Questions tagged [primary-education]
For questions about the mathematical education in the first years in school (ages approx. 5-10).
141
questions
19
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). ...
1
vote
3answers
204 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 ...
1
vote
0answers
86 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
68 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
534 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
104 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 ...
3
votes
1answer
149 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 ...
51
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&...
2
votes
4answers
212 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
252 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
221 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 ...
4
votes
2answers
133 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 ...
5
votes
2answers
279 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 ...
14
votes
8answers
4k 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, ...
3
votes
1answer
164 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 ...
1
vote
2answers
235 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 ...
6
votes
3answers
387 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
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 ...
10
votes
1answer
195 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
214 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
170 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 ...
11
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, ...
7
votes
3answers
355 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
100 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 $\mathbb{Z}$ ...
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
374 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 ...
5
votes
1answer
205 views
Corequisite remediation for “Mathematics for Future Elementary Teachers”
My university is eliminating its developmental math courses, and moving to a system using corequisite remediation.
I am trying to develop a coreq for the first course in our "Mathematics for ...
4
votes
5answers
3k 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 ...
3
votes
2answers
248 views
How many hours / school years does it take for the average child to memorize the $10\times 10$ addition and multiplication tables?
How many hours does it take for the average child to memorize the $10\times 10$ addition table?
How many school years does it take for the average child to memorize the $10 \times 10$ addition table?
...
6
votes
4answers
1k views
Real-life exceptions to PEMDAS?
What are some real-life exceptions to the PEMDAS rule?
I am looking for examples from "real" mathematical language --- conventions that are held in modern mathematics practice, such as those appearing ...
6
votes
2answers
214 views
Curriculum for Advanced 6th Graders
Next year I volunteered to lead the math class for a group of 6th graders (ages 11 - 12). Here are the pertinent details:
About 5 - 8 (U.S.) students, for about 45 minutes, 3 days a week (they'll ...
12
votes
1answer
300 views
Best practices in teaching math to future elementary teachers
This question is about references in current best practices in teaching math to future elementary teachers at a university level. I am asking it because I do not see any question so far on this site ...
5
votes
1answer
270 views
How is math taught in elementry school in Finland?
I read on the internet that Finland has the best education system in the world at that in Finland, students are taught to love mistakes and that's how they learn and become smarter. I could not find ...
5
votes
3answers
288 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 ...
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 ...
4
votes
0answers
136 views
What effect does giving numerical or written grades have on learning?
When I was in school, pupils were given numerical grades, or the equivalent of numerical grades but disguised as words, on their performance in various school subjects and also behaviour. A key ...
-4
votes
2answers
364 views
Could schools jump straight into teaching real numbers first then teaching fractions later?
Some students really struggle to learn fractions. Not only that but also, once they've mastered an understanding of real numbers, they can learn about fractions so much faster and more efficiently ...
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 ...
7
votes
1answer
213 views
Fun classroom exercise for mental rotation
I'm training to be a teacher and I am doing a maths lesson later next week. The topic is geometry, the students are 12-year-olds.
More concretely, I've been given a selection of exercises that I may ...
4
votes
1answer
107 views
Making modular arithmetic interesting for school kids
This is a pattern even school kids could discover (when gently pointed to). I never did conciously, and cannot remember to have been pointed to explicitly, neither at school nor later:
$$\color{red}{\...
11
votes
5answers
343 views
Intuition for the mean for elementary school kids
I was teaching elementary school kids (aged 10) about the mean. The intuition I gave them is roughly as follows:
You are trying to find a value such that the sum of all the distances from the mean ...
8
votes
3answers
570 views
Math Everywhere Activities
Question
Does anyone have a nice list of "no effort" activities that parents can employ to promote numeracy? I am primarily interested in K-8 activities.
Exposition
Often parents ask me about what ...
5
votes
4answers
835 views
How to correct visualization of mathematical expressions?
This happens a lot when I try to explain the commutative property, mostly in elementary grade levels. I say
2 + 3 = ?
and then the student usually replies with 5. Albeit they're not wrong, it's not ...
11
votes
3answers
951 views
Third Grade Question — This makes no sense to me
Third grade grandchild had this for homework. Can someone explain the intent here?
19
votes
1answer
399 views
Has Benezet's teaching experiment ever been reproduced?
In the 1930's, Louis Bénézet, a superintendent of several schools in New Hampshire made the interesting experiment of teaching no formal arithmetic until grade 6:
In the fall of 1929 I made up my ...
0
votes
1answer
118 views
How to present the order of factors and summands for the usual multiplication procedure
In the following multiplication example,
$$\begin{align}
34\;&
\\\underline{\times\;\; 7\;}&
\end{align}$$
first one would multiply the units digits, producing the partial product $28$ as ...
4
votes
4answers
203 views
Method of Showing Algebraic Work
I have seen two different methods of showing algebraic work when solving equations. I show both of them below for the same simple math problem:
\begin{alignat}{8}
x+3 &\;=&\; 5 \qquad&&...
5
votes
0answers
144 views
Textbooks explicitly showing the injections for the sum of sets
Asking for methods to produce the sum of natural numbers from the disjoint union of sets, it seems that the obvious way is to use the general definition, as coproduct, of the sum of sets. The accepted ...
1
vote
1answer
109 views
How to build addition with sets?
I was taught under the New Math, so I should know this, but I am afraid I was tricked.
Using the cardinal, it is easy to define a multiplication, as the cardinal of the cartesian product is the ...
