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Questions tagged [arithmetic]

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64 votes
17 answers
9k views

Is there a virtue to learning how to compute by hand?

I have been professionally tutoring a wide range of students (from elementary school through graduate school) for many years. Most of them are from the United States. I generally focus on helping my ...
Geoffrey's user avatar
  • 898
18 votes
4 answers
3k views

Does this property of subtraction and division have a name?

Addition and multiplication are commutative. Denoting $\circ$ as either such operation, we have $$x \circ y = z \Leftrightarrow y \circ x = z.$$ Subtraction and division have a similar property, where ...
Reinstate Monica's user avatar
15 votes
5 answers
319 views

Learning operator priorities by drawing trees

As far as I know (and here I am refering to my own math education), operator priorities of $+$, $-$, $\cdot$, $\div$, power and parenthesis are taught via some simple phrases like "pointy" ...
M. Winter's user avatar
  • 251
14 votes
1 answer
345 views

Do electronic calculators inhibit mathematical thinking?

I am interested in educators real-world experience or being pointed to any research in this area. I have a student whose arithmetic skills are weak for his/her age. The student counts on his/her ...
Clive Long's user avatar
13 votes
9 answers
2k views

Is it meaningful to add a number to itself a fractional number of times?

(Migrated from the math stack exchange, where I received an apt-seeming suggestion to pose the question here, at the math-educators stack exchange) I introduce my young kids to basic math concepts in ...
StoneThrow's user avatar
12 votes
6 answers
2k views

Why does the widespread erroneous definition of "irrational number" persist without being taught?

Among the mathematically ignorant one often finds a mistaken proposed definition of "irrational number", which says that it is a number whose decimal expansion does not terminate or repeat. The ...
Michael Hardy's user avatar
12 votes
13 answers
4k views

Different ways to multiply decimals

I am an undergraduate secondary math education major. In $2$ weeks I have to give a Number Talk in my math ed class on the problem "$3.9$ times $7.5$". I need to come up with as many different ...
FoiledIt24's user avatar
  • 1,281
11 votes
4 answers
487 views

For students who don't have instant recall with basic arithmetic, should I be stubborn about training them to have instant recall before moving on?

I'm a maths tutor, and my students/tutees are aged $11 - 18.$ Obviously I have limited time with students, usually one hour per week. Moreover, if parents don't see improvement over a year or two they ...
Adam Rubinson's user avatar
11 votes
3 answers
2k views

Arithmetic books for adults

I'm trying to learn arithmetic from scratch again. Even though I can use it, I'm not sure if I can teach it to someone and I believe if you can't teach something properly, there might be loopholes in ...
Harshit Rajput's user avatar
10 votes
7 answers
6k views

Is this primarily a "rote computational trick" for multiplication by 9?

I tried uploading a gif, but was unable to do so. What I can do, is share a link to the gif here. (SE software seems to have allowed me to share the link, but not upload it.) What it shows, ...
amWhy's user avatar
  • 2,095
10 votes
2 answers
412 views

Is it normal for a child to strongly prefer addition to subtraction?

My six-year-old daughter enjoys addition but not subtraction. When we walk together, I like to give her some "mental mathematics" questions, such as "What is 13 plus 33" and she ...
Zuriel's user avatar
  • 4,275
9 votes
2 answers
286 views

Generating system of equations with unique solutions

I have a similar problem addressed in System of Equations Generator. What I need is an automatic way of generating a system of equations with unique solutions, but the equations are not exclusively ...
Chaotic's user avatar
  • 191
8 votes
7 answers
1k views

What's the best technique to do math calculations in my head?

I wish to teach myself how to do math calculations–like $99\times 58$ or $2048+1296$ or $506+998$–inside my head. I know there already exist two methods–Abacus and Vedic Maths. I don't know of more, ...
Gaurang Tandon's user avatar
8 votes
3 answers
644 views

Is there a numerical base that is in any way “better” for simple mathematical calculations than others?

I want to know if there are any numerical bases that are notably well-suited for humans to learn and use at an elementary or grade-school level. I know that different numerical bases (i.e. decimal/...
Lawton's user avatar
  • 189
6 votes
7 answers
2k views

Adding things to bunches of things vs multiplication

"Suppose you bought four boxes of pencils having five pencils in each, how many pencils do you have altogether?" — "Nine." — "How come?" — "Because 4 plus 5 is 9." — "But you cannot add boxes to ...
Rusty Core's user avatar
  • 1,317
6 votes
6 answers
676 views

How to answer a three-year-old the question "Why is $2+6$ the same as $4+4$"?

I am teaching my daughter, who is currently about $46$ months old, additions. She is very curious and asks a lot of good questions. For example, when I told her that $2+6=8$ and $4+4=8$, she asked me ...
Zuriel's user avatar
  • 4,275
6 votes
4 answers
840 views

What are other strategies for a 7 year old for addition and subtraction besides counting fingers?

We recently received feedback from our 7 year old daugther's school teacher. One of the things mentioned was that our daughter still counts her fingers when she does addition and subtraction. The ...
sbrattla's user avatar
  • 161
6 votes
1 answer
319 views

Concentrations of Adult Math Phobia

Some professions have more math phobia than others. Few engineers hate math, but many teachers and journalists do. This means that university departments of education and journalism would likely have ...
WeCanLearnAnything's user avatar
6 votes
0 answers
182 views

Adding one to numbers bigger than ten

If someone asks you Tell me the next number (add one) after the number one million two hundred thirty-one thousand ninety-nine, do you known if it is a common error that the first number that ...
pasaba por aqui's user avatar
5 votes
5 answers
6k views

Are soroban (Japanese abacus) classes worth doing?

The companies that run these expensive abacus programs for children claim it has all kinds of benefits for their mathematics abilities and speed. Apparently it starts with a child learning the ...
Humanities Guy's user avatar
5 votes
3 answers
381 views

How to explain the motivation of parentheses in addition, subtraction and multiplication?

My kid, 5 years old, knows addition, subtraction and multiplication now, of course, in a basic level. Also he understands that parentheses means "whichever inside shall be computed first". When I ...
athos's user avatar
  • 777
5 votes
6 answers
689 views

What’s better: number bonds, or addition tables?

I’ve been teaching my kids addition tables (1+3=4, 2+3=5, 3+3=6, etc.) I only just found out about number bonds (1+4=5, 2+3=5, 4+1=5). This seems a better method because it’s mastering all the ...
Humanities Guy's user avatar
5 votes
1 answer
240 views

Sensible amount of repetition 7 year old

We are now in lock-down, so while homeschooling my son I get to se exactly what he does for math. He has been getting a huge amount of repetitive practicing of really simple math, despite being quite ...
Ivana's user avatar
  • 53
5 votes
2 answers
247 views

Grading a Simple Rounding Exercise

A student is given the question: "Round off each of the following numbers, correct to two significant figures. 32.4892 8.2673 475.98 0.078625" There are two marks for each. If a student answers ...
JP McCarthy's user avatar
5 votes
1 answer
265 views

Looking for a video about arithmetic disappearing in a few years

I saw a video 3 or 4 years ago. The video is about the idea that arithmetic will disappear in the future and only will be a sport, like hunting that passed from a need to a sport. In the video there ...
Mika Ike's user avatar
  • 401
4 votes
1 answer
178 views

Are ‘constant difference’ and ‘common difference’ synonymous?

I’ve seen at least two phrases to describe a fixed difference between two numbers, i.e., “constant difference” and “common difference.” For example, if Sibling A is 10 years older than Sibling B today,...
EJ Mak's user avatar
  • 329
3 votes
3 answers
261 views

How to train facility with numbers?

I have a student (age 14) who is valiantly striving to improve his algebra. He knows the "rules", and he more-or-less manages to apply them correctly, and hence is generally able to tackle ...
Prime Mover's user avatar
3 votes
1 answer
135 views

Mental/"Paper and Pencil" Arithmetic

Recently, I was watching this video and I began thinking about how much my arithmetic skills have declined in recent years due to over reliance of calculators in upper year (high school) math courses. ...
zachery moïse's user avatar
3 votes
0 answers
271 views

Quantifying arthmetical skill

Question for a research project: What is the standard way of quantifying a student's skill in arithmetic ranging from having to look up numbers on a times-table to computing large sums in their head ...
BostonBrooks's user avatar
2 votes
3 answers
545 views

Reduction of fractions

Last night I was fiddling with some equations and admittedly, I made a careless mistake because I was exhausted. However, in doing so, I began to question the process of what I used to understand as &...
Oofy2000's user avatar
  • 153
2 votes
2 answers
230 views

How do we explain to a little child that a date in 2020 and a date in 2021 are not necessarily a year apart?

I talked with my friend on December 29 2020. Then I talked with him again on January 03, 2021. Q: What was the year when you last talked with your friend? A: 2021. Q: And what was the year the ...
Alecos Papadopoulos's user avatar
2 votes
2 answers
271 views

Scepticism as the cornerstone for not making mistakes in arithmetic/algebra etc, especially for students who relentlessly make every possible error

As a maths tutor, some students I have tutored don't just make the odd mistake in arithmetic (including fractions) and algebra: they make every possible mistake and regularly. My go-to approach for ...
Adam Rubinson's user avatar
2 votes
3 answers
441 views

How many zeros do we need to add to get a nonzero value?

A student (kid) of mine asked this question to me. I am not sure what to make of it or how do I answer it. How many zeros do I need to add to get a non-zero value? ...
Ashish Shukla's user avatar
2 votes
3 answers
344 views

Logarithms chronologically before algebra

Do any textbooks or (somewhat?) standard curricula introduce logarithms and their applications in arithmetic without assuming the students know any algebra? (I do not mean just the use of logarithms ...
Michael Hardy's user avatar
0 votes
1 answer
293 views

Understanding common multiples

Imagine a class of students who don't know what smallest common multiples (LCMs) are, or indeed what multiples are. (Notice I said "smallest" rather than "least" so as to avoid ...
Michael Hardy's user avatar
-1 votes
2 answers
162 views

I'm in dilemma while solving arithmetic problems [closed]

I'm competitive exam student learning Quantative aptitude what should i choose over solving more questions and skipping the one i can't solve or spending hours on one question till i solve it and then ...
Abhishek's user avatar
-4 votes
1 answer
180 views

Is there an **official** name for the following "digit reduction" operation? [closed]

In one of my programs I have a function I call reduce(n) which associates to n the recursive sum of ...
mszmurlo's user avatar
  • 135
-6 votes
3 answers
248 views

The value of homogeneous divisibility rules and of a numeration

Everyone knows about several divisibility rules. But any teacher knows how difficult students are even with the criterion of three in base ten. For example, many teachers have encountered the classic ...
Stéphane Jaouen's user avatar