Homeschool Math Blog

(Note: I'm "resurrecting" an old post, with added information and a video. The topic is still very much valid.) Manipulatives are IN, in math education. But do they TRULY facilitate learning to such an extent as people promoting them claim? The entry at Text Savvy, Hands-on, Brains-Off , explains some of the pitfalls in manipulative use. Very enlightening! Quoting from an article at Education Week ( Studies Find That Use of Learning Toys Can Backfire ): In a similar series of experiments at the elementary-school level, the researchers found that children taught to do two-digit subtraction by the traditional written method performed just as well as children who used a commercially available set of manipulatives made up of individual blocks that could be interlocked to form units of 10. Later on, though, the children who used the toys had trouble transferring their knowledge to paper-and-pencil representations. Mr. Uttal and his colleagues also found that t...

Recently Brown Center published a Report on American Education with a special sector about the happiness factor in learning. The report is based on 2003 Trends in International Mathematics and Science Study (TIMMS) data. The TIMSS study found that countries in which kids report enjoying mathematics and feeling confident in it do worse in math than kids who report they don't like math and are not feeling confident in it. American students are much more confident about their math abilities than Singapore students, yet they do far worse: Even the least confident students in Singapore outscore the most confident students in America! Check the charts (slides) from the report... a PDF file. It's quick and easy to glance over for more details and charts. The report author Tom Loveless was questioning the idea of teaching math so that students like it... that we don't need to always make math enjoyable. I can almost hear my homeschooling readers' anger raising...! But wait a ...

This is what I've been working on behing the scenes so to speak... and now some of it is finally come to the fruition and is available to the public: (now comes the sales pitch as was made up by my dear husband) Meet Mrs. Maria Miller's Most Marvellous & Magnificent Math Mammoth Modified Modern Mathematics Meticulous Multiplication Methodology Major Madness - It's Mmm Mighty Majestic! Ok, back to normal... I have been making worksheets for SpiderSmart, Inc. tutoring company and the 6th grade ones are now available as two downloadable ebooks at: Math Mammoth Grade 6 Worksheets These aren't your run-of-the-mill worksheets, but more like carefully hand-crafted quality problem sheets, with varying problems that both emphasize understanding of concepts and computation. The worksheets do NOT have explanations and therefore best suit math teachers or others who can explain the mathematical subject matter to the student(s). I will later on (next year) be making more workte...

It's very good to know something about the most common misconceptions students might have. The website CountOn.org has 22 examples of them at http://www.counton.org/resources/misconceptions/ . Here are some examples: #2. Multiplication always increases a number... is that really so? Well, to small kids it appears to be so - but only if you just try whole numbers. Take 10 for example. If you multiply it by 2, 3, 4, 5, etc., it does get bigger. But all you have to do is multiply it by a fraction less than 1, or by a negative number, and 10 does not get bigger... 1/2 x 10 is 5. 1/4 x 10 is 2.5. -3 x 10 is -30. We must remember that repeated addition is not the only meaning or definition for multiplication . That's what it is for whole numbers. For fractions, 1/3 x 12 is better understood as 1/3 of 12. #3. As 1 x 1 = 1, then 0.1 x 0.1 = 0.1. This one was new to me. Quite curious. A child might think of 0.1 as some kind of "unit" like 1. But seriously, 0.1 is one tenth....

I want to blog again on Julie's great Living Math website. You can really get help there if you're one of those who don't care for math, or even hate math, but want to get rid of that feeling. She has suggestions on how to start teaching "living math" - teaching math in a way that makes connections to real life, takes away the dryness of it, takes away the 'kill' from "drill and kill" (note that drill in itself doesn't have to be always bad - drill is a tool amongst many), etc. On this page , Julie has book suggestions to many different situations... Consider finding one or a few (from library or bookstore). Reading a math book that's not a school book can do SO much good! For your kids too! As you probably know, I wish everyone would get to know some of the interesting, fascinating, fun, curious aspects of mathematics. Or, get to know a bit of math history. You don't get those in school books. Or, finally learn why things work. Thes...

Recently Spunky wrote about reform math, and I feel I want to say something about it, too. She was critizing the movement heavily. Some people call reform math 'new new math' or 'fuzzy math' (in a degrading way) - and like you can read in Spunky's post, sometimes when new ideas are implemented, it can cause math to become 'fuzzy' to the children. But that is not necessarily a fault of the reform on a whole - maybe the teacher in question didn't understand how to implement the methods, or for some reason (unwisely) totally abandoned 'traditional' math fact drills. I would say not all of the IDEAS that have come from this mathematics education reform are bad. For example, encouraging kids to explore and investigate mathematical concepts, or discovering their own rules, can be a good thing. Group work CAN be a good thing. The reformists promote understanding of concepts, problem solving, critical thinking. They try to distance themselves from the ...

I've been looking over the website LivingMath.net recently. Lots of good stuff there. What is 'living math'? How do you make math "come to life"? Well, I guess we could ask that when did math become 'dead' and who killed it? Some people feel that it is worksheets, tests, drill, and 'scope and sequence' that killed it. But I don't feel it's that simple. Those things are tools you can use, and they don't necessarily make math 'all dead'. There are many ways to make math 'living'. One important way, I feel, is to show your kids when you do use math in your daily life. I've written about it before. When YOU use math, it conveys the idea that math and numbers are things we use, not some obscure school subject that one does for half an hour five times a week, and then tries to forget the rest of the time. I have never understood mothers who say they didn't like math, hated it, etc. Don't say that! That attitude wi...

Recently I saw this kind of problem used as an example; it went something like this: We're in the grocery store. We're going to buy 6 watermelons, and divide each of them into fourths. How many slices will we get? I want you to think hard :) ... and find the answer to that question. Also note HOW you found it... Got it? Now listen how it was solved in this particular mathematics tutorial: They changed a fourth into its decimal equivalent, 0.25, and proceeded to divide 6 by 0.25 - going thru the motions of multiplying both dividend and divisor by 100 before getting to the long division of 600 ÷ 25, and then finally onto the answer!!! And this was for 7th grade math. Sad! What happened to mental math? What happened to solving problems with the most efficient and quickest way? Well here's a suggestion for an example instead of that one: You are considering buying notebooks for your school which are $0.42 each. Your budget is $200. How many notebooks can you buy? You can solve ...

I want to discuss this topic because of a possible confusion. Recently in a blogpost I linked to the article Math anxiety , which mentions this math-related myth: MYTH #4: IN MATH, WHAT'S IMPORTANT IS GETTING THE RIGHT ANSWER. Then, in another recent post I linked to an article Things not to learn in school where the author strongly convinces us that getting 70% in a test is not enough since in real life you need to get it 100% right. So is it important to get the right answer when doing a mathematics problem? Well, yes but it depends. This is not a simple cut-and-dried question. It IS important if you're drilling multiplication facts. But many times it's not your focus. For example, when a student is learning to do long division or multiplying 4-digit numbers, the emphasis should be in learning the procedure and why it works. Calculation mistakes might yield a wrong answer, but if the way the division was done is right, then some credit should be given. And obviously all...

Would your youngster enjoy a career in math? The article at Businessweek Math will rock you world tells us how mathematics is used more and more in advertisement world, in internet technologies etc. Use of mathematics is on the rise because it is used in more and more places to model various things, including people's behaviour. New math graduates can easily land a job - often with a 6-figure salary. Says Tom Leighton, an entrepreneur and applied math professor at Massachusetts Institute of Technology: "All of my students have standing offers at Yahoo! and Google." But math programs in universities and colleges aren't filling with enthusiastic American young people: estimated half of the 20,000 math grad students now in the U.S. are foreign-born. So it looks like math graduates are in need. And you don't have to be a boy to study math, remember.

I just started reading the book Mathematics : The Science of Patterns by Keith Devlin. I'm planning on writing a review of it for my site. I can already tell it's a good book, and I've just read the prologue, titled "What is mathematics?" The author says that yes, mathematics WAS the study of number - up till about 500 B.C. Then it became the study of number and shape. After invention of calculus, it became the study of number, shape, motion, change and space. But nowadays you can't say that any more, because the field of mathematics has expanded SO much: in 1900 it would have taken about eighty books to write all the world's mathematical knowledge. Devlin estimates that nowadays (or when he wrote the book about 10 years ago) it would take maybe 100,000 volumes to contain all knonw mathematics! You know, your average person doesn't realize that. I got a glimpse of it while in university, when I saw all these lists of subcategories of mathematics, and...

Some of us are math enthusiastics: we love math, think it is full of beauty, logic, and patterns; we think it can be fun, exciting, amusing even. (I include myself in this category.) And then some of us don't care for math, didn't like it in school, didn't do well in it, don't want anything to do with it anymore. And I'm sure there are people in between these extremes, too. As a teacher, you would like your students to belong to the first category, of course. Now, I sincerely think that the biggest factor in whether student ends up liking or hating math is what kind of math teacher and teaching he/she gets. Parents' attitudes play a role too, but teacher's attitude to math and the way math is taught are the weightiest factors, I feel. But books such as The Adventures of Penrose The Mathematical Cat by Theoni Pappas can help too. It is intended for fun reading, exploring exciting mathematical topics in an easy-to-understand way. The storyline includes Penr...

Today, Barry Garelick sent me an article of his which explores the topic of MATH WARS . You may have heard of them. Math wars refer to the debate or controversy about how math should be taught in school. There have been two main camps: those who emphasize discovery learning and calculators, de-emphasizing algorithms and memorization - and those who claim kids need to learn and memorize basic facts and algorithms such as long division. Mathematicians have been fiercely opposing the math education reforms that are based on the discovery learning postulate. In my opinion, I think kids surely need to memorize their basic facts, and learn the basic algorithms. Learning by discovering is a fine teaching method, but it shouldn't replace teacher telling or explaining how things work. I guess what I feel is that learning by discovery (or explorations) can be great but you need to use it right and not let it 'rule'. It is an instructional method or a tool - not a goal in itself. ...

In elementary school, I was under the impression that math was all about NUMBERS. Before 7th grade, I was thinking that there couldn't be much more math since we seemed to be doing the same things over again (spiraling curriculum). After that, the math I was learning seemed to be all LETTERS: x's, y's, a's, b's, f's etc. And soon it was Greek letters too! But math is actually neither. Math is all about PATTERNS. The whole structure of our base-10 number system is a certain pattern. Multiplication, division, etc. are full of patterns to notice. Functions and relations are all about making general rules for patterns. When first learning about sine in right triangle , it may seem to students like a disjointed piece of information - but if they could get past the initial stage and see the sine curve ! Patterns! But I especially wanted to mention trees, ferns, coastlines, snowflakes, and such. Because they have a pattern too, and mathematicians have unveiled th...