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How much math should 5th grader have retained?


redquilthorse
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We used Saxon 7/6 last year for math for my 4th grader (this is where the Saxon placement test had us start him, and he has a late birthday, so he could have been 5th grade if in a brick and mortar school). We did not school this summer due to a move. We started this week, and we spent the first two days reviewing. He has only about a 50% retention rate at this point. He did not remember pretty basic things like how to find the area of a square. When do I decide this is more than just your typical summer amnesia? I'm not sure whether we should just keep chugging away or re-do 6th grade math using another textbook. I was not sure by the end of the year whether he was really retaining what he was learning. He could get 100% correct on the lesson, but then miss several in the review. 

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Saxon just cannot be stopped and restarted in the middle of a book. Each book reviews the previous book, but the lessons really pick up pace in the middle of the book. So just as the variety of new topics is getting really challenging to juggle, is the wrong time to take a break. Saxon is written to be completed and then take breaks between books.

 

I personally do NOT think 76 is a 5th grade book, never mind a 4th grade book, so I personally would have no worries of being "behind". I personally would restart Saxon 76 and finish it before taking another break. I have restarted students in Saxon, because of breaks, and just because their speed and accuracy was falling. I have no problem redoing Saxon lessons.

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We don't use Saxon, but when my dd11 needs to go back to relearn something that she got in the lesson but got wrong in the review, I often let her just do the odd numbers or something.  If she can show me that she remembers it and can still do it, then I don't stress about it.  If it's still a problem, we do the evens.  Also, when I do need to go back, I'll have her do that type of problem every day for a couple of weeks (just one problem, before we start the other material).  That seems to help. 

 

I wouldn't expect my kid to remember formulas, as long as there's an "oh right!" moment at some point.  I'd either go back, or spend a week in review of the concepts earlier in the book, before continuing.  Then make sure the reviews are happening.

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If you're only 2 days in I wouldn't worry about it just yet. Expect and prepare to reteach old concepts on the fly for the first few weeks or so.

 

I don't have a whole lot of experience with Saxon, but I'm on my third 5th grader this year. My vote goes to summer brain rust, and I wouldn't blame the math book. My current 5th grader got every single double digit or bigger multiplication problem wrong the first day back (he uses Horizons). I reminded him of just multiplying the top number by the ones, then the tens, then the hundreds, and adding those products together. He had a total *facepalm* moment, and hasn't had a single problem multiplying since. Then we had that moment all over again when he couldn't set up the check yourself problem for an equation...lol.

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My apologies for the following stump speech on "area". This is my sales pitch for emphasizing concepts as opposed to mere formulas.

 

I.e. as a mathematician I am puzzled when I hear that someone can't remember how to find the area of a square. A square is a unit of area, so at first I didn't know what was meant. Actually I did, in a memorization sort of way, but I always want to emphasize what area means. Area is not a number, until one chooses a unit, and that is not possible in any natural way. So measuring area of a square really means comparing two squares, one of which you think of as a unit of area, and you want to know how many of the (say smaller) squares, fits inside the other.

 

When one asks it this way, it comes down to comparing first the sides of the squares. I.e. if one square has a side which is say X times the side of the other, i.e. if X copies of the other side will fit inside this side, then X^2 of the other squares will fit inside this square. That's easy to remember because they are called "squares". Or rather that's why X^2 is called "X - squared", the exponent "2" reflects the dimension of the figure. It's also easy to illustrate when X = 2 or 3 by a picture. It gets more interesting when X is a fraction like 3/2, and then it is not at all obvious, but still true.

 

So I would review this discussion of what area means, with lots of pictures and examples, and then the less meaningful bare area formula, may be easier to recall.

 

I.e. as a college professor teaching calculus, I cared less whether my class knew area formulas, than whether they knew what area means. I had students who might think the volume of a sphere of radius R was 4Ï€R^2, not realizing that a three dimensional figure cannot have a volume formula which is proportional to the square of its linear measure (the radius) rather than the cube of it.

 

I'll bet if the child figures out how to explain why a square of side length 3/2 has an area of 9/4, he will remember the formula for a longer time.

 

thanks for your patience. good luck.

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Mathwonk, I love it!  My dd10 has had a heck of a time remembering formulas, and it was frustrating till I realized it was telling me she really didn't know what these things - area, volume, etc., really *mean*.  As we've been studying exponents, I've really been working on helping her understand squares & squaring, cubes & cubing, as well as the relations between addition and multiplication and exponents.  I'm explicitly tying this to areas and volumes, and I think it's finally clicking.  

 

The whole discussion of figuring out the area of a triangle - I think it's in The Mathemetician's Lament? from thinking about a triangle inside of a rectangular box and figuring out how much of the space it took up - reading that was what led to my own personal epiphany about needing to teach this differently.

 

OP, I'm so sorry for the digression, I just get so darn excited about Mathwonk's posts I sometimes forget what we're talking about in the thread!

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I am glad this may be helpful. More briefly, for the child in question, I would just remind him, and show him, that when you slice up a square by lines parallel to the sides, which cut each side into three equal pieces, then the whole square gets cut into 9 smaller equal squares, and note that 9 = 3^2. maybe then do it for 4 pieces and 16 squares. that's about it. If he does this little demonstration for himself a few times, he will probably always remember the formula.

 

 

We can't be expected to remember formulas we don't understand. E.g., see this 50 page paper on my webpage explaining the Riemann Roch formula?

 

http://www.math.uga.edu/%7Eroy/rrt.pdf

 

Guess what formula I always had trouble remembering as a student?

 

 

Yep, but now that I know how it was actually derived by Riemann, I can remember it, well a little better anyway.

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We can't be expected to remember formulas we don't understand.

 

This, precisely.

A student who has understood how the area of a square is obtained will be able to reconstruct it.

A student who has memorized a formula, any formula, without understanding will most likely forget eventually.

 

Math curricula that conditioned students to memorize stuff without a deep conceptual understanding are the bane of my existence as a college instructor for physics.

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Totally agreed with Mathwonk's post.  

 

But as for the OP's conundrum, I second that it's early in the year to worry and you have to give kids time to clear the fog.  I also think that changing books is a drastic solution at this point.  However, if she's conceptually weak in a lot of areas, then this is exactly the weakness of Saxon as a program and in that case, you might consider switching or adding a supplement to help her think about the whys of what she's doing.  Just a thought.

 

I would also add that luckily much of middle school math is review in preparation for algebra.  So while I have some issues with that, it's nice that you really aren't behind and lots of other students are reviewing at this point.

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Honestly, I think this is why the beginning of each math book is review.  DD12 started back this week with math and totally blanked out the order of operations.  Oh... she remembered there was an order and an acronym but could absolutely NOT remember anything else.  Fortunately for her, lesson 2 this week was a blast thru order of operations and simplification.  She has a few more review lessons and I think we will be up and running towards the end of next week.

 

8/7 starts with a review of the 7/6 material - I would give it a shot and if he ramps his brain back up and is ready to move on, then good.  Otherwise, regroup and start over reviewing the 7/6 material.

 

Or did I misunderstand you and you are trying to pick up in the middle of 7/6 after the summer off?  That won't work - you would need to back up a ways and get a run at it again with a review of the earlier chapters.

 

 

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Some students do very well with Saxon. Other students, because of the incremental nature and constant review, do very well on daily work, but later courses which require them to apply their knowledge show that they did not receive more than a procedural understanding. That is, they understood *how* to do it, but not *why* to do it. One example of this would be a student who can faultlessly do 4-digit addition and subtraction, but when given a word problem involving 2-digit addition (such as "John has 83 dollars and Amy has 24. How many more dollars does John have than Amy?" cannot figure out whether to add, subtract, or multiply.

 

If what you mean by "not sure he understood what he was doing" involved the second type of problem, it may be that a more conceptual program would be a better fit. It could also just mean that his arithmetic skill outran his reasoning ability, in which case restarting would also be a good idea.

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Thanks for the input! Just to clarify a bit, we were moving at a slightly slower pace than normal, then we stopped at lesson 70-something because we moved. I was planning to finish 7/6 before going on to 8/7 because he is still so young. I had some doubts about doing 7/6 at this age, but he seemed to be handling it OK until halfway through the year. Then we slowed down. Then we moved.  :glare: So it sounds like we just need to back up to a place where we can review and keep going, maybe skipping the lessons he remembers well.  I think he started having trouble after lesson 46 or so. When we started this week, I had him do some practice problems starting at lesson 50, and he had trouble with them. When we were going through it last year, he would get the majority of problems correct, so I thought we were fine at the pace we were doing. If he missed more than that, we would review. He is very mathy, BTW. He is my math and science kid. 

 

I should also add that we use the DIVE cd. He likes it and it seems to explain things better than mom can.  :001_smile:

 

I do think it is good to know that Saxon could use some supplementation for conceptual teaching. Last year was our first year with Saxon. We used BJU up to that point. The example I gave re: area was just one concept he did not remember. He didn't remember what it meant to find the area of anything. So we were reviewing the concept as well as the formula. 

 

Any suggestions for a good supplement to reinforce concepts? Is LOF enough? We have Decimals and Percents and Fractions. We were still plugging through Fractions at the end of the year.

 

 

 

 

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Math Mammoth is really good for supplementing with conceptual teaching. It's also very inexpensive, which is good for a supplement. :D The "Blue" topical series makes it easy to pick out specific topics. The "Light Blue" series is broken into grade levels.

 

Personally, I don't think LoF always teaches conceptually. Some things he does, and some things he just teaches the "how". Also, my son did the Fractions book over a period of several months (so not rushing through it by any means), passed the Final Bridge, and last week, fractions fell out of his head. :lol: And he DID do math all summer! (note that he learned fractions in MM and Singapore before doing LoF, so he had a good conceptual foundation in fractions - he just lost them because he hadn't used them as much lately). I think that's why elementary math programs repeat and repeat and repeat. Kids this age sometimes have their brains leak out their ears. ;)

 

If your son was having trouble starting after lesson 46, I'd probably go back to lesson 46, and any concepts he's not quite sure on, pull out the MM pages to go along with it. Then move on within Saxon.

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OP, I'm not even a little bit surprised that this turned into a "Saxon isn't conceptual thread."  I have never, not even once, tried to talk someone into using Saxon.  I don't know that I would have started with Saxon if I had known about other math curricula at the time.  If Saxon turns out to be a bad fit, please use something else.  As a teacher and a parent, check often to make sure your student understands the concepts.  But take the Saxon comments with a grain of salt.  I just asked Ds9 (just turned 9, going into 4th grade) how to find the area of a square.  He did look at me blankly for a moment but then explained how to find the area - with a nice conceptual explanation, too.

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I do think it is good to know that Saxon could use some supplementation for conceptual teaching. Last year was our first year with Saxon. We used BJU up to that point. The example I gave re: area was just one concept he did not remember. He didn't remember what it meant to find the area of anything. So we were reviewing the concept as well as the formula. 

 

 

I disagree that Saxon needs any supplementation. There's enough constant review, and with that review expansion of concepts, that all concepts are well taught over time.

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Also, my son did the Fractions book over a period of several months (so not rushing through it by any means), passed the Final Bridge, and last week, fractions fell out of his head. :lol: And he DID do math all summer! (note that he learned fractions in MM and Singapore before doing LoF, so he had a good conceptual foundation in fractions - he just lost them because he hadn't used them as much lately). I think that's why elementary math programs repeat and repeat and repeat. Kids this age sometimes have their brains leak out their ears. ;)

 

My kids do this too, and we school year round. If we haven't used a concept in a while, it's going to be huh? when it comes up again. I'm going to try to to work in regular review of things like area, fractions, etc. for that reason given the programs I'm attracted to all seem to lean more toward mastery rather than spiral. Still, I think it's typical and that's why units begin with a review of previous knowledge often. I do agree that making sure the conceptual framework is there can help things stick...but I suspect some (many?) kids are still going to be use it or lose it.

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I'd start back at the beginning of 7/6 and try to complete the book in this school year.  I have a 5th grader and a 6th grader using 7/6 this year and a 6th grader using 8/7.  My kids have always used Saxon and it would be tough for them to stop a book in the middle and pick it up again a few months later.  In the past, we've used Teaching Textbooks as a supplement.  I don't really believe that a supplement was necessary, though.   

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I'd back up in the lessons and continue with Saxon. My dd had made it to lesson 44 in Saxon 5/4 and had been doing really well (92% or better on homework and 95% on tests). We took a break for 3 months, and she was LOST when we tried to start again. We simply started the whole book over again. We won't break in the middle this time. We may take a week or two off and the end of the book though. She is flying through the lessons now though, and rarely misses anything. I feel like this will definitely give her the best foundation to continue on. She was using it as a third grader, so we definitely had the time to back up. You have the luxury as well. :-)

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