Questions tagged [primary-education]

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

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32 votes
4 answers
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Books about elementary mathematics written like a good undergraduate textbook

I've never seen any really good expositions of elementary mathematics (middle school or earlier). A good college-level textbook, written for people with an interest in mathematics, reads like a novel ...
Jack M's user avatar
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36 votes
24 answers
6k views

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 ...
Mathdad's user avatar
  • 580
17 votes
4 answers
2k views

Teaching a very enthusiastic and bright 5 year old

I was asked to give extra lessons to a 5 year old boy who loves math (he says he likes 3 sports: football, swimming and math). However, I have never taught at this age and I am unfamiliar with the ...
Lucas Virgili's user avatar
13 votes
6 answers
4k 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 ...
Timothy's user avatar
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57 votes
15 answers
17k views

Student: Why not use a calculator?

The kid I am teaching math (subtraction for large numbers right now) just said this is all too easily done by a calculator, why don't we use it? Well, I did tell him that you can only learn more ...
Rijul Gupta's user avatar
  • 1,165
51 votes
3 answers
11k views

How do blind people learn mathematics?

I am interested in how blind people learn mathematics at any level, but particularly before college. Math is often taught using a lot of visualization; how does this work with blind people? My ...
Peter Flom's user avatar
46 votes
18 answers
12k views

How to explain the flipping of division by a fraction?

This question is inspired by @DavidButlerUofA's discussion of "$\div \frac{2}{3}$ as $\times \frac{3}{2}$" in "Are fractions hard because they are like algebra?" Q. How can one best convey to ...
Joseph O'Rourke's user avatar
7 votes
10 answers
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 ...
NotAgain's user avatar
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31 votes
11 answers
5k views

What are the arguments for and against learning the 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?
Markus Klein's user avatar
  • 9,438
17 votes
12 answers
7k 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 ...
Improve's user avatar
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16 votes
6 answers
2k views

Fun games for children [closed]

I'm looking for fun games for children (from 4 to 12 years) used in learning math concepts. They can be offline or online games.
Filipe Ferminiano's user avatar
15 votes
2 answers
4k views

Teaching 100 x 100 times tables

First, why bother: I teach and play math with my son in the mornings. It's a lot about letting him enjoy learning, so the curriculum (my intentionally vague vision of how we'll proceed) is flexible. ...
Hal's user avatar
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12 votes
8 answers
4k 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. ...
user26832's user avatar
  • 573
64 votes
17 answers
9k 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 ...
Geoffrey's user avatar
  • 898
15 votes
5 answers
1k views

Cost and benefits of compartmentalization in k-12 curriculum

This is a soft question perhaps not well suited for the format of the site but I'm interested to hear opinions from this community on this topic. K-12 mathematics textbooks (understandably) divide ...
NiloCK's user avatar
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55 votes
14 answers
6k 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 ...
Mike Shulman's user avatar
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42 votes
12 answers
7k views

Is it advisable to avoid teaching "multiplication as repeated addition"?

I've had this discussion with a couple of friends. I argued that teaching multiplication as repeated addition isn't a good idea because it doesn't help children differentiate between the two ...
Mark Fantini's user avatar
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32 votes
6 answers
2k views

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 ...
NiloCK's user avatar
  • 4,980
31 votes
1 answer
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\...
JRN's user avatar
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28 votes
7 answers
6k views

What value is there in requiring students to answer word problems in complete sentences?

This is related to my previous question What value is there in requiring students to declare the dimensions of an answer when it is already clear from context? , but with a different focus. A sizeable ...
Robert Columbia's user avatar
25 votes
5 answers
1k views

A Series of Unfortunate Examples!

All of us know, when teaching, the "right" choice of examples is important. Though, making the "right" choice is one of those things that are easier said than done. Here is the ...
Amir Asghari's user avatar
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25 votes
1 answer
765 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 ...
Joseph O'Rourke's user avatar
25 votes
23 answers
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). ...
user15257's user avatar
  • 351
24 votes
10 answers
4k views

How to encourage young student to think in unusual ways?

I tutor a young girl aged 11 (grade 4). She is doing OK for her age, but I have observed that she has a tendency for rigid ways of thinking. She is usually more inclined to follow rules and stick to ...
BKE's user avatar
  • 1,282
21 votes
13 answers
1k views

How can I familiarize elementary school students with infinities larger than $\aleph_0$?

Cantor's discovery of the existence of more than one infinity was a revolutionary change in human knowledge. He defined the notion of counting by bijections and showed that one can use infinities as ...
user avatar
19 votes
9 answers
3k views

What is the rationale for distinguishing between proper and improper fractions?

I cannot recall ever hearing the terms "improper fraction" and "proper fraction" outside of an elementary and middle school setting. At some point in my mathematics education ...
Improve's user avatar
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18 votes
14 answers
5k views

How to teach binary numbers to 5th graders?

I already tried the direct approach, starting with "this is how it works". That turned out ok but took too long and was boring for all of us. My second attempt was using the twofingered alien. This ...
Esmaya's user avatar
  • 191
15 votes
4 answers
41k views

When should a kid have memorized the multiplication table?

To contextualize: I know someone who is ten years old, and needed to use repeated addition to compute $4 \times 8$, i.e., needed to calculate it as $4 \times 8 = 8+8+8+8$. Question: By what age ...
Pichi Wuana's user avatar
15 votes
4 answers
3k views

Confirmation bias in math education

Confirmation bias is a quality of human mental processes which makes us tend to think in terms of positive examples and tests that would confirm our working hypothesis, rather than negative examples ...
dtldarek's user avatar
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14 votes
3 answers
752 views

The interplay of memory and mathematical performance

As mathematicians and mathematics educators we very often see the Dunning-Kruger effect in action. Our calculus students are certain that they are masters of Calculus because they took the AP exam. To ...
Jon Bannon's user avatar
  • 6,173
12 votes
2 answers
454 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 ...
Jon Bannon's user avatar
  • 6,173
10 votes
4 answers
292 views

Problems sets for instruction

What resources are available for any grade level K- 12 that are aligned with the Common Core Mathematics Standards and Mathematical Practices that have sets of problems or problem banks that can be ...
Sue Thuma's user avatar
  • 161
10 votes
7 answers
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, ...
amWhy's user avatar
  • 2,095
10 votes
4 answers
535 views

Interesting Physical Implements for the Classroom

I'm interested in gathering a list of physical objects of mathematical interest for occasional or permanent display in a classroom. Mostly I'm interested in things that are wall-mountable, but any ...
NiloCK's user avatar
  • 4,980
10 votes
6 answers
935 views

What value is there in requiring students to declare the dimensions of an answer when it is already clear from context?

When I was in late primary and middle school (east coast US, early 1990's), we were assigned a lot of word problems of the following general form: Mary has eight self-sealing stem bolts. She sells ...
Robert Columbia's user avatar
9 votes
4 answers
3k views

Should math for elementary teachers content be taught under the direction of the math department?

I recently was appointed math department chair at a small university. We have a 3 credit math for elementary teachers content course. Administration told us they will change this course into an ...
Paul's user avatar
  • 121
9 votes
3 answers
992 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=...
user13107's user avatar
  • 307
9 votes
6 answers
486 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" ...
Luísa Borsato's user avatar
8 votes
1 answer
296 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 ...
user8046's user avatar
7 votes
1 answer
199 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 ...
Nekochan's user avatar
7 votes
1 answer
444 views

How is math taught in elementary school in Finland?

I read on the internet that Finland has the best education system in the world and that in Finland, students are taught to love mistakes and that's how they learn and become smarter. I could not find ...
Timothy's user avatar
  • 499
7 votes
5 answers
834 views

What are some common fallacies students make when they learn $X$ concept?

What are some common mistakes students often make, which may seem logical at first? I'm a student myself, but I'm curious of what some of the most frequent mistakes which happens. I'm thinking of ...
Frank Vel's user avatar
  • 243
6 votes
4 answers
347 views

Fun resources and games for advanced elementary school math students?

My younger cousin (2nd grade USA) is advancing very quickly in his current math class. The school does not have much to support him in moving ahead in the material. What websites (preferably game or ...
MicFin's user avatar
  • 162
6 votes
1 answer
1k views

What is the justification to teach the (redundant) use of parentheses in multiplications?

Example: 5 x 18 = (5 x 10) + (5 x 8) instead of 5 x 10 + 5 x 8?
AJSF's user avatar
  • 61
5 votes
2 answers
347 views

How to estimate the time needed to solve a basic mathematics problem

I want a way to know the time needed to solve addition, subtraction, multiplication and division problems. Examples $15 + 10$ $500 - 132$ $10 \cdot 10$ $20 \, / \, 10$ Is it possible to create a ...
Peter's user avatar
  • 51
4 votes
1 answer
183 views

What is a good reference for (this way of) generating a logarithmic scale?

I am interested in answers to the title question without parentheses, but I found this method below rather interesting, and I am hoping to find it published somewhere, along with a teacher's guide ...
Gerhard Paseman's user avatar
3 votes
2 answers
702 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 ...
John Clever's user avatar
2 votes
2 answers
747 views

Preparing elementary teachers for the praxis exam

I'm teaching a class called "Math for Elementary Teachers." The main goal of the course is to prepare the prospective teachers for an exam that I believe is called "Praxis" (some ...
Ferris Boyler's user avatar
1 vote
1 answer
136 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 ...
arivero's user avatar
  • 231
0 votes
1 answer
350 views

What do kids(6-15) need to know in Math to be able to understand Math easily and effectively?

I teach kids in a village and I was wondering if there is a list of Facts, Procedures, things, a kid 6-15 years of age should know to be able to easily understand things at his/her level of Math. ...
Ashish Shukla's user avatar