Ideas for teaching basic arithmetic operations
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I was terrible, terrible at math as a high school student. I didn't know why. I was a fixed mindset on math too. I had a very smart honors-student friend and I believed he was just born knowing math. That fixed mindset was bad for me learning. I went to college and took an algebra class. I really wanted to get past the issues I had in high school. I decided to do every odd problem at the end of each chapter. I started thinking deeply about math just so I could hack my way into understanding math. Then something happened. I discovered that if you learned the rules of math and just applied those rules you could take on basically any math. You just simply memorize the rules because math is all made up by humans and someone down the line made up the rules for how things work -- for how we calculate. So, for example I started really looking at the simplest rules: Commutative property of addition: 1+2 = 2 + 1 No matter the order you add numbers, you get the same answer. Associative property of addition: (2+3) + 4 = 2 + (3+4) Now the student has a base of understanding from simple principles. Next, explain how the commutative property doesn't work on subtraction 3 - 2 != 2 - 3 Allow them to see that this is just a made-up way of dealing with numbers but it works out. It's not some huge subject that only geniuses can learn but learning these little things provide confidence. Next, the = property really helped me understand algebra. I had to really think about what it meant that two sides of = have to be the same. 5 = 5 5 = 7 - 2 7 - 2 = 5 So then if you do something to one side you have to do something to the other side to keep the = sign true. step 1. 7 = 7 step 2. 7(+2) = 7 Step 3. what do you need to do to the 7 on the right to get it to be equal? Later all of this helped me when we got to exponents for example I was like why can you just add exponents when multiplying exponents ? for example x^2 * x^4 = x^6 But, why? Well, because if I multiply out x*x * (x*x*x*x) that would be the same as X^6. So now I knew the rule and knew "ok, just add up the exponents when you multiply them". But what about if someone gives you this? x^2 + x^4 Well, you have to remember that is: (x*x) + (x*x*x*x) which is 2x + 4x = 6x and 6x is different than x^6. Now replace using a simple number: (2*2) + (2*2*2*2) 4 + 16 = 32 (2*2) * (2*2*2*2) 4 * (16) = 64 This was a lot, but I had to see these rules to really get them into my head. It's a first principl
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A very long time ago I found a book in the school library and read it. It was called "Quick and Easy Math" by Isaac Azimov (1964). Give it a read.
David Wright
Great book. Thanks for sharing.
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I try to explain things in a way that the kid can see it as something to understand, not to memorize. For example: Kid trying to count to 100 and you hear "forgetting" numbers. Explained: You only need to repeat from 0 to 9 (and you already know that) Once you get to 9, you move back to 0 and add 1 to the tens then I told the name of all the tens and once I got to 100 I just said, and now we repeat again, but with 3 numbers instead of 2, and told the name of the hundreds until 1000 and when the numbers behind the first one are not zero... you go back to the previous "scale" and add it so 234 = 200 + 30 + 4 The kid learned how to count to ten thousand in one afternoon. For arithmetic I use examples on everyday routines, i.e. preparing the meal box... How many pieces of apple do you want? 5, Ok... If I only pack 2 how many are you missing? And if I pack 9, how many additional pieces do you have? Multiplications... writing down the equivalent in times added on the side and saying, multiplication just save time and pencil. Question back, but daddy, 3x1 you need more pencil than writing only 3... me :doh: :doh: :laugh: :laugh: If the kid is curious (and that's almost by definition of Kid), you only has to find the way that particular kid needs. Playful, logical, by heart, laws of nature... whatsoever. If you find it, the kid learns way faster. Just try to find it.
M.D.V. ;) If something has a solution... Why do we have to worry about?. If it has no solution... For what reason do we have to worry about? Help me to understand what I'm saying, and I'll explain it better to you Rating helpful answers is nice, but saying thanks can be even nicer.
Thanks. Could do many of these things if the kid were in front of me. This kid is in a different city, and I am doing Skype sessions, so need to adapt this method to an online teaching session.
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If your student has learnt a bit of programming, why not write a calculator with him/her that takes two numbers represented as strings (one digit per character), and operates on them using the basic multi-digit arithmetic operations? I did that with my daughter, and it was fun for both of us.
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
Yes, perhaps need to introduce Programming to this kid.
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Tell him that there is really only one operator: addition. The other three just all reduce down to that.
"One man's wage rise is another man's price increase." - Harold Wilson
"Fireproof doesn't mean the fire will never come. It means when the fire comes that you will be able to withstand it." - Michael Simmons
"You can easily judge the character of a man by how he treats those who can do nothing for him." - James D. Miles
Exactly, that's what I'm doing. Transforming a Subtraction problem to an Addition problem. Need to continue this with Multiplication and Division also.
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I apologize beforehand that my reply is colored by my personal experience. Why not try to teach him something else than basic arithmetic? There are so many branches of mathematics you can choose from: geometry, sets theory, algebra. For me, the first 5 years were absolutely horrible. I had (and still have) no inclination for arithmetic and struggled to get mediocre grades. Luckily, in grade 6 I started basic synthetic geometry (triangles and stuff) and a bit of algebra. All of a sudden I discovered that math is about reasoning and first "reductio ad absurdum" proofs seemed like intellectual martial arts. Got hooked for life.
Mircea
The issue is that we've to adhere to the school syllabus schedule, because tests and homeworks are as per their schedule. And Integers, Addition, Subtraction come first.
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I am teaching basic arithmetic operations of integers - addition, subtraction, multiplication, division - to a middle school student. and am looking for innovative ways to teach these operations, in an easy-to-understand manner. Finding that the student at hand tends to repeat the mistakes, and is finding it difficult to learn; perhaps there's a basic fear instinct about mathematics in general. How to get the child overcome such fear, and make him successful? Any ideas are welcome, am open to experimentation here. Thanks a lot.
Whatever you do, don't use some beans[^]. :-D
Quote:
BA: Right Baldrick, let's try again shall we? This is called adding. If I have two beans, and then I add two more beans, what do I have? B: Some beans. BA: Yes... and no. Let's try again shall we? I have two beans, then I add two more beans. What does that make? B: A very small casserole. BA: Baldrick, the ape creatures of the Indus have mastered this. Now try again. One, two, three, four. So how many are there? B: Three BA: What? B: And that one. BA: Three and that one. So if I add that one to the three what will I have? B: Oh! Some beans. BA: Yes. To you Baldrick, the renaissance was just something that happened to other people wasn’t it?
"These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer
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We did a lot of things with blocks, and beads (in 5's and 10's, etc), and wooden pie pieces and toy grocery stores with play money when I was in kindergarten.
"Before entering on an understanding, I have meditated for a long time, and have foreseen what might happen. It is not genius which reveals to me suddenly, secretly, what I have to say or to do in a circumstance unexpected by other people; it is reflection, it is meditation." - Napoleon I
The real question here is how can I have -2 pieces of apple. And if multiply by 1 does nothing, how can I draw 2 apples out of thin air after multiply by -1.
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Whatever you do, don't use some beans[^]. :-D
Quote:
BA: Right Baldrick, let's try again shall we? This is called adding. If I have two beans, and then I add two more beans, what do I have? B: Some beans. BA: Yes... and no. Let's try again shall we? I have two beans, then I add two more beans. What does that make? B: A very small casserole. BA: Baldrick, the ape creatures of the Indus have mastered this. Now try again. One, two, three, four. So how many are there? B: Three BA: What? B: And that one. BA: Three and that one. So if I add that one to the three what will I have? B: Oh! Some beans. BA: Yes. To you Baldrick, the renaissance was just something that happened to other people wasn’t it?
"These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer
Richard Deeming wrote:
ape creatures of the Indus
Looks like my country India :confused:
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Richard Deeming wrote:
ape creatures of the Indus
Looks like my country India :confused:
Looks like the modern local name is the Sindh: Indus River - Wikipedia[^]
"These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer
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Looks like the modern local name is the Sindh: Indus River - Wikipedia[^]
"These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer
According to traditional scholars in India, Sindh is the name of the geographical region towards the east / south of the Indus river (Sindhu river). This Sindh became Hind, because the S sound became difficult to pronounce for some people. So, Sindh --> Hind. (Rather Sindh was the name given by people from other countries to this geographical region. The original name was Bhaarata, and earlier Ajanaabha. This is what is told in our age old Sanskrit scriptures). This further became Hindu, and India (because H sound also had some pronunciation difficulties).
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I am teaching basic arithmetic operations of integers - addition, subtraction, multiplication, division - to a middle school student. and am looking for innovative ways to teach these operations, in an easy-to-understand manner. Finding that the student at hand tends to repeat the mistakes, and is finding it difficult to learn; perhaps there's a basic fear instinct about mathematics in general. How to get the child overcome such fear, and make him successful? Any ideas are welcome, am open to experimentation here. Thanks a lot.
I taught all of my kids math using several methods because learning differs. Here are some: I made worksheets with hands on them to demonstrate making 5 (fingers up + fingers down), making 10 (same concept but with both hands), and adding to 5 (using the same diagrams as for making 10) I got a curriculum called Math U See with block-style manipulatives. This system comes with a great scope and sequence as well, the blocks are color-coded, and the lessons are all centered around "Decimal Street" which focuses on place value. Another curriculum called Life of Fred puts math into the context of daily life in an engaging and compelling way. This is great for those who ask "When will I ever use this?" and for those who love a silly story. There are other lessons embedded in the stories as well, mostly academic, but also critical thinking and philosophical thinking.
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I am teaching basic arithmetic operations of integers - addition, subtraction, multiplication, division - to a middle school student. and am looking for innovative ways to teach these operations, in an easy-to-understand manner. Finding that the student at hand tends to repeat the mistakes, and is finding it difficult to learn; perhaps there's a basic fear instinct about mathematics in general. How to get the child overcome such fear, and make him successful? Any ideas are welcome, am open to experimentation here. Thanks a lot.
When we learned our multiplication tables in school, we had to stand in front of the class and recite them to a vinyl record with background music. 2 times 2 is [pause] 2 times 3 is [ pause] … 2 times 10 is [ pause ] We had a “tracking dog bone” with 2 thru 10 or 12. If you recited them all correctly, then the teacher would use a hole punch to mark the number off. It was on a volunteer basis, but in hind sight, each student was super attentive to see if the reciter messed up or succeeded so the whole class was reinforcing each recital. Even people who never recited in front of the class were proficient by the end of the year. The next year we did a 3 minute timed test everyday progressing through addition, subtraction, multiplication, and division. Once you aced 3 tests, you moved to the next operation. Once you aced 12 tests, the teacher would call “pro time” at two minutes. The tests were very simple, basically a folder that you would wrap around a sheet of paper. It had holes to write your answers. Flip it the other way and it became the grader. I remember that my weak spot was 7x8. I would always answer 48 or maybe 54? Blocked me for weeks! Memorize memorize memorize!
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The real question here is how can I have -2 pieces of apple. And if multiply by 1 does nothing, how can I draw 2 apples out of thin air after multiply by -1.
The "-1" is a "transform" (translate?) ... you've simply changed the coordinate system; the "2" is still a 2.
"Before entering on an understanding, I have meditated for a long time, and have foreseen what might happen. It is not genius which reveals to me suddenly, secretly, what I have to say or to do in a circumstance unexpected by other people; it is reflection, it is meditation." - Napoleon I
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I am teaching basic arithmetic operations of integers - addition, subtraction, multiplication, division - to a middle school student. and am looking for innovative ways to teach these operations, in an easy-to-understand manner. Finding that the student at hand tends to repeat the mistakes, and is finding it difficult to learn; perhaps there's a basic fear instinct about mathematics in general. How to get the child overcome such fear, and make him successful? Any ideas are welcome, am open to experimentation here. Thanks a lot.
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I am teaching basic arithmetic operations of integers - addition, subtraction, multiplication, division - to a middle school student. and am looking for innovative ways to teach these operations, in an easy-to-understand manner. Finding that the student at hand tends to repeat the mistakes, and is finding it difficult to learn; perhaps there's a basic fear instinct about mathematics in general. How to get the child overcome such fear, and make him successful? Any ideas are welcome, am open to experimentation here. Thanks a lot.
Our kid had a grade 2 teacher who used math as a punishment when his classroom got out of control. Over the following years we worked past the anxiety with mathematical activities that are not obviously school work, like music and baking to name a couple. Also: candy works well, even with adults, as an immediate reward for getting something right. We used M&M's on an empty music scale; name the note first try, eat the note.
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jschell wrote:
math dyslexia
Maybe, but there should be a remedy for this.
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I am teaching basic arithmetic operations of integers - addition, subtraction, multiplication, division - to a middle school student. and am looking for innovative ways to teach these operations, in an easy-to-understand manner. Finding that the student at hand tends to repeat the mistakes, and is finding it difficult to learn; perhaps there's a basic fear instinct about mathematics in general. How to get the child overcome such fear, and make him successful? Any ideas are welcome, am open to experimentation here. Thanks a lot.
For me, there is no one thing that works Some calculations are memorised, some with patterns which still requires recalling what the pattern was 9s, are related to summing the number anything with 9 is 1 less, but 9x2 or 9+9 is memorised as 18, not the pattern of move 1 over Some is using "simpler" math like addition to solver multiplication. Visualisation is mixed in sometimes And then there attempting to make it THEIR fun. Do they have lots of books. Use that, how many pages can you read in a hour. So if you have 2 hours a day. How many days will it take to read the book. If first person shooter games, explaining the K/D ratio - how many klls to deaths you have.
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I am teaching basic arithmetic operations of integers - addition, subtraction, multiplication, division - to a middle school student. and am looking for innovative ways to teach these operations, in an easy-to-understand manner. Finding that the student at hand tends to repeat the mistakes, and is finding it difficult to learn; perhaps there's a basic fear instinct about mathematics in general. How to get the child overcome such fear, and make him successful? Any ideas are welcome, am open to experimentation here. Thanks a lot.
