9

I have some personal experience. I taught in a school that has Israeli students whose families had moved to the US. These children had Hebrew as their native language. Hebrew is written right to left. I never saw these students struggle with math because they learned to write from right to left. Furthermore all students in my school studied both Hebrew and ...


7

The list of topics you want to study corresponds rather to abstract algebra than group theory. You did not say why you are interested specifically in group theory, but I believe that acquaintance with various algebraic structures in addition to groups would be beneficial for any person learning mathematics beyond school mathematics. Therefore, abstract ...


7

A once per week ten minute session is objectively not using up that much of the kid's time. In addition, he's not even as much turned off on it as you are. Also, I think you will find that speed increases with volume, so it becomes nonlinear. None of this is to say that I love the particular drill. Sounds too easy for a smart 7yo. Just that it's not so ...


6

I am totally convinced that, in most cases, it is good for students to understand why mathematical rules work. I could write a very long text justifying this belief but, from an academic point of view, my personal opinion has no value. I need academic articles/books written by researchers of mathematical education supporting this idea. Is there an agreed ...


6

The key term you are interested in is "conceptual knowledge" (more specifically, "conceptual understanding"). According to this document from the National Council of Teachers of Mathematics, Students who lack understanding of a topic may rely on procedures too heavily. Without a flexible base from which to work, they may be less likely ...


6

This is not really an answer, but is too long for a comment. BTW, the downvote wasn't mine. I tried constructing something similar to this about 25 years ago, with some guidance from my mother, who worked in standardized testing. The details of the list of skills were different in my case, but it was a similar situation. The problem I would expect you to ...


5

To repeat my comments: I can recommend Fraleigh's classic introduction. It is easy to read for beginners, with many exercises, from easy to difficult, on which self-learners could check themselves. John B. Fraleigh A First Course in Abstract Algebra, 7th Edition. Pearson, 2002.           Because it's been around so ...


4

I think it's useful but can be overdone and/or can make things more difficult. For example, I actually think it is easier to learn ODEs first, in the mechanical way (e.g. solving the linear second order equation). Initial practice should be on more algebraic problems, not applied. This is because word problems are harder. After mastering the process ...


4

I am not familiar with this book, but the title alone suggests it might be worth examining for your purposes. Statistics for Mathematicians: A Rigorous First Course. Victor M. Panaretos. Compact Textbook in Mathematics. Birkhäuser/Springer 142 (2016). ISBN-10 : 9783319283395. Springer link. "Intended for students of Mathematics taking their first ...


4

I would suggest "All of Statistics" by Wasserman. It is reasonably concise and moderate in its demands on background, but much more mathematically serious, also covering a much wider range of material, than a typical first course in statistics.


3

Sue has linked to a great book (which I hope she turns into an answer), and here are two more quality ones that are free, at least, though less inquiry-oriented. Doerr and Levasseur, intended for computer engineers as well as CS Keller and Trotter, a bit higher level but has some very good material There are others at https://pretextbook.org/catalog.html ...


3

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

I'll echo @XanderHenderson in the comments that Hungerford's Abstract Algebra: An Introduction is a really nice textbook. It's what I had as an undergraduate, and I'm currently re-reading it for maybe the third time. It's one of my favorite, well-written, clear texts. Note that he's committed to a pedagogy that starts from the most familiar/concrete and ...


3

This is not a direct answer to your question, but it is literature that addresses at least one aspect of the issue you raise. Keith Devlin wrote an article entitled, "The Symbol Barrier": Link. The point of his article is to argue that video games can help overcome "the greatest obstacle to good mathematical learning." But setting video ...


2

Wilson, Robin J. "An introduction to matroid theory." The American Mathematical Monthly 80, no. 5 (1973): 500-525. JStor link. This is an elementary introduction, not even assuming much knowledge of graph theory. He explains enough transversal theory to proceed to matroids. He defines a matroid in several ways, so that you get different ...


2

Am Arabian Mathematician. In my country in all school we used to write math from right to left i scored very well in 12th grade 179/200. But in the universities we use English books so we write from left to right it was hard for me to get through that in the first course I scored 65/100 by the time I used to that and now am PhD student in the US. So my ...


2

One of my favorite resources has been the shell center’s mathematics assessment project. They have both lessons and more traditional assessment scenarios, however the rubrics provided focus on ways to give formative feedback rather than a strictly point based approach. https://www.map.mathshell.org/


2

Generally, is providing a context/big picture helpful or a waste of time when teaching "hard skills"? Disregarding the "added value" of the students knowing the big picture, being able to apply the skills, etc., does the learning of skills per se improve? From an emotional perspective, it can be helpful. It shows why what you're trying to learn is important....


2

The word imply has significantly different meanings in ordinary speech and mathematics, and has caused me some confusion in the past. According to this dictionary entry, the word indicates a suggestion (rather than a definite conclusion) that some statement is true. This gives rise to expressions that cover different degrees of strength in a connection ...


2

You can find articles and videos on teaching math to low vision and blind students from the Texas School for the Blind and Visually Impaired. https://www.tsbvi.edu/ In particular, you can find informative videos from Susan Osterhaus on that site. She is an instructor with 25+ years of teaching experience with blind and visually impaired students mostly in K-...


2

I think this is only a partial answer to your question. Ideals, Varieties, and Algorithms by Cox, Little & O'Shea presents affine varieties and their parametrizations in Sections 2 and 3, respectively, of Chapter 1. This material could complement or supplement the coverage of curves and surfaces in a multivariable calculus course. Then Section 4 of ...


2

Common Core includes Standards for Mathematical Practice. Those may be a good description of what you're looking for. I have seen a few other good lists of mathematical thinking skills. I enjoyed thinking about how I might use this one, put together by Avery Pickford, in my teaching. (You might find more good thinking in the comments.)


2

My answer is anecdotal, certainly not a reference to a study or anything of the sort. Background - I work in a high school, as an in-house tutor. I've also subbed, and co-taught a sophomore algebra class. Our sophomore math is offered at 4 different levels, presumably so an honors student on track for AP calculus (AP = Advanced placement, the student is able ...


2

Thanks for the advice everyone. After looking at many options and talking with faculty, it's been decided that we're using Lang's Undergraduate Algebra. I was leaning heavily towards Artin the past few days, but I was actually pleasantly surprised when I flipped through Lang's Undergraduate Algebra... far more standard organization, great exercises, and ...


2

In an attempt to answer your question: Are the PISA data detailed enough to measure effects by such AI based approaches in mathematics? I found three things that point to the answer being no. I dug through the 2018 PISA School Questionnaire, which is administered to school principals, and found no question on AI that would allow the data to be parsed in ...


2

Just a link to an xkcd symbols joke, posted just today [7Aug2020]:


2

If you can ignore the specific UBC context, this might be the type of paper the OP seeks: Eric Eich. "The Cognitive Science of Learning Enhancement: Optimizing Long-Term Retention." (2011). Univ. British Columbia. HTML link. Here's an excerpt comparing "massed" vs. "spaced" learning: "The advantage of spacing over ...


1

I'm a physicist and only rarely get to teach math, but I suspect the situation is about the same in both fields. I've visited a fairly decent-sized sample of classes for adjunct and tenure-track review at the community college where I work. My observations from visiting these classes are of course not really what you asked for, but I suspect they're pretty ...


1

Kevin Arlin already gave my "best" answer in All of Statistics. That said, statistics is a large topic. If you're looking specifically at inference and statistical learning and want a rigorous exposition of most of the different methodologies used I would recommend Elements of Statistical Learning, although it assumes a heavier mathematics ...


1

As a student of mathematics taking a statistics course next semester, I have been plagued with this problem. I have found a solution in "Lectures on Probability Theory and Mathematical Statistics" by Marco Taboga, which is a collection of many lectures and exercises from the website https://www.statlect.com/.


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