# Questions tagged [primary-education]

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

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### 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 ...
356 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 ...
207 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 ...
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### 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&&...
142 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 ...
5k views

### What was the problem with New Math? Why did it end?

During the 60s, people in the US (and also in Europe), school curricula introduces New Math where students began with set theory in the first grade before learning to perform addition or ...
107 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 ...
5k views

### Should we say that fractions “are” or “represent” numbers?

I never gave this a second thought until a friend who works in education brought it up the other day. Should we say that a fraction like $\frac{1}{2}$ "is" a number, or "represents" a number? In ...
651 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 ...
978 views

### Resources for Teaching Logic to Primary School Children?

What are some books or other resources for teaching primary school children logic?
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### 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 ...
924 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 ...
264 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 ...
168 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 ...
245 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. ...
303 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 ...
241 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 ...
242 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 ...
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### Online Resources to Explain Negative Numbers and Scientific Notation

I have to teach someone whose English isn't her native language (and her English skills aren't advanced) the concept of negative numbers + exponents, and how to read scientific / engineering numbers. ...
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### What is the rationale for the absent (+) in mixed fractions?

Why are students taught to represent one and a half as $1 \frac{1}{2}$ rather than $1 + \frac{1}{2}$? This mode of expression seems standard at least throughout North America. I believe that it is bad ...
195 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 ...
1k 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 ...
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### 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 ...
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### 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" ...
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### 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?
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### Imbuing a six year old with a sense of mathematical wonder

My six year old started school a few months back and he's loving it. This first year is more about social skills than anything academic and I like that approach. But we're spending some time at home ...
368 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 ...
313 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 ...
1k views

### Should students get full credit for getting the correct answer (without work)?

Pre-algebra If the student is taking this branch of mathematics, they are expected to show their work because they're expected to solve specific problems in a certain way. Ex, when they're solving ...
88 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 ...
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### Are women better math teachers for little children?

Once in a discussion a colleague told me that he thinks: It is better to use women to teach maths to little children including preschoolers and children in elementary school. Also it is better to ...
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### 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 ...
358 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 ...
158 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 ...
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### Community College Remedial Mathematics difficulties for students

I've been teaching remedial mathematics for the better part of a decade, and I've noticed a big trend in my classes lately. Many of my students are able to grasp the more complex ideas but still ...
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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: ...
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### 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 ...
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### 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 ...
544 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 ...
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### Teaching measurement to 4th grade students by projects?

I'm going to be teaching measurement to 4th grade students and I want something a little more hands on. I believe that they would enjoy that more. So any helpful ideas or things you think would work ...
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### Was math education following a western trend?

After some research on the recent history of math education in the U.S., from the new math movement to the beginning of the 21st century, I understood that the historic flow of the math education ...