16

Here's a silly example: Give students collections of the same type of thing, where each collection contains "good" objects and "bad" objects -- for example, a stack of Pokemon cards with both rare and common cards. We might assume common cards are worth $1$ and rare cards are worth $5$. Have ready another stack of cards that are all common -- call this the "...


14

I found out about the Prisoners' Dilemma as a kid from a book about the Harry Potter phenomenon, which had a chapter about the problem, but presented as a story about Harry and Draco being accused of breaking school rules. Each was offered the same deal as in the original problem, formulated with House Points being taken away instead of a prison sentence. ...


10

Since no one's posted an answer I will get things started with some general advice. Calculus 3 is my favorite course to teach, but it can be a bear to wrestle with the first few times. Some more specific information about your situation would be helpful (are you at Community College? Ivy League? Are the students Engineers? Math Majors? Is the class 20 ...


10

Quite a few universities publicly post the math exams their faculty write: UC Berkeley hosts an archive of their past exams, sorted by course. University of Michigan hosts past exams for some classes. There's not a consolidated repository though: past exams are hosted under individual course webpages. For example here are the past exams for Math215 ...


8

I like Nick C's idea more than modifying the typical formulation. The notion of snitching on a friend, regardless of the severity of the "crime", has real-world ramifications beyond the punishment put out by the authorities. Depending on your student population, that is possibly going to spur a conversation that will overshadow the objectives of your ...


8

I've heard very good reviews of the 2017 book, "An Illustrated Theory of Numbers" by MH Weissman. The book's main site is here; a write-up, along with some reviews, by the American Mathematical Society can be found here. To quote from the latter (emphasis added by me): An Illustrated Theory of Numbers gives a comprehensive introduction to number ...


8

Paul Lockhart's Measurement and David Foster Wallace's Everything and More incorporate history, language and art in their exploration of mathematics. 1) Measurement explores mathematics as art form, and covers deeply many high school mathematics ideas with an eye toward their beauty. Excerpts could be used as required reading in various high school math ...


7

You may find the SageMath knot and links capabilities useful for computation and visualization. The Knot Atlas might be a bit more comprehensive than you are looking for but is certainly a reference to be quite aware of.


6

I don't know much about knot theory but I know that Meike Akveld taught knot theory at both high school and university level. Here's a bibliography of one of her courses at ETH Zürich: https://www2.math.ethz.ch/education/bachelor/lectures/fs2015/math/knot/bibliography_FS2015.pdf It includes Englisch and German books both for high school and university ...


6

First, let's note that the terms as used by Rosen are standard definitions, as we can see on Wikipedia (here and here), as well as other resource sites. There was some question about this in the comments, so I thought to clarify this first. Perhaps reading those articles will give an added perspective for the OP. Now, I'm not going to offer a mnemonic -- I ...


5

Euclid the game is a set of challenges built in Geogebra. It allows the student to progress through the elements gaining additional tools as they go or solve each using only straight edge and compasses. It is accessible and enjoyable. I have used it with students from the age of 12. I don't know whether you were looking for something more formal.


5

The folks at Art of Problem Solving have what you need. It's not cheap ($559), but they work with many students like you, and are highly recommended. I think you will find it worth what it costs, if you can afford that. (And if not, ask them for a scholarship. I don't know if they'd do it or not...)


5

This won't help the OP for the summer of 2017, but let me put this here for future readers of this site: Michigan Virtual High School is (as I write these words) developing its own online Algebra 2 curriculum. The curriculum, which is expected launch in September 2017, consists of two separate half-courses (Algebra 2A and Algebra 2B) which can be taken ...


5

Researchers Sebastian Rezat, Mathias Hattermann and Andrea Peter-Koop have published a book "Transformation - A Fundamental Idea of Mathematics Education". You can find the link here. This is a description of the book: The diversity of research domains and theories in the field of mathematics education has been a permanent subject of discussions from ...


5

Possibly worth looking at is: Earth Algebra: College Algebra With Applications to Environmental Issues by Christopher Schaufele and Nancy Zumoff (1995 1st edition and 1998 2nd edition) See this review and this project/funding document. For what it's worth, in Spring 1993 I interviewed (on campus) for a tenure-track position at the university this was ...


4

The Florida Virtual School offers high school level classes in all subjects, including Algebra 2, and is very well regarded. They're considered a school district within the Florida school system so I would expect a course from them to be considered acceptable by another public or private high school. If you don't live in Florida, you can still take classes ...


4

I personally would prefer a textbook recommendation I can download or pick up that is [preferably] not old and does not make trigonometry intimidating to approach (especially one that emphasizes understanding proofs behind properties/theorems). I don't have textbooks to recommend, but I can recommend an approach to doing trigonometry that facilitates ...


4

Maybe a visual approach could supplement your study? There are many such resources available on the web, not in textbooks. E.g., Trig Intuitively:                     Note: the labels show where each item "goes up to." Another: Interactive Unit Circle. Another: Inverse Trig Functions.


4

Schaum's outlines are very practical in general and cheap. Well suited to an older learner. Often the answers are right after the problems versus at the end. And you get all the answers, not the odd/even gyp. Thus suited to self learning. I like this one, overall and own it: https://www.amazon.com/gp/product/0070026505/ref=...


4

The Open Syllabus Project presents a large amount of data about books listed on syllabuses of courses taught around the world (especially in the USA and not only about math/science). I think that it is not possible to ensure that the presented textbooks are indeed the most adopted (or bought or sold or used or read). However, they probably are (at least) ...


4

The Canvas class for Dartmouth's Spring 2020 course in Graph Theory, Math 38, seems to be mostly open. According to the syllabus, the course uses the 2nd edition of West's Introduction to Graph Theory. Course Description This course will cover the fundamental concepts of graph theory: simple graphs, digraphs, Eulerian and Hamiltonian graphs, trees, ...


3

It sounds like you wish to protect your students from the violence and greed of the adult world, while still making the dilemma real enough to keep them engaged. To that effect, I offer two solutions. One, replace prison with detention. Make the crime something like using cell phones in class or throwing spitballs. Two, have them arbitrarily grade each ...


3

A1/ I'm not sure why you would need a companion to Euclid. Euclid is already a textbook and you can progress through it as leisurely as you like... I prefer Sir Thomas Heath's version. But the two most popular works back in the 19th century (when Euclid teaching was at its height in the UK) were Todhunter's The Elements of Euclid for Schools and Colleges ...


3

If you are teaching a class for the first time, there is something to be said about using the same text as the last instructor. But if you are interested in trying something new, you might like "Operations Research: A Practical Inroduction" by Carter and Price. It covers all of the topics that you listed, but more succinctly than Hillier. It doesn't get into ...


3

As a software engineer, the book "concrete mathematics" by Graham, Knuth and Patashnik is a must. Chapter 4 is on number theory.


3

I think the OP asks a difficult question that will not have a succinct answer. Permit me to point to one publication, Schoenfeld, Alan H., ed. Assessing Mathematical Proficiency. Mathematical Sciences Research Institute Publications. 53. Cambridge University Press, 2007. (PDF download of book.) which addresses the question of what constitutes mathematical ...


3

(In before the close!) I'd say the PDE course looks more like a traditional course than the prob/stats course. Look at the hours expected, for example (~6.5 versus ~1.5), each times 8 weeks. The PDE course looks like a solid half to two thirds of a semester of a normal, engineering support course. You cover a couple of the 3-4 major equations. And get ...


3

Before listing 'resources', let me start with some official documents (e.g. to clarify the difference of sustainable math and math for sustainability, see xkcd:Sustainable :-). The official UN Site lists the 17 Goals for sustainability; especially Goal 4: Education. Still debating what this all means, I find the paper by Brundiers et. al. (2021, see below ...


2

Short answer: (migrated from comments by request) Hung-Hsi Wu (Berkeley) has a home page full of links to writings of this ilk. Two specific examples that may fit the bill are ones I mentioned back in MESE 1857 (April 2014); in particular, links to a text on Pre-Algebra (pdf) and an Intro to School Algebra (pdf). Further comments: Some of H.H. Wu's ...


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