Questions tagged [primary-education]

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

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6
votes
8answers
1k 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 ...
4
votes
6answers
278 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 ...
6
votes
1answer
163 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 ...
3
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4answers
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 ...
2
votes
2answers
199 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? ...
4
votes
4answers
504 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 ...
5
votes
2answers
120 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
225 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 ...
4
votes
1answer
197 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 ...
3
votes
1answer
121 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
345 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
124 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
313 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
688 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
186 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
91 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}{\...
9
votes
4answers
256 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 ...
7
votes
3answers
533 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
805 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 ...
7
votes
1answer
298 views

Third Grade Question — This makes no sense to me?

Third grade grandchild had this for homework. I don't even know the intent here?
16
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1answer
266 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 ...
3
votes
4answers
173 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
138 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
100 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 ...
7
votes
3answers
290 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
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2answers
616 views

Resources for Teaching Logic to Primary School Children?

What are some books or other resources for teaching primary school children logic?
16
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5answers
723 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
198 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
7answers
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
362 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
187 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
225 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
204 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
160 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
403 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" ...
11
votes
2answers
328 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
224 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 ...
13
votes
3answers
769 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
138 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
262 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
221 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
170 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
191 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 ...
11
votes
3answers
183 views

How can I teach the concept of before and after a given time

I'm teaching my 6 year old how to tell the time. She can read analogue clocks comfortably. We want her to be able to tell the time so when she wakes, if the time is past 6:15 then she is allowed to ...