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Slowing Down and Advancing


rochenan
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Slowing down and going deeper are two different things, imho.  Providing extra review is not the same as extra depth.  Extra depth is a different form of acceleration, where advanced but relevant material is introduced sooner, so that it is more readily digested when later presented on level.

 

For example, during pre-algebra (and even sooner!), you can introduce quite a lot of number theory.  That number theory makes the technical portions of algebra a breeze to learn.  During the acquisition of basic math concepts, such as during 1st-3rd grades, you can discuss how numbers are formed, how operations are formed, and how they interact.  Sets, domains, ranges, and functions can all be taught at a startlingly young age.  Those foundations simplify all mathematics going forward.  Yet, they are often taught only in later algebra, precalculus, and calculus courses.

 

Sometimes, you will see depth presented as intermediate courses.  For example, adding in a course on number theory, symbolic logic, probability, combinatorics, stereometry, or analytic geometry.  Using these allow you to accelerate freely, and fill in timelines with meaty content, so that the child stays relatively close to peers.  This is still not slowing down -- the material is highly advanced for middle schoolers and even many high schoolers.

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I'm assuming the ages in your signature are correct? I don't have many ideas for you, but my 4yo DD enjoys Penrose the Mathematical Cat. It introduces a lot of ideas that are not typically introduced to young children. In addition, the Time-Life I Love Math books cover a huge variety of topics appropriate to elementary math but not always in typical curriculum. The I Love Math books are out of print, but my library had some and I found several used.

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My 5yo likes to read Life of Fred. Then she asks me to re-read the chapters with her so we can do the Your Turn to Play. I ration her to about 2 chapters of this in a day. This way I feel like she gets some benefit from "sleeping on it" and doesn't zoom through faster than she can truly kick things over to long-term memory. LoF has a lot of great auxiliary math topics beyond just your typical elementary arithmetic too.

 

She also reads Beast Academy for fun.

 

My primary goal is to make the field of mathematics available and interesting to my kids, not to progress them through some predetermined path at a faster or slower pace.

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Jackie thanks for the suggestions. They look fantastic and he loves cats!

 

Sunnyday. I think making math more available to him is what I'm trying to do without it just being worksheets. It's not even that I think the book we are using is bad, but he doesn't need 300 pages and lots of review or at least he doesn't right now. I do think availability is a big thing. I have shelves of books about history and literature and I can't help but wonder if having more math books around for him would let him move along in math the same way kids start reading more difficult books. They pick up a book out of curiosity or at least that's how I started reading more literature.

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At the ages of your kids, My son and I did a lot of discussion about the concept of adding, subtraction, multiplication, and division. It was discussing the four or five different ways that addition can be looked at and then how subtraction could be described in the same way. How did they then relate to multiplication and division. Could he explain each operation in terms of addition? Did he understand origins, reciprocals, and identities. It was about the concept of math, not the actual usage.

 

But then, I am a pure math geek. Ultimately, Ds has gone humanities track. At least for now.

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My DD started LOF at 5 and really enjoyed it. It introduced more while still concentrating on basic math facts and concepts. We also did Math almost entirely through word problems and introducing Math concepts while out and about (which is how my 3 year old came to be having a discussion at a restaurant with my 6 year old about whether the time taken til breakfast arrived would be best measured in seconds, minutes, hours etc and wishing it was milliseconds). My eldest also likes Penrose the Mathematical Cat and she is also reading The Toothpaste Millionaire at the moment which introduces a lot of mathematical concepts as well as real world applications. And then we also read a lot of Living Math books to both the youngest and eldest. Many of the LOF concepts can be discussed in real life really easily too.

 

We run the extras and the Singapore and LOF curricula all separately not lining anything up - as far as I am concerned Math is everywhere and therefore to try to separate addition and multiplication and so on all the time is not how life works. Of course with the youngest I will show her more addition-subtraction concepts in my speech with her, but I won't prevent her from hearing about multiplication and division now - she hears it from her older sister anyway. The eldest did tell me Singapore 3a was baby work the other day so I may need to look at that again before she starts rebelling.

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I've been looking into the new Murderous Math Mysteries for Early Readers. They don't let you see samples though so I don't know how much of an early reader they really are. LoF was nice for apples but now that we've started Beast with color and monsters he doesn't want LoF.

 

For the first time though, we are using Beast and NEED more review. We finished chapters 1-3 in Beast 3 and he loves it but I don't know what's going to stick in the long run without a review every couple weeks. B-D books are coming in the mail but not fast enough. We did a chapter every two weeks which was way faster than expected. In the second week of every chapter we had two days that I made my own review sheets to do to stretch the chapter out.

 

I'll probably buy a Murderous Math Early Reader for Christmas to try for extra depth.

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We used the books Hippo Math (series), Murderous Maths (series), The Number Devil, I Hate Mathematics (unfortunate title, great book!), and Math for Smarty Pants which allowed ds to explore higher level math concepts while still learning arithmetic.  He also got to do Khan Academy in lieu of his regular math work one day per week.  He hated arithmetic but liked the mathematical reasoning in these books, so it kept him motivated to get through arithmetic.

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Others not yet mentioned (I think).

 

Basher Books-several math titles there (plus lots of science ones). If your child likes silly little creatures, this is great, because it personifies each concept and gives it a face and personality. No math work, just concepts.

 

Math is CATegorical by Brian P. Cleary. My DD loved these (and the accompanying grammar series) even after she knew the concept cold.

 

As she got older

 

(Fill in blank) for dummies. She's used these books to get an intro/overview of a lot of topics and will sometimes go back to them to review if she needs it. Some included math work, and some have workbooks as well. We have pretty much every math-related title they have. Nothing like having a kid carry "Calculus for Dummies" onto a plane for light reading.

 

Painless (fill in blank)-very similar to the Dummies books, and serve the same niche.

 

These both have served a need in letting my DD progress onward while enriching at a slower pace. We actually now use life of Fred for the same purpose.

 

Extra topics-lots and lots of Dover math books, logic books, and stuff like that. When she was younger, Prufrock Press and Creative Thinking company were helpful, too.

 

Math contest prep activities, like Continental Math league, the Canadian Math Kangaroo website, and MathCounts. We dropped doing these as an extra when we started AOPS, but before that point, they were DD's fun math.

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Thanks for all the suggestions!  Your posts have certainly made me realize I need to look at math differently and not just follow the next workbook. I guess I need to get over thinking he is too little to be doing something. I guess focus less on age and more on interest and ability.

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At the ages of your kids, My son and I did a lot of discussion about the concept of adding, subtraction, multiplication, and division. It was discussing the four or five different ways that addition can be looked at and then how subtraction could be described in the same way. How did they then relate to multiplication and division. Could he explain each operation in terms of addition? Did he understand origins, reciprocals, and identities. It was about the concept of math, not the actual usage.

 

But then, I am a pure math geek. Ultimately, Ds has gone humanities track. At least for now.

 

I wish I was more of a math geek... I am more into science so those conversations are easy for me to do but math is terrible. I remember hating math and was convinced I was bad at it because of how much review my mom was convinced I needed (I was homeschooled). I avoid Saxon math for this reason!

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  • 2 weeks later...

I've been looking into the new Murderous Math Mysteries for Early Readers. They don't let you see samples though so I don't know how much of an early reader they really are. LoF was nice for apples but now that we've started Beast with color and monsters he doesn't want LoF.

 

For the first time though, we are using Beast and NEED more review. We finished chapters 1-3 in Beast 3 and he loves it but I don't know what's going to stick in the long run without a review every couple weeks. B-D books are coming in the mail but not fast enough. We did a chapter every two weeks which was way faster than expected. In the second week of every chapter we had two days that I made my own review sheets to do to stretch the chapter out.

 

I'll probably buy a Murderous Math Early Reader for Christmas to try for extra depth.

I found some murderous maths aimed at a younger audience though I am not sure if they are the ones you meant. They have a kindle version though so if you have one you can get a sample.

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Oh, and thinking outside books, the Dragonbox apps are fantastic. I played through the algebra ones myself because they were so much fun :)

Absolutely, and I was quite suprised at just how much the conceptual/intuitive nature of it lends itself to actually algebraic concepts. We do Hands-on-Equations one day per week as a 'for fun Friday Algebra day' just because of the bug dd caught from Dragonbox.

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