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the difference –Discovery Math
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Part 1:
This is in response to:
I have used RS A for two children now. (I have a 20 year old that we tried just about every math program with and still didn’t find one we liked: making math meaningful, Singapore math, math u see, saxon, Bob Jones, Teaching Textbooks, etc. When I found RS for one of my younger children 6 years ago I was thrilled. However, after using Level A and him coming away with very little understanding I switched him to Systematic Math. With the next child, I started Level A late in Kindergarten and am having the same issue. I guess what I don’t like about RS is that I feel like it doesn’t teach the child. It leaves the child guessing and trying to figure out what he is supposed to be learning. I have to admit that I find this frustrating along with the child. In theory, I like RS but in everyday teaching I am pretty frustrated. Any suggestions? We are nearing the end of A and not sure what to do next.
pollysoup
this is a hard and complicated question.
i’m going to try to help you draw a parallel–I’m sure it will have holes. Please forgive me in advance. Have you ever had a topic (cooking, baking, gardening, knitting, whatever, math, science, physics, composition, how to change your car’s oil or tire or sharpen a knife, etc.) that you were learning whether you wanted to or not…and the teacher told you what to do…and you did it and passed or were able to do it in a rudimentary way but with little true understanding and immediately FORGOT it!…then one day you WANTED to ….YOU needed to…and you went back at it with gusto…and you took the little you knew and DISCOVERED cooking, baking, knitting, science, etc. Yeah, you might have had questions along the way or needed a bit more guidance here or there….but it became yours because you studied the problem, took what you knew, discovered the next step, added it to what you knew, went ah-ha…well if that worked what about this…etc.
how does this apply to math?
many people believe that math is just the teacher says blank, student does blank, student should get it right. end of story. if not…teacher is at fault or student is lazy or stupid or something.
not so. math is a SKILL…full of tools…and tool #16 can’t be obtained until tool #12-15 are thoroughly made MINE by the student.
When I taught I cared little for the right answer, let’s say a student took a page to answer an equation. A whole page of beautiful correct work. But as he wrote his answer, he transposed the numbers or left off a neg. sign. Now the line before the final answer was correct. Should the whole thing be wrong?
the answer is no! be more attentive, mark off a few points, praise the right, and continue on…this one is working!
what about a student with a very simplified concept of how to do something…he has memorized how to get the right answer but has no real understanding. He writes down the right answer, shows no work, and can not for the life of him tell you why, except that is what the teacher told him to do. And in many cases he knows it is right and is downright cocky, his pride is setting him up for a failure. In my class, his answer was not counted correct. Remember i taught 9th-12th grades. without explanation of his methods he is actually at a roadblock in his learning. because as math gets more and more complicated and advanced…he won’t be able to memorize a set of procedures alone without understanding…it won’t work. i would do a disservice to him to allow him to continue on a dead end path.
More in a bit,
I will get to the point, pollysoup. I promise.
jo
Part 2
When I taught I have mentioned that I chose to use, Key Curriculum Press’ Discovering series…Discovering Algebra 1, Discovering Geometry, Discovering Algebra 2 (which had a different name then) even when there was opposition.
Their approach was radically different. You introduced the concepts and the students performed “experiments” and you led them in forming conclusions, wording things properly, etc. At first, all the students HATED it. So of course, the parents hated it. etc. I got a lot of flak. but while i was there i refused to compromise what i knew was right. (later, i changed venues and taught homeschoolers the same way using the same methods. my tutoring methods differ to a certain extent due to several reasons.)
But then something interesting happened, as I walked around supervising the groups, I hear the students say to me…oh, please don’t help us…we want to get this one ourselves. I had started with 6 classes of 40 uninterested bored students each and suddenly they started waving me off cause they were busy learning …I smiled to myself and moved on…knowing they were on the right road in regard to learning!
Mind you I didn’t leave them to themselves. And they didn’t teach themselves though I was accused of that in the beginning. I was very very busy teaching them …to think. Not to regurgitate a bunch of facts that I had thrown at them. BIG difference. But with perseverence, the did have ah ha moments that they attached to what they knew and then more and more ah ha moments until they KNEW the why AND the how. If we came to a place where a lack of the basics was showing…I gave them the tool. They were too old to go back to basic whatever—and time was of the essence in that place. I taught it simply and concisely and these are the rules. And they grabbed the tools cause they needed them…and at that age…they feel pressure to get good grades and graduation and college are looming. so they have motivation to some extent.
the other thing that i did that made a sharp difference was I required hard work and a lot of it. i raised the bar…my expectations were way more than they were used to–on purpose, in that setting, mediocrity is actually pretty good if you can get it…excellence is pretty rare…and by requiring organization, neatness, completeness, timeliness (yes you can turn it in even though it is a week late, the grade will still be a zero, but I will be glad to look it over for you) etc. By requiring a work ethic and expecting their best, they knew that i thought they could…and they did. It was painful to watch at first, consequences abounded as they tested the limits…but a zero spoke quite clearly and i was always ready and willing to help them master anything…and suddenly homework was turned in timely, etc.
i told you all that to let you know two things…the why of the “discovery” approach and the neccessity of hard work and high expectations.
next i will relate this to the elementary levels of RS
jo
Hey Jo
My dad was a math teacher, and from a pretty young age, I marked test papers.
I remember the general proceedure for marking. He would give me a test page with the correct answers worked out, showing the steps.
My proceedure? (Say the question was worth 5 marks….)
If the student had the right answer, and the working it out looked pretty much like what the answer sheet showed (give or take) – they got 5 marks
If they had the right answer but didn’t show work… they got something like 2 marks
If they had the right answer, but how they worked it out didn’t look like the answer sheet – flag for my dad to check (maybe they had used a different, but still correct, method)
If they had the wrong answer, but the working out of the problem looked the same until the last step or two… they got 4 marks (and it was put aside for him to look at.)
If they had the wrong answer (or blank answer) without showing work – they got 0
If they had the wrong answer and had tried to work it out but it didn’t look similar to the answer sheet – flag for my dad to check.
I think I started marking high school math when I was about 5. (Probably as soon as I could write numbers….)
Anyway, sounds like it was at least similar in principle. You must SHOW the WORK!
Sometime I’ll have to tell you the method I used in grade 2 to subtract without borrowing. (It involved negative numbers.) Had my teacher baffled as to what I was doing until I explained it….
part 3:
pollysoup your descriptions of how you felt: “it doesn’t teach the child. It leaves the child guessing and trying to figure out what he is supposed to be learning. I have to admit that I find this frustrating along with the child.” led me to this topic.
I suspect it is relevant to more than just yourself. Please read what I am saying and what I am about to say with the lens of gentleness and respect. The written word can sometimes be read in a way it wasn’t intended so ahead of time…I am saying I am no way trying to be insulting or disrespectful.
there are many elements to rs that have the discovery approach woven into it…they want the child to have those ah ha moments and to connect what they are learning to what they already know…they use many modalities just as key press does (even in high school)…and they are after mastery not rote reproduction. they break it down into small steps.
it teaches the child, the child is not supposed to be left guessing…he is supposed to be LED. You need to lead him. Your comment about your frustration makes me suspect that you are very uncomfortable with this style of learning…yet if you gained confidence in the material yourself…that would translate to your child. AND it is possible to learn with the child and still lead! a lot of this is attitude. i have found that true in many subjects–my attitude leads-many times not where I was aiming!
I also suspect that you have been going through the motions in the lessons, maybe not realizing the point you are trying to get to…and then you end up with gaps…just memorization of when i see this i’m supposed to do this…etc.
I would suggest if you decide you want to take this on newly–that you begin with lesson 1 in Level B. The first X number of lessons in B review A. But maybe this summer you could just play around with the cards and abacus. Make sure number recognition without counting is there. That would be the first step. Watch the you tube videos from rs, go to their forum for possible answers if there is a specific problem area. But really, shift gears yourself and know that this is teaching him and you…but learning by discovery takes work …hard work to get your mind to accept that it needs to think through this…to get away from the expectation that someone should just tell you the answer or exactly what to do next.
RS is worth it, is a good program–but it is not required. there are other ways some will lead to understanding and some won’t. many will get you by, not everyone understands math…we are kind of taught not to…
For example, I tutored a fellow high school teacher who taught next door to me…she taught geometry. As we got to one section, I was explaining the concept and referred her back to the subject she was teaching. Her response was telling, oh, I have never understood that. I know to do this, so I show them that, take no questions, and go really fast. I immediately went to some serious teaching…till she “got” it and the light came on…yes i used a bit of discovery and lots of you do it now…i was trying to impact all of her students including her future ones.
However, all of that said, to anyone out there, not just pollysoup…anyone…pray over your choices, grow yes, take on hard things, yes, but don’t beat yourself up if you decide no to something.
I think you could do this…if you really want to and are willing to change your thinking first…but you don’t have to and no one is going to think less of you if you don’t. i don’t know about the rest of you, but i have a lot of things in front of me and sometimes i have to pick and choose my battles so to speak.
and being the kind of woman i am, i will say out loud, no i am not saying it is all your fault. I am NOT!
God Bless each of you.
Feel free to PM me if you need me, and I don’t seem to be answering on the forum.
joanna
Let me think it through again… lol….
Ok, say 34-7 (it would have been in a column format.) Instead of borrowing the 1 from the 3 in the tens.. I would just go… ok 4-7=-3 and 30-3=27. It works. It makes sense, and to me, it was easier. Conceptually it is also sound.
My grade 2 teacher was very impressed, figured I would grown up to be a mathematician, but made me do it the “right” way (which I could easily do).
the right way…yikes! shame on him!
that is great! great story and very very bright for a 2nd grader!
when i was in college i remember getting mad because i had been taught my whole life that triangles have 180 degrees.
well, in Euclidean geometry…that is geometry on a flat surface that is true.
on a not flat surface, like the earth it is not…and that is called Spherical geometry.
and on the inside wall of a ball it is different yet again…called Hyperbolic geometry.
and each of these has purpose and reason in the real world and how we make lens or measure distance in space etc. and is as real as euclidean’s 180 degrees.
my mind hurt as i tried to readjust my thinking…and i was mad cause why didn’t they tell me…on a flat surface, or most of the time…or something
my mind could have handled that…instead it got dumbed down and drummed into me…triangles always have 180 degrees…imagine my shock when I am about to graduate from college with a degree in math…to be holding a sphere with a triangle drawn on it….and am measuring and remeasuring the angles..and they do not add up to 180. My world rocked that semester.
It was a class called Differential Geometry…a kind of calculus based geometry…it was weird amazing stuff…but it blew what I thought was TRUE and FACT out of the water…
jo
Ah, I had an advantage on that one…. My HS math teacher taught us that in Euclidean Geometry triangles always have 180 degrees… but that there are other types of geometry where they always have less than 180… and other types where they always have more than 180…. but for OUR math class we were doing Euclidean Geometry. (I was in an International Baccalaureate class.)
My dad at one point also had a computer store (in the late 70’s) and so I learned about Binary Math, Octal Math, and Hex math… I learned that stuff at about age 9…. so I knew that 1+1 is not always 2… sometimes it is 10 (binary.) and that F is 15, and all sorts of fun stuff!
You want to know what really gets me when I look back though?
In grade 8, our city had a bus strike for a month or so…. and so I had to stay at school about an extra hour waiting for my carpool (along with many other students) and I always had my homework finished…. so for entertainment, I borrowed the grade 9 mathbook, and did the entire grade 9 math course on my own. Correctly. Ok, no problem (oh, and where I lived HS started in grade 10…) And so then I had to do the grade 9 math course again the next year in class, even though I had done it all on my own in about a month, correctly. And I sit and wonder…. why didn’t anyone suggest that I take the grade 10 correspondance course (my province had a very established correspondance course) during my math time. I probably could have finished the grade 12 math course by the end of grade 10 (instead of by the end of grade 11), done the grade 12 calculus course in grade 11, and started some university math.
In fact, in grade 7 (at a different school) the councellor would have recommended moving me into a more advance math except she didn’t know what I’d do in grade 9… so instead I would have to be bored in class…..
How set into the system people are!
And people wonder why I homeschool……
this and MANY MANY other reasons…oh the stories the public (and private) school teacher could tell…yikes
I’m really enjoying this thread.
I am not mathematical nor do I think mathematically…but I am learning. All I know in school is if I followed the formula it worked..usually. But I never understood why it worked.
Now that I’ve been teaching my boys with RS….I am having lots of aha moments. My children think it’s funny and just roll their eyes [in a kind way]
I will say when I first started using RS I wanted to tell my children the answer….and it wasn’t till about Level D that I realized I wasn’t supposed to. I was to lead them. But since I wasn’t really understanding math myself I didn’t clue in.
This last year I have had opportunity to tell others about RS at conventions. It’s rather humorous to me as until then I didn’t even understand the philosophy of RS. But reading the handout they have and the website and what’s written inside at the beginning of the math curriculum really helped me to finally start understading the program and being able to explain the program. Up till then I could only tell someone I loved the program…hahaha!!!
We really do a disservice to our children when we TELL them rather than let them discover. I notice this when children come to the booth and want to play with the balance. I will put a weight on one side of the balance and hand them another weight and ask them if they can place it on the oppostie side to make it balance. Most children get that concept and do well with it.
Then I’ll take the one weight they put on off, and give them two weights and ask if they can use two weights on the opposite side of the balance to make it balance the weight on the other side. This is where I see that the majority [98%] of the children don’t get the concept of the balance. It doesn’t matter the age either….young or old. If I have the weight on the 8 on one side….they will place one of their weights on the 8 on their side and then place the other weight on another number. Of course it’s too heavy and the balance won’t balance. Well I can see the puzzlement in their eyes so I’ll ask them….could you take one of the weights off and try another number. So they start experimenting.
But it never fails….if a parent is with the child…..the parent will start TELLING the child where to place the weight….very few parents will allow the child to continue experimenting until the solve it themselves. Or ask them questions to help them figure it out themselves. And since I am facing the child I can see in their faces the difference when they discover it verses when their parents TELL them.
This has really helped me to understand why Dr. Cotter has the children discover concepts rather than have us, the parents, tell our children. Yet it took me teaching through 3 levels before I truly understood.
The other thing about RS that I didn’t grasp at first is the importance of playing the games. The games are where we can see if our children are getting it or not. At first they will have to use the abacus…but after some time it starts to click and then they don’t need the abacus as much…and then they get to the point they don’t need it at all. When they don’t need it….they not only understand they facts they’ve been practicing but they have them “memorized”.
Not sure where I am going with this, nor is it directed to anyone…. but just wanted to chime in and hopefully help someone if they are considering or struggling with RS.
Whether its RS or another curriculum….look at the teaching philosopy…..read those first few pages in the books….read the website….call and talk to a customer care rep…..I think a lot of times we do a curriculum a disservice because we don’t understand the philosophy or we don’t implement it as we should….I know I’ve done that myself.
Plus I never realized there was more than one way to teach math…..or more than one way to solve a math problem….I was only taught one way in school and that’s how a I thought everyone had to do it….so using RS was an eye opener to me and so very liberating to find there are multiple ways to get an answer….I sure wish I’d have been taught this when I was in school.
Oh….one more thing I thought of…..at one convention I was talking to a guy who was very mathematical….he was a math athlete in school. We were talking about the stategies children in RS are taught and he said those are some of the very same strategies he was taught when he was a math athlete…..but NOT the way he was taught in regular math class….I found that very interesting….
Jo, You have not offended me in the least! I appreciate your straight-forwardness!
You are right! I have never been good in math. In 2nd grade I missed something in math and I stayed at that level until I started teaching my oldest with MUS. I agree that a child who discovers for himself is a very blessed child. And in all other subjects, I can lead and guide and give opprotunities for them to explore and discover. But, in math, that is just too risky. I’d rather let someone else do that. However, the very thing that frightens me about RS is what draws me too it…. Thank you for your time, thoughtfulness, and challenge.
Polly
I really, really want to try this RS, but it keeps coming back to money. My younger son should be in C, my older in E. I would be looking at about $300 plus — a really big investment –and if it turns out it isn’t a good fit for us…well I really don’t have the cash for that kind of mistake. I really like the idea of games and discovering for themselves, but I know transitioning would be a huge challenge — then of course there is the time consideration…I do work part-time weekday mornings. The 30-40minute lessons at this level –does that include playing games, or just the teaching portion?
I can see that an honest committment to this program and the right attitude going in can really work. But is there a way to make it more cost effective? Are some manipulatives replaceable with household or homemade items? Neither of the boys are crazy about work sheets, they love the idea of games and such. I’ve been considering Math Mammoth with math games on the side –there seems to be lots of ideas on line, plus board games that we have already. I’ve also been considering Miquon, but no one here has mentioned it really. Both programs seem to be cost effective mastery programs. I thought of just kind of doing my own thing, with online resources and games just stressing mastery of basic operations this year, then moving on to an official curriculum next year, but then again I am back to time constraints when I consider how much time I would need to build this type of program, and again, not really feeling that confident about teaching it all correctly.
I would like to decide on this math issue soon as how much I choose to spend here will determin how much I can spend elsewhere. I’ve already got my science and Queen’s Language Lessons for the Elementary Child for my older, but that’s about it so far. My budget is limited and I still have soooo much to get!
If you really want to ‘try’ RS— there are other ways.
If you look around on the website— you can purchase the Al Abacus and a manual just for it called-/ Activities for the Al Abacus.
A great way to add some hands on RS thinking into the math you already have.
If you read ALL the info on the website—- then add in things— like playing dominoes, and certain card games— you can use their philosophy and methodology with anything you have at home.
I am in no way slamming RS or their products.
I am only saying this for those who can’t afford RS or maybe just want to try it out.
Maybe you are like our family — 7 children — no way I could spend that much time with 1 child
But we bought the Al Abacus and workbook — and we are enjoying working through that.
I am enjoying these math threads
Mic
also, i saw someone trying to sell their rs level in passing on the rs forum
i didn’t stop so i don’t know if they are selling it cheaper or not or even what level
sorry…i don’t have a lot of ideas about this…but i do agree with mic that you could add things in…
the abacus which you can get for $10 @ rainbow resource and the activity book…the math games book might be helpful too. i don’t know how much it is from rs. but the other thing to consider is that both of your children will need to do the transition lessons to “get up to speed” with the methods. that you would only have to purchase 1 set of and use for both! that will take a while to work through…and then they would split off into their respective levels.
i find that it is all a hard decision…i try to remember to do my best and let God take care of the rest.
🙂
jo
You are right! I have never been good in math. In 2nd grade I missed something in math and I stayed at that level until I started teaching my oldest with MUS. I agree that a child who discovers for himself is a very blessed child. And in all other subjects, I can lead and guide and give opprotunities for them to explore and discover. But, in math, that is just too risky. I’d rather let someone else do that. 
However, the very thing that frightens me about RS is what draws me too it…. 
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