Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange
Join us in building a kind, collaborative learning community via our updated Code of Conduct.

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

5
votes
0answers
40 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
89 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
162 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
128 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
91 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 ...
5
votes
1answer
137 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
89 views

Resources for Teaching Logic to Primary School Children?

What are some books or other resources for teaching primary school children logic?
16
votes
5answers
637 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
118 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 ...
11
votes
7answers
1k 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
265 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
152 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. ...
9
votes
0answers
156 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
179 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
157 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
140 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
349 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" ...
10
votes
2answers
303 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
162 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
615 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
76 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
121 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
242 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 ...
15
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
252 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
203 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 ...
1
vote
0answers
136 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
172 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
179 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 ...
17
votes
3answers
510 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 ...
4
votes
1answer
126 views

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 ...
12
votes
0answers
258 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 ...
10
votes
1answer
937 views

When and Why are different division symbols taught?

There are 4 division symbols that I have learned/taught. Below is 18 divided by 3, shown with 4 different symbols. This question was sparked by the comments on my answer to the question on examples ...
35
votes
23answers
5k 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 ...
4
votes
1answer
4k views

How to teach “after-before” of numbers to a $5$ year old?

I am currently teaching basic mathematics like numbers and tables to a $5$ year old girl. She is in nursery. But I am facing troubles while teaching her what comes after or before of a given number, ...
6
votes
1answer
123 views

Advice needed to teach a problem about speed

I am currently helping a friend's child with his schoolwork. He is currently in primary school and being taught the topic of speed. I would like to give him the following problem as practice but I am ...
11
votes
2answers
121 views

Visual questions for 6th graders

I'm tutoring a 6th grader in math at the moment and because she never has a ton of homework I like to give her some interesting extra problems to do. It seems she really enjoyed a problem I showed ...
7
votes
2answers
158 views

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. ...
13
votes
4answers
14k 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 ...
10
votes
4answers
370 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 ...
13
votes
1answer
128 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 ...
8
votes
2answers
239 views

Is multiplication by zero clear for and understood by K-3 students?

For K-3 students, perhaps it is not acceptable to introduce multiplication by zero as a property or definition. Instead, the child may think about multiplication as, e.g., repeated addition. ...
4
votes
2answers
518 views

Hypothesis testing for children (grade 1-4)

What do you think, could hypothesis testing be taught, in some way (probably informal) to that age group of kindergarten to 4th grade? Ideas, some resources, published papers, and so on? This would ...
8
votes
4answers
361 views

1:1 iPads for K-3: how can an educator accommodate student(s) opting out?

My school district has decided to provide an iPad to every student in the district, from kindergarten to grade 3, starting next September -- although a handful of classrooms are piloting this ...
5
votes
7answers
918 views

Systems of linear equations in grade 3?

From a Grade 3 NAPLAN test: "Question 28 Joel draws 24 rectangles. He separates them into 2 groups so that there are 6 more in one group than the other. How many rectangles in the larger group? ...
13
votes
4answers
1k 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 ...
22
votes
1answer
369 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 ...
34
votes
12answers
6k 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 ...
7
votes
3answers
147 views

Looking for a tool to create a digital multiplication quiz

I'm looking for some site or software which can help me create an easy, digital multiplication quiz for my students. Some things which need to be included: The student need to be able to type in the ...