Pre Algebra - switch horses midstream?

[Emba]

DD is 7th grade, working on Saxon 8/7. I had already decided that next year we would not move on to Algebra, but would switch to a different program for a second dose of pre-algebra. We’re on lesson 67 and she is struggling. It’s the “teaching” through practice problems. She doesn’t do well when things are not explicitly taught. She has always struggled with math, but she’s really doing poorly now. Part of it is sloppy work and mistakes that she knows better than to make, but I’m beginning to think some of it is Saxon.

She claims to like Saxon, unlike Math Mammoth (a fail) and Rod and Staff Math (not a fail, but not great). I do think she does best with spiral curriculum. A curriculum that reviews frequently, daily if possible (like Saxon and Rod and Staff) is necessary.

i think cle would be a good fit but not sure I can switch into it halfway through the year like this.  Are there any traditional textbooks that have frequent review that might be suitable?

i hate to switch halfway like this but I am at my wit’s end.

[SoCal_Bear]

Is she working through just the textbook on her own? There are CD-ROM from Saxon, DIVE CDs and Al Reed's DVDs. Are you using this? If she needs things explictly taught, I would think you need to have something in place to do that. It seems like it is not the curriculum but how the curriculum is being used may be the problem?

Edited February 8, 2019 by calbear

[Emba]

No, I am teaching her most days myself. I also have a subscription to Nicole the Math Lady, which works slightly better for her than DIVe, but she doesn’t learn well from video. Too easy to tune out, I think.

She’s not good at recognizing when she needs to ask for help, which is probably also part of the problem, and i am having real difficulty getting her to actually show her work.

[kristin0713]

My DD is in 7th grade and just started CLE this year.  The 700 and 800 levels go through pre-algebra over two years with an extremely thorough review of all arithmetic and lots of geometry.  It has been excellent for her.  I wish I had switched her years ago!  If you work through the summers, you could get through both levels before starting algebra 1. 

[Doodlebug]

On 2/7/2019 at 3:31 PM, emba56 said:

DD is 7th grade, working on Saxon 8/7. I had already decided that next year we would not move on to Algebra, but would switch to a different program for a second dose of pre-algebra. We’re on lesson 67 and she is struggling. It’s the “teaching” through practice problems. She doesn’t do well when things are not explicitly taught. She has always struggled with math, but she’s really doing poorly now. Part of it is sloppy work and mistakes that she knows better than to make, but I’m beginning to think some of it is Saxon.

She claims to like Saxon, unlike Math Mammoth (a fail) and Rod and Staff Math (not a fail, but not great). I do think she does best with spiral curriculum. A curriculum that reviews frequently, daily if possible (like Saxon and Rod and Staff) is necessary.

i think cle would be a good fit but not sure I can switch into it halfway through the year like this.  Are there any traditional textbooks that have frequent review that might be suitable?

i hate to switch halfway like this but I am at my wit’s end.

 

I asked a question about curriculum a month ago for exactly the same reason.  

My seventh grader, a long time user of Saxon, was struggling with 8/7 (around lesson 60).  

I finally did the following... I became really familiar with DS's problems with Saxon.  I researched other textbooks, ordered, and perused Lial's pre algebra.  

And it came down to this, midyear... Saxon is the animal I know and it is easier for me to address the issue Saxon is bringing about than to start a whole new program.  Problems in Saxon at this stage can be intimidating to students -- because the arithmetical spoon feeding has stopped. Gone are the days of getting stuck on a problem, looking up the corresponding lesson number, plugging in your numbers, and moving on. 

My DS needed reminding that it takes courage to sit in front of something that appears complicated.  I encouraged him to see those problems as poodles dressed in dragon suits... the goal is to simplify the problem (to get to a friendly and familiar looking poodle) and to then use one of the tools Saxon has taught repeatedly in the earlier lessons to solve.  DS was struggling to make the intuitive leap to using the tools because 1) the problems looked scary to him and 2) he lacked confidence. 

Confidence and seventh grade seems to be a thing.  😉

  

 

[Emba]

On 2/9/2019 at 10:58 PM, square_25 said:

I think teaching through practice problems is generally not a bad thing. Can you give me an example of where you think it's tripping her up? 

Also, can you give me an example of the kind of thing she's messing up? 

Example (maybe): picture of a block made of cubes, 2 by 3 by 2. To me, obviously a volume problem. L x W x H. Question asks "How many cubes are in this block?" The answer was 12, but she got 28 by counting the cubes she could see and making up what she couldn't, except I have no idea how she got her numbers: 6, 6, 6, 6, 4, 4. To me it looks like this very simple problem is trying to help them see the concept of volume without saying the word volume itself - the idea that volume is the number of invisible blocks that make up something, so that they can "see" volume in a word problem without the word giving away the algorithm. I explained the exact same thing to my son with sugar cubes a couple of weeks ago and she was there watching. 

Things she messes up: today we went over a unit multiplier word problem she missed Friday. She did it right first, but because it was a decimal that went out several places, and she missed the word "about" in the problem, indicating the answer should be rounded, she thought it was wrong and did the same math with the unit multiplier's reciprocal to get an answer that was wrong and defied common sense(but which seemed right to her because it wasn't an unending decimal)

She got a fraction problem wrong because although she did order of operations right, near the end she did mental math and decided

27-18=14

It's quite common for her answers to be one digit off because of addition/subtraction carelessness.

Edited February 11, 2019 by emba56

[Emba]

38 minutes ago, Doodlebug said:

 

My DS needed reminding that it takes courage to sit in front of something that appears complicated.  I encouraged him to see those problems as poodles dressed in dragon suits... the goal is to simplify the problem (to get to a friendly and familiar looking poodle) and to then use one of the tools Saxon has taught repeatedly in the earlier lessons to solve.  DS was struggling to make the intuitive leap to using the tools because 1) the problems looked scary to him and 2) he lacked confidence. 

Confidence and seventh grade seems to be a thing.  😉

  

 

Dragons in poodle suits...that's good.

I do think it has helped (me) to go over her mistakes exhaustively every day and see where her repeated errors are. I now know she's got a problem adding\subtracting negative numbers. And unit multipliers, though I thought we had whipped that one.

Thirty problems is a lot and hard for her to concentrate on for so long, which I think adds to the # of careless errors. But she NEEDS repetition, so I feel stuck between a rock and a hard place there, no matter what curriculum i use.

[madteaparty]

So many horses, so many streams here. FWIW, we did prealgebra twice.

Also FWIW, I just signed up for Derek Owens (another stream, another horse!) to supplement a IRL algebra 2 class I’m not thrilled witj but stuck in for the year, and DS said, “in 10 years of homeschooling, those are the most understandable videos” (he exaggerates. He hasn’t been schooling never mind homeschooling for 10 years).  

[Emba]

12 hours ago, square_25 said:

Interesting. It sounds like she needs more concrete examples about how to work with things. It's not wrong to count the blocks per se, it's just not exactly what you want her to be doing (and obviously you want her to get it right.) Maybe building it with sugar cubes again would help... If the idea that you figure this out by multiplying isn't clicking, I'd start by seeing whether she knows it's multiplication when you just have one level of blocks. 

Same issue with negative numbers: what is her concept of negative numbers? What does she think she's doing when she's taking away and adding a negative number? 

To me, it sounds like she'd benefit from one on one teaching and concrete examples more than changes of curriculum :-). Especially if she's basically liking it. 

Well, she always has done better with hands on, and I’m fairly sure we did the sugar cubes a couple of years ago when volume first came up. But I’ll definitely be doing it again today.

You wouldn’t happen to have any concrete ways of explaining subtracting negative numbers, would you? Because that one is really giving me trouble. And that’s the problem as we get along in math. There are fewer and fewer things that can be explained hands on.

[Emba]

2 hours ago, square_25 said:

 

We worked with this for a while. It took us a bit of time and trouble to figure out the rule for negative number subtraction. I think we worked on it for a few weeks at least, doing scenarios like "OK, I have 10 apples but I also owe someone 5 apples. That means really in total I have 5 apples. But then say someone forgave my debt: that's like "taking away" the debt. Then I have 10 apples. So we get the equation 5 - (-5) = 10." 
 

Yeah, debt forgiveness is the only example i have been able to come up with for subtracting negatives. I was hoping you had something better. 😃

[Emba]

DD understood the analogy, but there wasn't any big light going on, if you know what i mean. I think negative numbers still are very abstract to her, even if she's starting to intellectually understand. It may just take some more repetition.

[alpacawalker]

If you are planning on doing prealgebra again for 8th and need very explicit instruction,  I would recommend Derek Owens using the parent grading option. We just finished it. It is a video program. He teaches each topic starting from the very beginning, so if you need any review at all you will get it. If she has mastered a concept already,  you can easily skip that section. The parent grading option keeps you involved so you know if there is a concern. It is different from Saxon though since it doesn't spiral.  You work completely through each concept before moving on. If spiral review is needed, you could work in a half page of saxon practice a few times a week for independent practice as the DO homework is usually only 8 to 10 problems.  The lesson itself has the bulk of the practice problems. We moved quickly through it which kept the cost down. Another plus for us.

[EKS]

Are you presenting the lesson to her and having her do the practice problems in your presence?  If not, that's where I'd start.  

[EKS]

15 hours ago, square_25 said:

Another thing I've realized after a whole lot of teaching is that we expect people to get the idea way too fast. So we show someone something, we justify it, and then we very rarely reference the justification. And as a result, a student spends maybe 1-2 days with the explanation, and weeks or months or years with the algorithm provided without justification.

Saxon's design makes this is a particular problem.  People like to say that Saxon teaches the concepts, and it does, but the excessive amount of practice is structured so that students end up focusing on quick execution of procedures and over time, concepts are forgotten.  

If I were you I'd switch to something like Derek Owens Prealgebra.  He reviews arithmetic and then introduces beginning algebra concepts in context.  I'd start at the beginning, and it will give your daughter a nice overview of the math she's learned since first grade.  I'd work with her, and allow her to move quickly through the parts that she is solid on and slow down for the things she needs to work on.

[Sherry in OH]

14 hours ago, emba56 said:

Yeah, debt forgiveness is the only example i have been able to come up with for subtracting negatives. I was hoping you had something better. 😃

 

Negative temperatures or distances below sea (or surface) level

[Monica_in_Switzerland]

I just want to point out that your dd's answer to the volume question was a perfectly reasonable answer to the wrong question.  She (correctly) got the surface area of the shape!!!  Four sides of 6cm^2, and two sides of 4cm^2.  I only want to point this out because her logic was SOUND... she just didn't understand what the question was asking.  

She may be able to continue just fine in the program with a bit of hand-holding.  

[Monica_in_Switzerland]

18 hours ago, square_25 said:

Another thing I've realized after a whole lot of teaching is that we expect people to get the idea way too fast. So we show someone something, we justify it, and then we very rarely reference the justification. And as a result, a student spends maybe 1-2 days with the explanation, and weeks or months or years with the algorithm provided without justification. And for a lot of students, that means the explanation (which wasn't fully absorbed) totally fades into the distance and all that's left is the algorithm, which feels mysterious and like a black box. 

As a result, I spend a whole lot of time reminding my daughter about what things mean and not very much time talking to her about "rules." I figure that once she works with a definition enough, she'll get an idea of the rules (and I nudge her towards them once in a while.) For us, it meant biting my tongue as she really slowly took away 69 from 71 when I asked her about 71 - 69, because she knew it was taking away and was comfortable with it (even though I'd have much rather she noticed 71 was 2 more.) And eventually she realized it was the same thing "how many extra are there" and starting just doing that quickly. But she never lost track of what subtraction was, and that was very helpful for us, because things she could fully conceptualize were easier for her to think about. 

 

This is a reason I enjoy teaching multiple math levels at the same time.  If I am going to demonstrate a basic concept to kid 2, I have kid 1 stop what he is doing and watch.  Same when I deomonstrate to kid 3, I get kid 2 to stop and watch.  Not to choose a controversial metapohor, but it's like a little vaccine booster shot to keep the ideas fresh in their minds.  😄  

[Monica_in_Switzerland]

57 minutes ago, square_25 said:

 

Interesting. That's a pretty serious misunderstanding of "number of blocks," though, since she's counting lots of blocks more than once. I guess it's a reasonable answer for "number of squares," though!  

I didn't notice that interpretation, I'm glad you pointed it out :-). 

Oh, and I like your vaccine analogy a lot. 

 

I see it as a potential mis-read.  The problem may have read, "number of cubes" and she interpreted "number of squares".  I have a dd who answers all sorts of questions (not just math) in the most ridiculous ways possible, but if you really dig, there is always some internal logic based on a small (but significant) initial misunderstanding of a question.  Frankly, it's exhausting!!! But knowing her mind is working logically helps me to be more patient with her misunderstandings.  It boils down to, "Slow down, read carefully."

[Emba]

Monica_in_Switzerland - thank you, I think you are probably right that she mis-interpreted number of blocks as number of squares. It does help to think that she got those numbers from somewhere.

eta - or forgot that multiple faces of some of the cubes would be showing, so counted each face  as representing a cube.

Edited February 13, 2019 by emba56

[Emba]

3 hours ago, Sherry in OH said:

 

Negative temperatures or distances below sea (or surface) level

Hmmm. I am not sure those are going to be clearer so far as the rule of “subtracting a negative is like adding its opposite” goes. I can kind of see it, though, and having another way of explaining  always helps.

Edited February 13, 2019 by emba56

[EKS]

2 minutes ago, emba56 said:

Hmmm. I am not sure those are going to be as obvious, so far as the rule of “subtracting a negative is like adding its opposite” goes.

Just to point out, subtracting a positive number is the same as adding its opposite--there is nothing special about subtraction of negative numbers.  All subtraction can be thought of in this way.  Just as all division can be thought of as multiplication by the inverse.

[Emba]

Just now, EKS said:

Just to point out, subtracting a positive number is the same as adding its opposite--there is nothing special about subtraction of negative numbers.  All subtraction can be thought of in this way.  Just as all division can be thought of as multiplication by the inverse.

Yes, but subtraction of positives are so ingrained as to be intuitive at this point. We’re not having problems with that concept. (I guess I’m just not sure why you’re pointing this out).

FYI - for anyone suggesting Derek Owens or similar, that’s really not something I consider an option. Video instruction has not proved a good way for her to learn. She really needs eyes on her, teacher demanding a response, or she sort of slips into passive “videos as entertainment” mode.

[EKS]

2 hours ago, emba56 said:

Yes, but subtraction of positives are so ingrained as to be intuitive at this point. We’re not having problems with that concept. (I guess I’m just not sure why you’re pointing this out).

Because it shows that subtraction of negative numbers isn't just some weird special case.  *All* subtraction is adding the opposite, and if she understands that subtracting a positive is the same thing as adding its opposite, it is just a small step to subtracting a negative being adding its opposite as well.  

Edited February 13, 2019 by EKS

[EKS]

2 hours ago, emba56 said:

FYI - for anyone suggesting Derek Owens or similar, that’s really not something I consider an option. Video instruction has not proved a good way for her to learn. She really needs eyes on her, teacher demanding a response, or she sort of slips into passive “videos as entertainment” mode.

We have that issue here as well.  The only way I have used Derek Owens effectively is to sit with my son and either present the material myself (having watched the videos beforehand) or to watch with him and stop the video to have him think through the example problems on his own first before being shown on the video.  The "reward" is that if he is able to do the example problem on his own with full understanding, we skip through the explanation.

[almondbutterandjelly]

Key to Algebra uses a football field to demonstrate negative numbers.  You might just pick up the booklet that covers that.

Mathusee uses his blocks to demonstrate negative numbers.  He flips the block upside down to represent the negative number.  So 10 + negative 5 would be the 10 block right side up, with the five block placed upside on top, and you look at how much of the original block is showing.  5.  Or, for instance, if you have -10 +5, that would be an upside down ten block, with a right side up 5 block placed on top.  The answer is how much of the original is showing.  (Clear as mud?)

[moonflower]

We did I think 3 different Pre-As.  Dolciani did the trick in the end.

Wendy had a magnificent concrete explanation of negative numbers.  Found it:

https://forums.welltrainedmind.com/topic/624923-re-how-mm-explains-multiplying-2-negatives/?tab=comments#comment-7212780

[Monica_in_Switzerland]

12 hours ago, EKS said:

Just to point out, subtracting a positive number is the same as adding its opposite--there is nothing special about subtraction of negative numbers.  All subtraction can be thought of in this way.  Just as all division can be thought of as multiplication by the inverse.

 

At some point during pre-algebra when my oldest realized "There is no subtraction/division" (Say this in the voice of Neo from The Matrix...), it was a real "aha!" moment.