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PeterPan

A thread to dump math stuff into...

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Since I've been monologuing threads (or we've been discussing) for reading and narrative development, I figured now I'd do a dump thread for math. :biggrin:  I'm digging in on this YouCubed and Build Math Minds stuff, and I keep finding things, seeing mentions of things. I thought I'd just put them here and people can explore and discuss. And really, it has relevance in some ways for SLD math. Like it's fine to criticize a method or a movement and say it's bunk for a population, fine. But I don't need to teach a population or have a grand theory--I just need to teach ONE. And all I'm trying to sort out is whether methodology would be good for my ONE. 

Realizing I need to clump here, because I'm totally overwhelmed!

Curriculum

https://im.openupresources.org  This is Illustrative Mathematics, which is problem-solving based and I think aimed at grades 6-8.

https://mathforlove.com/curriculum/  This is Math for Love, and I haven't wrapped my brain around this and need to look at the samples more. They're selling grade-leveled curricula, but at best something like that would be a supplement for my ds. I've never seen anything persnickity enough to connect with his brain but Ronit Bird. I keep looking, and I keep seeing lots of cool supplements. But for actually being careful enough to develop concepts and act as intervention for him, RB is where it has been at.

http://www.creativeteaching.com/product/hands-on-math-gr-45-ebook  Hmm, this is a lot more traditional, in the realm of how do we add hands-on to introduce concepts at home. 

https://incentivepublications.com/collections/common-core/products/common-core-third-grade-math This is a CC-driven workbook, so I guess I'm just very curious about the Dark Side, hahaha. 

https://crazy8s.bedtimemath.org/home/what  This is Crazy 8s by Bedtime Math. It got mentioned as something for weekly clubs, weekly challenges, that kind of thing. There seems to be a big call for weekly thinking math projects, something where they start at the beginning of the week and try to figure it out by the end. This requires you to set up a math club. Not sure if I can make that happen, as the activities are structured for 12-16 kids.

Software

https://www.stmath.com ST Math. Haven't done the demo yet, but it looks really sharp! Have we already discussed this and I just missed it? It could be really nice as independent math for ds on top of the together math and worksheets.

https://www.gomathacademy.com/  Here's another online math program that I thought would make a good supplement. Has a free trial, around $80 a year if you pay upfront. 

https://www.zearn.org  Zearn is based on Engage NY and reviews well on EdReports https://www.edreports.org/math/reports/compare-k8.html  Apparently GoMath scores well also, getting 13/14 to Zearn's 14/14. Zearn appears to have free teacher materials to go with the online lessons, making it a full, though not tiered intervention, curriculum option. For comparison, the major well-to-do districts in the city near us seem to use Bridges, which scores 12/14 and costs $$$$. Now Bridges looks really amazing, but obviously homeschoolers can't plunk out that.

Challenge Supplements

https://www.kenkenpuzzle.com/teachers/classroom You can sign up to receive weekly puzzles.

https://www.youcubed.org/week-inspirational-math/  

http://www.openmiddle.com/tag/robert-kaplinsky/  This is for that person seeking a challenging weekly problem to hand to the students, something they'd chew on all week, something that is not an immediate solve. I'm not sure about the levels, so maybe my ds isn't ready for it. The concept is interesting though. To me, anything you can structure, anything you can put on a whiteboard or a list, we can make happen. When my dd was young we did the problem solving books from (I forget the name, for the math contests, the AOPS people sell them), but this is just taking it farther. Seems good to me. Free. It looks like you can sift by grade, common core, or depth of knowledge level. Sharp. I almost think I could do this with my ds or that it would be fun to try.

https://solveme.edc.org/ I haven't figured out if this is an app or only through their site. It could be like reward math, transition time. Looks very fun! It has brainteasers to solve.

http://bedtimemath.org/apps/ Ok, so apparently Bedtime Math has an app that you play before bed to boost your dc's math scores. I'm guessing that needs internet if it's loading new problems each day. I'm looking at it, and it's actually really charming! It gives a real life scenario, complete with stories and pictures, and then gets them trying to solve it. Like!!! This may be a winner, and it's free to download.

Living Math

https://www.hmhco.com/products/do-the-math/math-reads/experience.htm  This is Math Reads by Marilyn Burns. She also has a new tier 3 intervention series (Do Math, Do Math Now), but it's not affordable. I wrote them to see if they would sell homeschoolers a kit with just the cards and instructional materials for the Math Reads, as the school sets are almost $600 and provide 5 copies of everything, overkill for homeschoolers. The living book lists here are FABULOUS and they're arranged by grade. 

Our math lives got totally way-laid working on language stuff, and his behaviorist was in favor of that. In fact, I would say that language was probably holding him back more from math than we realized, because it's hard to understand "two of something" if you don't understand OF. So we've come a long way getting behavior under control, getting more foundation, being more consistently in ready to learn, and he's bored enough that he would eat up anything that is clearly implemented and gently progressive. He can't handle a lot of frustration, so I think the collaborative challenge problems are more of a minor thing for him, not something he could do as major instructional approaches. He needs idiot-proof, gently progressive, anxiety-lowering. That is working with everything else. With Spelfabet, for instance, he started out flipping out about writing two words and is now writing all the words on the page! That's 12 words, which doesn't sound like much but with him is a BIG DEAL. That's good, solid progress that we get just by being disarming and getting material that is so stepped back and so right that he finally relaxes and can get there. Spelfabet has been brilliant for that. Maybe I should keep looking. Maybe I haven't actually found that for the math? With Spelfabet, it's an SLP and it was developed using PECS/Boardmaker, meaning she was teaching it to kids right where ds is, where spelling and reading and autism issues merge. Maybe she recommends something for math, hahahaha...

The other idea that has briefly flashed through my mind is to give him a calculator and more challenging word problems and see what happens. That's nuts, but it has crossed my mind. I got lots of stuff for fractions (some kits, the RS fractions book, etc.) to do with him, so we have that too. He's pretty good with fractions and basically usually fine when it's more conceptual. 

So that's all, just thinking out loud here. Feel free to dump things or respond or say what you're doing or whatever. I haven't actually looked for dyscalculia FB groups or tried really hard to get into the loop. That's how I found Spelfabet, but finally sneaking into some more serious intervention/professional groups. It just seems like there's less for SLD math, sigh. They talk about this one guy (whose site I've apparently mislaid), and I can't find samples there or anything to figure it out. Beyond that, they mention RB, which we already know. Maybe that's what I'll look for next.

Edited by PeterPan

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Multisensory is what people I know use, they start concrete then go pictorial.  SM was used by the school district here for special needs until MIF and Engage NY were developed and offered in the fully included multisensory classrooms.  

Is there a particular strand you need resources for?  Kinesthetic, visual preference, or multisensory ok? 

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HeighHo, you might be right. I might be needing more magic pixie dust than anything. I definitely want to round out our approach and step it up. If I landed on something brilliant that was even more scripted/structured than Ronit Bird, I'd go with it just to have it done. But I think mainly I'm wanting to have more categories of things we're doing for math so we can hit math multiple times. I used to, because we were doing some kind of online game and this and that. Really though, the online stuff wasn't brilliant. Some of this stuff I'm finding now is really sharp! 

Also, the challenge with ds is that he seems to benefit from seeing things lots of ways. So to me it's not overkill to do it with manips and software and worksheets and real life and and... 

His biggest buggaboo is that he seems so totally removed from learning. Like it's not that I'm neglectful, but every time I introduce things that are maybe typical, grade level math (multi-digit addition, whatever), it's sort of like asking if you'd like to teach an elephant to dance ballet, kwim? Like you could, but why?? He's just in this other world, where food appears and his does his thing and none of this stuff matters. 

Now if I get him on a conceptual level, sure he's totally into it and engages! The more challenging the better even, which is why I was looking for challenging stuff. I think I picked up the fractions kit from the HOE people. I have a pile downstairs and need to see. 

So those are my two biggest problems--my lack of mojo and his lack of why-jo. I'm working on the mojo thing, actually am going to get a GP and see one, am gonna take a little trip to someplace blazing hot till I roast away my fatigue with walking and hot tubs and breakfasts that magically appear... But his lack of why-jo I still feel really guilty about. It feels like it's an error on my part, like if I found the right something he'd engage. But it's more than that. He doesn't get the sequences of steps, doesn't have a reason to, doesn't have a need to, and frankly probably NEVER WILL. 

I mean, seriously, he never will. He will never ever ever EVER use the crap people spend 6+ years teaching in elementary math. None of it. He just qualified again with the board of disabilities. He's toast. He has a gifted IQ and whether he ever does 5th grade math WILL NOT MATTER. And I don't know what to do about that and I haven't figured out a way to make it better. The behaviorist says it may come in and gel with some maturity. Thing is, it doesn't MATTER. For his world, which is narrow and will probably involve living a supervised life with a part time job and meaningful hobbies, computation DOES NOT MATTER.

I don't know if there's something about math that would matter for him long-term. I hadn't thought about it. He might enjoy it if we read short biographies of mathematicians and did cool things. That might be interesting to him. Like I remember in high school there was this book of mathematicians with brief bios and nifty explanations of what they did (looking at patterns, etc.). He might like stuff like that. I don't know. I guess my tack so far has been to keep him thinking and not harp on the parts that aren't working. He sorta does computation stuff passably if he really needs to. I was looking at the summer homework packet for a nearby ritzy school for their rising 4th graders, and he could do everything in the packet. But just to sit down and do a page of computation, he'd NEVER do that. Right now it's pulling teeth just to get him to write 12 letters to complete words in Spelfabet (think Explode the Code for uber-dyslexics). He's just on his planet and doesn't get why he would need to write words, why he'd want to do any of that.

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So I guess my theory on some of these things was that they'd be idiot-proof and create their own why-jo. Like you're doing it because it's on there and we do the software every day at this time so you're doing it. That was my theory. That would leave me to do the interesting things I do really well. But that's what I was looking for, something that might create its own momentum and lure him in and help him progress without him realizing it.

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My theory is that computation doesn' t matter in comparison to developing the part/whole relationship understanding, as well as grasping that we can communicate our reasoning if we have some language to go with it. 

I don't know about the hook.  It is so personal.  If he enjoys concept, one could extend concept with relevant practical application. Not unusual for gifted children to not enjoy computation, it is rather boring when you know that multiplying say 3 digits by 3 digits is a lot of useless work since you already have the concept from multiplying 2 digits by 2 digits.

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4 hours ago, HeighHo said:

My theory is that computation doesn' t matter in comparison to developing the part/whole relationship understanding, as well as grasping that we can communicate our reasoning if we have some language to go with it. 

I really, really like that, thank you! You're right that it's a redefining of goals, and that for him just being able to communicate his thoughts involves a challenge and step just as much as computation. I thought of the goal so solely as computation and that needed to be redefined, yes, definitely.

Well I ordered some Teacher Created Resources Mathematics Readers that Gander sells in sets. I got some through the library and a few through ebay with a coupon. They may fill that need for giving an interesting/engaging context with a few questions. We'll see, but I think I might be able to get them to work. 

Well I'm going to keep chewing on your goals there. I think that's really important, the way you've defined them. You're right that it's a strong expression of what success with dyscalculia can look like and an expression of what would be accomplishing a lot with his language issues.

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When you look at elementary math done right, its SM type...concept, reasoning, application.  ime The part/whole concept is done many ways over the course of elementary school math, so many that the students that 'get it' are ready to ask themselves questions about fractions, and enjoy redefining parts as wholes  and vice versa for the purposes of their real world applications.  But also embedded are the properties...associative, commutative, distributive ,  identity, zero  ...and noticing patterns (trait of humans)...things that gifted children enjoy much more than a collection of computational procedures without reasoning.  Learning and using the properties are a heck of a lot more fun than memorizing with say, the nines finger trick for multiplication.  And presenting a solution instead of an answer allows acquisition of vocabulary, awareness of audience needs, and development of communication skills. 

Are you using gifted multisensory resources for math enrichment?  Play is so important. The units on other bases for example, can really add to a student's understanding of base ten.  Games give a success reward for using mathematical thinking.

A possible motivator is that you are letting him in on the fruits of mankind's knowledge.  No need to re-invent the wheel, but need to understand what's been learned and proven, and what's useful in his life. Things that will save him time, so he can focus on his priorities.

Edited by HeighHo
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On August 29, 2018 at 9:28 AM, HeighHo said:

Are you using gifted multisensory resources for math enrichment?  Play is so important. The units on other bases for example, can really add to a student's understanding of base ten.  Games give a success reward for using mathematical thinking.

Yup, basically everything we do is play. Yup, multi-sensory out the wazoo. 

I think my real problem is getting my butt in gear at this point. What usually happens is I find one really good activity and we milk it for 2-3 weeks. So it's not like I need so much at this point. I just have to get my butt in gear. He played store today with money and used a LOT of language, making coupons, doing subtraction, etc. I was just amazed at the language. We've come a long way from where we were, and he should be easier to work with and more ready to do collaborative problem solving. We should be fine. We just have a few odd weeks here, finishing up one of our therapies while also doing the other, so it messes up our whole easy continuity thing. When we drop down to one therapy day a week and have more consistency, that should help. But yeah, if I just go pick something and get us STARTED, we'll probably be fine. He actually counted by 4s by choice today. These are concepts that just weren't there before, somewhere where language and developmental readiness and math merge. Now I'm seeing it, which means I have openings to do more.

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Do you have a list of concept progression by strand?  that allows some planning.

Throwing out for benefit of lurkers:

There is so much in real life you can do at this stage.  When store gets boring do movie theater and sell tickets and popcorn, figure out how much is needed to be sold to pay the workers.  make some of the customers seniors and children with different prices.  Or zoo tycoon game...

What bothered me about public school here was the dropping of everything real life, especially measuring.  Pre-nclb the dc were measuring the room with paperclips and other found objects, then rulers and understanding why the distance from the king's thumb to his nose wasn't the best standardization.  measuring cups were used to water the plants and ready a science demo.  Farm kids would share how many eggs per chicken and everyone could figure out how many cartons  his family needed to use. After nclb it was up to the parent.  At youth group I had neurotypical boys who had no clue on how to read the gauge on the pump to fill the bicycle tire....think about that, in two years they'll be expected to pour and mix gas as they do yardwork.. it was a project to figure out how many boxes of grammies, bags of marshmallows, and choc. bars were needed for the whole group.  They had nothing beyond basic, whole number rote work. 

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58 minutes ago, HeighHo said:

What bothered me about public school here was the dropping of everything real life, especially measuring. 

Oh that's interesting. Yes, we do tons of real life. I hang on some of these math groups on FB, and you're right that what they're doing sounds so impressive (collaborating on strategies to solve things, etc.), but that's not the same as applying to real life. But I don't know what is really happening in their classroom. 

So yes, in general we're super strong on the real life part. I just try to have carefully chosen tasks that move him forward conceptually, something that is maybe too hard at first (a game) that makes him think and that we grow and make more challenging as he gets stronger. That's where we like to be. 

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measuring is being brought back in as part of middle school STEM. see the NYT ed article on integration of public schools yesterday, the first photo shows the STEM expectations  "1. Use rulers and scissors for measuring and cutting..".   

pretty much every student needs intellectually challenged; little steps are too little for many to have any sustained interest.  one thing classroom teachers do is put the science posters up on the wall so the students who don't need little steps or massive review can have something to learn while waiting.

Edited by HeighHo
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Oh that is HILARIOUS. I had no clue. Posters sound fun though. I'm thinking that would be fun for us to make as a way to discuss/narrate science topic books. He would totally get into that.

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http://ime.math.arizona.edu/ttc/Exploding Dots_Student Version.pdf

Came across a mention of Exploding Dots and it has a workbook by Tanton. Isn't Tanton the guy Heathermomster likes for math? Anyways, it uses different bases and dots to explore WHY we do trades for addition and subtraction. It then carries them over to multiplication, which I thought was really sharp. We're *just* starting to do addition with trades, and although ds is carrying the dot, I think the Exploding Dots work would connect it more tightly in his brain WHY he's carrying dots. And even the fact that we're carrying dots is from RightStart, which made me wonder which came first or where RS got the idea to go with dots for trades.

Well otherwise our math is going really well! I try to have at least 3 sections to our math a day, so we do some computation using a hands-on kit (Lakeshore Learning), do a page from Advanced Pattern Blocks, do some Ronit Bird stuff, and then do a bit from the Hands-On Equations (Borenson) fractions kit if we have time. He seems to be doing well with that. I also had missed that Ronit Bird had a page with all the addition strategies on it in one of the printed books (Toolkit probably). I printed that out and want to go back and make those strategies a bit more explicit for him. That's Common Core but it's also good sense. Somehow we learned them but didn't nail them to strategies. He's got enough brainpower now to think that way.

For our Ronit Bird time, we're working through her multiplication book, which is BRILLIANT, oh my. I'm just taking it slowly, letting it sink in, since it seems to be sort of rocket science for him. She builds her facts out of components, so 2X4 is the double of 2X2 which is a double, 2X7 is 2X5 and 2X2, etc. I can't believe I never thought to present it that way! And what it's doing is setting him up well for other concepts like prime factors. He was actually figuring it out for himself yesterday, so he's right on the cusp. Just blew my mind. And since the way we're doing the RB math has you using terms like double and half, I went ahead and threw in some as division, which let us then explore short division, which he seemed to get quite easily. 

So I'm pretty pleased. We're not necessarily where you'd like a student of this age to be, but what he has is solid and connected in his mind across lots of branches, not just one way. I had thought about adding in some printed math, but I just don't feel we have time. By the time we do all these explorations, we've already spent 45 minutes and are done. I looked at computer math, but I think they would use up valuable time without providing instruction as thorough as Ronit Bird. So I think for now it's better to stick with our Bird math and explorations and solve the other hurdles (word problems, language issues, etc.) when we come to them. I *may* get the BJU math just for some independent work, but I don't know. I always have way more ideas than we actually get done, lol.

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Do you think the euphimisms are helpful?  'trades', 'carrying'....it seems more straightforward mathematically to use 'group' and 'regroup'.

I think the dots are an abstract step, helping the student visualize and get away from trying to replicate the concrete in their visualization.  No need to get stuck on the step of detaching unifix blocks for ex., although I could see that a student who has used a domino representation for a particular number may be weak on knowing how many dots at a glance if not using that representation.

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Yes, there's a lot there! Your point on the terms is well-taken. I'm not sure I've noticed what RB calls them. I lost (mislaid, put somewhere, see my head hanging in shame) by coming of Overcoming Dyscalculia. That's what would have RB's take on the more advanced stuff, so it's killing me. I did some looking and I just need to find it, sigh. 

Yeah, one video I watched showed a girl at a whiteboard and she kept her dots pretty tidy. I don't know if it's so much that learning via patterns makes it hard or that the dyscalculia makes it easier to count by 1s than groups. Either way, it will be interesting. I prepped the first portion of the Tanton doc to play with him today, so we'll see. I think he may take to it. It's really just a stage though, definitely, not a long-term place to stay. I think if it makes it click super solidly WHY we're doing the dots at the top that would be good. And yeah, I'm gonna need to think about changing that term to group or something. You're right that trade means very little to him and that language matters in this.

You're right he doesn't stay at blocks long for anything. The Lakeshore kits I got have blocks, and I thought he'd stay there longer. Oh no, the kits were coins. We did blocks a different way. Anyway, I was surprised how briefly he stayed there. And you're right that even though it seems very physical, they're abstract. Tanton suggests having them do the dots with buttons, etc., which would be sort of an in-between. But it's still a representation of a different concept, inherently abstract, good point. And I think that's why it's good, as an in-between step, just like the Lakeshore addition it is in-between blocks and solely written. 

I have no clue where I left my Overcoming, sigh. I have some piles (more shame, more head down) to deal with from when I've moved things around, changed things up. I don't know. I must be more diligent. In my slight defense, my thyroid has been giving me fits. I'm getting my spunk back, so I need to tell myself to get stuff done.

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When I help with math at this level, I find explaining the place value system as a code most helpful.  The light bulb turns on when the student realizes we humans have picked this code, its not something mysterious that they don't find obvious. Its a tool we invented that helps us. That's why using the different bases help -- it turns the lightbulb on for place value for some students since they can't use memory, and are forced to step thru it to understand. Then I can eventually get the concept of analog clock as a counter and phrases such as 'half past five' understood. 

Counting dots at a glance is a learned skill in the progression. Counting a handful of change at a glance and telling time from an analog clock at a glance is too. 

I didn't use buttons, as  I find cardboard circles, same size with the number 1, 10, 100 written in same color/size/font to be the very best until ready to move to pictorial of same.  They aren't seen as something that needs explored with the senses, as poker chips and coins are.   After mastery, I move to coins... if the child has been pushed into nickel and quarter too fast, he has some lack of success emotion to overcome, and that's easier if he has place value understanding.  Same with inches/feet, grams/pound, imaginary part/imaginary whole of their choice....getting the whole/part and part/whole concept down and seen as useful. 

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Well we did the first lesson from the Exploding Dots and it was fun!! Definitely excited to see what connections he makes with this.

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