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Questions tagged [reference-request]

A reference request is a request to be provided with (links to) documentation, official papers, and specs related to one or more specific algorithms or mathematical procedures, to provide a trusted base for what's being said or written.

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76 views
+50

Flow diagrams and summarizing strategies in proof-computation courses: good or bad for learning? Unsuitable for Inquiry-based learning?

For concreteness lets keep our discussion to calculus courses where there is a balance of proof and computations (computing limits but also doing epsilon-delta proofs) I can understand that in more ...
3
votes
1answer
118 views

Books similar to “Teaching Developmentally”, but for high school math

I've been extremely excited by my reading of the book Elementary and Middle School Mathematics: Teaching Developmentally by Johan A. Van de Walle et al. Does anyone know of similar books (or other ...
7
votes
8answers
2k views

What is an intercept?

I have always taught my students that the $y$-intercept of a line is the $y$-coordinate of the point of intersection of a line with the $y$-axis, that is, for the line given by the equation $y=mx+y_0$,...
2
votes
0answers
58 views

Reference for study about good teachers in a US state

Several years ago I have read about a study in a US state where standard test scores were used to identify teachers whose students consistently improved far above the average and then film and analyse ...
5
votes
1answer
89 views

Tables of primitives with indication of solution method

I am looking for an extensive source (often called "table of integrals") listing primitives of various classes of functions including the "elementary" ones (rational functions, functions involving ...
9
votes
0answers
98 views

Recommend a vector calculus textbook/resource with an algebraic geometry flavor

Is there a resource or textbook that presents the basics of vector calculus, specifically the gradient, directional derivatives, curves and surfaces, and extrema, from a more algebraic geometry ...
5
votes
0answers
128 views

Textbooks explicitly showing the injections for the sum of sets

Asking for methods to produce the sum of natural numbers from the disjoint union of sets, it seems that the obvious way is to use the general definition, as coproduct, of the sum of sets. The accepted ...
3
votes
1answer
201 views

Are kindergartners supposed to be steered from squares being rectangles?

Question 1: What are the literature, status, debates, references, etc regarding this matter please? Apparently, some (woohoo weasel words!) consider that squares are rectangles too advanced a topic ...
8
votes
3answers
160 views

Resources on solving systems of polynomial equations in multivariable calculus setting

Whenever I teach multivariable calculus I find students really struggle with both finding critical points and the method of Lagrange multipliers. I think that the reason is the same: solving systems ...
14
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4answers
270 views

Why is polynomial factorization over the integers part of secondary school curricula?

By "polynomial factorization over the integers", I mean problems and solutions like the following: Problem: Find a factorization into irreducible polynomials for $24x^2 +x - 10$ and ...
2
votes
0answers
89 views

Which book to use concurrently with each of these mathematics texts?

I'm in search of a good book that I can read --- and recommend to my proteges to read --- along with each one of the following books. Topology by James R. Munkres, 2nd edition Introductory ...
13
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4answers
255 views

Pedagogical advice/articles for graduate student teaching assistants

Are there any good pedagogical resources or articles that you would recommend to math graduate student teaching assistants (TAs)? Is there any sweeping advice that you would give a TA to improve their ...
2
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0answers
83 views

Is there a mark scheme for math essays or research papers? [closed]

It is rather difficult for students to write an essay in mathematics because they are not clear about the requirements. It is also very hard to mark the essays. A mark scheme makes both writing and ...
6
votes
0answers
140 views

Adding one to numbers bigger than ten

If someone asks you Tell me the next number (add one) after the number one million two hundred thirty-one thousand ninety-nine, do you known if it is a common error that the first number that ...
-1
votes
3answers
140 views

Which book has functions and their respective graphs? [closed]

I am looking for a book, which has different many different types of functions and their graphs (like, Weierstrass function, Takagi function).
4
votes
0answers
104 views

Are there any high school level summer program that teaches Analysis?

All summer programs I know for highschool students focuses on number theory, combinatory, graph theory, logic, and all kinds of stuffs in discrete mathematics. (I am mainly interested in UK, US, ...
9
votes
1answer
122 views

Experimental results about the variability of grades on a math exam

"[Myth] that exams are objectively graded. Daniel Stark and Edward Elliot sent two English essays to 200 high school teachers for grading. They got back 142 grades. For one paper, the grades ranged ...
4
votes
1answer
101 views

Is there a class curriculum that studies the work of a mathematician?

Are there classes dedicated to understanding the work of a particular mathematician? I have seen courses dedicated to a theorem (I saw for example one that sought to prove and understand the Atiyah-...
12
votes
3answers
144 views

Tasks that encourage argumentation

I am looking for resources that have tasks such as the one below that encourage argumentation. I want tasks that 8th graders could do but would also be appropriate for high school students. I want to ...
10
votes
0answers
200 views

What is known about discrimination and difficulty in test questions?

I am interested in looking at any design resources or "guiding principles" on the distribution of different types of question difficulties on evaluative examinations. We can use Item Response Theory ...
5
votes
2answers
135 views

Material on tutoring university level math classes

Can anyone recommend online or printed sources on anything related to teaching university level math tutorials (that accompany a lecture course taught by someone more senior, but I'd also be happy ...
11
votes
1answer
130 views

Where can I find primary sources from the New Math movement in the 60s?

I'm interested in learning about the New Math movement from a historical perspective. I've located some secondary sources about the topic, mainly parodies, highly critical restrospective articles, or ...
2
votes
1answer
111 views

Reference or term for connected sage-on-the-stage?

I heard that there is evidence that a "connected sage-on-the-stage" teaching style is at least as effective as guide-on-the-side / flipped classrooms. I have been unable to find significant references ...
3
votes
0answers
62 views

Research on how to teach math to children - what proven approaches are there to teaching math effectively? [closed]

I posted a related question on the Math.SE, but was directed here where I'm asking an similar but different question. I've been tasked with helping to redesign a math curriculum for an enrichment ...
2
votes
0answers
191 views

Introduction of the power set as a collection of *labels* or *names* for subsets

The way that naïve set theory is usually presented in undergraduate education is via very concrete examples of sets, often involving non-mathematical elements. When power sets are treated, having a ...
7
votes
0answers
66 views

Resources for high school teachers about APOS theory

As far as I can find, the major resources available to the layteacher about APOS (Action, Process, Object, Schema) theory refer to "undergraduate" concepts such as group theory and vector spaces (such ...
8
votes
3answers
655 views

What did math educators think about the transition to widespread classroom use of calculators?

When we have discussions about which technology to include in our classrooms today, we are often somewhat conflicted with many standard arguments and worries being presented on both sides. To help ...
10
votes
4answers
580 views

Is Calculus Necessary?

That title is a quote from Fred Roberts: Fred Roberts. "Is Calculus Necessary?" Proceedings of the Fourth International Congress on Mathematical Education. 1980. p.52ff. "Calculus is not ...
3
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0answers
120 views

Quantifying arthmetical skill

Question for a research project: What is the standard way of quantifying a student's skill in arithmetic ranging from having to look up numbers on a times-table to computing large sums in their head ...
8
votes
0answers
80 views

Studies into the effects of having fewer classes per term

Have there been any studies done into the effect of having fewer classes per term on a student's comprehension of their mathematics course material? Also are there any examples of schools that have ...
9
votes
5answers
384 views

Math for Social justice curriculum

Recently, a friend of mine who plans to work as a "social-impact consultant" (she is currently a College senior with a background in intro statistics) requested that I offer some kind of curriculum ...
6
votes
2answers
169 views

Need scientific source to prove the difference between arithmetics/calculus and real mathematical skills

For research about cognitive information retention, I'm trying to find a scientific reference where they explain the difference between the capability to apply real mathematical skills (entailing ...
6
votes
3answers
309 views

Apply the inverse operation on both sides, or know the inverse function?

My old question here was about logarithms, but as I teach more and more (precalculus) algebra, I've generalized the question a bit in my mind. Should students do the same thing to both sides, or ...
10
votes
2answers
193 views

Styles of visualization in geometry

Some people talk about visual thinkers and non-visual thinkers, but I am interested in a contrast within styles of visual thinking. There are people who readily visualize complicated flow charts and ...
10
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0answers
87 views

Literature on student understanding of assumptions

In a discussion with a physics lecturer he mentioned that one major area where students fail is understanding assumptions - for example, if we are interested in two objects hitting each other and then ...
10
votes
2answers
419 views

“Good” and “Bad” student intuitions when teaching and learning mathematics

I'm a college math/science tutor and I'm really interested in STEM education. I'm currently starting work on a project I hope to present in a couple of months at a tutoring conference and I was ...
17
votes
2answers
496 views

Should we “program” calculus students, like the physicists seem to want us to?

If it is true that we first learn formalism...how to do things that we don't understand, should we regard teaching students mathematics as programming dumb machines with formal rules (to the greatest ...
2
votes
1answer
46 views

GRE Geometry Reference Request?

My brother is taking the normal GRE (not the math subject test), and I need to help him learn geometry. I know basic geometry myself, but I need a book that will present it well and will have good ...
4
votes
1answer
64 views

Research on the effects of simulation and interactive visualization

Are there any existing research on the effectiveness of computer simulation and/or interactive visualization for the learning of mathematical concepts? I ask because: There has been some efforts in ...
19
votes
2answers
383 views

Separating the roles of “teacher” and “assessor”

Teachers at the university level (at least what I've seen in the US) are responsible for both teaching students the material for a course, and assessing the students' understanding of the course ...
13
votes
3answers
656 views

Does the “how old is the shepherd” phenomenon occur for more relatable word problems?

A friend of mine just showed me this article about the "how old is the shepherd" problem: Link Of course, I'm shocked by the finding that 75 percent of kids give an answer other than "there isn't ...
6
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0answers
77 views

References for persistence of grades [closed]

I've recently been challenged on my proposal that a reasonable way to estimate a student's future GPA is to look at his/her current GPA. I am looking for any papers that study the correlation of ...
8
votes
2answers
136 views

Journals that feature challenge problems for high school students?

I'm interested in journals that present challenging problems for high school students and take answer submissions. I coach some talented high school students and would like to encourage them to ...
6
votes
0answers
44 views

Effectiveness of audio / video feedback

Hattie & Timperley (2007) mention a meta-analysis about video or audio feedback with a mean effective size of .64 (Table 2 on page 84). They state that this analysis was part of the meta-analysis ...
5
votes
0answers
156 views

Catalog of undergraduate's misconceptions / problems while proving

Selden & Selden (2011) listed 41 difficulties their students had in an experimental proving course into 9 categories. Unfortunately I haven't found similar work. Thus, my question is: Is there ...
10
votes
4answers
494 views

Is there any advantage of plotting graphs using traditional paper and pencil method?

Why don't we discard the traditional pencil and paper method of graph plotting in high schools and for freshers at colleges since there are many electronic devices doing the graphing? And please where ...
21
votes
2answers
2k views

Gender and groupwork

What does current evidence suggest: doing group work in mixed/balanced gender groups or doing group work in single gender groups? Setting College level mathematics/science course Group size ...
11
votes
2answers
242 views

Importance of exercises for learning mathematics

For me it seem to be obvious that exercises and exercise courses are important for undergraduates to learn mathematics and skills like finding a proof or writing it down. Was there any research ...
7
votes
1answer
149 views

Native language, writing, and mathematical problem solving

This question is meant to explore the intuition that mathematical thought does not most naturally proceed from writing in one's native language. The hackneyed and not entirely satisfying slogan that ...
4
votes
1answer
99 views

References on the effectiveness of manipulatives (virtual vs. physical) [duplicate]

I am in need to find references for my thesis proposal. My topic is "Virtual manipulative versus physical manipulative: which way do students learn faster?". Do you know any authors that worked on ...