# All Questions

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15 views

### Is there such thing as a 1 kg "decimeter cube?"

Base 10 sets are readily available from educational suppliers and retail sites, as are the largest element in these sets, sometimes known as "decimeter cubes" (10 x 10 x 10 cm). The "...
46 views

### More advanced (free) alternatives to Geogebra and Math3D?

I teach vector calculus. I love both Math3D and Geogebra. But I have reached a limit in terms of what these programs can do. Some examples of features that I wish Math3D had: Draw vector fields with ...
158 views

I have a new math pupil. She is an emotional 12 year old girl who starts to cry when she doesn't understand something. Her father said she is sensitive. I was asked to do more praising and encouraging ...
72 views

### What are differences and the examples of syntactic knowlede and substantive knowledge in mathematics?

There is a distinction between substantive and syntactic knowledge particularly in mathematics. There are several definitions for both knowledge. However, what are the indicators and the examples of ...
81 views

### Are ‘constant difference’ and ‘common difference’ synonymous?

I’ve seen at least two phrases to describe a fixed difference between two numbers, i.e., “constant difference” and “common difference.” For example, if Sibling A is 10 years older than Sibling B today,...
494 views

To prove, e.g., the identity $(a^2+b^2)(c^2+d^2)=(ac-bd)^2+(ad+bc)^2$, I remembered working, in high school, in the following way. Expanding the LHS gives (a^2+b^2)(c^2+d^2)=a^2c^2+a^...
3k views

### Why is there a disconnect in the usage of "domain" between high school and higher mathematics, and where does it come from?

In high school (in the US, at least), it is common to define the domain of a function as the set of real numbers for which the function is well-defined and returns a real result. Then students are ...
154 views

### How do I get started as an online math tutor?

I have a master in math, teaching experience as a graduate student, TA experience and tons of in-person tutoring. I feel like a pretty prime candidate to be an online tutor. Can anyone give me some ...
55 views

### Where can I find the solutions manual to Beginning Statistics with Data Analysis by Mosteller, Fienberg and Rourke?

I am planning to teach a course on Statistics using Beginning Statistics with Data Analysis by Mosteller, Fienberg and Rourke. On page xii of the book, the authors said "A solutions manual is ...
6k views

### How should I teach logarithms to high school students?

I have some very basic questions about how to teach the logarithm to high school students: First of all, is it better to introduce it as a function with a graph or is it better to treat it like a ...
56 views

### Search for educational articles

I am looking for articles in French preferably (or in English otherwise, but my english is bad..) on the following topics: study of assessments made in class after a problem; phase of conclusion of a ...
273 views
+100

### How to balance between teaching to the standardized test vs understanding?

For people teaching high school standardized curriculums such as AP, IB, or A-Levels, how do you find the balance between preparing students for the standardized test compared to ensuring they ...
109 views

### Line segments on a geoboard

To make a polygon on a traditional geoboard, one usually stretches a rubber band around the vertices. No problem there. When making a simple line segment, however, a rubber band is typically stretched ...
197 views

### Average Cost to Velocity Analogy

In my Business Calculus class (U.S. college-level), we discuss three aspects of cost: Total Cost $C(q)$, Marginal Cost $MC(q)$, and Average Cost $A(q)$ where $q$ is quantity produced. The defining ...
216 views

### Is Stewart Calculus a good book for AP calculus exam prep?

I have some background from completing Silvanus Thompson's book, but I didn't fully grasp the later chapters in it. I'm going to use khan academy and maybe other resources as a supplement. How useful ...
118 views

### Teaching Solving Linear Equations before teaching evaluating expressions

Traditionally, I have always taught evaluating expressions before teaching linear equations. But, I was recently given a remedial class of students that have to cover the bare minimums (and we have ...
540 views

### Simple combinatorics problems using division

I would like to introduce counting principles associated with each of the 4 basic operations (addition, subtraction, multiplication, and division) before introducing permutations and combinations in ...
163 views

### Rational Powers of Negative Numbers on Basic Calculators

Context: I teach at a small liberal arts school in the US. The students of interest in this question are generally in their first year. In courses like precalculus and calculus I like to use ...
8k views

### Student asked me if it is necessary to simplify fractions at the end of answering a question. I'm not sure how to respond

I was just tutoring someone and we went through some sort of diagnostic test thing, when the following question came up. Question: Here is some information about $50$ people who took the driving test:...
123 views

### Solved , open problems and levels of difficulty

What are the advantages and wins of solving already solved problems? Does it help me know how to become better at problem solving and test my abilities on it? Does it help me become better and have ...
179 views

### How to Effectively Implement a "Notice and Wonder" Activity?

I am a first-year Pre-Calculus teacher at a public high school in the United States. The curriculum I am using often contains "Notice and Wonder" activities whenever a new concept is about ...
75 views

### Quiz in locked mode without managed Chromebooks?

Google Forms enables locked mode (where students cannot move to other tabs or apps without submitting the form) only if students use certain laptops called Chromebooks. I'm looking for any platform to ...
281 views

### Effective Strategies for Helping Students Recognize Nonsensical Expressions? (HS - Undergrad Level)

I'm not entirely how best to pose this question, so that it fits within the guidelines (so edits / suggestions for modification are warmly welcome). I'm interested in exploring effective strategies ...
8k views

### Combative students in proofs classes

When teaching my first discrete math class recently, I found a subset of about 5 out of 35 of my primarily computer science students who I struggled to reach. If these students simply struggled with ...
85 views

### What is Algebra 1 "Number and quantity; Interpreting Data"?

My sister received her scores for "End-of-Course Examination Program" test results. There is a section "Algebra 1" and underneath a table with rows: Algebra Functions Numbers and ...
148 views

### To what degree can the legally blind, with computer induced medical problems, study statistics?

My son graduates from secondary school in 2022. But he shall attend university in Australia or UK — where you must apply for ONE major — not liberal arts in the USA. He wants to pick BSc Math with ...
418 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 ...
107 views

### Number of students taking a particular course per year

I'm wondering, where can I find the following information: How many students take a particular course (like "Calculus", "Linear Algebra", etc.) in a particular year (2010, 2011, ...
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 ...
2k views

### Teaching Math for Elementary Teachers

What would you guys say the requirements for teaching "Math for Elementary Teachers" should be? Is this generally agree'd upon? Would you recommend it be taught by somebody who has a ...
4k views

### Why the fear of polynomial long division?

Why do people think long division of polynomials is complicated ? I heard this expressed recently and it seems like an odd sentiment. For me, synthetic division is complicated and totally adhoc ...
232 views

### Distance from the wall when reading a sign? A Calc I/II problem

Here is a question on a test I asked recently in a Calculus I class I teach on Saturdays. These are students who are planning to major in Math, and they are already taking AP Calculus BC in their high ...
100 views

### Which function is more elementary: Constant function or identity function? [closed]

I am not a mathematics teacher, I just want to know which function is more elementary and is more reasonable to be learnt first: Constant function (f(x)=1) ...
150 views

### Which context of the two contexts of the linear function concept should be taught first?

It appears in the current version of the Wikipedian article Linear function: In mathematics, the term linear function refers to two distinct but related notions:1 In calculus and related areas, a ...
257 views

### is it beneficial to encourage high school students to conduct their own 'research' in mathematics?

Is it good idea to encourage students to look up more about particular topics that interest them? The idea is that I don't think they will understand how to read math literature. for example, if a ...
576 views

### Write calculus multiple choice questions with only numerical answer choices?

What are the best type of answer choices for multiple choice questions? Numerical only like the probability and financial math actuarial exams? I have an opportunity to utilize a multiple choice ...
338 views

### Solving math problems and learning

Should i solve math problems by writing the answers to papers or notebooks with pencils or should i try solving them in my head at undergraduate studies at university? Also, sometimes after learning ...
286 views

### Is it possible to understand decimals without understanding fractions?

It is common for students to come unstuck by there inability to manipulate fractions (eg calculating gradients, algebraic fractions, etc) yet these same students can handle decimal numbers competently....
853 views

### Is there a blog platform that renders LaTeX well? [closed]

I've been using wordpress.com, but it renders LaTeX terribly! There must be a blogging platform that does a good job of this. Can someone recommend one?
167 views

### How to explain the difference between a constant function and a linear function?

Both function types contain a straight line on a plane, so if a student asks for the difference between them what would be a standard or recommended way to explain it?
172 views

### What is the most fundamental continuous function in calculus after a constant (totally straight) line?

What would be to teach in most countries and education systems? (Taught before "high education frames", i.e. before doing bachelor of arts in mathematics).
1k views

### Where can I find public repositories of past math exams?

I'm looking for public repositories/banks of past undergraduate math exams. No solutions necessary. I just want inspiration for writing my own exams and practice exams. It'd be nice to collect links ...
205 views

### How can I encourage students to show up for exercise classes?

I am doing a maths PhD and naturally that involves leading exercise classes for undergraduate students. The idea is that the students just show up and work through the problem set and I'm there to ...
214 views

### How to train facility with numbers?

I have a student (age 14) who is valiantly striving to improve his algebra. He knows the "rules", and he more-or-less manages to apply them correctly, and hence is generally able to tackle ...
83 views

### How to make progress as an independent student?

In recent times, I have been studying mathematics (topics related to mathematical logic, more specifically) independently and I feel a great deal of passion about it. However, although I have made ...
210 views

I am a high school student really into algebra and algebraic geometry. I want to expose this sort of math to other high school students that have the motivation and ability. For a long time, I had no ...
346 views

### Where can I buy a compass that can hold an "Expo" dry erase whiteboard marker?

Question in title. I'd like to draw a perfect circle on the whiteboard using "expo" dry erase markers. Is there a store I could buy such a compass at? Thank you
3k views

### I want a "true" proof by contradiction of an implication P => Q

When teaching proofs by contradiction of an implication P => Q, one starts by assuming both P and (not Q), and then reaches a contradiction. The problem is, most elementary proofs of this type are &...
This is an example of the AC Method: $x^2 + 16x +63$ (1) $x² + 7x$ (2) $9x + 63$ (1) $x(x + 7)$ (2) $9(x + 7)$ so we have: $x(x + 7)+ 9(x + 7)$ (1) with (2) The Result is: $(x+9)(x+7)$ I have more ...