Teaching Less Math, Makes Sense

A friend of mine came across this article a while back and I am finally getting to blog about it. This is from a March 18th blog on Psychology Today's website. The author of the article talks about schools teaching LESS math to young elementary school students. Yes, LESS math! Now, I am all for less math, but seriously, the article points to several studies that show that this "less math" idea has a lot of merit. Here is the proposal:

"One of the recipients of this challenge was L. P. Benezet, superintendent of schools in Manchester, New Hampshire, who responded with this outrageous proposal: We should drop arithmetic! Benezet went on to argue that the time spent on arithmetic in the early grades was wasted effort, or worse. In fact, he wrote: "For some years I had noted that the effect of the early introduction of arithmetic had been to dull and almost chloroform the child's reasoning facilities." All that drill, he claimed, had divorced the whole realm of numbers and arithmetic, in the children's minds, from common sense, with the result that they could do the calculations as taught to them, but didn't understand what they were doing and couldn't apply the calculations to real life problems. He believed that if arithmetic were not taught until later on--preferably not until seventh grade--the kids would learn it with far less effort and greater understanding."The roles of play and curiosity as foundations for learning.”
(Peter Gray, March 18, 2010)

This makes sense to me since MOST kids today do not understand WHY math works the way it does. Memorizing the formulas and memorizing the "math facts" does not lead to understanding. I know, I am the product of the 1960's - 1970's NEW math that really just did not make sense to me. I learned math while homeschooling. Sure I knew how to do algebra and the "math facts" that are drilled into our heads in school but real understanding did not come until much later.

"Today whenever we hear that children aren't learning much of what is taught in school the hue and cry from the educational establishment is that we must therefore teach more of it! If two hundred hours of instruction on subject X does no good, well, let's try four hundred hours. If children aren't learning what is taught to them in first grade, then let's start teaching it in kindergarten. And if they aren't learning it in kindergarten, that could only mean that we need to start them in pre-kindergarten!"
(Peter gray, March 18, 2010)

The above statement reflects my children's generation. The competitive aspect of school really cranked up in the 1990's when parents were routinely doing the work that their kids should have been doing so that Johnny and Mary could get an A. Parents were concerned that their little genius get into the BEST most competitive preschool for goodness sakes! This all lead to certain subjects such as math being taught WAY too early for the child to grasp. The researcher, Benezet, then asked schools to try an experiment in math.

He asked the principals and teachers in some of the schools located in the poorest parts of Manchester to drop the third R from the early grades. They would not teach arithmetic--no adding, subtracting, multiplying or dividing. He chose schools in the poorest neighborhoods because he knew that if he tried this in the wealthier neighborhoods, where parents were high school or college graduates, the parents would rebel.
(Peter Gray, March 18, 2010)

This experiment was a success!

“By "recitation" he meant, "speaking the English language." He did "not mean giving back, verbatim, the words of the teacher or the textbook." The children would be asked to talk about topics that interested them--experiences they had had, movies they had seen, or anything that would lead to genuine, lively communication and discussion. This, he thought, would improve their abilities to reason and communicate logically. He also asked the teachers to give their pupils some practice in measuring and counting things, to assure that they would have some practical experience with numbers”
(Peter Gray, March 18, 2010)

The results were fantastic! The students who did not learn formal math caught up within ONE year! Plus they did better on word problems.

Please read the whole article here:
Psychology Today
When Less is More: The Case for Teaching Less Math in School

Natural Math

"I love algebra! It is like a puzzle!" A friend of mine once told me this several years ago. Do you think her algebra teacher loved the subject? You bet! Math is a 4-letter word to some people (well it IS a 4-letter word, after all) me included! My math teachers basically just said, "this is how it is, I can't tell you WHY!" I think the WHY is way more important than the end result. My daughter's 5th and 6th grade Catholic school math teacher taught math one way. If your student had a hard time understanding it she would, very nicely, stay after school to go over it. The exact same way! Isn't that the definition of insanity? Seriously, these poor kids just never got it, over and over again. The teacher never understood that she was the problem.

Now, if you are a homeschool parent, then YOU are the teacher. Which leads me to the point of the post. Research the math before you have your kids learn it! Math is basically a series of relationships and patterns. That's it! Like a game, math also has rules. Approach math in this way and it won't seem so scary! (scary to you and your child!) I never liked math but I always did "ok" in it. The reason? I have a pretty good memory. By memorizing the math "facts" and the rules, you can get the correct answer. But, is this really learning? I never learned the relationships and patterns that make up what we call "math." Fast forward to our homeschooling days, and I was forced to see that math is actually these patterns and relationships! This was my "a-ha" moment! Did this realization make me want to run right out and take a college math course? NO, but I feel much more secure in my math abilities.

Take a look at this website for some natural math learning ideas. These are great for both parent and child!

Learning Math Naturally

Cooking for Science and Math

My last post was all about sourdough baking and making a sourdough starter. Pretty cool stuff and my starter has made some great bread for me! Gets me thinking about cooking as science, since it IS science!

Here is an interesting link: Science of Cooking

Looks like a lot of cool ideas! This website can keep you in science experiments for a long time!

Many of you will see the science in cooking, but where is the math? Have you ever tried to halve a recipe? Or maybe double it? If you are doubling a recipe and it calls for 3/4 cups of flour, how much flour do you need? These are all valid math "problems" all in the guise of simply cooking!

What if cooking is not really for you? You can use cup measures and spoon measures with water to show the relationships in the fractions. Take the same "problem" above but use water to figure it out. A large liquid measure and a couple small ones would work wonders! Your child can fill the smaller liquid measure to 3/4 and then pour into the larger one, then do 3/4 again. She will see that she gets 1 1/2 cups of liquid. This is ALL math! Design a math and science program using cooking!

Why I Think of Math as Coins

Weird title for the blog post but I am running on empty and could not think of a better way to put it!

My brother had a paper route when I was just a little one. He is eight years older than I am and I always wanted to hang around with him. I was about four or five when he was starting with his route. I guess I was a pest because, to keep me busy, he would have me stack his coins from his route into one dollar piles. As a four or five year old, before any "formal" math lessons, I learned that there were 10 dimes or 4 quarters or 20 nickels to make up one dollar. My brother knew that I could count at least up to 20 and so I could help him out by stacking up coins into dollar piles. As we both got a little older, and he started with both local papers as a paperboy, my duties increased to making the coin piles for the paper coin wrappers. Now, I was counting out 40 quarters for 10 dollars, 50 dimes for five dollars and 40 nickels for 2 dollars. My fingers were still too small to get the coins into the wrappers but I was accurate and fast with the sorting and counting.

This "lesson" in math has stayed with me to this day! I think in terms of money when thinking out math problems. I can actually SEE the quarters etc. when I am figuring out something with math. Weird.

This is one way to naturally teach your child math. Math is not numbers, it is patterns and relationships! Once a child "gets" the pattern and the relationship, he will be able to understand the math concepts.

Learning Math for Kids and Adults

I am not a math person. let me get that out there right now. I majored in English in college and back in the 70's math was not required for an English BA degree. I could choose a math or science. Ha! Science won hands down!

Back in elementary school and middle school, math was not so difficult for me. It made some sense and algebra was pretty easy. The following year was geometry and that made NO sense to me at all! I think I really needed something more tactile than a damned book! Jeez! When my kids asked me "why do I need to learn this?" I always had an answer. "See that tile floor? It required geometry for Dad and I to put it down!" It also required algebra and basic addition, subtraction, multiplication and division. Thank goodness I have my husband for that! Really, it is pathetic. He is really good with math and numbers, he is a programmer.

My kids were 10 and 13 when we started homeschooling so the math fear for them was already there. My daughter a little less so than my son. Third grade, in Catholic school, brought math speed drills. Now I understand that the purpose was to have them learn the basic multiplication tables by heart to make math easier later on. Sounds good in theory. Sadly, for a dyslexic child like my son, who WAS good in math, they were simply torture. Of course, because it is school, the name of the game is ridicule and shame. There was a lovely chart up on the wall with each student's progress or lack thereof. Naturally, everyone could see the "smart" kids and the "dummies." His teacher never "got it." I talked to her, my dad (who is also dyslexic) talked to her but she either didn't gave a rat's a** or she was too stupid to understand that not every kid learns that way. My son changed that year and has never really been the same. Luckily she left teaching after one more year. Of course the damage was already done to MY son. Thanks Mrs. B.

Learning math is very natural if a child can learn on his own with some manipulatives. Legos work just fine! Of course I would love a whole set of Math-U-See manipulatives but, well, it was not in the budget for kids who were already 10 and 13. If they were younger, and I could have gotten more years out of them, maybe.

My theory about teaching math is that a child will learn, with your help, how to "do" addition, subtraction, muliplication and division.
Addition: Mom, I have two cookies, can I have one more?
Subtraction: Hold on, you have too many cookies there, let me take a few. Dinner is in a few minutes.
Multiplication: Sally is coming over. I have three cookies, do we have six so Sally can have three, too?
Division: I have six cookies, here Sally, you take three and I take three.

Very natural stuff. To make it even more clear you can use those Legos. Set up three piles of four Legos each pile. Your child can count them to see there are twelve. Now ask him to put them in two equal piles. He then divides. Make sense? There is NO SENSE making it much harder than that until your child "gets" the sorting. He can SEE what math looks like. Once he is good at it and can understand the relationships in the math, he can start learning the terminology. I think schools get so caught up with the terminology that it scares kids away from math. Oh and did YOUR school have nice manipulatives for each student? I didn't think so.

Unschooling Math Idea

When we started homeschooling back in 1998 my daughter was 13 and had just finished 7th grade at the Catholic school. I didn't have any particular math plan for the homeschooling right away since I was not sure she was ready for Algebra so I made up something for her to do. I drew out a very basic house floor plan with two bedrooms, a kitchen, living room and bathroom. Some of the walls had length in feet and some did not although one could figure out the dimensions of the entire house with the information given. Along with this floor plan I gave her a budget (can't remember the dollar amount anymore) and then I gave her various "projects" that she had to do on her house. Sadly I can't remember the whole thing anymore but one of them was to buy carpet for one of the bedrooms where she had to figure out how much she would need (figuring out room dimensions in feet and carpet sold by the square yard). Another was to figure out how much paint she would need to paint the walls of one room if the ceiling was 8 feet and she needed X number of gallons to cover Y amount of square feet. The last thing she had to do was buy furniture for the house all within the budget. There was much more to it but I can't remember it now. Damn getting old! She actually liked this project a lot! Maybe it prepped her for last summer when she and her husband bought a house that needed a lot of cosmetic work! They painted all the interior walls and had all new flooring installed. Oh and they bought furniture as well. I wonder if she had thought of this project? Maybe I prepared her for it back in 1998 when she was 13!