(Part 2) Best study & teaching mathematics books according to redditors
We found 156 Reddit comments discussing the best study & teaching mathematics books. We ranked the 63 resulting products by number of redditors who mentioned them. Here are the products ranked 21-40. You can also go back to the previous section.
I'd recommend against Khan Academy or similar resources in this situation. They are great resources for students who are missing basic skills, or even learning at grade level and struggling a bit. But for a student who is already doing well and wants to do something special, the last thing I'd look for is to give him an early repeat of what he's going to see in math class next year anyway, or the online version of drill worksheets.
Okay, I guess that means I owe some positive suggestions. That's harder given the age, but this is my best try.
First, you might want to start with /r/matheducation. They’re actually experts in this subject.
You can read work by hundreds of experts in child psychology/development, pedagogy, the philosophy of mathematics, the intuitive/psychological foundations of mathematics, etc. Personally I’m a fan of Piaget, Bruner, Papert, and like-minded thinkers, who advocate a child-centered “constructivist” approach to education. But there are certainly respectable educators and researchers who favor a more structured and top-down approach.
If you want to read concretely about the differences between typical US instruction and Chinese instruction in the 1990s, read Liping Ma’s book Knowing and Teaching Elementary Mathematics
Or watch this video from a few years ago discussing the TIMSS study and criticizing Khan Academy.
Or to see what a particular group of young children could learn with some expert guidance, check out Zvonkin’s book.
You might have read Lockhart’s Lament. He provides an alternative way of teaching high school mathematics in his book Measurement.
I like this concise theory of mathematical learning. YMMV. Here’s a short essay by Minksy about why mathematics is hard to learn.
If you want lesson plans and curriculum guidance, look to the American NCTM, who have been making detailed materials available for decades. Also look up math circles (both online materials and physical groups meeting in your area).
You might like this book by Van de Walle about general elementary teaching, or this book by Lenchner about problem solving.
Many people seem to like the Singapore math books. Read about Singapore’s curriculum.
If you ask homeschooling parents in your area, you can probably find strong opinions about curricula. Just searching around the web, many keywords about elementary math books etc. seem to lead to homeschooling sites. (This makes some sense: they have some free time, like to write about their experiences and form online communities, and do more personal evaluation of curricula than schoolteachers can necessarily have time/political power to do.)
There are hundreds of available books of mathematical puzzles and games, dozens of different types of physical manipulatives, and thousands of books, papers, essays, etc. about how to organize, order, and teach students of every imaginable age and background
If you have a particular age group / level of prior preparation / desired set of topics in mind, there might be some more specific materials people can point to. Are we talking about 4-year-olds? 10-year-olds? High school olympiad preparation? Are you interested in basic arithmetic? Geometry? Algebra? Do you have 1 advanced student to teach? 50 students of varying skill levels?
In welcher Klasse bist du denn jetzt?
Wenn du dir Nachhilfe nicht leisten kannst: pauk Buecher. Such dir Buecher, die den Stoff enthalten, der dir fehlt. Sie sollten vollstaendig, nicht zu ausschweifend sein und dabei moeglichst verstaendlich.
Fuer das Abi sind die Trainer von STARK sehr zu empfehlen:
https://www.amazon.de/Abiturpr%C3%BCfung-Bayern-Mathematik/dp/3849036774/ref=sr_1_1?__mk_de_DE=%C3%85M%C3%85%C5%BD%C3%95%C3%91&crid=1GVKF7JG2BST9&keywords=abitrainer+mathe+bayern+2019&qid=1554226375&s=gateway&sprefix=abi+trainer+mathe+%2Caps%2C171&sr=8-1
und
https://www.amazon.de/AbiturSkript-Mathematik-Bayern/dp/3866688636/ref=sr_1_2?__mk_de_DE=%C3%85M%C3%85%C5%BD%C3%95%C3%91&crid=1GVKF7JG2BST9&keywords=abitrainer+mathe+bayern+2019&qid=1554226375&s=gateway&sprefix=abi+trainer+mathe+%2Caps%2C171&sr=8-2
>die attestierte überdurchschnittliche mathematische Fähigkeit und die überdurchschnittliche analytische Fähigkeiten
Wer hat dir das attestiert?
So eine Diagnose ist dermassen gefaehrlich. Vergiss das. Du brauchst ein Wachstums Mindset https://www.youtube.com/watch?v=JC82Il2cjqA.
Du musst dir einreden, dass der Mathe Teil deines Gehirns waechst, wenn du ihn trainierst, und du dadurch besser in Mathe wirst.
So eine "ich bin so intelligent" Haltung hat 2 massive Gefahren. 1) Strengst du nicht richtig an (ich bin ja so toll und muss nicht lernen). 2) Wenn es mal schwierig wird, faengst du deswegen an, an deiner Intelligenz zu zweifeln, und wirst panisch. "Das ist schwer. Bin ich dann doch nicht so intellgent? Oh Gott, ich schaffe das nie!" usw.
>Ab heute Online den Stoff lesen, den er online stellt. Auch wenn das wenig bringt wenn ich es nicht kapiere, weil mir beispielsweise das Vorwissen für die Anwendung fehlt.
Lehrer sind empfaenglich fuer spezifische Fragen. Wenn er sieht, dass du dir wirklich den Arsch aufgerissen hast, und versucht hast, es zu verstehen, und du eine spezifische Frage hast, muss er dir auch helfen.
Die Profi Variante ist es, dann zu versuchen, das fehlende Vorwissen nachzulernen. Ich weiss nicht, ob man das als Schueler schon kann, ich habe sowas erst in der Uni gelernt.
Eine moegliche Strategie ist: das, was ich nicht verstehe: wie heisst das? Welcher Begriff ist das? Wenn du dann herausgefunden hast, das heisst "lineare Gleichungen mit einer Unbekannten loesen", dann kannst du auf Google nach Lernvideos und Tutorials suchen, und die entsprechenden Kapitel in Mathebuechern aufmachen.
Die andere Strategie ist, du besorgst dir Buecher, die den Stoff beinhalten, den du nicht kannst. Dann liest du dir die Inhaltsverzeichnisse durch, und streichst alles durch, was du schon kannst. Und den restlichen Stoff gehst du dann von vorne bis hinten durch.
>Verständnisvoll auf dem Lehrer einzugehen, auch wenn die Methodik mich ankotzt!
Arschkriechen ist nicht verkehrt. Im akademischen Wettkampf gibt es wenig Raum fuer eigenen Stolz oder die eigene Wuerde.
Es ist scheisse, da muss auch was passieren. Aber du kannst da aktuell gar nichts machen. Ich hatte damals die Haltung "Schule ist wie anale Vergewaltigung. Es tut so oder so weh, aber es tut weniger weh, wenn ich nicht zappel."
>Die 3 auf meinem Hauptschulzeugnis
Hauptschulmathematik ist viel einfacher als Gymnasialmathematik, und dann noch nicht mal eine 1? Fuer mich ist das gar kein Argument fuer gar nichts.
>Die 3 auf meinem 1. Halbjahreszeugnis, welches pädagogisch sinnvoll in Betracht gezogen werden muss vom dem Lehrer, weshalb eine 6 unpassend wäre.
Das ist in der Tat ein starkes Argument. Was ist denn da passiert? Hat sich der Stoff geandert? Lehrer geaendert? Hast du auf einmal viel weniger gelernt?
>Immer die Hausaufgaben Liniengenau, wo ich eigentlich ein Schmutzfink bin
Top. Auf jeden Fall.
>Das ist mir doch Schnuppe, eigentlich. Denn wir sind hier auf einer Schule die dafür sorgt, dass Hauptschüler ihr Zeugnis verbessern können in einer höheren Qualifikation.
Wenn der Lehrer sagt, das ist Stoff der 7. Klasse, dann holst du dir das 7. Klasse Buch und paukst das nach. Kauf das Buch, geh zu ihm hin und er soll auf die entsprechenden Kapitel zeigen, die er meinte. Und die lernst du dann.
Du kannst dich nicht auf das Schulsystem verlassen. Du musst dich selber darum kuemmern, dass du den Stoff lernst. In deinem Kopf hat die Schule hauptsaechlich die Funktion, dich abzufragen.
>Ich lerne regelmäßig für meine Zukunft nach der Schule.
Wie viel ist das denn? Wie viel konzentrierte Lernzeit schaffst du am Tag / in der Woche? Wie sieht das Lernen bei dir aus? Wirst du dabei abgelenkt? Hast du das Gefuehl, es ist effizient?
Certainly:
The first and second link are all-in-one books for the first and 2nd year of university respectively. The 3rd and 4th links are the all-in-ones for the third year for analysis and algebra respectively. They're pretty damn good, and it's like reading a Bourbaki but with colored boxes and random historical blurbs that you'd expect to find in a freshman calculus book like Stewart.
You need some grounding in foundational topics like Propositional Logic, Proofs, Sets and Functions for higher math. If you've seen some of that in your Discrete Math class, you can jump straight into Abstract Algebra, Rigorous Linear Algebra (if you know some LA) and even Real Analysis. If thats not the case, the most expository and clearly written book on the above topics I have ever seen is Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers.
Some user friendly books on Real Analysis:
Some user friendly books on Linear/Abstract Algebra:
Topology(even high school students can manage the first two titles):
Some transitional books:
Plus many more- just scour your local library and the internet.
Good Luck, Dude/Dudette.
I suggest reading How to Study as a Mathematics Major.
Go to office hours.
Go to college-sponsored tutoring hours.
Teach others how to do the problems you're working on.
Your metric for success is whether you can do the math at the end of the day or not, and for math, you need to do a TON of problems to get it into your skull.
Lectures are inherently bad systems for teaching math, so you need to take advantage of other, more conversational options if you're having trouble with concepts. Since the professor is nice, talk with him/her every chance you get about the problems you encountered in the homework.
Bad initial question: "I don't get partial fractions."
Good initial question: "When I worked on #6, I had trouble figuring out how to solve for the numerators for each of the parts of the summed fractions. How do I do that in this case?"
I wonder how much of it has to do with how the arithmetic is taught though. I read Knowing and Teaching Elementary Mathematics even though I teach high school because I found it fascinating. Basically it contrasts US elementary teachers with Chinese elementary teachers and the difference in approach to teaching the basic techniques is pretty amazing...
The columnist is a completely clueless fscktard who somehow missed the concept of researching before writing an article. Danica McKellar is a math major who actually has an Erdos number of 4, and is a math advocate. The most cursory net search would have showed her that McKellar is a math advocate, not some bubblehead. And why is she reviewing a book that was published over a year ago as if it were brand new? Heck, McKellar's newest book, Kiss My Math, is hitting the stands next month! I hope this was posted as a wry joke to poke fun at the columnist Chloe Angyal for writing without a clue.
I bought the ETS "Official Guide" and went through the quantitative reasoning section and made notes on any math concepts I needed to brush up on (I haven't done any geometry since high school, which was...uh...a few years ago). I wanted more practice problems, so I bought a Kaplan book that just covers GRE math and that's what I'm working through now. It's this one: https://www.amazon.com/Math-Workbook-Kaplan-Test-Prep/dp/1625232993/ref=mp_s_a_1_3?ie=UTF8&qid=1543244179&sr=8-3&pi=AC_SX236_SY340_QL65&keywords=kaplan+gre+math&dpPl=1&dpID=511IWfCnykL&ref=plSrch
Once I finish with this workbook I'll probably do the two free practice tests on the ETS website, and then if I'm still not happy with my scores I might pay for the two additional practice tests.
As far as making it fun, I'm just a weirdo who genuinely enjoys doing math problems. I'm super fun at parties, lol.
That's a fair point tbh. A lecturer at my uni specialises in undergrad maths education so she really knows how students learn best. She actually gave us a document of a chapter on time management from her book on how to study for a maths degree, but I have to be honest, I haven't read it yet. If anyone's interested it's this one. We also have a Maths Learning Support Centre where we can drop in and ask lecturers for help on something, not like office hours.
this one
and
this one
and yes I keep them on my shelf. Personally, the pre-calc is still helpful from time-to-time and the Math Power book I keep because it made me love mathematics.
1)
Resources:
Maybe try something like udemy?
https://www.udemy.com/singapore-math/
Or sift through videos here:
http://www.watchknowlearn.org/Category.aspx?CategoryID=4912
If you want to pay for it (or maybe try to find it at a library), this is a great book that goes over the foundational skills taught the singapore math way.
http://www.amazon.com/Why-Before-How-Computation-Strategies/dp/1934026824/ref=sr_1_13?ie=UTF8&qid=1405976198&sr=8-13&keywords=singapore+math
This is a great book about how to teach singapore math based model drawing to solve word problems.
http://www.amazon.com/Step-Model-Drawing-Problems-Singapore/dp/1934026964
Teacherspayteachers also has some free resources:
http://www.teacherspayteachers.com/Browse/Search:singapore+math/Price-Range/Free
2)
Rote practice is necessary, but if you can make it more interesting in any way possible that would probably yield better results. There are plenty of apps out there that make computational practice fun.
You need to make sure he can explain to YOU different ways to solve a problem so he gets practice making those connections on his own and verbalizing it to someone else. It will cement those skills so he can recall the information on his own and independently think of a variety of routes to solving a problem.
3)
This is probably a huge factor in his scores, and super important to work on nixing bad habits. I used to do this ALL THE TIME and it's a hard habit to break. One thing you can do to show him the difference between his way and your way of doing things: Give him a quiz at the start of session. Then focus the session on minimizing mistakes and slowing down, not skipping steps. At the end, give him another mini quiz w/ similar questions & difficulty. The next session, have them graded and most likely there will be a big difference between the first and last, and the difference will most likely be preventable errors. (If it's not...then it would be a first!). Show him both quizzes and ask him why he did better on the second one, process with him the importance of doing the steps every time and double checking work, etc.
It will also help if you have him explain to you why he got a problem wrong, and to keep track of the reasons. Once he sees how many he is missing because of little errors, he will better understand the impact of skipping ahead and not checking his work. (This worked for me when I was studying for the GRE. It's hard to see the big picture, I only see the current moment. Tracking the big picture helped me connect my actions to the future consequences)
4)
Lame techniques are awesome because they remember them and it's fun to tease them a bit. :)
I'm not like a wunderkind, but I 710'd my dry run after a few weeks of study. The best book I saw for math is Nova, linked here:
https://www.amazon.com/GMAT-Math-Prep-Course-Kolby/dp/1889057509/ref=sr_1_1?ie=UTF8&qid=1484443227&sr=8-1&keywords=NOVA+gmat+math
Be aware that the Kindle version has a bunch of typos because of shitty OCR. But the price is right and it's a very solid book. For the verbal I'm wanting to say I used the basic GMAC book and maybe Kaplan.
What score are you shooting for?
When Borders was closing, I was studying for 5161. I picked up several books absurdly cheap. Most of them were crap, but the Cliff Notes one was so good that I actually kept it as a math resource. The topics were clear and well organized, and the practice tests were the most helpful of all the simulations that I took.
If you want to only teach middle school, do the middle school math Praxis. It might hinder your flexibility later if you want to move up later, but at least you'll get started. Additionally, as a math teacher, you shouldn't have as much difficulty finding a job.
However, I strongly encourage you master topics above the level that you teach. It'll give what you teach context, and you'll know what you're preparing your kids for. I didn't take that much calculus and no stats in college. You bet I had to study my ass off and practice to teach myself in preparation for 5161.
https://www.amazon.com/CliffsNotes-Praxis-Mathematics-Content-Knowledge/dp/0544628268/ref=sr_1_2?ie=UTF8&qid=1536453143&sr=8-2&keywords=praxis+5161 try this. Go through Khan Academy on areas you're weak in for a quick refresher. There are plenty of youtube videos on specific problems in regards to praxis 5161. YOU CAN DO THIS! good luck!
I'd suggest this mathematics resource book by Van de Walle and colleagues if you really want to understand mathematical concepts. It is really well-written, easy to read, based on mathematics education research, and even fun!
It's a common occurrence in mathematics to come across some Greek you don't know, which then means that you'll have to do "the usual yoga" -- make up exercises and examples until you've worked yourself into whatever you're looking at, as opposed to expecting to understand everything by reading about it.
From what you say I infer that you can do and have done that, as such I doubt you can really put yourself into the mother's shoes -- because this fundamental stumbling block of not learning a thing because you believe you can't ever learn it vanishes once you've had the experience that with some yoga, everything can suddenly very well work out.
How can you invest time and effort into understanding something if you haven't learned that you can understand things that way?
That's btw also why not few people who aced maths in school drop out of maths at university: The smarter you are and the easier and "obvious" things for you are in school, the less likely are you to actually develop that skill. If then on top of that you're arrogant enough to miss the pointers your professors throw at you, you've set yourself up for failure.
Raw intelligence without grit and the wisdom of how to apply it to things amounts to little. And makes you quite likely to end up linked on this sub. Have grit and sufficient wisdom, however, and it doesn't matter much how much raw intelligence backs it up, you'll excel in one way or the other.
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Thinking about it, I guess /s would've been a better choice than :) in my previous post. I do get it, I just have enough practice to usually overlook that path.
I'd recommend asking the school/teachers, but each board usually publishes a book for each qualification. These are usually available at shops like Waterstones and online. For example, here is the Edexcel GCSE Maths book (for this year, I think). So just find out which qualifications are being done (and also which exam board) then buy accordingly.
I would suggest Spivak for a rigorous, proof-based treatment of calculus and Sally's Tools of the Trade for an introduction to real analysis, linear algebra, and proofs all at the same time. My school uses both of these books for its introductory classes for math majors and they're very good. Note that Sally can be very terse, so it would be beneficial to find some online lectures and resources to supplement your reading.
Hat nix mit flutschen zu tun. Du kannst der schnellste Bieber des Westens sein, trotzdem dauert's bis du durch den Wald durch bist. Wissen und Verstehen braucht Zeit.
> Ich kann [...] noch nicht einmal das Problem herausfiltern.
Das ist sehr gut so, da steckt auch keins drin :) Das nur eben eine typische "Eröffnung" eines Beweises: wir definieren ein paar Symbole, und bauen darauf unseren Beweis auf. (In der Analysis gibt es wahrscheinlich dutzende Beweise, die genau so beginnen können.)
Beweise werden vorwärts geschrieben, aber rückwärts verstanden. Ein typischer Beweis startet "irgendwo im nirgendwo", marschiert in eine scheinbar beliebige Richtung los und kommt bei der Behauptung an. Das ist verwirrend, vor allem weil "formale Korrektheit" und "Verständlichkeit" zwei verschiedene Paar Schuhe sind. Oft ist es erhellend, sich rückwärts vorzuarbeiten: Ja, Y folgt logisch aus X, aber wie kommt er auf X?
> Ich bin schon mit überall stetig nicht vertraut. Google würde da sicher helfen
Google eher nicht, weil die Definitionen wieder nur auf anderen Dingen aufbauen mit denen Du wahrscheinlich auch noch nicht vertraut bist. Du brauchst eine strukturierte, "lineare", didaktisch durchdachte Wissensvermittlung (früher hieß das "ein Buch").
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Kernaussage meines Kommentars:
Stetigkeit ist ein schönes Beispiel für die Beziehung zwischen einer mathematischen Definition und dem Verstehen des dahinterstehenden Konzepts:
"Stetig" bedeutet anschaulich, dass sich eine Funktion zeichnen lässt "ohne den Stift abzusetzen". Das ist leider nicht exakt genug und in einigen Fällen ist das intuitive Verständnis dieser Beschreibung sogar falsch.
Es gibt verschiedene exakte Definitionen, die aber - selbst wenn man die Symbolschrift dekodiert und alle Annahmen versteht - nicht unbedingt geeignet sind, eine anschauliche Vorstellung von Stetigkeit zu bekommen.
Letztere gewinnt man normalerweise, indem man die Stetigkeitsdefinition anwendet -
insbesondere auf Sonderfälle, und die formalen Ergebnisse mit seinem intuitiven Verständnis abgleicht.
Die vielbeschworene Schönheit der Mathematik beginnt an der Stelle, an der man versteht, dass alle diese Definitionen äquivalent sind, also die gleiche Idee, das gleiche Konzept beschreiben, und zwar aufs i-Tüpfelchen identisch - obwohl die für die Definition verwendeten Konzepte aus ganz verschiedenen Bereichen der Mathematik kommen, die eigentlich gar nichts miteinander zu tun haben (Zahlenfolgen, Infinitesimalrechnung oder Topologie.)
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Empfehlung:
Lerne, die Kurzschreibweise zu lesen. und damit meine ich tatsächlich erstmal nur: zu lesen - so wie man russisch lesen kann, wenn man das Alphabet kennt, auch wenn man noch nicht weiß, was die Worte bedeuten. Einfach formal das "Gekrakel" in deutsche Worte übersetzen.
(Mathematik und eine Sprache zu lernen haben tatsächlich viel gemeinsam. In dem Sinne: ist die Symbolik eher eine Phrasensprache, eine einzelne Zeile in "Mathe" entspricht einem ganzen Absatz in Deutsch. Der Sprachumfang aber gar nicht so groß, auch wenn jedes Buch und jeder Lehrer da so seinen "Dialekt" hat.)
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Das bringt aber, knallhart gesagt, nur etwas, wenn man sich mindestens ein Jahr mehrere Stunden pro Woche mit Mathematik beschäftigt.
Was cool wäre, wenn Du das auf die Reihe bekommst, denn zl;ng: es wäre schade, wenn Dein Interesse an Mathe daran scheitert, daß Du lieber drei Studen am Tag daddelst. ;-)
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Experiment 1: Ignoriere Vorwort und Einleitung unbedingt, Beginne mit "0 Naive Mengentheorie". Das ist knallharter Tobak und leider ziemlich kompakt geschrieben - ist aber ein Weg, der einen großen Sektor Mathematik aus den fast-nichts erschafft. (Und vergiss nicht: eine Zeile Symbole ist wie ein ganzer Absatz, mehrmals lesen, auseinander nehmen etc.)
Kann gut sein, dass Du darüber abstirbst: nicht Deine Schuld, dann habe ich das falsche Material gewählt ;) Wie gesagt, dass ist ein Experiment.
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Experiment 2: D.F.W. ist nicht der beste Didakt und definitiv kein Mathematiker, aber ein brillianter Geist, der sich hier mit brutaler Wucht durch ein Kernproblem der Analysis "durchprügelt". Dies ist definitiv kein Lehrbuch! Der Blickwinkel des eigentlich-Geisteswissenschaftlers könnte für Dich aber interessant sein.
Uff.
Math content knowledge on a subject is pre-requisite to pedagogical knowledge. If a teacher can't divide fractions, xe won't be able to effectively teach xir students how to divide fractions either. This point was highlighted in Liping Ma's book that has been making the rounds in math ed community.
You are right that just knowing how to divide fractions doesn't mean that you can effectively teach it; that's where the jingle "ours isn't to ask why/ just invert and multiply" came from: well-meaning teachers who are trying the best they know how to get their students to pass the tests.
If this counts: http://www.mattboutte.com/SATandACTMathGuide.pdf
Other than that, I use prep books. You can get digital versions via Kindle for some of them, such as Steve Warner's 28 SAT Math Lessons.
https://www.amazon.com/Cracking-SAT-Subject-Test-Math-ebook-dp-B071PCMQ6C/dp/B071PCMQ6C
I have two suggestions:
Firstly: There is a nice book called The Beauty of Everyday Mathematics, which has a terrible name that find misleading, and which I think is excellent. Each chapter centers around a question, and then performs a level of analysis that would top /r/theydidthemath absolutely.
I routinely incorporate ideas from this book and others of similar depth and breadth in talks I give for undergraduates.
Secondly: If you were to invite graduate student speakers from nearby schools, they would come. You see, to a graduate student, giving talks is both an opportunity to give back and an opportunity to introduce yourself to a potential employer/practice speaking for when you do introduce yourself to a potential employer.
The downside is that sometimes grad students are good speakers, and other times they're lousy speakers. But I think it would be exciting nonetheless.