math curricula question

[dragons in the flower bed]

It seems to me that RightStart, Miquon, and even Life of Fred all lead children to discover, deduce or otherwise figure out the math concepts. Singapore, Saxon, BJU, Horizons, and Key to... directly explain these concepts or else the "how to do it" that is based on the concepts, not expecting kids to sort them out themselves.

 

What math program do you think directly explains the concepts best? Not a program that gets the concepts across by asking children to figure out what's going on, not a program that teaches kids the applications of the concepts so they can function as people who will need to multiply and divide and pass tests, but a program that explains outright the concepts so that kids deeply understand what is going on when they are multiplying, etc.

 

Embedded in my question of course is the notion that children can deeply conceptualize mathematical principles from plain explanations. Feel free to explain to me why that isn't true if you think it isn't. I've been thinking about this stuff a lot lately.

[Faithr]

I think Saxon has good explanations but I know some complain that it isn't conceptual enough. I think Math U See might be what you are looking for. We used that for a year. My kids didn't like it because it went too slowly for them. But it took you through every step and explained the 'why' very well.

[LizzyBee]

The Key To series is very straightforward. My kids rarely got stuck with it.

 

I only used Saxon for a year (5/4), but some of the explanations were not mathematically correct, so I had to tell my dd to ignore what the book said and re-teach the lesson a different way.

 

I love Singapore and I think most of the explanations are clear and accurate. The word problems force kids to apply what they've learned, so when my kids can do the word problems accurately, I know they really understand the concepts.

 

Life of Fred leaves some gaps in the instructions, so kids who don't infer easily will struggle with it. I found that my 13 yo needed to use something else to learn the material, then use LOF for review and to take the knowledge to the next level, so to speak.

 

I haven't used the other programs you mentioned.

[Capt_Uhura]

RS does want kids to discover the concepts themselves, but then a few lessons later, it explains it. For instance, you do area of a rectangle a lot. Then you're presented w/ area of a right triangle and my son quickly deduced that the area is just half the area if it were a rectangle. Later in the lesson, you do demonstrate this concretely for DC. It was done similarly in SM I believe but you actually cut up rectangles into triangles and rearranged to prove the algorithm. RS doesn't just say, "To find the area of a triangle use the formula A=1/2 bxh."

[Karen in CO]

I think the answer is maybe none of them. I've actually used every program you listed (plus MUS and MM), and I agree with the way you seperated them. I am biased by my own understanding of math and by what worked for my children.

Singapore, I've used EB, 1,2,3,4 and NEM 1&2. My dd hated it. She hated that the problem sets were designed to be used with on type of solution which was explained in too much detail. She didn't think there was enough variety in the problems or variety in the types of solutions.

MUS - she despised it. Again, because there was a straight and narrow path from the explanation tot he answer and not a lot of variety in the types of problems. The explanations were great, but it relied on one type of solution, and she views every problem as having multiple paths to resolution.

BJU - Used level 2 and 3. she actually really like the explanations. It had a good variety of problems, and a terrific variety of ways to solve the problems. We switched from this because the relgious content became unpalatable. I don't know if this holds true for the upper levels. I plan to use this for my K child along with Miquon and Singapore CWPs until we get through at least 3.

Saxon - The explanations are sometimes off. We often don't use them, but these are the best explanations we have found. The word problems are too easy, but my dd thinks long division is the coolest thing ever because it broke the problems down and explained them in clear, concise terms. At first she hated that there was math vocabulary included in the lessons, but now she loves understanding what those things mean. She is taking things she has learned in Saxon and using them at a higher level in other mathematical situations - she helped her dad ficgure out how much concrete to use for sinking posts based on the diameter and depth of the hole.

Keys to are Great, but they don't cover early math - I've used a couple of the geometry ones for my ds.

[Karen in CO]

 

Embedded in my question of course is the notion that children can deeply conceptualize mathematical principles from plain explanations. Feel free to explain to me why that isn't true if you think it isn't. I've been thinking about this stuff a lot lately.

 

I'm answering twice, because I was interrupted earlier and never got to the interesting part of your question.

 

I used to be a big believer in discovery based math, until I met a group of high school kids who were a product of discovery math programs. I know that they aren't all alike and that there is a certain amount of teaching that still must be done to follow up, but I realized that there is some serious balance that needs to happen.

 

One of the things I love about the idea of CM is the value it places on kids having experiences in the real world. I really think that kids need to play in the mud and build towers and bridges. It allows them to discover some basics about the world and continue to look at the world in wonder. Those experiences make a good foundation for real learning later on. That is kind of my feeling about discovery math. It creates a contrived environment in which a child will discover things about mathematical relationships and principals. It doesn't replace a skilled teacher explaining the principles; it enhances the learning.

 

I went through every math program I could get my hands on and frustrated my math-teacher brother before I realized that what I was looking for in a math program was SOMEBODY to teach math to my kids. I wanted that clear explanation that stopped short of spoon-feeding. I had one terrific math teacher in highschool and a few terrible ones in college. That one terrific teacher taught me more math than I learned before or since. He isn't in a book. The best I can do for my kids is to learn the math, pick a book that explains it well, and have somebody on call that can explain it better.

 

I do discovery mathy things with my kids because they are fun, and I do work so some discovery math thing can count as math when I'm really busy. It isn't my main math, and I don't count on it to teach, just to provide opportunities for experiences.

[Corraleno]

What math program do you think directly explains the concepts best? Not a program that gets the concepts across by asking children to figure out what's going on, not a program that teaches kids the applications of the concepts so they can function as people who will need to multiply and divide and pass tests, but a program that explains outright the concepts so that kids deeply understand what is going on when they are multiplying, etc.

I would say Math Mammoth does. The explanations are quite conceptual but also concrete. IOW, she explains the concept, and walks the student through it step by step, usually with concrete illustrations. There is some discovery mixed in (especially in the Puzzle Corner problems), but not so much that it would frustrate kids who don't inherently think that way.

 

I think a lot of people look at MM in the lower levels, and don't see much of a difference from other curricula, except maybe the problems are a bit more challenging. It looks like a lot of grouping colored circles or whatever, and the subtle introduction of higher level thinking may not be so apparent. But by the time you get to 4th grade, she's introducing algebraic equations using "scale" illustrations (like HOE) with numbers and colored shapes. Then she has them solving simultaneous equations with two variables (where you have to calculate the value for one variable and plug it into the second equation to calculate the 2nd variable). In 4th grade! And kids think it's just a fun game, not realizing they're doing algebra.

 

Once you get into 5th & 6th grade, I think MM's strengths become even more apparent. Her explanations of fractions, decimals, ratios, and percents are very advanced, yet completely understandable. She has kids prove for themselves why "moving the decimal" in decimal division works by having them create equivalent fractions, rather than saying "here's the trick, just do it this way." The problem sets are quite varied, so kids see the concept from multiple angles. Her explanation of integers in 5b is very very similar to that in Foerster's Algebra, and she logically leads from integers and number lines into functions and graphing in a coordinate grid. When a student has seen these concepts and worked these kinds of problems in 5th & 6th grade, by the time they get to algebra, they totally understand what they're doing — and why.

 

I think what sets MM apart is that it not only explains mathematical concepts in a very clear, explicit, and concrete way, it links those concepts together, and I think that's a key component that's missing from many math curricula. To understand why dividing by a fraction is the same as multiplying by its inverse, you need to really understand what division is and what fractions are and how all of the operations relate to each other. When a student truly "gets" the underlying grammar of math, it's so much easier to learn the language at higher levels.

 

Jackie

[Closeacademy]

I've found that Singapore explains some things well and clearly and Rod and Staff is rather explicit when it comes to explaining math--so much so that I can pretty much take their diagrams on how to do something new and my dd can create a notebooking page for that concept and add it to her math resource/reference folder.

 

Rod and Staff also has lot of review.:001_smile: