Questions tagged [arithmetic]

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-4
votes
0answers
109 views

What would be the advantages and disadvantages of having alternative bases like binary taught primarily in the language department? [closed]

What would be the advantages and disadvantages of having alternative bases like binary, quaternary, octal, hexadecimal, and/or vigesimal taught primarily in the language department? Perhaps using a ...
52
votes
15answers
7k 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 ...
5
votes
1answer
186 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 ...
2
votes
2answers
205 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 ...
3
votes
3answers
297 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 ...
17
votes
4answers
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 ...
9
votes
2answers
180 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 ...
6
votes
4answers
236 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 ...
12
votes
13answers
2k 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 ...
3
votes
1answer
109 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. ...
6
votes
3answers
422 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/...
10
votes
7answers
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, ...
6
votes
6answers
493 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 ...
6
votes
8answers
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 ...
5
votes
6answers
395 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 ...
4
votes
5answers
4k 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 ...
5
votes
3answers
301 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 ...
5
votes
1answer
289 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 ...
6
votes
0answers
165 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 ...
9
votes
6answers
384 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, ...
5
votes
1answer
236 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 ...
3
votes
0answers
267 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 ...
9
votes
3answers
159 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 paranthesis are taught via some simple phrases like "pointy" operators (...
14
votes
1answer
254 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 ...
5
votes
2answers
197 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 ...
11
votes
6answers
1k 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 ...