Questions tagged [middle-school]
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29
questions
3
votes
2answers
178 views
The value of making students copy your derivations exactly
I have a hypothesis that I have not yet implemented, and am seeking guidance before I do. I have always taught algebra (and above) in such a way that the students understand the derivations. I check ...
3
votes
2answers
190 views
Teaching words with multiple meanings in Mathematics and English
We want to teach about words that have multiple meanings, in mathematics and
English for middle school children (e.g., function, root, or, volume, angle, constant). This is for students who are ...
21
votes
9answers
4k views
Why do we introduce the notion that triangles are "congruent" instead of just saying that they are "the same" or "equal"?
The assumed age of the students is 10-15 years old.
What is the danger in saying that two triangles are "the same" or "equal" instead of saying that they are congruent? It seems to ...
7
votes
2answers
301 views
When working with 12-16 year olds, how should I graph functions when the domain technically isn't $\mathbb{R}$?
Let us assume that I want to graph any of the functions below.
A) A can of soda costs $\$1$. Draw a graph depicting the total cost as a function of the number of cans you buy.
Comment: One cannot ...
7
votes
7answers
4k views
What is the preferred way to denote the Pythagorean theorem equation?
I am teaching 12-16 year olds.
How should I write down the Pythagorean theorem equation?
Some alternatives:
$a^2 + b^2 = c^2$
$\text{leg}^2 + \text{leg}^2 = \text{hypotenuse}^2$
$\text{leg}_1^2 + \...
57
votes
15answers
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 ...
3
votes
2answers
245 views
Looking for a rigorous middle school self-study math course
My son is in 5th grade (US) and since he is doing remote learning, we have been doing a lot of topics in pre-algebra just using worksheets. I'd like to start him on a formal middle school curriculum, ...
1
vote
1answer
75 views
Resources for Unit Rates
I am currently mentoring my little brother in mathematics. There is an issue with the pedagogy of unit rates. For example when given the following concept " 11.00 U.S. Dollars to 20 Planet X ...
3
votes
1answer
148 views
Ramanujan results for middle school?
Pls I wonder what Ramanujan's results could be explained to middle school level audience, ie without using integral etc that is up to university curriculum?
For example Ramanujan's infinite radicals ...
1
vote
2answers
169 views
What are the resources to learn prerequisite knowledge to latter High school and undergrad prep textbooks?
I use textbook study and am planning on studying Spivak's Calculus, Mathematics It's Content, Methods, and Meaning, How to Prove it by Velleman, etc. However, I'm worried I lack the prerequisite ...
7
votes
2answers
524 views
Logic and proofs in secondary school
Inspired by the question When do college students learn rigorous proofs?, I became curious when pupils in secondary schools learn about proofs, what kinds of proofs they are, how rigorously they are ...
4
votes
2answers
138 views
Teaching Approach at primary, middle and higher level
I would like to have a comparison or a big picture of how and why the approach for teaching math varies from primary (or pre
primary) to middle to higher classes.
I understand at every level one ...
0
votes
2answers
137 views
I find high school math very hard compared to middle school? [closed]
i hope i can get some help on how to get better at high school maths i find them very difficult compared to middle school.
Whats the big difference so i can work on it ?
4
votes
5answers
340 views
Patterns that unexpectedly fall apart at large $n$
I am constructing a learning sequence for middle grade students designed to convince them that empirical arguments (arguments by example) are not sufficient in mathematics. To motivate this, I am ...
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 $\mathbb{Z}$ ...
17
votes
8answers
5k views
Prisoner's dilemma formulation for children
I am preparing an introductory course on Game Theory for children (between 10 and 17 years old). In the course description, I want to include a prisoner's dilemma in order to catch children's ...
-2
votes
4answers
319 views
Inefficient methods
I see many teachers use slow methods to solve a given problem where there's another faster methods that doesn't demand much more effort. I'm not looking for mistakes like saying that $a$ is the slope ...
3
votes
3answers
208 views
How to explain to pupils that "$\frac n{100}$ OF $a$" is equivalent to "$a$ TIMES $\frac{n}{100}$"?
How to explain to pupils that "$\frac n{100}$ OF $a$" is equivalent to "$\frac{n}{100}\times a$"?
There is some difficulty in explaining that the first sentence, containing "OF" (which could suggest ...
9
votes
4answers
3k views
Is the constant term a coefficient?
I'm a baby boomer who was taught that the constant term of a polynomial is a coefficient, being the constant factor for the x^0 term.
That's not what's taught today.
Current text books are vague on ...
7
votes
6answers
176 views
Simple Number Theory Task
I am doing exercises with middle grade students and looking at their capacities to create arguments for simple number theory conjectures. I want three tasks, and I have two so far: 1. The sum of three ...
5
votes
2answers
401 views
How to Teach Middle School Students to Read Square Roots?
This exact quote from my standard American Algebra 1 textbook states when first introducing rational square roots:
$\sqrt{49} = 7$ is read "The positive square root of $49$ equals $7$."
$-...
18
votes
10answers
3k views
How to Write Steps of Solving Equations?
This is a common way to write the steps during solving equations:
But in GeoGebra the steps are shown this way (the highlighted part):
I'm going to use GeoGebra to teach equations. Is it OK to let ...
8
votes
5answers
1k views
Exponents with Negative Base; with or without Parentheses
How can I convincingly and mathematically explain the reason behind difference between $(-1)^2$ and $-1^2$?
I used to add "negation" to the order of operations, in the same row as multiplication and ...
2
votes
4answers
284 views
Might it be helpful for students to have different symbols for subtraction (-) and negation ( _ )?
Might it be helpful for students to have two different symbols for subtraction (-) and negation ( _ )? Subtraction, after all is a binary operation (with 2 operands). Negation is a unary operation (...
3
votes
1answer
180 views
"Seeing" GCD and LCM in Word Problems
Last year, I taught GCD and LCM and then gave my students word problem relating to these concepts ("Two runners with given different speeds; when will they meet again?", "Having three kinds of flowers ...
6
votes
4answers
328 views
Am I too formal teaching this middle school student?
Solve for $x$ the equation below, writing the universe set and the solution set:
$$\frac{a}{b}+\frac{b}{a}-\bigg(\frac{a^2}{bx}+\frac{b^2}{ax}\bigg)=1$$
Let's choose $U=\{x\in \mathbb R;x\neq 0\}$ as ...
4
votes
1answer
310 views
how to prove my 6th grade son knows algebra 1?
My son is taking pre-algebra in 6th grade. He mastered algebra 1 in detail more than what school can teach. How to prove to school that he mastered Algebra 1? He wants to start Algebra 2 in 7th grade. ...
0
votes
1answer
147 views
Using Substitution in place of the balance model
How does substitution work as an alternative to the balance model in introducing solving equations? My biggest worry is that, lacking a concrete representation, is too abstract for middle schoolers. ...
8
votes
3answers
193 views
Mathematical Task with Various Solutions
I need to come up with a mathematical task for middle school (9th grade), which involves either algebra, functions, probability or statistics (anything but geometry actually). My problem is, that the ...
