Questions tagged [primary-education]

For questions about the mathematical education in the first years in school (ages approx. 5-10).

Filter by
Sorted by
Tagged with
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 ...
1
vote
2answers
150 views

Which works better for learning 6 * 7 = 42: saying “six sevens are forty-two”, or “six times seven equals forty-two”?

When memorizing and recalling the times table, I learned to say "six sevens are forty-two", and always wondered what it would be like to learn to say "six times seven equals forty-two&...
28
votes
11answers
3k views

What are the arguments for and against learning multiplication table by heart?

I think, a lot of students are bothered by learning multiplication tables by heart, in particular when it comes to numbers greater than 10. Why should one learn (or not learn) these things by heart?
10
votes
8answers
2k views

How early and how much can you teach kids and teenagers about vectors?

I have met kids and teenagers who I believe are capable of understanding the concept of a vector. However, I have only heard of a select number of schools who teach it to young people. Here's my main ...
23
votes
5answers
945 views

A Series of Unfortunate Examples!

All of us know, when teaching, the "right" choice of examples is important. Though, making the "right" choice is one of those things that are easier said than done. Here is the ...
17
votes
14answers
4k views

How to teach binary numbers to 5th graders?

I already tried the direct approach, starting with "this is how it works". That turned out ok but took too long and was boring for all of us. My second attempt was using the twofingered alien. This ...
27
votes
1answer
5k views

Which product of single digits do children usually get wrong?

(I was inspired by the comments in this answer to ask this question.) I have some multiplication table cards from Kumon that have a list of commonly mistaken multiplications: $7\times 8,4\times 8,11\...
2
votes
0answers
154 views

Why students do not notice sign of plus/minus?

My child in grade 3 often needs a reminder because in a task where he needs to do addition he would subtract instead of adding or v.v ignoring the signs given in a task. He would also forget adding ...
23
votes
23answers
5k views

How can I explain why we need proofs to someone who has no experience in mathematical thinking?

I know someone I really like, but sadly, that person has absolutely no experience in math or mathematical thinking above third grade mathematics (+, - are fine, but division already makes problems). ...
0
votes
4answers
323 views

Defining mathematics to primary/elementary school teachers

I'm looking for a simple way to define mathematics to primary/elementary school teachers and explain some of the confusion children have. I'm hoping some Algebraist could help me properly state the ...
24
votes
1answer
639 views

Is there a Piagetian age at which proofs can be comprehended?

I am wondering if there is literature on the developmental age (pre-adolescent?, adolescent?) at which the notion of a "proof" can be understood? I am less interested in mathematical proofs and more ...
2
votes
2answers
332 views

How actually are prime numbers taught in elementary school in United States and how easily do students learn what they're being taught about them?

I read the question https://math.stackexchange.com/questions/1593091/how-to-explain-why-study-prime-numbers-to-5th-graders and according to the body of the question, some students sigh. Also according ...
5
votes
1answer
185 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 ...
5
votes
0answers
178 views

Is there a name for 'simple' two-input-one-output word problems?

Andy has 4 apples, and then eats 2. How many does he have left? Beth drives for 3 hours at 80 km/h. How far did she go? Carl, Debbie and Earl earned $30 together shoveling driveways. How much does ...
16
votes
15answers
20k views

How to explain the difference between the fraction a / b and the ratio a : b?

I found it difficult to explain the difference between the fraction a / b and the ratio a : b. This subject is for pupils of grade 5. So is there a real difference between them and how to explain the ...
0
votes
0answers
93 views

What notation do they use for mathematical expressions in Polish schools?

I thought of something like Polish notation all by myself and asked the question https://cs.stackexchange.com/questions/111067/could-we-define-the-decimal-notation-of-a-natural-number-as-a-series-of-...
1
vote
1answer
73 views

Resources for Unit Rates

I am currently mentoring my little brother in mathematics. There is an issue with the pedagogy of unit rates. For example when given the following concept " 11.00 U.S. Dollars to 20 Planet X ...
2
votes
2answers
544 views

Teaching Mathematics to a Younger Sibling

I always wanted to teach my siblings mathematics, and one, ten years of age, is particularly eager. For the purposes of specializing recommendations, I will add he can use arithmetic up to ...
1
vote
0answers
107 views

Mental visualisation ability test for each age?

What are standard tests for mental visualization (image, representation) for kids? So far I know about mental arithmetics and spatial rotation tests. Is there any other way to check mental vision ...
8
votes
4answers
1k views

Why do some students struggle so much with fractions?

I read on multiple web pages something that implies that that some students really struggle with fractions but I could never find a detailed explanation of why. This question is different from Are ...
3
votes
1answer
184 views

Is there an arithmetic book similar to “Teach Your Child to Read in 100 Easy Lessons” by Siegfried Engelmann?

I have found Engelmann’s book (mentioned in subject) to be extremely effective. Is there an equivalent to this book for teaching Arithmetic? I believe the overall approach or method is called Direct ...
52
votes
4answers
4k views

Future educators writing nonsense questions

I teach future elementary educators mathematics content courses. We play a lot in class with tasks like "Write a variety of word problems which would require the student to multiply 2.3 by 1.4&...
4
votes
2answers
136 views

Teaching Approach at primary, middle and higher level

I would like to have a comparison or a big picture of how and why the approach for teaching math varies from primary (or pre primary) to middle to higher classes. I understand at every level one ...
29
votes
4answers
3k views

Books about elementary mathematics written like a good undergraduate textbook

I've never seen any really good expositions of elementary mathematics (middle school or earlier). A good college-level textbook, written for people with an interest in mathematics, reads like a novel ...
2
votes
4answers
272 views

At what age are most children able to convert between rational fractions and decimals?

At what age are most children able/taught to convert between rational fractions and decimals? For example Convert 0.25 to a fraction consisting only of whole numbers. What is 3/4 expressed in ...
6
votes
5answers
313 views

Concrete way to teach addition and subtraction of fractions

I am teaching 4th-grade kids. The topic is Fraction. Basic understanding of a fraction as a part of the whole and as part of the collection is clear to the kids. Several concrete ways exist to teach ...
6
votes
4answers
233 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 ...
5
votes
2answers
290 views

Have there been attempts to base early math education on category theory?

The New Math curriculum built math eduction on set theory. Have there been any attempts to do something similar with category theory? I was fortunate to grow up in a relatively enlightened ...
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, ...
14
votes
8answers
5k views

Fun set theory for kids

Are there some fun results in set theory to set as landmarks while introducing to kids? For example, while introducing graph theory to kids, I could explain isomorphism via a pentagon and pentagram, ...
13
votes
4answers
2k views

Confirmation bias in math education

Confirmation bias is a quality of human mental processes which makes us tend to think in terms of positive examples and tests that would confirm our working hypothesis, rather than negative examples ...
6
votes
3answers
421 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/...
3
votes
1answer
165 views

The spatial thinking course for primary school - what to use?

We're planning to run the project for first two grades of the elementary school kids, in which we want to facilitate the spatial thinking development along with the regular arithmetic course and make ...
7
votes
10answers
2k views

How to explain fractions to 7 year old kid

I am finding it difficult to convince my kid that 2/4 and 1/2 are same. As per the kid, 2/4 is more than 1/2 since in first case the boy gets 2 candies out of 4 and in second case he gets 1 candy out ...
43
votes
17answers
9k views

How to explain the flipping of division by a fraction?

This question is inspired by @DavidButlerUofA's discussion of "$\div \frac{2}{3}$ as $\times \frac{3}{2}$" in "Are fractions hard because they are like algebra?" Q. How can one best convey to ...
10
votes
6answers
6k views

Is short division taught these days and if not, why not?

tl;dr I'm interested in opinions on short division. Below I discuss my experience dealing with young children and long division versus short division. For those that don't know of it, wikiHow has a ...
15
votes
4answers
31k views

When should a kid have memorized the multiplication table?

To contextualize: I know someone who is ten years old, and needed to use repeated addition to compute $4 \times 8$, i.e., needed to calculate it as $4 \times 8 = 8+8+8+8$. Question: By what age ...
47
votes
3answers
7k views

How do blind people learn mathematics?

I am interested in how blind people learn mathematics at any level, but particularly before college. Math is often taught using a lot of visualization; how does this work with blind people? My ...
9
votes
1answer
203 views

Equality as “makes” vs equality as “equals”

A problem I often encounter while introducing students to equations is that of changing the conceptual image of the equation symbol $=$ from "results to" to "is equal to". To be more precise: In the ...
6
votes
3answers
217 views

Are there standard notations for 'number talks' / ‘math talks?'

I’m a homeschool teacher of a nine-year-old, and we sometimes have one-on-one ‘number talks’ (a.k.a. 'math talks') similar to the activity used in primary school classrooms. Part of this process ...
4
votes
2answers
171 views

Resources for Learning Multiplication Facts

A recent question (@Namaste) made me realize that it would be good to pull together the best resources for learning the multiplication facts. When seen as a rote memory task, this can turn students ...
6
votes
3answers
368 views

How do I convince my teachers that a book on maths must focus on conceptual understanding?

I am a senior teacher at this school. We have to select the textbooks for the upcoming session. I am proposing that we have to select books (in maths) that focus more on conceptual understanding and ...
1
vote
1answer
102 views

How to address opportunities for improvement with a teacher

My daughter’s 5th grade teacher gives some pretty impossible questions and I don’t think she understands the material she’s teaching. For example, this question has no context from previous questions ...
22
votes
15answers
6k views

Explaining why (or whether) zero and one are prime, composite or neither to younger children

There are lots of discussions out there about whether $1$ is a prime number (such as this one) and even about zero (such as this question, though note zero does generate a prime ideal in $\mathbb{Z}$ ...
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 ...
11
votes
3answers
1k views

Third Grade Question — This makes no sense to me

Third grade grandchild had this for homework. Can someone explain the intent here?
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 ...
11
votes
5answers
347 views

Intuition for the mean for elementary school kids

I was teaching elementary school kids (aged 10) about the mean. The intuition I gave them is roughly as follows: You are trying to find a value such that the sum of all the distances from the mean ...
12
votes
8answers
3k views

How to teach sum of fractions to students?

I think almost every middle school student in my country has learned sum of two fractions in this non reflexive way (I'm included when I was kid), doing the following steps: They calculate the lcm. ...
8
votes
3answers
541 views

Subtraction using Addition (Austrian Method), is it useful to learn this method instead of the usual “borrow” method?

I came across this method to perform subtraction using addition and not using the "borrow" concept, apparently because it is harder to learn it that way. Video - https://www.youtube.com/watch?v=...