comprehend what I read because he was focusing so hard on trying to be still! It took some rethinking of what "learning" meant to allow me to accept my son's hyper-learning style. It wasn't a discipline problem, but how he learned. One of the reasons I decided to homeschool him was because he was very advanced but not when still. Can you imagine how that would have translated to a classroom setting?

He seemed to be learning in non-conventional ways. He learned better when he played educational games or read what he wanted to read or researched what he wanted to research. He was so far ahead that we didn't use curriculum for a few years - just let him collect and label bugs or focus on whatever other hobby he wanted to dive into. He had the audacity to continue to learn without school or without the aid of ‘schooly’ things! I experienced what Mark Twain meant when he said, "I never let schooling get in the way of my education." I don't know if I would have ever understood that quote before I saw it lived out in front of me.

For third grade, we tried to use Abeka again and we lasted a whole year! We did the tests and kept report cards! (Though that's not required in Texas.) He made all A's, of course. When you homeschool you don't move on to the next concept or lesson until the child has mastered it, so you can't make a C or fail! It's not possible. (No pass no play? No pass no turn the page!) I was so proud of his A's and it was a very fun year and I felt so productive! Maybe playing school was the ticket.

The next year I decided to start out by quizzing him with some old tests that he had previously aced. I was shocked and appalled that he couldn't remember most of the answers! The facts and details of what he had learned for the tests the year before didn't seem to make their way to the long term memory or to survive the summer! Had we wasted a whole year? That's when I realized that I probably didn't remember the answers to many of the tests that I had passed either! He could still read, thank God. I guess learning to read is like learning to ride a bicycle, without the skinned knees.

I decided that "tests" and "grades" would not be our educational goal, but rather skills that he could use for the rest of his life. For example: What if we focus on finding the answers and asking the questions instead of memorizing the answers? What if we made research a major part of how we learn here in our home? This skill can come in handy when he is in college and expected to write a research paper or thesis. My favorite quote is by Roger Lewin, "Too often we give children answers to remember rather than problems to solve." While looking into Classical Education I ran into another quote that I really love. It is by Dorothy Sayers: "Is not the great defect of our education today...that although we often succeed in teaching our pupils subjects, we fail lamentably on the whole in teaching them how to think: they learn everything, except the art of learning." If I remember correctly, she was referring to the Nazi educational system. They had taught much about what to think, but no one seemed to be able to think for themselves or to think. She warned that when people are not able to think for themselves they will easily be controlled by a tyrant.

Instead of doing a traditional study or course called "English" what if we learned all we could about our language by learning where each word originated and what the history behind how the word came to mean what it means today? What if we focused on our language and its rules in action and in context by reading often, aloud to each other and silently to ourselves? We could learn the rules of our language from a deductive approach instead of an inductive approach. (I asked ZOLAonAOL to define 'inductive' for me and she said, "The act of eating waterfowl" so I am not sure if I am using 'inductive' and 'deductive' right.) Becca I. had mentioned that Jack London taught himself to write by copying the writings of his favorite writer, Mark Twain. We would learn Greek and Latin roots as a family and read together often!

Focusing on a Greek or Latin root a week gave us a small history lesson, as the root usually had a story behind it. Focusing on roots also introduced us to a list of new words (spelling) and helped with our vocabulary! I made it my goal to find other ways to combine several subjects into one - to free up time for more important things like playing or traveling or visiting friends.

Each time we read a book together something mentioned in the book sparked an interest or curiosity about some other topic. When we read "Charlie and the Great Glass Elevator" we became interested in researching and learning more about orbits, satellites, and eventually the solar system. I guess we allowed literature to provide us with ideas on what we could research and learn more about. The children's curiosities provide the energy, but following those curiosities is a bit like trying to steer a sailboat without a rudder: we are moving, forward maybe, but I don't know what our destination is or when we will 'arrive.' There is always more to learn about any topic or subject!

I pray for God to be our curriculum guide and to bring educational opportunities into our lives and to help me be able to recognize and take hold of 'teachable moments' in our every day lives. When I start out our day with that prayer and mindset the random dots that pop up throughout the day seem to become connected and to form a more tangible picture of where we are going.

(WOW, I need to take my own advice!)


"Let the questions be the curriculum" Socrates

Monday, September 18, 2006

Play is synonymous with learning

Here is the e mail I wrote when Kelsey “discovered” the concept of multiplication in her room while playing with her many beanie babies:

I believe and have observed that there is a direct link between children's play and the development of common sense. A common sense intuition about how the world works. It is through play that children learn and internalize scientific or mathematical concepts that they won't be formally taught or required to put a name to until jr high, high school, or maybe even college. Without this experience - this internalization, the book knowledge is empty. (No one ever said that books were better than experience, I know.)

Children are naturals at the scientific process and experimentation; they are wired to learn about the world they live in - by playing. Watch them on a slide; they are gaining experience and living "object in motion stays in motion" until they hit the ground. They learn about friction when they realize that if they take off their socks they can slide much faster or that the baby doesn't go down the slide very fast if he is naked. Rub your socks on the carpet and shock your friends and family members, literally. Then try it in the dark and see the spark! How many times did it take the cat to run when he saw you rub your feet on the carpet? Hmmmm association and conditioning?

You know, the more children are seated on a merry-go-round, the harder it is to stop? The children seated on the inside of the merry-go-round aren't actually spinning as fast as the children on the outside? A child in a bathtub causes displacement, experiences some buoyancy, and learns about what type of toys float and what types sink. Some of the toys that usually float will sink when filled with water. What about those bubbles? Children might notice that when they get out of the bathtub, the water level seems to drop. (When mom gets out it REALLY DROPS!) After playing in the mud, there might be a ring around the tub! A washcloth appears darker when it is wet. The wet cloth can actually stick to the side of the tub, but a dry one can't. The wet cloth, after a few days falls off of the tile and hardens - molds if left in the hamper... (great time to talk about seeds, spores, and buds)

I've observed my children's discovery of mathematical concepts through play! And not just with the abacus and Math Blaster at the computer. When my daughter ran out of fingers and toes to count on, she found that beanie babies were great for counting. She learned that she could divide her 25 favorite beanie babies into equal groups of five's, but she couldn't divide them up into equal groups of 3's or 4's, however, if she tossed ONE beanie baby and only played with 24 beanie babies she would divide them up into equal groups of 3's or 4's!!! This discovery thrilled her and she explained it all to me. When I realized that she had discovered the concept of division and multiplication on her own, I knew that she would be able to understand these concepts if I explained them to her. It was her hint to me that she was ready. I just participated in her play and showed her many other ways to divide up beanie babies. "By the way, you know how to divide and multiply, Kelsey." My daughter also discovered, on her own that, "If ten plus ten is twenty, then ten plus eleven is twenty-one!" She announced this to me before she ever heard of place value or had any type of lesson on adding two digit numbers.

These simple concepts that children discover or experience while playing have scientific explanations that they won't have to learn until later, but they have internalized examples of these concepts. What if instead of letting my daughter play with her 25, then 24 beanie babies, I had made her sit down to do seat-work for math? I could have filled up her busy play days by teaching these concepts in a very organized and structured way. Maybe she would have learned these concepts earlier. Maybe I could have bragged to my homeschool friends or family members. Would the lessons have been as important to her? Would these same concepts that she learned on her own, been as important to her if I had sat her down and taught them to her?

My daughter learned many similar mathematical concepts by playing with her many beanie babies! Not only did she learn these concepts on her own while playing, but she OWNS these concepts. They weren't mom's ideas or some concepts dictated by a scope and sequence, they were HER discoveries. She is learning to learn from life! Unfettered play is soooo important to learning and common sense.

Go play.

"Watching" a basic math "course?"

I never thought I would find myself using a basic math course to teach basic math to a 10 year old. I have a degree in elementary education and elementary math is pretty easy and fun! I didn’t even intend to use this course for instruction here at home. But, it’s the best thing that ever happened to us.

So, if I could do it all over again, here is what I would do for math:

1. Nothing!
2. Nothing for a few more years!
3. Play fun games that teach basic math skills like “Math-It,” “Multi-flyer,” and “Knock-out” when the child is about 9 or 10. This would give competency in the subtraction, addition, multiplication, and division fact tables. By this age the child has already discovered and has a working knowledge of these basic concepts. (I remember that Kelsey “discovered” the concept of multiplication while playing with her many beanie babies by organizing them, sorting them, and grouping them - I wrote about it and maybe I will share that in another post.)
3. “Basic Math” over the course of 1-4 years or as long as it takes to ease and relax through math. No hurry!
4. I guess then, when they are ready, programs like Teaching Textbooks, Classmates Math, or Video Text could be used for high school math courses….

This system seems to be working for us today, September, 18, 2006, but, as anything does when you follow your child’s lead, it could change tomorrow! But, it will “change” to something that works better, so it’s ok! Well, there might be a bumpy transition…..

Cool things about MATH

I thought I would share some of the cool things I’m learning while watching my 10 year old’s “basic math” course with her. (“Watching” a basic math “course?” You might wonder. I’ll defend my silliness in another post.)

Did you know that the sign for multiplication (the little line with a dot on top and underneath) actually symbolizes a fraction? I had never heard of such a thing, but it makes so much sense. AND in a multiplication problem the remainder is always the numerator when you express the problem in fraction form. I guess when my teachers taught me math (they had their work cut out for them) they never used mathematical language. Math is so deep and rich if you go beyond the memorization of steps to get an outcome. I was just told HOW to solve mathematical problems; how to get a correct answer with little regard for the layers and layers of conceptual information that could be pointed out and used to further expand my knowledge and understanding of math!

When I compare Kelsey’s experience with formal math to my experience I feel joy. I feel a sense of freedom for her that I didn’t feel: the freedom to do in life what you want to do without being limited by your mathematical ability. The freedom to declare a major without concern for the math requirements… Ok, she’s just 10. But, she did factor trinomials with her brother when she was 9…. (that's really just basic math)

I hated math...

…until I had to teach it to my children!


I am learning so much from Kelsey’s basic math course.  (I’ll tell you some cool things in another post)  It amazes me how little I know about math as an adult, after attending public school for 13 years, and then college for what ended up in a bachelor’s degree.  (That’s nothing to be impressed with, let me tell you, if I can get a degree anyone can.)  I was never good at math and I took Algebra twice in high school and twice in college.  I was ahead in math up until I hit Algebra. 


I don’t think that my inability to grasp Algebra was because of a lack of intelligence but rather because of a lack of maturity and interest.  I was one of those goofballs that had to take a Basic Math course in college.  The first time I took Algebra in college I got a D and then I tried again a few years later and I got an A or a B, can’t remember, but it was easy for me in my 20s.  I later took Trigonometry in college one semester because it fit my schedule and I got a B.  Math wasn’t as difficult anymore, but I had chosen a major which did not require much math so I was free.


Teaching my children is teaching me to enjoy and not to fear Math.  I’ve learned that sometimes people aren’t ready for a topic or a concept and if they aren’t ready it’s a waste of their time and life to force or demand proficiency in that subject.  This is easy to see with reading and children but I can now see it with children and teenagers when it comes to math.  


Just a thought on how I was terrible at math and always hated it until I was older.





Thursday, September 14, 2006

Math workbooks have PROBLEMS!

I don’t know if any of you knew that Kelsey was very “behind” in Math. You might ask, “Behind what?” To which I would answer, “You know, like if a comet fell on me and she had to go to public school NOW, she would be considered behind – grade-wise.” (Grades are for eggs?) Anyway, we had been so relaxed here and I just didn’t make her do the tedious work found in her math workbooks. She was always drawing, playing with the cat, or pretending that she was a cat. She was happy and free. But, she was 10 and still hadn’t finished, and maybe I should admit, hadn’t really started her 3rd grade math workbook! More confessions: We never bought the kindergarten, first, or second grade math books! This was starting to make me very stressed out.

I got nervous and decided to just get out the game “Math-It” and NUKE the basics within her. I wanted to make sure that she at least knew her basic math facts. I created a plan that would guarantee proficiency in all her facts in just three weeks. I learned that “Math-It” could be just as boring as workbooks! I guess anything can become boring when forced on a child. We also played around with “Multi-flyer” on-line so that she could get extra practice with her multiplication facts.

I decided to buy a “Basic Math” course from the Teaching Company. The course was geared towards high school students who needed remediation in Math. It was taught by a college professor but for some reason I thought it could help. Looking at the workbook that came with the program I feared it would be worthless to us. We had just learned our basics and here was a book with big problems. All math books have problems. Well, for example, the division section started out with long division! That’s the only concept that gave Matthan a problem in Math – which meant dividing monomials and polynomials would be our next stumbling block….

Kelsey loved watching the lectures. She had no problem doing the big problems in the work book. I only made her do five a day. This was not tedious! She now loves Math! And guess what? Long division came easier for her than it did for Matthan!

I’m not saying it’s this particular program that helped. I think it was the waiting until she was more mature to begin formal math coupled with avoiding the tedious work.

Now WHEN Kelsey does math I only require that she work just five problems; five challenging problems. She works each out on a dry erase board so that I can watch her every mathematical move.

Now if a comet falls on me she will be right on track like a good little train.

Friday, September 08, 2006

Biology test boo boo:

Today, Matthan took his second Biology test over Module #1. (Don't ask.) Anyway, he was doing so well and I thought he would score 100% until he got to this question:

To which Kingdom does mankind belong?

a. Monera
b. Animalia
c. Fungi
d. Protista

Well, Matthan answered "a. Monera" to which I wrote in big red letters:

Is mankind a bacteria or a pathogen?

How come we don't know the obvious things, but can grasp the hard stuff?????

Christian's first day of art:

Before we left for art, he was counting on his fingers. It all went fine until he counted down from five. When he got to "two" he held his fingers like we all do, but when he got to "one" he put down his pointer finger instead of the OTHER finger!

You know how if you make a big deal out of some act, gesture, or word it is sure to create repeated incidences? I was trying to get him to not count like that without telling him why or he would be sure to do it ad nausum in front of the other homeschooled children..

It caused some nervousness around here.

I didn't want to be the mom with the 5 year old who knows how to sign - with a very limited vocabulary.

Friday, March 17, 2006

In Memory of Kitty

Kitty was given to us when Kelsey was just 3 years old. The two watched cartoons together on the couch. Kitty quickly replaced Kelsey’s baby dolls and could often be found strapped in Kelsey’s baby doll stroller. Sometimes you could find him in that stroller rocketing up and down the hallway. He seemed to enjoy these rides! He knew to just jump up in the baby-doll stroller so that he could go for rides. He enjoyed jumping in empty laundry baskets on cue. We could carry him around in boxes or laundry baskets – he was a very brave kitty!

When he would attack our arm we could calm him down by rubbing his nose. We don’t know why this would tame him.

He thought he was one of the children and would follow them if they crossed the street. He always wanted to be where we were. He would sit with the family on the couch if we were all watching tv or a movie. Kitty slept at the feet of our bed waiting for us to fall asleep so that he could sneak up to our pillows and sleep by our heads. Well, after he outgrew the “attack feet under the sheet” stage. Sometimes he would stay out all night, but he was always meowing at the door in the morning.

Kitty got hit by a car two years ago and with some time and $$$ was almost back to normal. After he got hit he was never as playful as he had once been. I attributed much of it to age as he was probably about 5 years old. He did still go up in trees and follow us around, but he never jumped in a laundry basket again.

Because of infections resulting from those many injuries we had to put him down yesterday. We had two extra years with him.

Kelsey and I have cried off and on for days. For days because we had made the decision a week ago but couldn’t follow through with it.

I thought the boys weren’t too concerned, but today while I was talking on the phone to a friend, Christian, (4 years old) told me that he had something to say - so I handed him the phone. He whispered, “Kitty is dead” in a very serious tone. So, I guess though he doesn’t cry with us he still thinks about it. Christian is right here with me while I type this and I told him, “I’m writing about Kitty what do you want to say?” and he said, “Kitty died.”

Little children are so black and white sometimes.

Sunday, March 05, 2006

University of Texas' Open House

This event, though wonderful for families who are interested in attending UT or visiting college campuses, was not just for teens! There were even activities for the young ones, like Christian. This was basically a big 'show and tell' and 'science fair' all in one. UT students from each dept.

or professors had set up demonstrations, experiments, and activities. We visited many different types of labs, We made slime, got to see a solar powered car (I asked many questions about the car and the solar panels), saw a wind tunnel, saw a trebuchet, saw water flowing uphill and what happens to objects as they move along that flow, watched the vortexes created in flowing water when the water has debris or an obstruction in its path, felt an earthquake thanks to T-Rex, built structures out of gumdrops and toothpicks and then tested the strength of the creations with weights, looked in a few microscopes.. So much to see and do!!!

The next UT Open House is on March 3, 2007. So let's go! The drive was easy and the day was so much fun and it was FREE.

My favorite part of the day was when our children, inspired by all the experiments they had seen, decided to try to break the world's record for the longest string attached to a set of balloons. They collected string from other balloons, took donations even, and tied the strings together until the balloons soared above a nine story building. It didn't take them long to encounter problems and make some very scientific observations about their endeavor. Eventually the string broke and this huge group of balloons floated off dragging behind it well over 100 feet of colorful string! It was quite a spectacle and some of the UT students were taking pictures of our kids as they did this.

We want to recreate this again when the wind is not as strong - maybe at the beach.


Tuesday, January 17, 2006

FW: John Taylor Gatto (Sudbury School in Houston, Tx)

During the question and answer time at the end of the talk, a tenth grader who attended a performing arts high school stood up and asked what he could do to make a difference? The suggestion: “Create groups of 3-5 students who go to nursing homes and children hospitals and put on free performances…..” I really got the idea that instead of rocking the titanic we could make a difference in a more grass roots – community minded type of way? Not causing a ‘stink’ but DOING what works.

Though he didn’t mean to, I was motivated to stop trying to make things feel and look so official. Why? That’s not working. Form organizations and offer support or build real relationships with people and support each other on a more personal level.

I’m still working these things out in my mind, so I’m sure these thoughts will marinate and make more sense later…….


Too often we give children answers to remember rather than problems to solve. -Roger Lewin

Homeschool Victoria

FW: John Taylor Gatto (Sudbury School in Houston, Tx)

The Sudbury School in Houston invited John Taylor Gatto to speak.  Is anyone familiar with that school?  It is a parent created democratic school where the children plan what they are taught each week.  They don’t turn anyone away and they are in desperate need of donations.


One thing that John Taylor Gatto said that stuck out was that, “short answer tests are making us dumb.”  He said that when parents and teachers say, “No thank you, I’d rather not” that maybe that is how we could make a difference?  When he said, “No thank you, I’d rather not” everyone started clapping and standing up.  So I assume that the audience was against testing.  This is Texas after all and most teachers hate having to teach to the test. 


“Short answer tests are making us dumb.”  John Taylor Gatto seemed to solve the mystery of WHY Public Schools were making America stupid.  It was like an answer to the problems exposed by John Stossel.  How can short answer tests make us stupid?  That wasn’t a ‘true’ or ‘false’ question so we will have to think about the answer and use sentences and discuss, disagree, explain and maybe change some as we learn.  Make our minds grow.  Oh, we are going to THINK!  See!  We will have to use our brains. 


Short answer tests don’t allow us to think.  Retrieving information isn’t thinking.  Recall isn’t thinking.  Being able to discuss, debate, and convince someone of your opinion is really thinking.  Working an idea out verbally or in writing is doing more for your brain than simply answering , “Do you think a short answer test accurately measures knowledge?  Yes or no?”  To think we need the “Why or why not” and the “But Tammy doesn’t agree let’s try harder to explain it or maybe we aren’t finished thinking it out….”  That’s thinking.  Now we can be “man-thinking” instead of “man parroting.”  (Someone find the latin words for those two terms LOL)


Why don’t we allow daily Socratic (?) teaching and discussion in schools?  Because there isn’t enough time in the day and real knowledge can’t be quickly evaluated.  In a room full of 22 students how can time be given for everyone to speak?  Short answer tests save time and can be graded quickly and the results seem to please everyone.  It’s like learning in a microwave, only thoughts are half baked and nothing was marinated.  YUCK  But there is no test created that can measure real learning – just retrieval.  A scantron machine can’t think so it has to be fed mindless answers.  Our fast food society has already come to the place where people want learning measured quickly and in a way that they can compare their children to others and say, “Look, he learned something, because it says so right here!” 


As Homeschoolers we have the perfect opportunity to do what WORKS in the long run and not get caught up in and not model our homes after a failing method of “education.” 


Here is another thing that John Taylor Gatto said that stuck out in my mind.  “The homeschooling movement is the greatest populist movement of the last 2 centuries.”  So, be encouraged!  or scared of rocking the boat? 


Public school?  “No thank you, I’d rather not.”  (the “no thank you I’d rather not” quote had a story about someone who ‘said it all the way to jail,’ so there is a bigger story there that I can’t RECALL.  Does anyone remember that?)





Too often we give children answers to remember rather than problems to solve. -Roger Lewin

Homeschool Victoria


Thursday, January 12, 2006

Teaching Reading Idea:

Let your child tell you a story. Write their words down on a piece of paper. Let the child (if they want to) illustrate their story. Then let the child read their own words back to you.

Let the child create many books to read. Take printer paper and cut it in half, fold the paper to form a little book. Maybe you could make a cover out of construction paper - the child can illustrate that too.

I think this helps them learn to read - because they are reading their own words.

And making books is fun! You have the crafty stuff, art, reading, and grammar in one swoop.

Just telling a story helps with language - formation of sentences etc.

we use our dining room table for school

Everyone pretty much does their school work at the dining room table in our house.  We have a dry erase board, books, maps, and a computer in our dining room.  Oh, and a fish tank.


Yesterday we caught Christian drawing on the dining room table with markers!  At first I got mad and said, “Christian, what are you doing??”  We use these markers for our dry-erase board – not the table! 


“It’s ok, it comes off,”  he assured me.  He erased the green scribble with his fingers and sure enough it came off!  I never thought of using our dining room table as a big dry-erase board!  It’s glass, after all. 


I told a friend about how the kids were drawing on our glass dining room table with dry-erase markers.  She told me that she knew of someone who would slide a workbook behind a plexi-glass book holder and let her child fill in the answers using crayons or dry erase markers!  The worksheets could be filled out without any marks ever being made in the book!  I thought that if we taped a picture under the glass table that the image could be traced – an image from a coloring book.


So today as Matthan works out Algebra problems with a black dry erase marker on the dining room table, Christian draws pictures and makes us guess what they are.  Kelsey is making up some math problems and solving them on her own.  When Matthan needs help with Algebra I can grab a dry erase marker and work out a problem right there on the dining room table with him! 


So we use our dining room table for school…..


Isn’t that fun?  I never thought of using the dining room table this way!  I guess we could do math on windows too!  Just so the marker doesn’t slip and hit the wall!



Teaching Math (number recognition) Idea:

My 4 year old, 9 year old, and 13 year old are playing darts (magnetic not the dangerous kind) right now. We are asking Christian "what number did you land on?" when he hits the board so that he can work on number recognition.

We don't ask him for every throw, or he would catch on, but every few throws and when he lands on a number that might be familiar with, like 1-9.

Anyway, I thought I would share that in case someone wanted to know a fun way to teach number recognition.

Of course, the older kids could keep a running score in their heads or they could add or multiply their HITS to have a total for each throw - to work on that.

What else? I guess you could pretty much use a dart board much like you use the game MUGGINS!

Wednesday, January 11, 2006

factoring trinomials with children

Matthan, my 13 year old, is factoring trinomials again today in Algebra. Remember how to do that? If you are an average person who didn’t major in math or go into pipefitting, you might not remember much about your advanced math courses or factoring trinomials! Don’t worry, it’s perfectly normal to have taken a course in high school or college and then not remember a darn thing after you’ve lived your life in freedom for a few years. Factoring trinomials is when you have something that looks like this:

x(squared) + 6x + 9

and you have to make it look like this:


You will remember that a factor of 9 is 3? This is the same thing only with some parenthesis thrown in there just to trip you up. You are finding the multiples of a number only now the number has googely eyes and fangs.

When I asked Matthan, “What number gives you nine when multiplied by itself or 6 when you add it?” or “What numbers when multiplied give you 8 yet when added give you 6,” I realized how elementary basic Algebra really is. It’s all the other stuff that confuses me like the parenthesis and the ‘unknown variables.’ We can all add 3+3 and multiply 3 times 3; add 4 and 2 and multiply 4 and 2, so why do we get all tripped up when we see it in the context of Algebra?

I think I know why. When we were in elementary school we were taught that “X” means to multiply.


We were very impressionable and we accepted that fact and used it most of our little math lives. Then one day, we are told that the very symbol with which we have come to associate multiplication is now an unknown variable. “What?” Then we are told instead of using an “X” you can put 4 in a parenthesis and 2 in a parenthesis and that now means what the “X” meant all those years before. Oh, and your ABC’s are now coming to join us for math class – well, Algebra. We learn one thing and use it all of our lives and just when it becomes second nature we have to give new meaning to old symbols and learn all new ways to do the same old things. Algebra seems to be a whole new world and it’s not peaceful to some of us.

It shouldn’t be new or scary at all. In fact, it’s not new, it’s just playing around and rearranging and expressing numbers that we are familiar with in many different ways. Why did it feel different? Why did we learn that multiplication could be expressed by putting an “X” in between two numbers when the whole time we could have just put those numbers in parenthesis? If we are expecting children to grow up and learn Algebra why don’t we just start Algebra in third grade? Maybe I’ll figure the answer out one day. Until then, we are going to play around with Algebra from the get go.

When I asked Matthan, “What numbers when multiplied give you 8 and when added give you 6,” so that we could factor a trinomial, I looked at Kelsey and thought, “She could do what we are doing!” So, I wrote a trinomial out: “x(squared) + 6x + 9” and under it I wrote two parenthesis with an X in each one like this: (x + ) (x + ) and let her decide what numbers should go after the plus sign. She picked up on this pretty fast!

When I told her that she was doing high school Algebra she became very excited. Her confidence in Math was boosted. I hope that when Kelsey enters the world of Algebra and is greeted by my googely eyed monster, that it won’t be something frightening for her.

She can factor trinomials now because that takes basic elementary math! And of course, as her understanding of math expands so will the complexities of the trinomials.

A few years later, as my daughter was learning how to convert Fahrenheit into Celsius, my six year old was inspired to play around with equations and variables. Here is the post.

Too often we give children answers to remember rather than problems to solve. -Roger Lewin

Tuesday, January 10, 2006

Teaching Reading idea - Dictation:

Let your child tell you a story. Write their words down on a piece of paper. Let the child (if they want to) illustrate their story. Then let the child read their own words back to you.

Let the child create many books to read. Take printer paper and cut it in half, fold the paper to form a little book. Maybe you could make a cover out of construction paper - the child can illustrate that too.

I think this helps them learn to read - because they are reading their own words.

And making books is fun! You have the crafty stuff, art, reading, and grammar in one swoop.

Just telling a story helps with language - formation of sentences etc.

Greek and Latin Roots (weekly activity)

Equus = horse (latin) equine

Caballus = horse (latin) cavalry

Hippos = horse (greek) hippology-study of horses (a hippopotamus was literally a "water-horse")

I got these from English from the Roots up vol II. Of course, there are more words associated with each root.

The big children can use the words for copywork, handwriting, vocabulary, and spelling as they write the derivatives and their definitions and thesmaller children can draw a picture to illustrate the meaning.

We usually just take one root a week, but we took these three for the past two weeks.


Darts for Math! Making Math FUN!

Matthan just reminded me that for many throws you are required to multiply your hit by 2 or three and the whole game you are adding your totals. A family game of darts could be educational for all age levels. An older child could keep score for the younger child who is focusing on recognizingthe numerals.

I know that when we play darts with Rodney he is able to keep a running total of everyone's score in his head. He played darts competitively and I bet that helped his brain store those numbers that way! He got used to doing math in his head and keeping a total for multiple sets of numbers. Mental math! So a game of darts will work on more than just multiplying andadding - there is something else going on!

And you are doing a family activity and teaching (modeling) taking turns....

Hey! When you guys catch yourself or your children learning on accident share your ideas!

A family game of darts can help with number recognition:

My 4 year old, 9 year old, and 13 year old are playing darts (magnetic not the dangerous kind) right now. We are asking Christian "what number did you land on?" when he hits the board so that he can work on number recognition. We don't ask him for every throw, or he would catch on, but every few throws and when he lands on a number that might be familiar with, like 1-9.

Anyway, I thought I would share that in case someone wanted to know a fun way to teach number recognition.

Of course, the older kids could keep a running score in their heads or they could add or multiply their HITS to have a total for each throw - to work on that.

I guess you could pretty much use a dart board much like you use the game MUGGINS!