math enrichment for natural aptitude (but weak at mechanics?)

[fdrinca]

My son intuits mathematical concepts really well. He's in first grade, but taught himself place value, carrying and borrowing, and other concepts in kindergarten. Yesterday, he articulated the relationship between fractions and decimals, two concepts we've only talked about in passing. 

 

BUT: he's really bad at mechanics. He struggles with memorizing math facts. He has to solve 15-8 each and every time. We do a bunch of different drill type exercises, but the facts aren't sticking. 

 

We use Singapore, which we're happy with, but I don't see the value in moving forward until the gets these math facts. He'll understand the concepts, but computation will be time-consuming and frustrating for him. 

 

So, I'm looking for non-computational based enrichment activities to keep him in the process of intuiting mathematics without begin boggled down by the arithmetic. We do logic puzzles, play lots of games, but I think he'd enjoy our more formal school time more if I could change up math a little. 

 

We've looked at Life of Fred, but it wasn't a big hit. 

 

Any suggestions? 

[quark]

First grade is still young for memorizing math facts in my humble opinion. One strategy people I know have used is to have a chart of common multiplication tables (for e.g.) next to the child and to allow the child to refer to the chart and then just move on with the math. This is especially helpful with an already intuitive math learner. Repeated practice (but not necessarily repetition of the same concept) often helps cement the facts. By having the chart next to him, you can reduce frustration and keep his motivation and interest in math high. Just a thought.

 

For enrichment, I'm not sure if you've looked at the Living Math site. The booklists offer lots of parent-tested math literature titles, organized by concept. We also enjoyed the Family Math books at that age.

[fourisenough]

Or just keep an abacus handy and allow him to perform his computations on it.

 

Rather than thinking of his computational skills as being behind, I'd put a positive spin on it and just note how advanced his conceptual skills are! 😄

[fdrinca]

Or just keep an abacus handy and allow him to perform his computations on it.

 

Rather than thinking of his computational skills as being behind, I'd put a positive spin on it and just note how advanced his conceptual skills are! 😄

 

Good perspective. He's just getting so frustrated that math is "hard," and I'd like to save him from that. I hoping for an open-and-go not-arithmetic math book, but that probably doesn't exist for this age level. 

[PeterPan]

Good perspective. He's just getting so frustrated that math is "hard," and I'd like to save him from that. I hoping for an open-and-go not-arithmetic math book, but that probably doesn't exist for this age level. 

 

Many kids who are VSL are going to be this way, really great at conceptual and slower with the fact memorization.  My dd's didn't become solid till her teens, in spite of all our work.  Btw, one of the things that happened then was we switched over to TT.  

 

Anyways, have you looked at Family Math?  There are two levels of it, and that will allow conceptual exploration where you just open it and do the activity.  Not independent, but it would work.  My dd loved living math books, and there are tons of them.  We didn't do as many as there are, and with ds I plan to explore even more.  There's a website with that in the name, so just google it.  

 

Also, people are suggesting to me the Peggy Kaye math books.  I think I have one coming in through the library today.  Marilyn Burns is in my pile of stuff to go through.

 

He might also turn out to be really good at geometry and things spatial, so try to find activities in that vein.  I had a paper plate geometry book when she was young, and you could build these wild things with folded paper plates and bobby pins.  

[redsquirrel]

my boys are exactly the same way. I just let them use manipulatives or fingers or whatever (I have even allowed 'cheat sheets') until they get it memorized. We have tried timez attack, Xtra math, drill sheets, flash cards, songs, workbooks etc etc, but it just takes them more time. It got really stressful until I decided that it was what it was and I should just let them do it in their own time. My older boy absolutely had facts pretty much memorized by the end of 5th grade, but even then he made the occasional mistake or needed to skip count.

 

As they got more confident they realized that using their fingers or cuisinaire rods or base 10 or skip counting, just to 'check', took more time than was worth it.  That was when it actually started sinking in.

 

FWIW, my older boy is in a challenging algebra program. In fact, as I type this he is at the local university at a math club meeting led by math grad students. He is learning about knot theory today. So, clearly this disconnect between aptitude and memorization didn't hurt him over time.

[kbutton]

Good perspective. He's just getting so frustrated that math is "hard," and I'd like to save him from that. I hoping for an open-and-go not-arithmetic math book, but that probably doesn't exist for this age level. 

 

Have you checked out Education Unboxed videos (free online) or Miquon? Miquon has calculations, but you use C-rods, and they teach making tens, number bonds, etc. Education Unboxed has ideas for helping to cement facts that involve play, some of which is conceptual. My younger one really likes them. Miquon introduces fractions and all operations early on, not sequentially. They also introduce arrays and factoring very early on for multiplication. Education Unboxed has a lot of compatible information. In addition, the c-rods help a person visualize the numbers if they are picture people. My little guy will sometimes use the rods mentally, not physically.

 

My older one has an intuitive number sense and just "gets" shortcuts of his own, but only some of the facts stick. He uses the facts he remembers to figure out the rest (since 8 + 8 = 16, 9 + 9 = 18). (Miquon uses a lot of these techniques also.) He started out going to school, so we didn't do things at home until 3rd grade. He still has trouble with math facts (he's in 4th and using Singapore), but he slowly learns them over time by using them in context on more difficult problems rather than through fact drills (the difficult problems are more interesting to him). We use fact charts as well. The biggest thing that has helped him with multiplication is factoring and talking about multiples. He can circle multiples on a dry-erase 100 chart. He can find common factors, greatest and least common factor, prime factors, etc. It is more fun than drilling. It's especially fun to factor with c-rods. I made a set of cards that goes up to 100 (with multiples of many of the numbers), and it it's for factoring. We place a number on the table, and he lays out the cards underneath to factor down to primes. All the numbers are one color, but the primes are also outlined in a second color (and he understands what a prime number is). So, we place the number 50 onto the table, and he can choose which direction to go after that (2 x 25 or 5 x 10). If he chooses 2 x 25, he knows that 2 is already prime, so it stays there. Then, he places cards below 25 to factor that down to primes (5 x 5). Once he is down to the primes, he knows he can multiply them together (2 x 5 x 5), and if he has all the correct primes, it will multiply out to 50. He can then gather the cards and find all of the multiplication and division facts with those cards. It comes in handy when you get to equivalent fractions and finding common denominators.

 

If you can trust your son to use the calculator with some specific directions, some kids find that using the calculator over and over for single math facts helps them solidify them mentally in the way that some people remember phone numbers by the pattern you make pressing the buttons. So, if your son is working on 134 - 59, he wouldn't be allowed to punch in the whole number. He would have to know to take a ten and regroup it with the ones, and then input 14-9 into the calculator, and so on. Then he'd write the individual answers on his paper as he would if he were figuring out the problem in his head. Over time, he might remember the individual math facts through use. My son likes to do this, but he does take liberties if I'm not explicit about the rules.

 

Computation is time consuming for my older son, but drill doesn't help. To accommodate that, we skip anything he knows well and let him spend more time on the harder stuff. We also use the IP (on level) in place of the workbook (this is not as designed by Singapore, but it works for us).

 

[fdrinca]

Lots of great suggestions here - thanks! Some of the math games (Peggy Kaye) and living math books would be a great fit for us, since the younger kids might like to listen/play in.

 

A hesitation I have about charts or calculators is that he'll never really *learn* his facts. I need to reframe how this is memorizing facts, which I can do intellectually. It's just a leap from the drudgery of flash cards I remembered as a child. This is why we homeschool, right?

[PeterPan]

If you have a little time, you might see if your library has Dyslexic Advantage by the Eides.  Even though his label isn't the same, there's so much overlap and crossover in these kids.  They've been doing MRI research on brain structure, and it's pretty fascinating stuff.  You have these mini-columns in the brain and the spacing, with learning represented by making connections between those columns.  So in these quirky kids (Right-Brain, pick your label), you get this scenario where the columns are farther apart (what they're seeing with MRIs) and take a  LOT longer to make connections between.  However along the way they bump into all sorts of stuff.  End result is these kids who are really slow to memorize and get fluency on these fast recall things but AMAZING at making connections and problem-solving.  Sound familiar?

 

So then when you realize there's a physical REASON behind all this, you go hmm, how do I most facilitate making those neural connections?  DA breaks that down into categories, but it's basically realizing how your kid learns and getting enough of those exposures in the way that he learns that you finally get the click.  With my dd, it needs humor, narrative, visual, and LOTS of repetition.  Honestly, the much derided Teaching Textbooks math has been AWESOME for her.  The year we started it her computation scores jumped 20%!!!  At that point her computation finally matched her conceptual.  I wouldn't be crazy for TT on its own necessarily (caveats, there's room for discussion there), but as part of a balanced approach where you're thinking about the abilities of your student and supplementing if necessary to meet their ability conceptually, it can be a REALLY good part of the mix.  Super short lessons, humor, multiple modalities, spiral.

 

Yes, we did charts.  They were helpful for learning visual patterns, and we did them for several years before her testing.  After her testing/evals, we went to TT, ditched the charts, and went to calculators.  THAT was when her scores went up so dramatically.  So you really have to view things in context, knowing your kid, knowing WHY something is happening, kwim?  Like with my dd, her processing speed is in the dumps.  If I let her use a calculator and she does it only for the really involved stuff (starting in pre-algebra, some people decide earlier), the goal is to ease the processing burden.  So what I did was actually sit beside her and say USE THE CALCULATOR FOR THIS, no, not the calculator for that.  I actually had to sit there while she was doing the math and do that.  End result was that she was doing short computation in her head (which helped make her faster!) but the more tedious stuff that was wearing her out with the calculator.  

 

When we did division, we did one problem a day off the worksheet, only one.  So it took weeks to get through that one worksheet, but by the end she really knew it.  She never struggled with division as a result.  Sometimes you don't need to do a lot, just a little with dramatic engagement, them being all the way there, present.  On days when we did stuff like that, I'd throw her a page of geometry or measurement or something like that from later in the book, since she's super fab on geometry, being able to visualize well.

 

Don't be afraid of charts.  My dd did really nifty things with her multiplication tables because she had filled them out herself and really UNDERSTOOD them.  You can do a lot worse than build visual memory that way. 

 

There's a middle school family math book.

 

Family Math : The Middle School Years, Algebraic Reasoning and Number Sense

[jennynd]

I will not worry about add/sub facts and I will not drill it especially for a math intuitive kid. I have one of those. I had never ever drill him fact, giving time, he will remember it. What is the worst case, he has to use his fingers? God knows I still do and I have a master degree in engineering.

My younger has her multi table down b4 her add/sub facts. I will definitely keeping moving him along without worry too much on add/sub facts. You really don't want to make him feel that math is hard or boring because facts.

[deerforest]

Honestly, DD was like that. Math concepts came easily and she loved math until suddenly math facts and operational practice really stressed her out. I ended up switching completely to living math for almost a year. Near the middle/end Beast Academy came out, we switched to it and math was a joy again. She was older and BA played to her strengths.

 

She still isn't fast with any of her facts but she can work them out just fine. I refused to hold her back and she continues to thrive in math, and is working in Singapore 5 now.

[Trilliums]

My kids had some similarities to what you describe in your child.  The one curriculum they enjoyed was Visual Math from:

 

http://catalog.mathlearningcenter.org/free

 

The curriculum is expensive, imo, but the website has many free downloads which can help fuel ideas for covering math.

 

GL! 

[FO4UR]

Lots of great suggestions here - thanks! Some of the math games (Peggy Kaye) and living math books would be a great fit for us, since the younger kids might like to listen/play in.

 

A hesitation I have about charts or calculators is that he'll never really *learn* his facts. I need to reframe how this is memorizing facts, which I can do intellectually. It's just a leap from the drudgery of flash cards I remembered as a child. This is why we homeschool, right?

 

 

I've got a kid just like that.  Using C rods was the best thing b/c he quickly only needed to visualize the rods...and soon had all +- facts memorized cold from use.  I didn't wait for memory.  I went on to multi-digit and practiced tons in that range.  x facts are still not down cold perfectly.  I let him use a chart.

 

He loathes drill/practice outside of games. He loves word problems & geometry.  

 

 

It's a wild ride finding a curric, let me tell ya'   Ditch the advice about sticking with one curric k-12.  Buy a semester at a time, keeping options open.  I find that I am see-sawing between developmental leaps and the need to practice in the meantime...Singapore is easy to accelerate through...CLE had great spiral review.  I will never buy a whole yr at a time again.