There are even free online albums (linked to in that post), where you can see pictures and instructions for all the Montessori materials, including math. Also you can google the name of any math material to find out more about it.

Actually, children are using paper & pencil in Montessori math from the very beginning – in elementary, every time they use a material (the golden beads, the bead frame), they are asked to record some of their problems and answers on paper. In that case, they are writing down the numbers, but they are still using the materials to figure out the answer.

However, the leap from concrete to abstract starts as early as 3rd grade. They are given materials that require more abstract calculations and less help in the concrete realm. By the time they shift completely to abstract work, by 5-6th grade, they have almost no problems because they understand the “why” of what they are being asked to do, whether it is carrying, borrowing, or doing long division.

Also, because of the concrete materials, they have a very good grasp of basic math facts (addition, subtraction, multiplication, and division for numbers 1-9), which makes doing work on paper fairly easy.

The intention is always to move away from the materials when the child is ready – long before college entrance exams

First of all, if workbooks or worksheets are used, I do not think they should be “graded”; I totally agree about the extrinsic nature of this kind of evaluation, and have written about it extensively. However, just as a child may need help to correct answers on the Multiplication Bead Board, they may need someone to help them correct answers on a worksheet. I love it when children can do this themselves, rather than have someone do it for them. But never, ever, should it be graded or given a grade.

Secondly, I do mention all of the math games and they are definitely a wonderful way for children to master their math facts. Do they work perfectly for every child? Does any child ever need another way to “view” math equations? I leave it to individual parents and teachers to answer that question because I think that children and circumstances vary.

While I studied the Pink, Blue, and Green Series quite thoroughly in my training, my observation was that when using things like Word Lists for spelling tests, it becomes a little bit of a “hit or miss” process (I haven’t heard of the “box” method). My Pink, Blue, and Green Spelling Cards use all the same words that are in the Pink, Blue, and Green Series but in a way that insures that no words are skipped and that words are approached in order of difficulty. If you have another way of doing that, that’s great. I’m sure there are several approaches that still stick to the Pink, Blue, and Green Series pattern.

Still, might you have to agree that children do need to learn testing skills, and that there are not Montessori materials to teach things like that? I would be interested in hearing your thoughts on that.

My aim in this post was definitely not to encourage parents and teachers to rely on worksheets (as I mentioned early on, I have seen Montessori schools that do that and it’s disastrous). The Montessori materials are fantastic and teach in a hands-on way that no worksheet can duplicate.

My thoughts were more directed to skills that Montessori materials may not address – or learning styles which may benefit from more than one approach. Unfortunately, sometimes students leave a Montessori school with “gaps” because only Montessori materials are used and certain skills (like testing skills) are not learned. When a student enters public school and tests poorly despite a rich Montessori education, it reflects badly on Montessori. I would love a world where students could stay in Montessori until college and never be tested, but that does not seem to be a possibility for most children.

Thanks for stopping by!

Which is purely extrinsic threats, and we know what studies show about that: when you remove the motivation they perform more poorly. It is our task as directors to spark their interest and foster their love of learning. Quality, not quantity.

I am surprised you do not make mention of the Montessori Mathematical Memorization Materials. There are so many of them! Specific step-by-step, easy to make didactic materials which bring the children to the point of memorization in such a simple way, through learning which appeals to multiple intelligences. They have been proven for 100 years!

I also wonder where you received your ideas for pink, blue and green materials. There in fact IS a formal Montessori spelling curriculum, as taught to me with the St. Nicholas method, involving a series of 4 pink and then 4 blue boxes, then a series of green boxes. In the elementary, the bulk of spelling addressed with the green boxes, and spelling is addressed with every single lesson in every area of the curriculum when new words are presented by dissecting them into their roots, prefixes and suffixes, and the parts translated to their original language and definition.

I am very concerned at the way of American Montessori when I see that directors are more and more using tests, workbooks, worksheets and quizzes in the classrooms. What a waste of time and energy when there are so many wonderful and awe inspiring works to be created, manipulated and actually UNDERSTOOD! Don’t fall into the trap of pressure. Do the research on the imperical data if you must, but trust the Montessori Method!

I feel similarly about them – if used, it should be done with thoughtfulness and care, and not just as busywork.

In elementary, there’s a temptation to give a child a page of math problems instead of using the wooden math materials, and that’s what I was trying to address in this post.

Thanks for stopping by!

One of the biggest negatives for the overuse of worksheets in traditional education is the waste of paper! That really takes my breath away. That’s one reason I recommend turning worksheets into re-usable materials instead of just making a copy for each child.

Thanks for stopping by!