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Grube's Method of Teaching Arithmetic: Why haven't I heard of this????


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I have been reading your posts about math, and this one caught my curiosity. I just looked over much of the Grube's Method book, and it seems very similar to MEP. This text appears to be great for extra reinforcement for the MEP lessons. I wonder if some of MEP is drawn from this, as it is a Hungarian program. Anyway, I thought it was very interesting how the two seemed so eerily similar.

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Oooh, thanks :-) It looks like books 3 and above, have at least some of the answers in the back.


Most of the lessons will print out beautifully, for people that like to plan ahead by weekly folders.


It really helps me to see the first book that launched so many of my favorite methods and curriculums. I guess I don't like the wideness of most modern conceptual curriculums, but I do like Grube followed up by vintage "common" arithmetic.

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  • 1 year later...

Rand McNally Primary Aithmetic seems to be based on Grube's



Since this thread Simply Charlotte Mason has put out a good pdf on teaching math vintage style



Waldorf math is based in Grube's. Here is a link to the free African math pdfs.



Manual of Methods has a section on teaching math.


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  • 4 months later...
  • 6 months later...

Oh, you.  As if we needed more choices.   :p    :D   


With these methods, at what age do they start?   


I was looking at Ella Frances Lynch's advice (which has some similarities to Grube's), and she recommends holding off on teaching arithmetic until the child starts asking a lot of questions about numbers.  In her experience, this is usually after age 6, and sometimes as late as 8 or 9.  


I'm not sure if it would be feasible for most little ones to learn all four operations at once.   Since the schools now seem to be doing quite a bit of arithmetic by 1st grade, that might be a reason most modern books start with addition and subtraction.   

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Waldorf, using the Grube's method, teaches the 4 operations to first graders, but that is to SEVEN year olds. The Manual of Methods first year, which I'm assuming is aimed at 6 year olds, says NOT to teach all 4 processes, that first year. Strayer-Upton Book One is THIRD grade, even though it is for the first year of formal instruction. I'm not sure if any of that is helpful.

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Thanks, Hunter.  It looks as if the Lippincott books did start teaching all four operations in the first half of first grade.  That was in 1915, so I think they would have been six year olds.  I wonder how that worked out in practice.  


I've just been skimming all this so far, but here are two of a series of critical articles by E. E. White.   The author has philosophical concerns about the way the processes are taught, but also believes (from personal observation) that it's too confusing for most children in the first year.  


The Grube Method II



The Grube Method, Again



Then there's an even more critical book by Saul Badanes, who disagrees with both Grube and White.  


The Falsity of the Grube Method of Teaching Arithmetic



Fun times!   ;)

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ElizaG, thanks for those links!


My ability to pick through the meat and leave behind the frosting and commercialism of modern Montessori, Waldorf and CM comes from reading the sources that they read before developing their own educational philosophies.


Vintage used smaller books, readily available manipulatives, paper/slates instead of workbooks, and assumed students would spend fewer hours on task. Even when vintage sources disagree, I still find helpful tips in all of them, on how to get this done more efficiently.

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I'm no help. I've mostly just done this with all these resources.  :willy_nilly:


MEP, I haven't even tried. WAY too much ink! At least these vintage resources are more concise.


I was using How to Tutor as my main curricula, but I have switched over to the Ruth Beechick guide for Ray's and my plan now is to look through the resources to see what I want to add to Ray's, when a few pages of Ray's are scheduled for weeks of drill.


Even without officially using these resources the "right" way, reading through them has influences my teaching, and I have added ideas from these book informally when teaching from How to Tutor and other books.

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I have going through the Franklin primary book and once it got to larger numbers and multiplication, I found myself thinking my oldest could really use this. I was going to get Strayer Upton PA, but I'm wondering if I should just use the Franklin book, since I like it. But I really prefer a real book.


Hunter, you've used SU, how does it compare with the Franklin book?


I'm sorry, but I don't remember the Franklin book well enough to compare it to S-U. Some of these books I used while I was still seizing so much more often and my memories of that time are pretty spotty.


Just the other day a friend was asking me about the storm the night before, and I realized I had a total blackout of the night before and knew NOTHING from the late afternoon to the next morning. Oh well.


This is one of those cases where I can't help you. Sorry. :) I'm just thankful I remember as much as I do remember!

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Okay, as for that much, Franklin Book 1 is a grade 1 book right, and SU Book 1 is grade 3/4? I remember much more about SU than Franklin.


SU reviews and covers Grube's at an accelerated rate, for the 3rd graders that did not have formal arithmetic in grades 1 and 2, which was a common method at the turn of the 19th/20th century.



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That's basically what I figured. Im looking at Franklin primary, i wonder if it is grades 1-2 and Franklin book 1 is grades 3-4 like SU. I will have to check .... So SU is based on Grube's? Good.


Eta: wow Franklin book 1 looks very different from SU samples. It keeps on working every number up to 100. I stopped looking after that. I really like the primary book, but I think I prefer SU, as far as I can tell from samples, over Franklin book 1. I am quite excited to use these!


Eta 2: found this great review of SU, including some pictures. http://desertramblings.wordpress.com/2012/10/05/strayer-upton-practical-arithmetics-review/

After reading that I feel like I'd rather cover multiplication using SU instead of Franklin.


It might help to read about Pestalozzi (1746-1827), who was the grand-daddy of modern elementary math teaching.   Montessori and Froebel were both heavily influenced by him, though they went in different directions.  Steiner seems to have been reacting more against his ideas, but might still have used some of them.  I'm not sure what "Waldorf and vintage number recognition lessons" are, but number recognition and "object lessons" were an important part of Pestalozzi's system. 


Lessons on Number, As Given in a Pestalozzian School


PestalozziWorld -- Methods


The teacher encourages the pupil in the development of language, observation, and mental skills which proceed from the "three elementary powers" of making sounds, forming images, and imagining concepts, powers on which Pestalozzi based his whole educational practice. In aiming to make education "a steady, unbroken development of these fundamental powers", and to ensure certain progress "from obscure to definite sense-impressions, from definite sense-impressions to clear images, and from clear images to distinct ideas", he seeks to base all teaching on sound, form, and number. (...)


From such a conviction grew his methods in elementary education. All activities were planned to enable correct ideas of number, form, and language to be developed from good and full perception. 


From what I've read, Grube's innovation was to take Pestalozzi's approach and change the order of the lessons, to teach all four operations at once.   The "Manual of Methods" doesn't follow Grube; they specifically say, "do not teach multiplication and division in the primary class" (p. 110).  I don't know what Strayer-Upton does (can't find my copies), but the review linked above talks about the section on multiplication starting part way through the book, so I'm thinking maybe it doesn't follow him either.    

Anyway, it seems as if Pestalozzi laid the groundwork for all of these methods.  He isn't talked about much these days either, but he does get a mention in all the "history of education" textbooks.  
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Waldorf is based off of Grube's 4 processes, but I never knew what the other parts of Grube were based off of, I heard that it was someone earlier. So I guess that is Pestalozzi. I figured the Manual of Methods was talking against Grube's 4 processes, but not the rest of it. So I guess it would be better to say the Manual of Methods is based off of Pestalozzi.


I like the SU order of presentation. I think a review for 3rd graders using Grube's is good, but I'm not sold on Grube's 4 processes for first grade. I am sold on the rest of Grube, which I guess I'm finding out is more accurately attributed to Pestalozzi.


Vaquitita, that is a nice SU review!


ElizaG, thanks for these links!

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So I guess it would be better to say the Manual of Methods is based off of Pestalozzi.

Some aspects of it, anyway.  I'd guess that there were other influences as well.  


The teaching approaches in these manuals were often called "common school methods," referring to the American system of public (common) elementary schools that got started around 1840.  I just came across a book from 1895 titled The Dawn of Common School Methods Or, Pestalozzi The Disciple of Rousseau and Inspirer of the Herbartian System.  Unfortunately, it's not online, but the title is long enough to get the author's point across.   :001_smile:


Before Pestalozzi, the big name in education reform was Locke, and before Locke it was Comenius.  They were all considered progressives, even radicals, though they've now been around long enough to have their own tradition.  

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