Mad Math Minute [pdf] is a worksheet given to grade school kids, helping them learn multiplication tables by repetition. What sorts of criticisms are there regarding these? Did kids treat them as a game or contest?
Isn’t that pretty much the only way to learn multiplication tables? The summer before I started first grade, one of my birthday gifts was a laminated times table sheet that I had to memorize before September. Once you’ve got the basics down, and you’ve worked out the pattern you can go from there.
You have to memorize basic math facts. It doesn’t mean they don’t understand the concept of multiplication, it’s just that not having the tables memorized slows kids way down once they reach the stage (~4th grade) of needing to use them in more complicated ways like dealing with long division and fractions.
It’s a service to kids to get them to be as fast and automatic as possible in rattling off their multipication tables. Making it a contest or game might help.
Having stuff memorized doesn’t make you stupid. It just saves time in the long run.
So many kids have trouble with algebra because they can’t handle fractions. And they can’t handle fractions because they don’t know their basic math facts. Drilling, like with these Mad Minutes or the Kumon program can make a big difference even for kids who are well beyond when they’d normally be learning this stuff.
I did something similar. I gave my fifth graders a sheets of 60 problems and told them to do as many as the could in a minute. The goal was to finish the whole sheet. I knew most of them wouldn’t archive it, but that was the goal. The kids liked it as it was something that they could see concrete improvement on. They might get ten or twenty in the beginning, but with study they might get fifty or even all sixty. I also found it good for helping them to see how not having them memorized is a problem. Pointing out that it took them six whole seconds to do to a basic problem helps to make it sink it that is not acceptable.
I made it somewhat of a contest myself as those who could do all sixty three times within the year got a prize. I’m sure some of the more competitive ones measured themselves against their friends, but I didn’t encourage that. I tried to focus them on beating themselves and that is what most of them seemed to focus on.
Memorization of basic tables aids when it comes to doing higher math. It saves time and prevents mistakes. I find it also builds confidence as at least some part of a difficult problem will be as easy as breathing. Personally I find it promotes good study habits as sometimes study does require memorization and this teaches that skill. Problem solving and reasoning are great, but if you don’t have the basic tools then they aren’t nearly as useful. However, for me the sheets weren’t tools for study in and of themselves. They were tools to measure the effectiveness of study. For their actual study I encouraged the use of flashcards and, to a lesser extent, songs as I found those to be more effective than worksheets.
When I was in third and fourth grades (Roosevelt died when I was in third) we were not asked to memorize the times table. There was a large times table posted on the side wall of the classroom and we were encouraged to feely consult it. Long before the end of fourth grade I had, of course, memorized it, but memorization of it was never an assigned task. In a way, it is a bit like learning to speak. Or kids (but not grownups) learning a foreign language by total immersion.
I still think that’s the best way to learn the times table, but I’ve never spoken to anyone else about it who learned it that way. Pity.
I remember doing that when I was a kid; it helped me far more than being told to just memorize times tables. I think a lot of people learn better by doing than by being told “memorize this”.
In third grade, we had a similar one-minute time test that was given every day and that never varied. By the end of the year, many of us had memorized the whole thing (it ended, I recall, with “0,0,0,0,1”, so it must have been great fun for our teacher to see the looks on our faces when, during the last week or so of class, she gave us a scrambled version. :eek:
I, for one, had learned my times tables pretty well (flashcards, etc.), but after the first row, I had to fight my muscle memory to stop myself from filling all of the non-scrambled answers in.
I was always fairly frustrated in teaching a freshman consumer economics courses when we were learning to figure percentages/profit and loss/taxes and we were in the middle of a 47-step problem and came up against a kid who didn’t know what 5 x 6 was. They were definitely at a disadvantage, since they either had to look it up or figure it out, which put them behind the others. Multiplication facts should be memorized as a base for other concepts.
Agreed. I took an excellent class on IP traffic prioritization last week - at what I’d gladly call expert level - and I was amazed at the time some of these geek types would take to do basic addition and multiplication. You shouldn’t need a calculator to figure that a 20 msec sampling rate means 50 samples per second.
That’s awful. That teacher didn’t teach you anything - and wasted all that paper! It’s one thing to memorize the charts, it’s another to just memorize a list of numbers (which is what happens with a non-randomized list).
Is the basic question of the OP whether this worksheet is an effective memorization tool, or are we discussing whether memorization is the right approach to learning multiplication?
The one thing I can say for sure is those worksheets are not a new idea.
I’ve done something similar with my music students and note names. The idea of a race can be a motivation to students to be focused. It works well with young age levels.
I used “Mad Math Minute” as an example of a “contest” or “race” form of learning. I was wondering if teaching kids to race is good the children. I am partially inspired by the “Awards for Every Kid” thread in the Pit. Is it good to promote hurried competition at such a young age? Since the worksheet requires you to be done in a minute, and since you might sacrifice accuracy for speed, is it a good lesson for children to be trained to work through their in-class work (tests, etc) very fast?
I don’t see how one assignment out of all the ones you do teaches them to “sacrifice accuracy for speed”. First – if it’s not also accurate, it’s wrong, right? But second – if it was all you did, that would be one thing. But as long as you have regular tests and assignments, why should this one speed assignment outweigh them? I think kids are smart enough to understand that sometimes you work fast, and sometimes you work carefully.
Anyway, there are times when you have to think fast. What’s wrong with teaching that too?
I’m surprised by the comments on this thread.
When I was at school, we were told to memorise our times tables. But I never bothered. I found it simpler to use tricks such as appending a zero for x10, doubling and doubling again for x4 etc.
6x5 for example I would think of as half of 60 (although now of course, I wouldn’t need to think that way about numbers that common).
And I assume it hasn’t held me back because I am a very confident with my maths and did very well academically in that area.
If you must teach your child to memorise the times table, I would recommend putting emphasis on memorising the squares because of the frequency with which they appear in real problems.
I will do whatever it takes to get my students to memorize their multiplication facts. Whether using the logical number sense of Mijin, or the patterning that occurs with the 9x facts, or repetition through Mad Minutes, or computer games, or competitions, or little stories and mnemonics and rhymes to remember certain tough ones – I’ll try anything. Because, as other posters have said, the instant recall of multiplication facts makes all subsequent mathematical learning much easier.
BUT, in my experience, it all comes down to whether the kid wants to learn them or couldn’t care less. (Learning disabilities aside. I’ve taught plenty of kids whose brains aren’t wired for memorization the way most (?) of us are.) When it comes down to it, no matter what I do to teach and encourage automaticity of mult. facts, it is up to the individual to say, “Yes, I will commit these to memory,” and do the work to make it so.
I had to do these from the first grade to the fifth. They were called “Math Facts” and we’d do them every Friday afternoon. You started on addition then moved to subtraction, multiplication, division, and mixed. There were sixty problems on the sheet and they had to be completed in a minute or less. Kids who completed them correctly were test again, and if you passed the test you got a certificate. If you passed all of them you received a T-shirt. Most of the years I got a t-shirt (the damn mixed sheet always tripped me up!)
I think it helped me immensely later on in middle school and high school because I could glance at 6X7 or 72/8 and know automatically what it was, while my peers were still having a hard time trying to figure it out.
I teach my second-graders both methods with addition facts (we just barely touch on multiplication near the end of the year).
That is, I want them to memorize everything. But if they don’t have a particular fact memorized, I want them to be able to solve 8+3 faster than the default method, which seems to be laboriously holding up 8 fingers one by one, then peering at them, then holding up two more fingers, then thinking for a minute, then putting all their fingers down and holding up one more, and finally saying, querelously, “Eleven?”
So I teach tricks:
-Doubles problems are, for some reason, really easy to memorize. 7+7 is the only 7’s fact that comes quickly for kids.
-If you know 7+7=14, and if you have a good sense of number, you should be able to figure out 7+8=15 quickly: you added one to the seven, so you need to add one to the sum. All doubles-plus-one facts should be solveable through this technique.
-The facts that equal ten are a great benchmark: learn them in order (0+10, 1+9, etc.). Then, if you know that 8+2=10, you can figure out 8+3 very quickly.
-When you add 9 to a single-digit number, take one away from the number and stick it in front. For 9+5, you take the five, subtract one to make it four, put a one in front to get 14, hey presto!
-Adding zero to any number is super-easy. Adding 1 to any number is easy. Adding 2 to any number is fairly easy. No reason not to memorize these, or at least solve them superfast.
-The commutative property is invaluable. If you’ve forgotten 2+9, for God’s sake don’t start at 2 and add 9 to it: start at 9 and add 2.
The goal is to use these tricks to become familiar with the answers, and then to memorize them once they’re familiar. Knowing a rationale for saying 7+8=15 (it’s doubles-plus-one) makes the memorization easier. And if you get all these tricks under control (easier said than done), there are only a handful of difficult facts to memorize, bastards like 8+5 or 3+6 or the like.
Similar techniques can be extremely useful for multiplication. Many adults have trouble spouting off the product of 7 and 8 quickly–but 7 and 7 sticks in folks’ heads much better, and if you can reason that 7x8 must be one more group of 7’s than 7x7, so it’s 49+7, you can reach the answer much faster than if you need to add 7 to itself 8 times. If I ever get moved to third grade, I’ll certainly drill kids on multiplication, but I’ll also scaffold their learning through the use of tricks like that one, or the awesome raised-fingers tricks for learning the nine-times tables, or whatever.
Daniel
All those good tricks are taught in my daughters’ math curriculum–they do the facts in batches, like doubles, doubles plus one, sums of 10, and at the end, the “oddballs” like 8 + 5. They have a math facts sheet to do with every lesson. I think it’s really, really important to learn those math facts and I intend for my kids to do it. My younger one likes yelling them while jumping on the trampoline!
When I was in 3rd grade, we had frequent multiplication facts quizzes–60 in one minute, kind of thing. I think they were very good for me and I actually remember them pretty fondly. My brother never saw the point of memorizing the times tables–he had the whole thing right there on his binder, so why bother? He has said many times that he really wishes he’d done it then, because it’s a lot harder to do as an adult and it really is important to be able to know the answer right away without thinking it through every time.
IMO without memorized math facts, algebra will be frustrating and too difficult. Racing encourages kids to learn to snap the answers right back.
Young kids under 10 or so are mostly whizzes at memorization, it’s the best time to memorize lots of things. Just look at Pokemon. Memorization can be quite enjoyable for the young’uns, take advantage of that!