Rod &Staff math...conceptual?

[Mama2four]

I recently saw a post where someone listed R&S math as a conceptual math curriculum. I've been teaching with R&S math for my son from levels 1-3 because he needs the repetition it provided. On the other hand, both of my daughters grasp math concepts easily and I use math-u-see with them mostly with some R&S thrown in. Math-u-see did not work for my son when he was younger, hence the switch. But I've been trying to figure out where the conceptual teaching is in R&S. It seems more rote teaching to me. There have been instances where my son will make mistakes because he doesn't seem to know the "whys" of math, he is just following the algorithm, so I will go back and reteach the concept the mus way. I feel some attachment to R&S, but I would like my DC to have a good conceptual knowledge of math that is provided in curricula such as Singapore, Rightstart, Math Mammoth, etc. I'm leery to jump ship completely with him because he literally needs to do the same kind of problems alot of times to get it, but then he has difficulty with word problems and knowing when to add or subtract even though I go o er the key words with him. He rarely can do a word problem on his own. If R&S is conceptual, can someone point out where to find that info. I've looked in the tm's with no luck. Thanks.

[MamaHappy]

That's funny because I've only seen R&S math described as more rote. Maybe you're confusing R&S with RS (RightStart)??

[Mama2four]

I may have confused the two. I could use some suggestions on how to transition to a conceptual program with him. I'm so used to all the repetition R&S provides and I'm not sure if the other programs provide as much.

[lotsofpumpkins]

When it comes to repetition of math facts vs. conceptual math programs, I have found CLE to be a "best of both worlds" kind of program. We were combining R&S and Singapore prior to finding CLE 2+ years ago.

 

That being said, if you want to stick with R&S, then here is a copy-and-paste from another board I frequent. It's long, but it does discuss conceptual understanding as found in R&S. It was directed at someone who was using Singapore.

 

Here are some comments about R&S I've saved over the years:

 

From Laura in TX:

 

Rod and Staff is a traditional math program, more similar to the math programs used in the 50s and 60s to many of the programs used today. These were excellent math programs, and most would acknowledge that Americans were better at math when we used these traditional math programs than students are today who are using all of these programs that are emphasizing “conceptual understanding†every step of the way. Traditionally, math was taught with the classical model, where there was more emphasis on drill and memorization in the early years, with an increase in conceptual understanding or analysis occurring each year. R&S does teach conceptual understanding, but it is quite difficult to see until you are perhaps 2 or 3 months into the program because it is done in the early years with little baby steps.

 

The best example I can think of this is the instruction with fractions. My daughter’s understanding of fractions, now in the fourth grade, is absolutely wonderful. Rod and Staff began with the traditional dividing of shapes into halves and thirds and fourths in the second grade, and also advancing to two-thirds or three-fourths, and the idea the three-thirds or four-fourths equals one. In the third grade, they apply this knowledge to math in all types of contexts - what is one half of a foot, what is one-fourth of a pound, what is one-fourth of a dollar? What is three-fourths of a dollar? This is done pretty much off and on in the daily lesson, all year long, and is seen in MANY word problems. My daughter really understood fractions and applying them to numbers and real problems.

 

Then you move to fourth grade, and they introduce counting by halves, by fourths, and by eighth, using a ruler as a visual aid at first. So they count 1/4, 1/2, 3/4, 1, 1 1/4, 1 1/2, etc. and also 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8, 1. After doing this exercise for several days, they do equivalent fractions, but it is almost not necessary to explain anything, because they have already figured out that 4/8 = 1/2 and that 2/8 = 1/4 because of the counting exercises. They just now learn the algorithm that shows that this same logic can apply to numbers which can’t be visualized, such as 27/36. By the time my daughter reached the lesson where they taught how add fractions, she already ‘understood’ that you could just add the numerators of like fractions, that you couldn’t do that with a fractions like 1/8 + 1/4, but that you needed a common denominator. This understanding was about 2 months in the developing and it would have been difficult to see by just flipping through the book.

 

Somewhere around this general timeframe, they are also doing long division and giving remainders as an answer, but combining it with word problems so that it is obvious why the remainder is actually a fraction such as “3 boys share 4 peaches. How many peaches will each boy get? What part of the remaining peach will they get?†After a couple lessons with word problems like this, they have division problems where they are supposed to give their answer with the remainder as a fraction, and they are then introduced to the term “mixed numbers.â€

 

So, yes, I would say there is wonderful teaching in R&S that leads to conceptual understanding, it is just done in a different way than many modern math programs, and that it occurs very slowly in the lower grades. Because there is a strong emphasis in the primary grades on drill, particularly fact drill, people often get this misperception of R&S, especially if they look primarily at the student workbooks or text instead of at the TM. The real lesson and the real learning takes place in the daily lesson at the whiteboard. The workbook and/or textbook is mainly just review problems and/or drill.

 

I recommend that you read this article which is linked on The Mathematically Correct Web page by Dr. H. Wu called “Basic Skills Versus Conceptual Understanding: A False Dichotomy in Mathematics Education.†This article will help you understand why it is essential that students get plenty of drill and review as well as lessons that work towards conceptual understanding; and also why conceptual understanding can only get you so far - no one can visualize a problem such as 2/97 divided by 31/17; eventually a student must become fluent with the algorithms, which means to have them memorized to the point of automaticity. This only happens with drill and review.

 

One more thing, since you are currently using Singapore, I can compare it a little to that program. Singapore pushes conceptual understanding more than many math programs. It has some drill and review, and the assumption is that teachers in Singapore are providing much more drill and review, but this program pushes to the limit for conceptual understanding in the early grades. It doesn’t take small steps in this area, it wants total understanding in one lesson of some concept that R&S might spend two or three months developing. Additionally, Singapore wants them begin applying this new understanding immediately to problems and word problems. This is excellent for some children, especially the math-bright among us, but for many, it is too much too soon. My daughter needed the slow and steady approach of Rod and Staff for the primary years. I knew this, but I couldn’t really verbalize it, until I read the excellent review of Singapore math by Susan Wise Bauer of the Well-Trained Mind which you can find on her Web page.

[Mama2four]

Thank you so much for sharing that information. It was very helpful. I know my son needs the kind of teaching R&S provides, I guess I need to be patient in knowing that more understanding will come eventually. Since I own MUS also, I will continue incorporating teaching with the blocks hoping more seeps into his brain. I know alot of his problem is that he just wants to hurry and finish his lesson so he can do other things. He doesn't want to think about math. Thanks again for the information lotsofpumpkins.:)