# All Questions

2,344 questions
11 views

### Modula Arithmetic

Three friends Kingsley, Kelvin and Karen take in turns to visit their farms on Mondays to Fridays. It is not allowed to visit the farms on Fridays and Saturdays. Kingsley, the leader of the group was ...
61 views

### Teaching three-year-old subtraction using the number line

I am aware of questions such as this one. On the other hand, I still believe that teaching a bright three year old subtraction is possible. He counts from $0$ to $100$ and backwards from $10$ to $-10$,...
37 views

### Difficulty in teaching the coordinates of a vector with respect to a basis $\{v_1,v_2,\ldots,v_n\}$

Let $V$ be a finite dimensional vector space and let $B=\{v_1,v_2,\cdots,v_n\}$ be a basis of $V$. If a vector $v$ can be written as $$v=a_1v_1+a_2v_2+\cdots+a_nv_n,$$ we call $(a_1,a_2,\cdots,a_n)$...
92 views

### Good textbooks for a college Basic Geometry course?

I will be teaching geometry for the first time ever this summer. I teach at a community college, and we only offer this course in the summer. (Mostly high school students take it, but it is a college ...
53 views

### Studies about group tutoring sessions

I’m not sure if this question belongs here, so I apologize if it doesn’t. I work in a tutoring center at my university where we tutor every subject. Mathematics is in high demand, and occasionally my ...
212 views

### How does knowing more about mathematics help one's teaching of lower level course, such as calculus?

A question has been asked about why great mathematicians are not necessarily great teachers. On the other hand, I am wondering if knowing more mathematics actually helps with one's teaching of lower ...
78 views

### Mathematics acts as a filter to higher education [on hold]

I need to comment on this topic. I think it indirectly asks about the importance of Mathematics in higher education. Am I correct ? Kindly provide the desired arguments. Thanks& regards
37 views

### Time for a mass-spring system to retract [on hold]

Let's suppose that i have the following mass-spring system: My question is: If I start from the deformed state, how much time does it need to go back to its initial position ? What I tried: ...
167 views

Throughout my geometry course, I was given many theorems and postulates, which I was were expected to memorize and apply. At the time, I sorta went along with it, but I couldn’t help but wonder where ...
15k views

### The concept of infinity for a 5 year old

My son, who just turned 5, has been interested in the concept of infinity since long. He asks me a lot of questions regarding infinity. For example, not accepting my infinity + any number = infinity, ...
56 views

### Possible Educational Outcomes of “Riemann Hypothesis” [closed]

I know the consequences of Riemann Hypothesis which are used in Number theory and Analysis. But I want to know what could possibly be the Educational Outcomes of Riemann Hypothesis, if it is ...
207 views

### A question from a young student to mathematicians

I'm a young math student. And I live with the effort of always wanting to understand everything I study, in mathematics. This means that for every thing I face I must always understand every single ...
89 views

### Activities for calc based physics

I was sort of thrown into teaching calculus based physics to a bunch of non-physics majors, who have taken one semester of calculus, and are poor with that material. It is only a 50 minute per week ...
183 views

### Would teaching nonstandard calculus in an introduction calculus course make it easier to learn?

Nonstandard calculus is a reformulation of calculus that is based on infinitesimals instead of epsilon-delta definitions. Of course, people had tried to use infinitesimals in calculus before; in fact, ...
5k views

### How to deal with a “protest” assignment?

I just received one assignment (by email) from a student. Out of 6 questions, "I don't know" is the answer to 4 of them. There is also a comment at the end of the assignment which suggests my ...
130 views

### Calculus workbook suggestions

Context: I am an assistant professor of mathematics at a small institution in the US. Our department uses Stewart's Essential Calculus for our calculus sequence, but I find that my students and I are ...
52 views

### Is there a point at which it makes decidedly more sense to learn about a “linear approximation” to a function, rather than a “tangent”?

I'm tutoring a first-semester calculus student, and we were looking over the slides the teacher has used. After teaching (or rather, repeating, for those who completed AP high school math) basic ...
112 views

### Analogy for nested loops/integrals

In teaching students how to do iterated integrals, I would like to find some analogy using a finite task nested inside another finite task. It would be especially nice if it satisfied the following ...
71 views

### PGCE University College of London Institute of education vs Kings College London [closed]

I have received an offer to study PGCE secondary mathematics at both UCL institute of education and King's college London. I would like to know which is more reputed particularly in the context of ...
213 views

### Book recommendations on mathematics education focusing on geometry

I will be teaching Euclidean geometry to future teachers, and I am feeling a bit lost (I know geometry, but I am not that familiar with mathematics education). Is there some recent (as concise as ...
179 views

Most problems require the student to simplify the final answer and in many context the meaning is obvious: For example, $3/9$ should be simplified to $1/3$ and $\sqrt{16}$ should be simplified to $4$. ...
464 views

### Is it a problem if a senior student majoring in mathematics could not prove the quadratic formula?

According to a recent experiment conducted by user Steven Gubkin, nearly one half of his students in a senior level Real Analysis course do not have any idea how to prove the quadratic formula. Is ...
131 views

### What is a good format of tutorial sessions?

At my university, traditionally a few lectures of a course should be tutorial sessions. The idea is that instead of covering new materials, the teacher should go over many exercises so that student ...
232 views

### Which examples should we mention when teaching the concept of derivatives?

I am teaching Calculus for non-maths major students. As far as I know, when we teach about derivatives, we should mention "the rate of change". There are some practical examples to motivate this ...
2k views

### Is Linear Algebra Done Right too much for a beginner?

I have asked in Mathematics stackexchange, but I think asking here is more appropriate. I am self studying the book Linear Algebra Done Right. That's how I started using the great Stack Exchange in ...
119 views

### According to Nathan Jacobson, what is Intermediate Algebra and Advanced Algebra?

Nathan Jacobson's Basic Algebra I, II covers many topics in Algebra that is probably even beyond many pure mathematics full professor's scope of knowledge, unless the professor is specialised in ...
105 views

### Published papers for Intro Stat students to read

I am looking for studies and experiments in the literature that I can share with undergraduate students in an intro statistics course. I do not expect students to understand everything, and I plan to ...
412 views

### How to balance the difficulty level and speed of lectures for students of very different levels?

I noticed that in my undergraduate class a few students understand things quite fast and some times see the proof before I even explain things. But some of them also have trouble understanding quite ...
186 views

### How to prepare for lecturing in a non-fluent foreign language?

I am giving some lectures on a calculus course in Norwegian. My Norwegian (or, rather, Scandinavic) is good enough to do so mostly without resorting to English, but I would, of course, like to improve....
117 views

### How to explain linear approximation to an equation to calculus students?

I am, at the moment, teaching calculus to students whose majors are, for example, biology, biochemistry, chemistry and geology. The course book is Claudia Neuhauser's "Calculus for biology and ...
155 views

### Favorite datasets to use when teaching statistics

There are so many datasets available that it seems difficult to sort through them all and identify the best ones to use when teaching an introduction to statistics class. What are your favorite ...
60 views

### Practical Implication for Correlation (Lay individual vs Scholarly Group)

Can you please explain or provide resources that explain this issue (esp. to a lay audience): How to understand the significance of a co-relation number that studies (esp. meta-analyses) produce. The ...
99 views

### Is there any alignment on what a maths grad should know?

This more specific question relates to a more general question of what is a maths degree aiming for. Do any universities define a high level goal for pure mathematics degrees at all? If so, are there ...
2k views

### Are students majoring in pure mathematics expected to know classical results in mathematics very well by their graduation?

For example, I am confident that very few students majoring in pure mathematics can write a complete proof to the Abel–Ruffini theorem (there is no algebraic solution to general polynomial equations ...
150 views

### Vector calculus texts that are free-as-in-speech?

I'm looking around for a text that covers vector calculus and multivariable calculus, and that is also "free as in speech," not just "free as in beer." In other words, I'm looking for texts that are ...
105 views

### What effect does giving numerical or written grades have on learning?

When I was in school, pupils were given numerical grades, or the equivalent of numerical grades but disguised as words, on their performance in various school subjects and also behaviour. A key ...
102 views

### Easy examples of visualizing passive transformations in the plane?

I teach mostly physics and a little math at a community college in California. When I teach special relativity, my preferred pedagogy is to describe the Lorentz transformation using an almost purely ...
116 views

The title is self-explanatory, but what is the appropriate response to "motivate your answer"? Should you prove your answer? Should you just explain it, or give the intuition for it? For example, ...
99 views

### Mathematics Research at Secondary Level (High school Level)

I am a future teacher and am interested in incorporating a mathematics research unit where my students do their own research on an unsolved problem. I have a couple ideas on problems, but am ...
68 views

### Tactile Learning Activities in Mathematics

Julie Barnes, Jessica M. Libertini. Tactile Learning Activities in Mathematics: A Recipe Book for the Undergraduate Classroom. 2018. MAA Press. AMS Bookstore link. Can anyone comment / review ...
366 views

### Should theorems be proved to students who are not majoring in mathematics?

My impression to students majoring in mathematics is, whenever we teach them a theorem, a proof should be given in the class, or at least as a reading assignment. However, how about students not ...
204 views

### Could students learn a lot more from school if they're only taught number theory until way later?

According to https://www.inc.com/bill-murphy-jr/science-says-were-sending-our-kids-to-school-much-too-early-and-that-can-hurt-th.html, when students get taught a concept when they're so young, they're ...
451 views

### Are there any negative consequences in applying operations/functions to a whole equality?

Some of my students solve equations not by applying the same operations on the left and right sides of an equation, but by applying the operation to the whole equality. For example, they may write ...
61 views

### Long-form, multi-step, skills-integrating applied mathematics problems in calculus I, II, III

When recently teaching Calculus II to college students, I instructed my students to read and be ready to work through the first 8 or so questions of James Walsh's climate modeling differential ...
145 views

### Viewing arithmetical operations as processes-possibly wrong and detrimental to long term math performance of the students [duplicate]

I think that the standard practice in the first grades when addition (or other operation) is taught as a "process" may be not so good. I always wondered why so many children lose interest in math ...
95 views

### How can I measure the mathematical computation skills of high school students through a test?

How to analyze the level of difficulty of mathematical computation of a problem on a standard mathematical test designed for high school students? I mean how to choose some indices that can reflect ...
281 views

### How to deal with students who object to me teaching material that won't be in the exam?

I sometimes encounter students who ask questions like 'Why are we learning this if it won't be on the exam?' If there is time to spare I like to teach interesting applications or natural extensions of ...
88 views

### Desmos Assignment: Make a graph that does this

I am interested in collecting/creating a compendium of lesson plans that are essentially just this. Lesson Plan: Appropriate for a precalc class and an algebra 2 course. Show the following graph: ...
316 views

### Is $180^\circ = \pi$?

I want to ask a question that causes confusion. In the trigonometry, we use some units of measure of angle: degree and radian. Which is/are correct? $$180^{\circ} = \pi$$ or  180^{\circ} = \pi \...
137 views

### How can I help a student who is constantly struggling in an honors Algebra II (high school) class

I am tutoring a student who is in an honors Algebra II class. The class is definitely advanced and the student hasn't been exposed to this kind of material. The teacher is going beyond algebra II and ...

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