geometry disconnect

[Noreen Claire]

DS10 is finishing up BA5, and is having trouble with remembering/understanding the definitions of, and relationships between, perimeter, area, surface area, and volume, which has come up again in chapter on exponents. He gets stuck with questions such as, "Given a cube with volume of 27 cubic cm, what is the surface area?" He has absolutely no trouble with the algebra, it is only the geometric concepts that he is struggling with. I looked back to the section on shapes in an earlier book and he went through it quickly and without much trouble (that I remember, and from the info saved in BA online).

We were planning on starting AoPS Pre-Algebra in the fall, after spending the summer working through the first two chapters of Jacobs Mathematics a Human Endeavor, which I think he will enjoy. However, I think we should add in some geometry practice/review over the summer related to perimeter, area, volume. Now that BA online has videos, I will have him go back and watch the videos from the earlier sections that relate. Can you recommend any other textbook, workbook, novel, video series, website, manipulative, whatever that will help him get a better grasp on these *specific* topics? Thanks very much.

[PeterPan]

Is it more an issue of the language and the visualization? You might need to help him make index cards with each word and a picture of the concept on the back. He may have gone through the materials so quickly or easily that he didn't really engage with the language.

44 minutes ago, Noreen Claire said:

"Given a cube with volume of 27 cubic cm, what is the surface area?"

If you stop and elaborate on that word problem, expanding each phrase, can he visualize it and get there? 

[Noreen Claire]

49 minutes ago, PeterPan said:

Is it more an issue of the language and the visualization? You might need to help him make index cards with each word and a picture of the concept on the back. He may have gone through the materials so quickly or easily that he didn't really engage with the language.

If you stop and elaborate on that word problem, expanding each phrase, can he visualize it and get there? 

He specifically mixes up concepts of perimeter, area, and volume. If I ask him for the area of a rectangle, he asks if that's adding the sides or multiplying. If I ask, what's the perimeter of a square with area of 25, he doesn't see how they are related. It's like his brain just doesn't register or remember these few, specific topics. It's something I've seen in classes of public school 10th graders with weak math backgrounds, but this kid has excellent algebra skills, so I'm struggling to find the disconnect. I'm wondering if he needs hands-on materials to work with?

[Noreen Claire]

Alternately, he *just* turned 10. Maybe I should just give it time, until we come to it in algebra in 6th grade?

[HomeAgain]

I would bring in Sir Cumference. Putting a story with a term helped immensely here and I added little activities to go with.  Also, an easy tool to remember area: call it squarea.  Keep reiterating that it's the number of squares inside. Peri walks around, but we find the squarea inside his footsteps.

[Momto6inIN]

1 hour ago, Noreen Claire said:

Alternately, he *just* turned 10. Maybe I should just give it time, until we come to it in algebra in 6th grade?

This is what I'd do. If he's 10 and really advanced in some math areas, it may be that his brain just isn't there yet with geometry. My just turned 11 year old still gets perimeter and area mixed up. She's not particularly math oriented but does solidly well at grade level.

[Noreen Claire]

3 hours ago, HomeAgain said:

I would bring in Sir Cumference. Putting a story with a term helped immensely here and I added little activities to go with.  Also, an easy tool to remember area: call it squarea.  Keep reiterating that it's the number of squares inside. Peri walks around, but we find the squarea inside his footsteps.

We've read a few of these books. I'll request then again from the library. Thanks!

[PeterPan]

The Real World Math series has been good for my ds for getting concepts away from memorized to real world application. 

                                            Perimeter and Area at the Amusement Park (Real World Math - Level 5)                                       This was GREAT and worked you into concepts so naturally, with context.

                                            [(Hot Air Balloons : Volume)] [By (author) Dianne Irving] published on (May, 2009)                                     

There are more in the series, and all of them have been excellent. I got them through the library. We usually do 4 pages a day, because there's text and then some application problems. 

[SoCal_Bear]

You could do something fun and hands on like Paper Paper Geometry. Geometry requires a lot of visualization. Hands on could help a lot with that. https://www.amazon.com/Patty-Paper-Geometry-Michael-Serra/dp/1559530723

Also AOPS pre-algebra has geometry chapters in there as well.

Compared to math progression when I was growing up, geometry concepts are introduced a lot earlier and in more depth than before. 

 

 

[SoCal_Bear]

It also may help teach him about the root word peri-. 

[fourisenough]

Not sure where we picked these up (probably this board!), but I’ve long used these memory aids to help my kids remember which is which:

pe-RIM-eter = walking the rim of a shape

squAREA = number of squares on surface of the shape

[almondbutterandjelly]

Lakeshore Learning has tons of great manipulatives for those concepts.  We used them even in high school geometry as refreshers.

Build and Learn Volume Kit: https://www.lakeshorelearning.com/products/p/TT567

Build and Learn Area and Perimeter Kit:  https://www.lakeshorelearning.com/products/p/TT566

Fold and Learn Geometric Shapes (useful for figuring out the shapes involved in surface area): https://www.lakeshorelearning.com/products/math/shapes-geometry/fold-learn-geometric-shapes/p/FG349

[Noreen Claire]

14 hours ago, PeterPan said:

The Real World Math series has been good for my ds for getting concepts away from memorized to real world application. 

                                            Perimeter and Area at the Amusement Park (Real World Math - Level 5)                                       This was GREAT and worked you into concepts so naturally, with context.

                                            [(Hot Air Balloons : Volume)] [By (author) Dianne Irving] published on (May, 2009)                                     

There are more in the series, and all of them have been excellent. I got them through the library. We usually do 4 pages a day, because there's text and then some application problems. 

Will check these out, thanks!

[Noreen Claire]

12 hours ago, calbear said:

It also may help teach him about the root word peri-. 

We've done this, but it's not sticking - yet. Will keep circling back to it in between our regular math and hope it eventually sticks.

[Noreen Claire]

5 hours ago, fourisenough said:

Not sure where we picked these up (probably this board!), but I’ve long used these memory aids to help my kids remember which is which:

pe-RIM-eter = walking the rim of a shape

squAREA = number of squares on surface of the shape

I'm going to post these on the board for him to look at as he needs. Thanks.

[Noreen Claire]

1 hour ago, perkybunch said:

Lakeshore Learning has tons of great manipulatives for those concepts.  We used them even in high school geometry as refreshers.

Build and Learn Volume Kit: https://www.lakeshorelearning.com/products/p/TT567

Build and Learn Area and Perimeter Kit:  https://www.lakeshorelearning.com/products/p/TT566

Fold and Learn Geometric Shapes (useful for figuring out the shapes involved in surface area): https://www.lakeshorelearning.com/products/math/shapes-geometry/fold-learn-geometric-shapes/p/FG349

Awesome recommendations, thanks!

ETA: I found a $25off coupon online! Woot!

Edited June 1, 2019 by Noreen Claire

[Noreen Claire]

12 hours ago, square_25 said:

In my experience, not having a mental model for a mathematical concept is far and away the most common cause of mathematically able kids having this kind of trouble. 

This is it; he's lacking the mental model. Everything else mathematical comes so easily to him, so this one's weird. We will just make sure to do a few problems every week, in between regular math work, to see if we can't imprint these models into his brain.

[cintinative]

I think this has already been mentioned, but perhaps if you bring out some 3D shape models that will help him to visualize what he is calculating. 

I am not very strong on visual-spatial stuff and often find these things helpful. Even if you don't have official models, you can use a Rubiks cube, cereal box, soup can, ball, etc for the various shapes.  When I am calculating surface area of a 3D object, I usually draw a picture or use a model. 

[Farrar]

I know that the true math people disagree, but for me and my kids, the disconnect with geometry is that it's all vocabulary. My kids are not good at the vocabulary element of it. Math and algebra are in the numbers and procedures. Geometry involves a ton of vocab recall. Again, some math person will step in to say, no, there's no more vocabulary in geometry than any other math, but if you forget the word dividend, you can still do the division problem in front of you. Or if you forget the phrase distributive property and monomial, you can still procedurally distribute and multiply two monomials. If you forget the difference between perimeter and area and surface area and so forth and you get that problem, you're completely screwed. There's nowhere to go with it. The question is in the words.

So, my recommendation is to do some drills with the words and see if the concepts begin to click eventually.

[Farrar]

7 hours ago, square_25 said:

 

I think I qualify as a true math person, and I agree that geometry has a LOT of vocabulary. It's a lot of stuff to remember. Sometimes, what people mean by "there isn't a lot of vocabulary" is that they don't put a lot of emphasis on it. For example, I'm just not teaching "shape names" to my kid because I don't see the point, and whenever I teach middle school kids math I have to unteach them what they've learned, anyway ("Yes, a square IS a rectangle, and also it's a quadrilateral, whatever you learned in grade 1.") But yes... when you get to proof-based geometry (and for some odd reason, most people only see proofs in geometry), you might wind up feeling overwhelmed by all the words. 

However, at the level of area and perimeter, that's just two words, and it's not so different from knowing the words "divide" and "multiply" or something like that. But yes... word drills seem like a good idea, because knowing what the words mean is certainly part of the mental model thing I was talking about.

I've been smacked down several times on this board and told that no, geometry is not all about the vocabulary. But if you have kids who are going to be slow on the recall - yes, even of only a couple dozen or so key terms - then it feels that way to them. Like, when my kids get a review of, say, all the different types of triangles, they can easily understand the concepts of how they're named by types of angles and sides and how that works and they do fine. But a few weeks later, it's gone. And the time to recall it - ugh. For one of my boys, this is tied to a specific issue. And I think it's especially hard on him because he's a really good mathy thinker usually. Yeah, word problems trip him up for similar reasons, but he's great with hard algebra problems that don't start as word problems. This year has been high school geometry and it's honestly sucked for all of us. I remembered that I hated it in school too. And I'm fine at it, but it's just... different from other math in this way. It wasn't fun at all the way algebra was for us. I'm looking forward to moving on in a couple of weeks when we finally finish.

[Farrar]

40 minutes ago, square_25 said:

 

Well, it's not ABOUT all the vocabulary, but if you can't remember the vocabulary, you can't do it! I would think it's totally fair to have the vocabulary posted up somewhere as you do the problems. And I'm not even sure that helps enough, because you are also supposed to remember the properties that come with the words. I'm not sure how I'd troubleshoot this one... when I did contest math, there were a lot of people who loved lots of math but despised geometry, and I'm now wondering if this was part of the issue for them. (I loved geometry, for the record, lol. I have a good memory and am very visual.) 

I'd be more worried about a hard time with word problems than about the inability to remember the long list of geometry words. Most of my college kids could do hard algebra but they couldn't set up the problems to actually get to the algebra. The set up is a harder skill.  

I only meant it in a colloquial way. There's no way to troubleshoot it. One of my kids could just study harder and he'd be better - and really he has. He's done fine. The other one - it's like foreign language - it'll never be his thing. That's fine. No big.

The word problems issue isn't anywhere near as acute. He can do them. He's just much slower than with other math. They'll also never be his thing, but he can do them. The geometry... he grasps all the concepts, but I doubt he'll ever be proficient in it in a deeper way. But that's fine. I don't see it as necessary to his future beyond the sort of stuff we all use geometry for in life. And the stuff he applies when he uses design software and so forth comes very naturally to him (no vocab involved there), so it's all good.

[Farrar]

50 minutes ago, square_25 said:

 

Sorry, maybe I wasn't clear: I didn't think you needed troubleshooting, I was just musing that I don't know how to deal with that issue :-). Because I can totally see what you're saying. 

Oh, I understood. I think for average students who just don't have great vocab memories, then the fix is just to focus on drilling the vocab. I'm actually pretty good at vocab. I didn't find geometry hard in school... just boring as all get out. So the reason I found it... ahem... mildly difficult to teach is that it turns out I still find it too boring to remember for long. It's funny because I like a good puzzle problem and I love logic. You'd think I'd enjoy it. And maybe there's some magic book that would make it work for me. Oh well. We survived. On to Algebra II.