Farrar Posted May 1, 2015 Share Posted May 1, 2015 So, it's nearing the end of fifth grade and both my boys are pretty solid on arithmetic. One of my boys is starting pre-algebra with Jousting Armadillos, the other is using MEP grade 5. But I am increasingly just embarrassed by their geometry abilities. It's not pretty. We have seriously covered this stuff, but they both struggle to remember things like... * the names of shapes other than the kindergarten ones - so things like hexagon, octagon, etc. as well as things like right triangle, acute triangle, etc. and terms like polygon and quadrilateral * degrees, such as that a line has 180, a circle 360, etc. * how to do area of triangles * how to do volume of solids and surface area of solids * terms of vertices, plane figure, etc. * measurement units and conversions both metric and English They're good about perimeter, I guess and area of rectangles - and they don't really confuse the two, which is good. And plotting points on grids and that sort of thing. And my ds who is in JA even sort of enjoys shape puzzles like pentaminos and tricky things where you have to calculate perimeter or area of weird polygons without it spelling out all the sides (Beast Academy had some of these and we've seen them other places). I feel like I need some perspective. How bad is this? Some of it is just dismaying. I spent three weeks off and on quizzing one of my ds on measurement units and felt like he basically had it, but he had a word problem with some the other day and it was like totally new information again. Argh. We aren't really drill and kill types. I feel like what I need is something like daily elementary geometry and measurement review with just a few problems to keep these skills in practice. Will this stuff get recovered if we do a full geometry program? Quote Link to comment Share on other sites More sharing options...
quark Posted May 1, 2015 Share Posted May 1, 2015 Just some thoughts: When you say you have seriously covered this, how was it covered? Do the boys have a chance to construct with compasses, measure angles with the protractor, etc? I know you were working on building projects. Have they applied these concepts in their building? Could they just work with the shapes, applying them in whatever way you see ideal for them without worrying about the names first? If they know area of rectangles, e.g. a square, can they intuit what happens if they fold the square in half diagonally (ETA: and also cutting the triangles and putting them back together to re-form into a square)? Would that help them intuit the 1/2 of base x height? 1 Quote Link to comment Share on other sites More sharing options...
Jyhwkmama Posted May 1, 2015 Share Posted May 1, 2015 My kid (same age, currently using CLE) has geometry issues with confusing definitions of different polygons too. I do not sweat it. I think back to when I was in school and we barely learned any geometry at all until we took it in high school. I turned out fine and even went on to excel in math in college and become an engineer. If you think about it, it is not really all that necessary in terms of building knowledge for future math levels. Except for the Pythagorean Theorem, when do you really use geometry before actually taking the full year course. By the time you take trig or math analysis (translate, rotate), you have already had geometry. Just keep talking about it when it comes up in their curriculum, but don't sweat it. 4 Quote Link to comment Share on other sites More sharing options...
quark Posted May 1, 2015 Share Posted May 1, 2015 I agree that you don't need to feel dismayed. And you definitely haven't failed! Plus, kids are pretty good at picking up on the fact that you are stressed and this might further hamper their desire to learn geometry in more detail. The Key to Geometry series might help for some gentle reinforcement. There are samples here -- click on each book for additional views. You probably won't need all of them. 2 Quote Link to comment Share on other sites More sharing options...
Chrysalis Academy Posted May 1, 2015 Share Posted May 1, 2015 I was feeling very similarly - we didn't like the geometry in MM, and despite my good intentions, didn't reallly end up doing much else for Geomeetry instead, although I did have her work on the chapters in BA 3A when it came out - she was in 5th at the time. Then this year, I tried her on the CTC book Understanding Geometry, and she just wasn't getting it. The real game-changer for us has been School Yourself/Edx's Intro to Geometry, which we've both done this spring. Their platform is so great, the way they show you visually exactly what is going on, and keep you engaged with the short, super interactive lessons. It's totally changed her attitude about Geometry - from fear/dislike to now enjoying it and finding it understandable. I am thinking about what's next - even though the EdX was supposed to be the equivalent to high school Geometry, I don't feel like it has enough practice for full mastery. But I'm thinking she can now do the UG book, and maybe Khan's Geometry mastery, and be in good shape. She is at least confident in her skills and ability, and has found a method of presentation that really seems to work for her. So, sort of just sympathizinig, and sort of suggesting that you check out the School Yourself platform and see if it works for one or both of them. I actually think the teaching is quite great. Its weakness as a full program is simply that there isn't enough practice for mastery. 2 Quote Link to comment Share on other sites More sharing options...
go_go_gadget Posted May 1, 2015 Share Posted May 1, 2015 I have a math degree, and some of the things you mentioned are things I don't have memorized, but re-derive when I need them (I remember volume of a sphere, but only remember circumference of a circle as the anti-derivative of volume). I'm a big-picture thinker, whole-to-parts learner, and can never remember that things work a certain way unless I completely understand *why* they work that way. I find that my kids retain trivia best when they see it on a regular basis, and that's one of the reasons I plan to use the AoPS books in an integrated way, working all the Intro books concurrently so that we don't go more than a few weeks without touching on a topic. The names of shapes with Latin stems should be easy once those Latin terms are retained, and ones like ''trapezoid'' I wouldn't worry much about. Similarly, ''acute'' and ''obtuse'' are intuitive if the meanings of those words in general speech are known. Metric conversions are just place value, with more Latin stems. Imperial ones are harder because nothing else is in base 12, and then there being three feet in a yard is just arbitrary. I'd recommend, not as a parent since my kids are a bit younger, but as a math lover, that you take a more spiral approach with geometry and also work in some Latin stem study. I don't think it's cause for alarm, at all, at this stage. 5 Quote Link to comment Share on other sites More sharing options...
Farrar Posted May 1, 2015 Author Share Posted May 1, 2015 How covered? Oh, many ways. One of my boys with MM through 4th grade. Then with other programs. We've actually done part of the Key to Geometry. And we did some special units on this stuff. We read Savage Shapes. We've done a bunch of hands on stuff. We've done a number of projects where measurement is key and they have to use it. I mean, when we do it again, except for some of the vocabulary issues, they generally pick it back up. But I have to show them how to pick it back up every single time. And it's always like new information. Like, oh, there are different kinds of triangles? We've done the proof for why area of triangles is 1/2b x h a ton of times. And they always get it. And then they always forget it. It's good to know other kids aren't necessarily on the ball with this stuff either. At least I don't have to reteach how to multiply fractions or do long division every time it comes up. It's just frustrating. But I don't think I've overly stressed about it up to this point. I kept thinking, honestly, that it was going to be like telling time - something we covered, and then covered, and then covered and they could never seem to remember it. Until one day it just seemed natural to them. And I thought, oh, this was a waste of time to worry about in first grade. Clearly, I just needed to wait for them to developmentally get it. And I thought of geometry that way to some extent. I thought, we'll just keep covering it, but when ds today referred to a hexagon as "that shape, you know, it's something," I began to wonder if maybe we'd really missed the ball, you know? 4 Quote Link to comment Share on other sites More sharing options...
Arcadia Posted May 1, 2015 Share Posted May 1, 2015 For names of polygons my kids remember by word roots so penta is 5 and hex is 6... By the time your kids are done with proofs in geometry, they'll probably remember all the rest. My 9 year old forgot how to spell isosceles correctly :lol: He had to look up the spelling to verify after he wrote. ETA: Link to polygon word roots http://strader.cehd.tamu.edu/Mathematics/Geometry/PolygonLesson/polyname.html Quote Link to comment Share on other sites More sharing options...
Farrar Posted May 1, 2015 Author Share Posted May 1, 2015 Good grief. I'm a decent speller and *I* forget how to spell isosceles. My kids definitely don't need to spell isosceles. BalletBoy maybe could learn but I'll just be happy if Mushroom can spell his own name some days. 3 Quote Link to comment Share on other sites More sharing options...
Loesje22000 Posted May 1, 2015 Share Posted May 1, 2015 I don't think There is a need to worry. In my area they should know it inside out at age 13 the vocational track at age 15... But I understand your problem, we have it with grammar... I might be a matter of interest. Interesting things will be easier remembered then not so interesting stuff, and what is interesting depends on the child :) 2 Quote Link to comment Share on other sites More sharing options...
wapiti Posted May 1, 2015 Share Posted May 1, 2015 Everything you've covered so far will most likely be covered again in prealgebra (though I don't know what's in JA, my kids loved the geometry chapters in AoPS Prealgebra). And then again in high school geometry. They will remember more when they're deeper in the weeds using this stuff. I wouldn't worry a bit :) 2 Quote Link to comment Share on other sites More sharing options...
Farrar Posted May 1, 2015 Author Share Posted May 1, 2015 Well, it's definitely not covered in JA. But I have Lial's BCM and could just have him do that chapter. In fact, I was, and he found it really easy... But didn't seem to be retaining anything and was complaining about wanting to only do JA so I set it aside for now. Quote Link to comment Share on other sites More sharing options...
JoJosMom Posted May 1, 2015 Share Posted May 1, 2015 Put me firmly in the "no big deal" camp. My DD is 12, so just a bit older than your boys. She does well with most math, but HATED the elementary geometry material (we did MM through 6th, the earlier progression.) Honestly, it's seems more like just stuff to memorize at that level, and I don't think she ever really connected with the material. She's doing AoPS Intro to Algebra this year, though, and did her first proof. When I told her that "real geometry" would be more like that, she lit up and said, "Oh, I think I'll like geometry then!" HTH 2 Quote Link to comment Share on other sites More sharing options...
madteaparty Posted May 1, 2015 Share Posted May 1, 2015 I don't know anything about geometry specifically, but it recently dawned on me (I've only been homeschooling 2 years) that for my particular child, we need to touch something (more like wrestle and struggle and cry) at least three times, at different periods of time, for anything to have a remote chance of sinking in. It should be double and triple spiral all the time here. Fun times. 2 Quote Link to comment Share on other sites More sharing options...
EmilyGF Posted May 1, 2015 Share Posted May 1, 2015 I'm having my 10-year-old use Khan to review geometry. Not sure what is up with it, but it seems like he's forgotten all that he's learned... Quote Link to comment Share on other sites More sharing options...
Chrysalis Academy Posted May 1, 2015 Share Posted May 1, 2015 I don't know anything about geometry specifically, but it recently dawned on me (I've only been homeschooling 2 years) that for my particular child, we need to touch something (more like wrestle and struggle and cry) at least three times, at different periods of time, for anything to have a remote chance of sinking in. It should be double and triple spiral all the time here. Fun times. It's really true. I never have liked spiral elementary programs, because I feel like my kids have needed the concentrated attention on a topic in order to learn a new concept in the first place, but boy do they need spiral review! Luckily it's pretty easy to do this if you use more than one math program, or take advantage of the various computer math programs, free or otherwise, for practice/review. It's invaluable to be faced with a problem that you know you've learned but can't for the life of you remember how to solve - and then go back and review, and solve the problems. Such repetitive/spaced practice is what learning is made of. I also saw a huge, huge benefit to having Shannon do Algebra 1 and Geometry at the same time (using the Edx/School Yourself classes). Granted, you need to be competent at solving basic equations before you start with geometry, but she was, and she was so benefitted by not only practicing the concepts in the context of Algebra and Geometry at the same time, but it also showed her the relevance of both - how both use concepts from the other, and how both are applied to real-world problems. I'm definitely a convert to the idea of integrated math for PreA level and beyond. If there aren't good Integrated materials that work for you, nothing wrong with going through subject-dedicated books concurrently. That's our future plan as well. 1 Quote Link to comment Share on other sites More sharing options...
madteaparty Posted May 1, 2015 Share Posted May 1, 2015 I also saw a huge, huge benefit to having Shannon do Algebra 1 and Geometry at the same time (using the Edx/School Yourself classes). Not to veer too off topic, but this is what I plan for 7th grade year as well, Geometry and Algebra 1 or 2 at the same time (depending how 6th grade year goes. We may repeat Algebra 1 in any event, for the sake of review and the fact that it would be nice to be competent at something for a change). 2 Quote Link to comment Share on other sites More sharing options...
Chrysalis Academy Posted May 1, 2015 Share Posted May 1, 2015 Yeah, we're ending up dedicating 7th & 8th grade to combined Algebra plus Geometry. We'll definitely get through Alg 1 and Geometry, we may start into Alg 2 in 8th, but I'm really not in a hurry, I'd rather take a whole 'nother year to cement the Alg 1 stuff, if need be. I feel like we're rock solid on the "first half" of Alg 1, and we've had a nice intro via EdX to the rest of the topics. For Geometry, we've had a good intro to all the topics, now just need to cement it. And memorize formulas! And I suppose think about writing proofs . . . 1 Quote Link to comment Share on other sites More sharing options...
dereksurfs Posted May 1, 2015 Share Posted May 1, 2015 Put me firmly in the "no big deal" camp. My DD is 12, so just a bit older than your boys. She does well with most math, but HATED the elementary geometry material (we did MM through 6th, the earlier progression.) Honestly, it's seems more like just stuff to memorize at that level, and I don't think she ever really connected with the material. She's doing AoPS Intro to Algebra this year, though, and did her first proof. When I told her that "real geometry" would be more like that, she lit up and said, "Oh, I think I'll like geometry then!" HTH I completely agree with this. While they are still very young and simply toying with these concepts and terms its more like memory work, almost like memorizing words of a foreign language. Since they are not really using them regularly it's perfectly normal to forget them. However, once the child is old enough to actually take Geometry all of those things begin to make more sense within the 'context' of regular usage. We never gave it much thought and at most looked at it as simple enrichment, an introduction to basic shapes, concepts and simple calculations. The brain develops so quickly at this stage while transitioning from concrete operations to abstract reasoning that your dc will be in a totally different place once they are ready for the actual course. Honestly, ds13 did very little pre-geometry and is really excelling in it this year after solid Algebra 1 training with AoPS and TabletClass. The real effort involves working the proofs and solving more complex problems. The terms are almost an afterthought compared to the more challenging aspects of the course. I'm doing the same thing for ds13 now in showing him introductory lessons to Calculus *way* before he is ready to take the course. This is simply to introduce big concepts and some of the associated terminology. While its interesting to him as 'oh, that's what I'm working toward,' I don't expect him to memorize and retain the formulas or terms before he actually gets there. To do so would be overkill and cause unnecessary stress/worry, IMO. 3 Quote Link to comment Share on other sites More sharing options...
The Governess Posted May 1, 2015 Share Posted May 1, 2015 My dd struggled with geometry at first. It finally started sticking when we went through Singapore 5 last year, and then this year she recalled more than I expected her to when we went through AOPS pre-A and easily picked up the new material. I feel like she is good at it now, where a couple years ago it was her weak spot. I think it was probably just a developmental thing. What if you have them make their own geometry books? They could have sections for the different shapes and all of the rules and formulas they have learned for each. They can add to it as they go and review it as needed. I did this for my dd for grammar one year and it really helped her organize her information and see how everything fit together. Also, AOPS has some fantastic videos in their pre-a section that cover properties of triangles and other shapes. 1 Quote Link to comment Share on other sites More sharing options...
daijobu Posted May 24, 2015 Share Posted May 24, 2015 I have a math degree, and some of the things you mentioned are things I don't have memorized, but re-derive when I need them This. I agree that you and your students need to get in the habit of re-deriving things they have forgotten, NOT memorizing. Maybe not even formal derivations, but motivations can help spark a memory. Next time they forget the formula for the area of a triangle, open your pad of paper to fresh blank page and draw a rectangle with diagonal. See how the area of the rectangle is base * height, and the area of each triangle is half that? Spend a good amount of time discussing triangles and the area formula, as if it were for the first time. Do this every. single. time. they forget the area formula. One day, my dd forgot what negative exponents meant. This despite having just learned it a few weeks earlier. So we began again with the motivation for our definition of negative exponents. 3^3 = 27 3^2 = 9 3^1 = 3 3^0 = 1 3^(-1) = ...see the pattern? We had already gone through this exercise, but it's important that she think about these derivations so she can do them herself when she needs to. 2 Quote Link to comment Share on other sites More sharing options...
happycc Posted May 24, 2015 Share Posted May 24, 2015 I have a child like this and mneumonics seem to help her. My other two kids ---just introduce and they have it down. So with the one that struggles---flashcards, memory games, go fish games with these terms. Talked about right angles made around the house. Place labels around the house labeling the angles and shapes seen. Making them out of popsicle sticks, rubber bands, building a fence, Legos...make up a board game with these terms., write songs about each of the shape (seriously my daughter finally remembered the shape name because of making her write a song about pentagons) Using stories and mneumonics ===repetition and drill and kill, overteaching. We switched to CLE for the summer to get these terms down. Going back to grade level work in the fall. And maybe use CLE for things she needs more review on. We are finally get pints, gallons etc down... we write a BIG G and then four Q's inside and within the Q's, 2 P's and then within the two P's, two C's. I had to remind her that P's and C's only get two in each. We taught the gallon man but soon found that was too cumbersome during test situations. She needed something small and quick. I also wanted to add to go slow with these terms and concepts. Work a lot with one before adding another. My daughter needs to play with a concept a lot before she can own it. 1 Quote Link to comment Share on other sites More sharing options...
Clear Creek Posted May 25, 2015 Share Posted May 25, 2015 So, it's nearing the end of fifth grade and both my boys are pretty solid on arithmetic. One of my boys is starting pre-algebra with Jousting Armadillos, the other is using MEP grade 5. But I am increasingly just embarrassed by their geometry abilities. It's not pretty. We have seriously covered this stuff, but they both struggle to remember things like... * the names of shapes other than the kindergarten ones - so things like hexagon, octagon, etc. as well as things like right triangle, acute triangle, etc. and terms like polygon and quadrilateral * degrees, such as that a line has 180, a circle 360, etc. * how to do area of triangles * how to do volume of solids and surface area of solids * terms of vertices, plane figure, etc. * measurement units and conversions both metric and English They're good about perimeter, I guess and area of rectangles - and they don't really confuse the two, which is good. And plotting points on grids and that sort of thing. And my ds who is in JA even sort of enjoys shape puzzles like pentaminos and tricky things where you have to calculate perimeter or area of weird polygons without it spelling out all the sides (Beast Academy had some of these and we've seen them other places). I feel like I need some perspective. How bad is this? Some of it is just dismaying. I spent three weeks off and on quizzing one of my ds on measurement units and felt like he basically had it, but he had a word problem with some the other day and it was like totally new information again. Argh. We aren't really drill and kill types. I feel like what I need is something like daily elementary geometry and measurement review with just a few problems to keep these skills in practice. Will this stuff get recovered if we do a full geometry program? The Daily Mental Math series covers most of these things. 2 Quote Link to comment Share on other sites More sharing options...
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