Unlearning New Math

[Pilleyhillmom]

I am going to be homeschooling our soon-to-be 5th grade foster daughter this coming school year. She has done very well in the public school, but when I gave her a math placement test to find out what math level she needed here at home, I saw that she solved multiplication problems using new math techniques, which are foreign to me. Her answers were correct, but none of the math curriculum I have used over 18 years of homeschooling has looked anything like the math she was taught. I will be teaching her traditional math techniques, but I'm afraid we will have to back up quite a bit in order to teach her traditional math methods. I don't want to slow her down or discourage her too much, but this may take some time to relearn traditional methods. Has anyone navigated this before, or would anyone be willing to share suggestions? We have used Saxon, Right Start Math, PACES, and Teaching Textbooks for 8 of our kids over the years.

[Kiara.I]

I would have thought that some of the techniques would be similar to Rightstart, given how it focuses on breaking down numbers and manipulating them. Is it not? Partial products, for instance?

If you can, it would probably work best to use her techniques and gradually bridge them over to a more traditional notation form; which, presumably, was what the school would have done anyway.

The Rightstart materials may work well for that.

[EKS]

Perhaps instead of forcing your foster daughter to learn traditional techniques, you might consider learning the techniques she knows and then move from there.  You could have her teach you.  If she has been successful so far, I'm sure she will continue to be. 

Edited July 21, 2019 by EKS

[lulalu]

If she is understanding math and getting correct answers, I wouldn't make her learn a different way. It will be just as beneficial for you to learn the way she understands. Look at Math Mammoth or Singapore. 

[HomeAgain]

4 hours ago, lulalu said:

If she is understanding math and getting correct answers, I wouldn't make her learn a different way. It will be just as beneficial for you to learn the way she understands. Look at Math Mammoth or Singapore. 

This.  If she is efficient at her method, there's no point in forcing her to do it another way.

My ds does math weird.  It's a mixture of the methods taught in MEP and his own way of thinking/visualizing with c-rods, and he's quick with it, so I carry on and teach him why things work.

[8filltheheart]

2 minutes ago, HeighHo said:

My dc learned both at school. It took two days in grade three to master the traditional add/subtract algorithm as he already fluently composed and decomposed.  You don't want to undo her understanding, she'll need that for future coursework.  Consider Singapore Math.

I agree.  If she understands what she is doing, there is no reason to dismiss her approach.  I would focus on integrating her understanding with the more traditional methods.  They are completely related.  It should be easy to show her what her methods are representing in a more algorithm representation. 

[sweet2ndchance]

Why make her feel like she's doing it "wrong" if she is getting the answers right and she understands it? There are many ways to arrive at the correct answer to a math problem. If she is doing partial products, that's really nothing more than "foil-ing" the problem the same way you work out an algebra problem. Lattice multiplication is the same idea, different format. Do you know for sure she can't do it with the traditional algorithm? Just because that's how she chooses to solve the problem doesn't mean she can't do it another way, she just prefers to use the method that makes sense for her. Even if she doesn't know how to do the traditional algorithm, there is no reason she can't learn it while still moving forward. And there is no reason for her to have to go back if she is using a valid method that consistently arrives at a correct answer. As long as she can both arrive at the correct answer and explain how her method gets to the right answer then I don't understand why she has to unlearn a valid method for solving a problem.

 

[daijobu]

I had the opposite issue with a gal I was tutoring.  She had been taught the traditional long division algorithm but it just wasn't sticking with her.  Each time, it was like she was having to memorize it all over again.  I thought the partial quotients method might resonate better with her, especially as it's described in Beast Academy.  

I described to her the new long division algorithm, and we tried a few problems.  Then I compared it with the traditional algorithm and showed that we arrive at the same answer.  And then we discussed the advantages and disadvantages of each approach.  (Neither one is perfect in IMO, so it's really a matter of preference.)  I asked her to try out the new algorithm with some homework problems and let me know which she preferred.  

Learning new and different algorithms and comparing them to others is a great learning experience, particularly when you can explain why they arrive at the same answer.  After that, you can proceed with the one you think is most efficient and gets the job done.   

Edited July 21, 2019 by daijobu

[Pilleyhillmom]

Thank-you for your suggestions. Practically speaking, I will not be teaching myself new math techniques this year. Our home of 13 children, six of whom are foster children, does not permit me the time or energy to begin a brand new math method with anyone. Our home is full of special needs, and thus I spend a great deal of time personalizing our kids' education, tailoring it, etc., and the curricula we are using works beautifully for the children using it (and does include Math Mammoth, which I forgot to mention). With the 4 different math programs we are currently using, I just won't be making any drastic changes to what I teach. One momma and a big, needy crew means we forge ahead with what we've got.

But our foster girl is very bright and learns quickly. I'm sure she will be able to learn traditional math methods, perhaps quicker than I was expecting. I just want it to be a gentle process and was hoping someone had some experience they would be able to share as they made the change from new math to traditional techniques.

[Lecka]

https://en.m.wikipedia.org/wiki/Lattice_multiplication

Maybe it is lattice multiplication?  

 

[Lecka]

Maybe look for a YouTube video comparing the algorithms?  If you know the name of the algorithm then it might be easy to search a video and then let her watch it.  

[Lecka]

If it is lattice multiplication here is a video.  

[Lecka]

I think she might also already know how to do both ways, but she happened to do one way on the placement test.  

It’s possible if you say “this time use the other way” and she knows it, too.  

I think this would have been the case for my nieces.

Edit:  my nieces did Everyday Math in elementary school.   

Edited July 21, 2019 by Lecka

[Pilleyhillmom]

Thank-you, Lecka. Yes, it is Everyday Math and the lattice multiplication. I am happy if she has been taught a variety of ways of thinking in order to solve math problems. One particular "way" is not really right or wrong, just impractical for our household. Perhaps you're right and she will already know how to use traditional multiplication. I that case I may have been too hasty in posting a question 🙂 . We will see how this goes!

[HomeAgain]

One gentle way is to look up the montessori checkerboard.  It is very similar to the lattice method but with color coded squares to show exactly how it works.  I tend to use that as an introduction to carrying before giving graph paper with the same color squares in columns (instead of diagonals) to show the traditional method.  It requires working with blocks, though, or at least being aware of the colors (I made ours to go with MUS blocks)

[Lecka]

My nieces loved to do it and “wow” their older relatives who didn’t know how to do it.  They loved to show it off and to draw the little boxes. 

But I think at a certain point they get tired of drawing the boxes all the time.  

[EKS]

4 hours ago, Pilleyhillmom said:

Thank-you for your suggestions. Practically speaking, I will not be teaching myself new math techniques this year. Our home of 13 children, six of whom are foster children, does not permit me the time or energy to begin a brand new math method with anyone. Our home is full of special needs, and thus I spend a great deal of time personalizing our kids' education, tailoring it, etc., and the curricula we are using works beautifully for the children using it (and does include Math Mammoth, which I forgot to mention). With the 4 different math programs we are currently using, I just won't be making any drastic changes to what I teach. One momma and a big, needy crew means we forge ahead with what we've got.

But our foster girl is very bright and learns quickly. I'm sure she will be able to learn traditional math methods, perhaps quicker than I was expecting. I just want it to be a gentle process and was hoping someone had some experience they would be able to share as they made the change from new math to traditional techniques.

I get that you have a lot of competing needs in your household.  But if you're interested in personalizing the education of the child in question here, you might want to spend the few minutes it will take to understand the way she has been taught to this point.

[ChocolateCake]

I don't know if Everyday Math has changed since I used it when teaching PS (about 14 years ago) but I don't remember anything being taught until mastery.  I would spend only one day teaching a method to do long division.  I think there may have been about three different methods (including the traditional algorithm).  I would just tell the kids to do the work any way they wanted after they learned the different algorithms.  So, if she was using Everyday Math, she may have learned some traditional math as well as other methods.  I would just show her the traditional way but also let her do the non-traditional way as long as she can get correct answers (maybe have her do half and half).  

Edited July 28, 2019 by ChocolateCake

[Guest]

Eureka math is a common core method and is free online (thanks to the New York department of Ed). https://www.engageny.org/

 

if you look up what atandards she has been working on, you can see how it is taught and if she already likely knows the standard algorithm. Chances are high she does. 

[Storygirl]

My children used Everyday Math in elementary school in fourth and fifth grades. They had been homeschooled before that, using traditional methods. I had to familiarize myself with the new methods they were being taught, so that I could help them with their homework. It really was easy for me to understand partial quotient division and lattice multiplication just with a quick explanation -- you will be able to learn it easily, in just a few minutes.

I am not saying that you need to switch over and teach a different way, but that you can quickly figure out what she is doing. Partial products division, in particular, is really very helpful, because it diminishes the need for guessing/estimating what numbers should go in the quotient.

Everyday Math teaches both the traditional algorithms and the other methods. The teachers my children had then encouraged the kids to use whichever method they preferred. So there is a good chance that your foster daughter has already been shown the traditional ways, and that it won't be all new to her. 

[Monica_in_Switzerland]

If she understands what she is actually doing with her method, and you understand what is actually happening with the traditional stacked algorithm, this should take about 30 minutes in an "aha!" sharing session.  If either of you does not have the full grasp of your method, this will be trickier.  

 

My kids are excellent multipliers, but I still take the time to regularly remind them of what is happening in the stacked algorithm, just to be sure they remember they aren't doing magic.  

I write out the problem like this:

36

42

_______

answer          <----- 2x36

answer          <----- 10x4x36  (it's 10x4 rather than 40 because when we add the placeholder 0, we really mean we're multiplying by 10)

________    add together to get a total of 42 copies of 36.  

final answer

 

 

Hope that makes sense.  Now, just do the same demonstration with the lattice (It will take you less than 5 minutes to understand with one of the above linked videos) and there you go.  Just show that in either case, you get a total of bottom number copies of top number.  Then have her do a few problems your way each day for a week.  I really don't think this will be a big deal at all.