Questions tagged [primary-education]

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

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52
votes
14answers
14k 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 ...
52
votes
4answers
4k 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&...
51
votes
14answers
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 ...
51
votes
14answers
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 ...
47
votes
3answers
7k 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 ...
43
votes
17answers
9k 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 ...
36
votes
12answers
6k 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 ...
35
votes
23answers
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 ...
29
votes
4answers
3k views

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 ...
28
votes
10answers
3k views

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?
28
votes
6answers
1k 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 ...
27
votes
7answers
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 ...
26
votes
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\...
24
votes
1answer
636 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 ...
23
votes
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). ...
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 $\mathbb{Z}$ ...
22
votes
4answers
829 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 story of a series of ...
20
votes
1answer
438 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 ...
19
votes
11answers
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 ...
19
votes
3answers
1k views

What is Discovery-Learning, and why is it so controversial?

In my home province Discovery Learning is getting a substantial amount of pushback. I've been trying to follow the discussions, but have been struggling because I can't seem to get a clear answer as ...
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 ...
17
votes
3answers
213 views

How can creativity be incorporated into elementary school mathematics?

Creativity is the core of research mathematics. However, most introductory math consists of learning fixed rules to perform basic, essential mathematics. Thus, for many elementary school students, ...
16
votes
15answers
19k views

How to explain the difference between the fraction a / b and the ratio a : b?

I found it difficult to explain the difference between the fraction a / b and the ratio a : b. This subject is for pupils of grade 5. So is there a real difference between them and how to explain the ...
16
votes
6answers
1k 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.
15
votes
13answers
4k 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 ...
15
votes
4answers
30k 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 ...
15
votes
5answers
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 ...
15
votes
2answers
3k 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. ...
15
votes
5answers
804 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 ...
15
votes
3answers
983 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 ...
14
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, ...
14
votes
12answers
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 ...
14
votes
4answers
3k views

Traditional “long” method of multiplication versus grid and partial products — evidence of better outcomes?

I'm not a math teacher but am actively involved in teaching my children mathematics (elementary age). I learned the traditional "long" approach to multiplication, but the school systems now emphasize ...
14
votes
3answers
629 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 ...
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 ...
14
votes
4answers
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 tought at this age and I am unfamiliar with the ...
14
votes
3answers
249 views

According to Common Core standards, what math skills are beginning Kindergarteners supposed to have?

I remember looking once at what chikdren in Kindergarten were expected to know, and it was quite a bit. I have a young son, and would like to know: What is a Kindergartener expected to know about ...
14
votes
5answers
729 views

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 ...
14
votes
1answer
153 views

How do online practicing websites decide how much practice / repetition is 'enough'?

I've worked with a few online programs that present students with drills / exercises / etc. for a period of time before deciding that they've 'done enough' for the day (e.g. Reflex Math). How do these ...
13
votes
3answers
1k views

Mathematical Knowledge for Teaching

Does anyone know of any course called Mathematical Knowledge for Teaching? Where is this course taught? If it's not a course, is there any workshop about this? Or possible a book? It's not knowing ...
13
votes
4answers
2k 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 ...
13
votes
1answer
142 views

Seeking Concise Article on Motivations for and Benefits of Standards-Based Grading

I am preparing for my second year of implementing standards-based grading (SBG) in my 5th and 6th grade math course. I was thrilled with the benefits of using SBG with my students but found that I ...
13
votes
1answer
177 views

Teaching functions/mappings early

Functions and mappings are usually introduced late in the curriculum, and functions of arity two or more are considered "advanced" (many don't even see them before college). On the other hand, the ...
13
votes
0answers
309 views

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 ...
12
votes
2answers
838 views

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 ...
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. ...
12
votes
1answer
398 views

Teaching K-8 math in the style of “A Mathematician’s Lament”

Here's a link to the full paper, colloquially known as Lockhart's Lament: Link: https://www.maa.org/external_archive/devlin/LockhartsLament.pdf In the context of K-8 learning materials that take ...
12
votes
2answers
369 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 ...
12
votes
1answer
321 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 ...
11
votes
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, ...