Questions tagged [primary-education]
For questions about the mathematical education in the first years in school (ages approx. 5-10).
156
questions
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1answer
63 views
Reference request: an introduction to triangular, square, and other figurate numbers
There are dozens (maybe thousands) of websites that explain what triangular numbers, square numbers, etc. are. I'm searching for a printed book that includes this material, preferably at a level that ...
3
votes
2answers
179 views
Teaching words with multiple meanings in Mathematics and English
We want to teach about words that have multiple meanings, in mathematics and
English for middle school children (e.g., function, root, or, volume, angle, constant). This is for students who are ...
4
votes
5answers
295 views
Is it a good idea for elementary school students to observe and discover the “circle perimeter formula” themselves without being dictated to?
Let them discover $\;\ell=2\pi R\;$ by their own, at least the invariance of $\ell/R$
Do you think that the following method works well in a mathematics class of elementary school? What do you think ...
21
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9answers
4k views
Why do we introduce the notion that triangles are “congruent” instead of just saying that they are “the same” or “equal”?
The assumed age of the students is 10-15 years old.
What is the danger in saying that two triangles are "the same" or "equal" instead of saying that they are congruent? It seems to ...
13
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11answers
6k views
What can (and should) an educator do about ambiguous terms like “triangle”, “square”, etc?
The imagined students are in elementary school, say around 9-13 years old.
I want to use rather precise terminology when talking to my students. However, it seems like we typically use the same ...
2
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3answers
188 views
What are strategies that a 10-13 year old could use to convert 6/27 into decimal notation?
Background:
I am working with 10-13 year olds.
I saw a problem which requires the students to convert $6/27$ into decimal notation. I can think of some methods, but I have not tested using any of the ...
20
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2answers
2k views
What does research indicate about how one should treat units in elementary school?
Background:
My friend told me that when she was in elementary school, the teacher would ask questions like "If you have $6$ apples and eat $2$ of them, how many apples do you have left?" A ...
3
votes
2answers
171 views
Looking for an educational game from long ago, possibly called Mother Goose [closed]
OK so this is really old school. Back in the 1980s, as a latchkey kid, I played on the computers in the library in elementary and middle school. There was this one bizarre educational game that I'd ...
15
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3answers
2k views
How many of “The Seven Laws of Teaching” are still relevant for teaching maths today?
Wikipedia shows that in 1886 John Milton Gregory outlined his "The Seven Laws of Teaching"; asserting that a teacher should:
Know thoroughly and familiarly the lesson you wish to teach; ...
-1
votes
2answers
166 views
What research has been done on the effects of requiring students to learn to count in an alternative number base such a binary or base eight? [closed]
What research has been done on the effects of requiring students to learn to count and do some easy arithmetic in an alternative number base, for example binary, base four, base six, base eight, base ...
1
vote
2answers
190 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
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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\...
54
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 ...
2
votes
0answers
166 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 ...
5
votes
1answer
192 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 ...
23
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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
332 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 ...
0
votes
0answers
98 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
74 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
557 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
113 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
241 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
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4answers
5k 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
365 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
403 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
246 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
138 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
307 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 ...
15
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, ...
3
votes
1answer
167 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 ...
3
votes
2answers
390 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
430 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
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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 ...
9
votes
1answer
213 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
220 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
176 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 ...
10
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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
3answers
373 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 $\mathbb{Z}$ ...
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
424 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
219 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
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 ...
4
votes
2answers
324 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?
...
8
votes
4answers
2k 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
272 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
330 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
310 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
302 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 ...
