Math curriculum that is both conceptual AND procedural?

[bluejay]

I read an article by Susan just now where she talks about the importance of both procedural and conceptual approaches to math.  Now my family uses Saxon.  We are okay with it but as I said in a different thread, I am looking for something of a hybrid between mastery and spiral.

 

I generally follow Saxon textbooks, but I let the kids play with manipulatives, explore concepts and find solutions aside from what's in the books.  I am okay with teaching them the procedures of "borrowing," etc.  but I want to make sure they understand why these things work.  DS especially, is a very hands-on type of student.  I do not want them to miss on anything and DH says he'd prefer a mastery-based approach.

 

Do you folks think Saxon is fairly good at covering both conceptual and procedural methods?  Can we use a program like Math Mammoth to supplement (or even completely replace) it?   Also can you buy MM and then use it multiple times (unlike Saxon consumables)?  The price seems very reasonable for a digital download.  The Blue series for Grades 1-3 is only $45 if I read that correctly.

[EKS]

I think Singapore does a great job melding the two.

 

The problem with Saxon, IMO, is that all that practice makes kids forget the concepts.  They never have to go back to the concepts in their minds to reconstruct how to do something.  I think the extreme amount of practice also eliminates the need to develop problem solving skills--Saxon works best when its easy (or else it takes *forever*), but tackling hard problems is the only way that I know of to learn how to solve hard problems.

[Farrar]

I think MM has the most split focus between the two - lots and lots of practice for algorithms, lots and lots of conceptual activities, word problems, etc. and requiring kids to think though things.

 

But I don't think that MM's balance is the right one for all kids necessarily. I mean, Beast Academy has very little focus on the procedural element of math and it could still be enough for some kids. Saxon might be right for others, though I admit I agree with EKS's assessment above that it's too procedurally focused for most students to keep a good grasp on the concepts.

[Tenaj]

 

The problem with Saxon, IMO, is that all that practice makes kids forget the concepts.  They never have to go back to the concepts in their minds to reconstruct how to do something.  I think the extreme amount of practice also eliminates the need to develop problem solving skills--Saxon works best when its easy (or else it takes *forever*), but tackling hard problems is the only way that I know of to learn how to solve hard problems.

 

I've always heard that Saxon doesn't teach the concepts and also that kids who use Saxon can't transfer their knowledge when the wording is changed from what they are accustomed to (i.e. other curriculum, or standardized tests).  I found it interesting that this year when I got their Iowa tests back, all my kids, from the first grader to the ninth grader had improved and scored their best ever in the categories of Problem Solving and Math Concepts after using Saxon for about three years.

 

I understand that it doesn't work for everyone but I do think that Saxon teaches the concepts, just in a different way than Singapore.  I will admit the drudgery of some math days with Saxon and I will also admit that my fingers have been cruising myself over to the Math Lessons for a Living Education website quite often lately because I'm so tired of those Saxon lessons (especially the second grade and third grade books, just shoot me now!) but even if I decide to bail on it, it won't be because it doesn't work, it will be because I'm so bored with it!

[jer2911mom]

I feel like BJU does this well in the elementary years.

[EKS]

I've always heard that Saxon doesn't teach the concepts and also that kids who use Saxon can't transfer their knowledge when the wording is changed from what they are accustomed to (i.e. other curriculum, or standardized tests).  I found it interesting that this year when I got their Iowa tests back, all my kids, from the first grader to the ninth grader had improved and scored their best ever in the categories of Problem Solving and Math Concepts after using Saxon for about three years.

 

I understand that it doesn't work for everyone but I do think that Saxon teaches the concepts, just in a different way than Singapore.  I will admit the drudgery of some math days with Saxon and I will also admit that my fingers have been cruising myself over to the Math Lessons for a Living Education website quite often lately because I'm so tired of those Saxon lessons (especially the second grade and third grade books, just shoot me now!) but even if I decide to bail on it, it won't be because it doesn't work, it will be because I'm so bored with it!

 

I wasn't saying that Saxon doesn't teach the concepts because it absolutely does, frequently in exactly the same way that Singapore does.  My point was that the extreme amount of practice with the procedures can make kids forget the underlying concept because they never have to use the concept to reconstruct the procedure.

 

The Iowa tests are, frankly, not very difficult.  The problems are straightforward and meant to be solved quickly and by rote, even the problems in the concepts and problem solving section(s), which is just what Saxon is preparing kids to do.

[mamamoose]

I think Math Mammoth is a good combination of both but I will say Righr Start taught borrowing and carrying the best of the two. It is manipulative heavy though, and honestly we don't use half of what we bought, which is frustrating, so I'm not sure it's worth the entire package. The AL abacus is amazing at teaching that part conceptually, along with multiplying and dividing. I've also used Saxon and my older kids came from public school where they used Saxon, and my oldest is very very bright at everything and she didn't understand conceptually what she was doing. She did a year of right start (D) and I can't believe the difference in her math skills overall. We then jumped to math mammoth.

[Rosie_0801]

The minicomputer lessons in CSMP are great for a hands on way of teaching borrowing.

[Spy Car]

Primary Mathematics (Singapore).

 

Bill

[bluejay]

Thank you, everyone!   I think the problem with the Saxon exercises is that they are repetitive and worded the same every time.  There is no variation.  So the child does not have to think about what is going on; he or she just hears a keyword and remembers the formula. 

 

One way I can think of to remedy this situation is to give the child new problems, and require him or her to explain the solution (easier with manipulatives).  I have also been using manipulatives to help explain concepts and allow the child to think in new ways. 

 

I'm thinking of getting MM samples to see if my kids can solve problems from other math curricula. This may supplement or fill in gaps in Saxon.

 

Saxon does have concept teaching.  But it could use more of it instead of mostly drills.  Also, while memorizing things like "the number at the top is ten less than the number below it" is fine, the child needs to understand WHY that is. 

Edited May 22, 2017 by bluejay

[8filltheheart]

Most decent mat programs do both. But I am actually confused by what you are looking for. SM and MM, for example, are mastery bc they focus on a single concept at a time. That focus on one topic at a time is what makes them mastery, not conceptual. Saxon is spiral bc it intersperses multiple concepts at a time. Sometimes the conceptual teaching ina spiral program is far less obvious than in a mastery program. I do not use Saxon, its repetitiveness is unnecessary for my kids bc they master concepts more quickly, but I do use a spiral program, Horizons, and I am always left wondering at the comments that it does not teach conceptual math bc the concepts are presented throughout. If you simply flip through it, it is not the same as actually teaching it.

 

Fwiw, my kids absolutely despise manipulatives. They don't need them and they are just a cumbersome nuisance. I taught my granddaughter this yr, and oh my goodness, she is a completely different learner from my 8 and the only way for her to really grasp what she was doing was with manipulatives. So much is really going to come down to what type of child you are teaching and their ability to integrate concepts mentally. Some kids need mastery. Some do better with spiral. Some needs hands on. Some don't. Not all kids learn the same way.

 

If Saxon is working other than the word problems, instead of getting rid of the entire program, you might want to look at Hands On Equations' Verbal Problems book. It contains three levels of challenging word problems. They are easy to use with any program and I have used them with both Horizons and Math in Focus (similar to SM). Fwiw, I owned 3 levels of MM and did not find the content much different from Horizons at all. I taught 3 levels of MiF (4th, 5th, and Course 1 (6th).) While the word problems were more challenging in MiF, I found little difference in content between it and Horizons, My Dd actually bounced back abd forth between them. (It was a personality thing, not a math learning thing.)

[bluejay]

Thanks for the tip, 8FillTheHeart!  Sorry for the confusion.  Maybe Saxon just approaches the idea of "mastery" differently from what I'm expecting.  It feels like a little bit of everything-- the child is not expected to master a concept before going on to another.  It's slowly over time.  And it can be confusing and frustrating when the child forgets the lessons.  I guess I have an issue with both the "heavily procedural" and "heavily spiral" approach that Saxon seems to do.  

 

I apologize for the confusion.  I have no experience with other math courses, so I don't know how they differ from one another. 

 

I agree kids are different.  My DD has a strong memory, but DS is more hands on and likes to feel everything with his hands.  I wouldn't be surprised if we end up using different courses for them. 

Edited May 22, 2017 by bluejay

[8filltheheart]

Thanks for the tip, 8FillTheHeart! Sorry for the confusion. Maybe Saxon just approaches the idea of "mastery" differently from what I'm expecting. It feels like a little bit of everything-- the child is not expected to master a concept before going on to another. It's slowly over time. And it can be confusing and frustrating when the child forgets the lessons. I guess I have an issue with both the "heavily procedural" and "heavily spiral" approach that Saxon seems to do.

 

I apologize for the confusion. I have no experience with other math courses, so I don't know how they differ from one another.

 

I agree kids are different. My DD has a strong memory, but DS is more hands on and likes to feel everything with his hands. I wouldn't be surprised if we end up using different courses for them.

It is confusing terminology, but I think if you can understand how to use them correctly in reference to scope and sequence, it will help you find what you want more easily. A mastery math program will have a money unit, a time unit, a double digit addition unit, etc. A spiral program introduces smaller amts of info and has multiple concepts per lesson. For example, my 1st grader's lesson today (in a 2nd grade textbook) covered multiplication, fill in the missing subtrahend/minuend, writing number sentences from word sentences, triple digit addition, 4 digit subtraction with borrowing, a word problem, and coin problems. A mastery program would focus mostly on 1 of those concepts with a few review problems interspersed.

 

With a spiral program, mastering concepts is spread over a longer period of time vs a unit.

[Vida Winter]

It is a struggle to get the right balance sometimes. The math programs we have used successfully are CLE, BJU, and Saxon. To get practice with differently worded problems, Khan Academy is a nice supplement. We have also done some of the AOPS books. There really is no perfect all-in-one program.