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
6 answers
359 views

Why is $a+b = b+a$?

In primary school, it's extremely easy to show that $a \times b = b \times a$, as follows: The surface of a rectangle can be calculated using the formula $\text{Basis} \times \text{Height}$, as in ...
14 votes
18 answers
6k views

What are some "deep" questions to explore in elementary school math?

My first grader is very advanced in math. Rather than doing more and more math and making school math even more boring for him, I recently decided to start going "deeper" rather than "...
8 votes
3 answers
209 views

Pi Day Celebration Ideas?

I realize it is probably a little late seeing as Pi Day is tomorrow.. but for the future, or late celebrations on Monday, what are some things that you do with your students for Pi Day (any grade ...
31 votes
8 answers
8k 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 ...
-2 votes
2 answers
194 views

Staircase method of small integer addition

I found the Math Games: Math for Kids to be excellent (if not extremely, excellent) at teaching elementary school math. But it made me think of some tricks, that could be displayed when teaching at a ...
2 votes
2 answers
154 views

International mathematical olympiad-type competitions at lower levels, and if they exist, their educational usefulness?

Educators in many countries have found that preparing highly motivated students for national and international mathematical olympiads can be useful in training them in mathematical ways of thinking. ...
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 ...
11 votes
8 answers
8k views

Is short division taught these days and if not, why not?

tl;dr I'm interested in opinions on short division. Below I discuss my experience dealing with young children and long division versus short division. For those that don't know of it, wikiHow has a ...
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 ...
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 ...
11 votes
3 answers
3k views

Third Grade Question -- This makes no sense to me

Third grade grandchild had this for homework. Can someone explain the intent here?
2 votes
5 answers
1k views

At what age are most children able to convert between rational fractions and decimals?

At what age are most children able/taught to convert between rational fractions and decimals? For example Convert 0.25 to a fraction consisting only of whole numbers. What is 3/4 expressed in ...
22 votes
2 answers
2k views

What does research indicate about how one should treat units in elementary school?

Background: My friend told me that when she was in elementary school, the teacher would ask questions like "If you have $6$ apples and eat $2$ of them, how many apples do you have left?" A ...
9 votes
5 answers
3k 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 ...
8 votes
1 answer
144 views

Where to distribute free math ed materials for informal settings?

I am a psychologist studying mathematical thinking and learning and I have been organizing a monthly math night at a local library. Each math night consists of a short presentation followed by several ...
1 vote
3 answers
181 views

Whole numbers as sets vs abstracted properties of sets

I recently landed on a book written for elementary school teachers which introduced the concept of whole numbers in the following manner: We have a set $\{\alpha, \beta, \gamma\}$. There are other ...
13 votes
0 answers
509 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 ...
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 ...
8 votes
2 answers
238 views

A few quick sentences to inspire an 8 year old in Maths

I have always been passionate and fascinated with maths, my job revolves around the subject, but I'm not an educator. Today I met the 8 year old son of a friend, I had the opportunity to speak to him ...
20 votes
5 answers
1k 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 ...
2 votes
1 answer
118 views

Reference request: an introduction to triangular, square, and other figurate numbers

There are dozens (maybe thousands) of websites that explain what triangular numbers, square numbers, etc. are. I'm searching for a printed book that includes this material, preferably at a level that ...
3 votes
2 answers
680 views

Elementary Teacher Math specialist/ Basic Math Minor

I'm the math department chair at a small university. Our general education program is non-traditional. The university is split into three areas. Students are expected to complete a major in one of the ...
3 votes
5 answers
531 views

Why do we explicitly state the equality of two things when we know they're equal

Recently my brother in high school and I were talking about some math when he said If we know two things are the same i.e. equal why do we need to state that they're the same? What he was trying to ...
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 ...
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?
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 ...
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 ...
11 votes
3 answers
2k views

Arithmetic books for adults

I'm trying to learn arithmetic from scratch again. Even though I can use it, I'm not sure if I can teach it to someone and I believe if you can't teach something properly, there might be loopholes in ...
3 votes
3 answers
755 views

What is the maximum value of the sum of the digits of the sum of the digits of a three-digit number?

The following is an elementary-level Math Kangaroo multiple choice question: What is the maximum value of the sum of the digits of the sum of the digits of a three-digit number? A. 9 B. 10 C. 11 D....
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 ...
2 votes
6 answers
656 views

Why is calculus important for pre-service Math basic school teachers?

Why should pre-service math basic school teachers take calculus courses? Should this course be different from calculus courses offered to engineering?
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 ...
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 ...
8 votes
3 answers
637 views

Is there a numerical base that is in any way “better” for simple mathematical calculations than others?

I want to know if there are any numerical bases that are notably well-suited for humans to learn and use at an elementary or grade-school level. I know that different numerical bases (i.e. decimal/...
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?
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 ...
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 ...
-2 votes
1 answer
335 views

math syllabus US education system 1-12th Grade

Please share links to websites / pdf files containing syllabus in subject mathematics in US education system Grades 1-12. Thank you.
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 ...
3 votes
2 answers
991 views

Is there an arithmetic book similar to “Teach Your Child to Read in 100 Easy Lessons” by Siegfried Engelmann?

I have found Engelmann’s book (mentioned in subject) to be extremely effective. Is there an equivalent to this book for teaching Arithmetic? I believe the overall approach or method is called Direct ...
4 votes
6 answers
634 views

Is there an agreed upon difference between how we represent $\frac{a}{b}$ and $a \cdot \frac{1}{b}$?

When teaching addition and multiplication of fractions, I seem to recall some advice on this site that one should first treat the cases $a \cdot \frac{c}{d}$ and $a + \frac{c}{d}$ before moving on to ...
1 vote
2 answers
389 views

What is the MOST efficient paper/mental multiplication algorithm for integers?

What is the most efficient (fastest) multiplication strategy that can be done mentally or with a pencil/paper? We can include strategies that use interesting tools like Napiers Bones or Soroban math. ...
3 votes
5 answers
915 views

How do I teach the difference between Linear Equations and Equation of a Line

I am more of an Intuitive Learner and Teacher so while looking at Linear Equations chapter I see that they are teaching Equations of Line there, which in my opinion is wrong. See How I understand it ...
19 votes
16 answers
37k 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 ...
0 votes
6 answers
888 views

Finding an analogy to explain the function of a binary adder

I want to find an intuitive analogy to explain how binary addition (more precise: an adder circuit in a computer) works. The point here is to explain the abstract process of adding something by ...
5 votes
0 answers
333 views

Word problems written in past tense, present tense, or future tense

Does anyone have extensive classroom experience regarding the best verb tense to use when writing word problems at an elementary or middle school level? I have been writing some lessons recently and I ...
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 ...
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 ...
1 vote
2 answers
782 views

Pro's and cons of number line model vs color counter model

Pro's and cons of number line model vs color counter model When teaching multiplication to elementary schoolers, the "number line model" and "color counter model" are both widely ...
6 votes
7 answers
1k views

Are these fraction problems different enough to warrant individual consideration?

Consider the following problems: A) You have 20 problems for your math homework this week, and you want to do 1/5 of them today. How many problems do you need to do today? B) You need to read a 20 ...