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22 views

Measures to quantify complexity of algebra equation

Like the title says, I am looking for ways to measure the complexity of an algebra equation. For now, I am focused on linear equations, but I would think any metrics could be generalized for ...
2
votes
2answers
87 views

Is copying working and explanation plagiarism in this context?

In my institution I have a friend who is part of this Math ambassadors club where they write blog posts and share them online at medium.com. However, there is an issue with my friends post.After they ...
2
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0answers
62 views

For 15 year olds, are there exercises — with full solutions — on the Fence Post or Off by One error?

Which books contain practice questions — preferably with full solutions — to assist 15 year olds with the Fence Post or Off by One error? Most students at my institution have not heard of this name, ...
0
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0answers
95 views

Mental Health in Mathematics

I am not sure if my question is relative to this meta but I still want to put forth my thoughts and concerns and questions because I think its not just me but others too who have similar issues. My ...
0
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0answers
56 views

Problem solving approach to learning and psychology

I try to have a problem solving approach to learning math. What i mean by this is if someone sets some questions or problems regarding the material i am reading how should i answer or what questions ...
3
votes
2answers
150 views

How do you study subjects you're not that interested in

I'm an undergraduate who doesn't find analysis particularly interesting, but I'm taking a calculus on manifolds course next semester, so I'm reviewing measure and integration theory since my grasp on ...
2
votes
1answer
99 views

Why is my 8th grade Algebra 1 tutoring student learning mean absolute deviation and standard deviation?

I’m tutoring an 8th grade student in Algebra 1, and he showed me that their class learned how to find standard deviation and mean absolute deviation using the following formulas: $SD=\sqrt{\...
1
vote
1answer
141 views

Math outside of undergraduate studies and proofs

I read sometimes mathematical works of others outside my undergraduate studies. I think i can not follow the understanding of the proofs of theorems sometimes. What should i do? Should i read other ...
6
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2answers
3k views

Should proofs include a third “context” column?

Proofs, or any mathematical derivation, appearing in any real setting, such as a book or textbook or talk, or even when we're teaching it in class, includes a great deal of surrounding explanation. ...
9
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0answers
119 views

Should I upload slides before or after a class

I used to post my slides before a class. But I noticed that many students simply read it while in class instead of listening . So I am thinking not doing it in the future. But they can still get it ...
1
vote
1answer
111 views

Best books for mathematical statistics self-study?

I'm hoping to start a masters in mathematics in the fall, and am hoping to find a good book on mathematical statistics to study so that I'll be able to take graduate level mathematical statistics once ...
2
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4answers
184 views

How can 17 y.o. high school students intuit that P(n, r) stops at $n - (r - 1)$, not $n - r$?

Every year, some 17 y.o. student makes the mistake of stopping $P(n, r)$ at $\color{darkorange}{(n - r)}$, rather than $\color{forestgreen}{(n - (r - 1))}$. Because they are in their last year of high ...
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0answers
82 views

What books teach the formula for the # of k-permutations of n objects, with x types, and $r_1,⋯,r_x$ = the number of each type of object?

Some of my 16 year old students hanker after the formula for the # of k-permutations of n objects, with x types, where $r_1, ⋯, r_x$ = the number of each type of object. This is more generalized than ...
3
votes
4answers
976 views

How long would it take someone to master the topics in the book like Book of Proof by Hammack and similar?

If someone never had any experience with mathematical proofs and had only classes like Calc I-III (which he passed) without paying any attention to the proofs present in the textbooks, how long would ...
4
votes
2answers
189 views

Why has the chapter on second-order differential equations been moved to the website instead of being put in the book in Stewart Calculus 9th edition?

From the book The chapter on Second-Order Differential Equations, as well as the associated appendix section on complex numbers, has been moved to the website. It doesn't mention a reason in the ...
6
votes
1answer
200 views

How to convince a high school student that the $=$ symbol denotes identity?

In French language, arithmetic statements are often read, at the elementary school level, as , say, " deux et deux font quatre" , i.e. something like " two and two make four". Out ...
3
votes
1answer
87 views

Questions to help better understand the textbook

I am teaching a linear algebra class for math majors and non-majors out of the first 4 chapters of Lay's book. My plan is to have the students read a section prior to each class, have them answer a ...
5
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0answers
127 views

What do you think, is teaching on an actual board more efficient than using an online board?

I am a sophomore math undergraduate and so far all of my university courses have been online due to the pandemic. I am really curious what you guys think about the efficiency of teaching mathematics ...
13
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3answers
905 views

Is there a measurable learning goal related to understanding proofs of important theorems?

I believe that good math courses are structured around measurable learning goals. For example, "can correctly replace a line integral with an equal double integral using Green's Theorem" or &...
3
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0answers
154 views

Doctorate and examples of difficult solved problems

Okay. My questions are: How do some people do doctorates in mathematics and spend so much time like three to six years trying to answer one or two open problems? How do they have the patience, ...
1
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0answers
349 views

Is it more efficacious, productive to jump to perusing full solutions — before and without attempting to solve problems?

Too many students lack the luxuries of time and effort to mull exercises and problems. They must juggle MULTIPLE jobs to pay exorbitant tuition fees. Single parents or adult learners must prioritize ...
1
vote
1answer
168 views

Introducing direct substitution in an intro calculus course

I'm revisiting the materials I've put together for students taking a non-proof-based intro to calculus, and my goal is for them to have a clear but rough sense of a limit as a bound (basically enough ...
0
votes
3answers
251 views

How can I visualize differential equations and Integration in real life?

How can we understand differential equations and Integration in real life so that we can understand calculus easily. All we do here, at university level is memorize calculus and get the answer. We ...
0
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0answers
60 views

From primary school to higher mathematics all mathematical abstract concept summary

is there any books or articles for summary abstract concepts from primary school to higher mathematics? we know such as mathmatical operations ...
7
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8answers
2k views

Nice examples of limits to infinity in real life

I have to teach limits to infinity of real functions of one variable. I would like to start my course with a beautiful example, not simply a basic function like $1/x$. For instance, I thought of using ...
9
votes
14answers
8k views

Why's math way more puzzling, abstruse than law and medicine? [closed]

Most students find math unfathomable, labyrinthine by the time of univariate integration (Reddit). Even overachievers – who ace undergraduate math without studying – will eventually be convoluted by ...
9
votes
3answers
377 views

Explaining the intuition for why finding roots of polynomials is hard

I'm currently teaching a mini-seminar to high school students, most of whom have at most a background in Algebra/Algebra II (in the US high school system) about finding roots of polynomials. In ...
1
vote
1answer
189 views

Limit from both sides or from left? [closed]

Is it possible to write a problem statement as follows: A function $f$ is defined on $]0,1[$ as $f(x)=x$. Determine $\lim_{x\to 1}f(x)$. Or should one write always as: A function $f$ is defined on $]0,...
3
votes
2answers
226 views

Preparing to be a linear-algebra teacher: Any tips/suggestions?

I'm engineer and I love linear-algebra. I finished a couple of days the Linear-Algebra on OpenCourseMIT to refresh my memory and I have been doing ton of exercises. I would like to teach to engineer ...
0
votes
0answers
76 views

Code for Urn (containing colored balls) generator? [duplicate]

I am interested in code that generates an urn with various colored balls for an economics experiment. I came across this thread: Urn (containing colored balls) generator? However, the server that the ...
21
votes
10answers
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 ...
5
votes
2answers
228 views

What's the best ratio for algebra tiles?

A good model for algebra are Algebra Tiles. See: https://calculate.org.au/wp-content/uploads/sites/15/2019/03/lesson-sequence-for-algebra-tiles.pdf In this presentation they recommend an aspect ratio ...
1
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2answers
178 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
10answers
3k views

How do I explain the distributivity of multiplication to a student without using the analogy of areas?

I am tutoring a student who doesn't really understand how multiplication works or what distributivity is, I want to explain him how distributivity of multiplication over addition on an abstract level ...
2
votes
2answers
184 views

ELL textbooks for core university math?

Any references for core textbooks aimed at English language learners at the university level? I have need of them for: Calculus I-II-III, Linear Algebra, and Differential Equations. Most of my ...
9
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0answers
204 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 "...
4
votes
1answer
156 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 ...
6
votes
5answers
558 views

Advice on how to tutor a twelve year old that starts to cry?

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 ...
2
votes
0answers
110 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 ...
4
votes
1answer
97 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,...
4
votes
2answers
591 views

Questions about proofs

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 \begin{equation} (a^2+b^2)(c^2+d^2)=a^2c^2+a^...
17
votes
5answers
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 ...
1
vote
1answer
200 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 ...
2
votes
0answers
60 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 ...
18
votes
10answers
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 ...
2
votes
0answers
61 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 ...
15
votes
3answers
426 views

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 ...
3
votes
2answers
112 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 ...
4
votes
4answers
221 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 ...
2
votes
1answer
275 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 ...

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