Questions tagged [primary-education]
For questions about the mathematical education in the first years in school (ages approx. 5-10).
117
questions
21
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
284 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 ...
7
votes
1answer
171 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
2k 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
209 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
541 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
126 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 ...
11
votes
1answer
232 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
204 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 ...
4
votes
3answers
196 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 ...
4
votes
2answers
382 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
126 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
321 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 ...
6
votes
8answers
736 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
191 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
93 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:
$$\color{red}{\...
11
votes
5answers
325 views
Intuition for the mean for elementary school kids
I was teaching elementary school kids (aged 10) about the mean. The intuition I gave them is roughly as follows:
You are trying to find a value such that the sum of all the distances from the mean ...
8
votes
3answers
544 views
Math Everywhere Activities
Question
Does anyone have a nice list of "no effort" activities that parents can employ to promote numeracy? I am primarily interested in K-8 activities.
Exposition
Often parents ask me about what ...
5
votes
4answers
815 views
How to correct visualization of mathematical expressions?
This happens a lot when I try to explain the commutative property, mostly in elementary grade levels. I say
2 + 3 = ?
and then the student usually replies with 5. Albeit they're not wrong, it's ...
11
votes
3answers
565 views
Third Grade Question — This makes no sense to me
Third grade grandchild had this for homework. Can someone explain the intent here?
16
votes
1answer
279 views
Has Benezet's teaching experiment ever been reproduced?
In the 1930's, Louis Bénézet, a superintendent of several schools in New Hampshire made the interesting experiment of teaching no formal arithmetic until grade 6:
In the fall of 1929 I made up my ...
0
votes
1answer
113 views
How to present the order of factors and summands for the usual multiplication procedure
In the following multiplication example,
$$\begin{align}
34\;&
\\\underline{\times\;\; 7\;}&
\end{align}$$
first one would multiply the units digits, producing the partial product $28$ as ...
4
votes
4answers
177 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
139 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
101 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 ...
8
votes
3answers
330 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=...
2
votes
2answers
693 views
Resources for Teaching Logic to Primary School Children?
What are some books or other resources for teaching primary school children logic?
15
votes
5answers
740 views
Why is multiplication taught using cross notation at first?
Alert: I am not a math educator.
It seems to me that multiplication is first taught using the cross notation, for example $3\times 5=15$.
First question - is that even correct? Maybe not all schools ...
7
votes
2answers
206 views
“Personalized System of Instruction” (PSI) vs. “Individually Prescribed Instruction” (IPI)
This question may be a bit overly-broad for MESE, but I am hoping to find some responses that can help to fill in my understanding of two similar forms of instruction that had their heyday in the ...
12
votes
8answers
2k 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.
...
10
votes
4answers
405 views
How to teach a weak student?
I am tutoring a 9th grade student. And he is terribly weak in mathematics. He doesn't remember the multiplication tables, can't divide efficiently. Doesn't know how to proceed with solving a ...
4
votes
2answers
190 views
What's the word for addition and subtraction without borrowing or carrying over?
Is it regrouping? Upon googling it seems regrouping is borrowing or carrying over collectively. What's the word for not borrowing and carrying over? It's supposedly to train mental computation.
...
10
votes
0answers
234 views
Shanghai math — what is it, and how good is it?
Some schools in the UK are adopting English translations of a grade school math textbook from Shanghai. The book appears to be designed to work with a specific teaching approach, the only specifics ...
3
votes
2answers
207 views
The Order in Which Arithmetic Operators are Taught
Should multiplication be taught before addition and subtraction?
The obvious answer for most people is 'no'. However, I think there are a few valid points that could change the way students approach ...
8
votes
1answer
159 views
Multiplying two decimals using (camouflaged) binary representation
This post is largely copied from a response to the
17 Camels Trick MO posting.
Here I ask:
Q. Does anyone (in any country) teach this
binary method of decimal multiplication?
It strikes me ...
8
votes
1answer
163 views
Introducing the concept of variables to kids
Today I had a discussion on how to introduce the basic concept of variables in math using real life examples. We came up with ideas of using boxes containing matches, or M&Ms representing the ...
9
votes
6answers
409 views
Motivation in School
I live in Brazil and here we have some problems with teaching mathematics in High School. In some point of the students' life (I think it happens in the 5th grade), they start "hating mathematics" ...
12
votes
2answers
337 views
Correctness in learning mathematics
I came to mathematics via physics, in part because of the reputation of physics as allowing "non-rigorous" reasoning. The subject felt more free and less anal-retentive than mathematics. This is not ...
8
votes
1answer
233 views
Where can I find a set of these 'logic' blocks?
(It will be difficult to answer this question without 'advertising' for a retailer, but I've searched for these several times in the past few years, to no avail.)
In Math From Three To Seven (The ...
14
votes
3answers
790 views
Does the “how old is the shepherd” phenomenon occur for more relatable word problems?
A friend of mine just showed me this article about the "how old is the shepherd" problem: Link
Of course, I'm shocked by the finding that 75 percent of kids give an answer other than "there isn't ...
3
votes
2answers
85 views
Reinforcement mathematics thinking of 10 years old child by teaching `patterns`
As Lynn Steen in The Science of Patterns says, I think Mathematics is the science of pattern ...
14
votes
5answers
1k views
Soft questions for 8 - 12 year olds
I am concluding my second year in mathematics at the university of Milan.
I also happen to be an educator for 8 - 12 year old children (as a Scout).
Recently I have tried to fill some dead time by ...
7
votes
1answer
143 views
Subtraction Methods in School Mathematics
I have studied long ago different method for subtracting numbers, for instance the borrow method or the Austrian method (I hope I am using the right names; I am not an English native speaker and these ...
5
votes
4answers
267 views
Average time to solve basic arithmetic problem
I am a game developer currently making a game based on basic arithmetic problems for kids and teens.
Are there any research papers on the average time to solve basic arithmetic problems or on how to ...
18
votes
12answers
2k views
Explaining the order of negative integers
Today I happen to have an interesting discussion with a primary school kid.
I asked him "Which is the smallest one - digit integer?" He instantly replied $-1$. I told him that he's wrong and the ...
4
votes
3answers
276 views
The meaning of equal sign in unit conversion
Recently, I read a paper about student's understanding of fraction. Most students mentioned in the paper had given $5/8$ as their answer to the following question:
...
9
votes
5answers
224 views
Primary/Elementary Math Resources for Homeschool
I'm a homeschool mom, my daughter is 7. She will be in second grade next year. I appreciate the different ways of doing math, rather than just stacking the numbers and adding/subtracting. I'm not sure ...
2
votes
0answers
173 views
Cognitively Guided Instruction (CGI) for 5th Grade
Are there any schools out there successfully using CGI with a 5th grade curriculum? Our students have poor number sense, and we'd like to remediate using CGI. I'd love to compare sequences of lessons ...
7
votes
1answer
194 views
Teaching Neural Networks to 6th grade students
I've been thinking if it would be possible to teach something about the basic mathematics behind Neural Networks / Deep learning to a class of 6th graders (12-13ys old). A 90-minute (max) lecture must ...
