How to master math facts?

[squirtymomma]

My first grader is using Singapore 1A and we've gotten through the chapters on addition and subtraction up to 10. The next chapter (which is addition to 20, I think) says that the student should have mastered facts to 10 before beginning this chapter.

 

I made flashcards of all of the addition/subtraction facts to 10, and it is a THICK stack. We've been going through them a few times a week for a few weeks, and she and I both hate it. I think she's improved some, but she still has a long way to go for them to be automatic.

 

She's a bright kid with an incredible memory, so this has me a bit stumped. She certainly understands the concepts. We're doing CC this year, and she seems to hear something once and have it forever in that context.

 

She's done some of the math facts games on the Shepperd Software web page, but it seems like that's been more an exercise in how to use the mouse than in learning the math (we don't do much on the computer at this age).

 

Today I printed out the mental math pages from the back of the IG. We've worked through them already, but I thought she'd be motivated by a timed exercise. I thought I might try going through the same ones over and over until they become more automatic.

 

This is a long post for a pretty simple problem. LOL Any suggestions? :tongue_smilie:

[3monkeys]

Personally, I would move on and just keep practicing the facts. MUS said to do the same thing but I didn't. Only because my son can get the answer quickly by adding in his head and he has done fine. I felt like i shouldn't hold him back when I know he at least knows the process. I know I learned them by just doing it over and over. I was never officially taught addition facts, only multiplication. Again, only my opinion. Others using singapore may have a better idea!

[arghmatey]

Are you using the mental math drills in the back of the home instructor guide? That is similar to the drills we use in from the book 2 + 2 Is Not 5.

 

We are in CC, too. For my children, singing memory work is rather breezy compared to saying and learning it.

 

ETA: wow! I completely ignored the second half of your post. I'm sorry. How about trying Holey Cards? I loved them in elementary, and so does my little one.

Edited December 8, 2011 by arghmatey

[ErinE]

We're at the same place and i just pull out the c-rods. I ran into a similar situation with ds and multiplication facts in 2B/3A. I drilled at first which led to tears and frustration. And you should have seen my son!

 

I saw how playing games, fact raps (I like rap), and working extra problems led to mastery with minimal tears. My dd hasn't mastered her facts, but I'm shocked at how many she knows and I haven't drilled, not once. Our schedule is SM and a Miquon worksheet daily, with games 3x per week. If you're only using SM, I'd recommend supplemental activities in addition to your daily math.

[ErinE]

I should add, play the games together. I'm working with ds on speed drills for addition. We played war: ds tried to beat me in adding two numbers together. If he beat me, he got the cards; otherwise, I got them. He loves to beat me. We play Go to the Dump as a family and dd loves to get a match from me. Something about beating a parent makes them really motivated to work harder.

[Spy Car]

My first grader is using Singapore 1A and we've gotten through the chapters on addition and subtraction up to 10. The next chapter (which is addition to 20, I think) says that the student should have mastered facts to 10 before beginning this chapter.

 

I made flashcards of all of the addition/subtraction facts to 10, and it is a THICK stack. We've been going through them a few times a week for a few weeks, and she and I both hate it. I think she's improved some, but she still has a long way to go for them to be automatic.

 

She's a bright kid with an incredible memory, so this has me a bit stumped. She certainly understands the concepts. We're doing CC this year, and she seems to hear something once and have it forever in that context.

 

She's done some of the math facts games on the Shepperd Software web page, but it seems like that's been more an exercise in how to use the mouse than in learning the math (we don't do much on the computer at this age).

 

Today I printed out the mental math pages from the back of the IG. We've worked through them already, but I thought she'd be motivated by a timed exercise. I thought I might try going through the same ones over and over until they become more automatic.

 

This is a long post for a pretty simple problem. LOL Any suggestions? :tongue_smilie:

 

This is a much discussed matter where the Singapore HIG is (in my estimation, and the experience of many others) just way off track.

 

There have been many threads on this because it is a problem. I'd say ignore the HIGs on this point and keep working the strategies and move along.

 

Games are a good way to have practice. The RightStart game "Go to the Dump" is a classic for learning pairs that make 10 (directions are on YouTube).

 

Otherwise don't stress over memorizing all the math facts at this point. The HIGs (which are pretty good otherwise) are just developmentally "off" on this issue.

 

Bill

[go_go_gadget]

I second the suggestion for the RS games, and would also suggest some kind of drilling software (we use Math Rider, but Dreambox seems very popular here, if expensive), once the number bonds are rock-solid. I would move on in the curriculum in the meantime, though.

[Halcyon]

Flashmaster! And I happen to have one for sale.........:lol:

[Embassy]

I would just continue on in Singapore and review math facts a couple times a week. My boys have done well learning math facts by continually using them in more and more problems. I'm using Road Rally Race for math facts. I have them go through addition where they must master facts like +1 problems before they move on to +2. After addition they head to subtraction then multiplication and division. My oldest is almost done mastering all his subtraction facts (25 correct in about 1 minute) and he has already learned long division. He will know most of his multiplication facts when we get there from repeated practice using them. We do all the mental math exercises in the HIG too. It helps with facts as well.

[Michelle My Bell]

I have skip counting songs that my kids listen to every morning. I am planning on making more and posting them to my youtube account. Here is a link to my page. Click on all my uploads to see more videos.

 

The other thing I would highly recommend is https://www.xtramath.org/

[mskelly]

We are in the same boat. My plan for December is put all other math plans on the shelf and just play LOTS of math games. We play the RS games, card games, apps, etc. I just bought the math wraps, which he seems to like and a game called Math-a-Kazam. Wow! What a hit that one is. It has a magic wand to pick up the numbers. That makes it instantly cool to a 7 year old! :) You have to use the numbers to make equations so there's lots of math going on there.

I'm trying not to stress about him not being able to spit the answers out quickly. Trying, trying, trying...

[squirtymomma]

Thank you for all of your responses! I think you're right about not halting forward progress while we work on the facts. Thanks for affirming that for me. I'm looking into all of your suggestions. I might just have to break down and get the RS games. My 2nd will be in kinder next year, and I think those will be a good fit for her too.

[TracyR]

I don't think learning math facts at this age is developmentally inappropriate at all. Actually they need to learn them. I made that horrible mistake with my oldest daughter. I remember many years ago asking the same question and being told. Don't worry about it. Keep moving on. She'll get it.

 

Well as she got older , though she understood the steps to math , her computation got slower and slower. Making math time drag terribly. I finally last year had to go through them all just to see where she was at because math time was just crazy and she was still counting on her fingers to get the answer.

 

My middle two have learned their math facts early on and I can honestly say math is fun for them. They take a reasonable amount of time to get their math done and that's it.

 

Instead of NOT doing drill. You can make it fun for you both. I remember those flashcard days. I learned after doing this for so long that you tend to neglect the things you both don't enjoy doing. I've come up with some fun games that you can do in the meantime.

 

1. Go fish. Use either index cards, or if your a crafty person, cut out some fish from construction paper. Write the math problems on them. Then use a wooden spoon with yarn at the end and a magnet as your ' fishing rod'. Put some paper clips on the index cards/fish and have her go fishing. Have her pick up a fish and when she does have her answer the math fact. If she gets it right she gets to keep her fish. If not , throw it back into the pond (floor).

 

2. Have board games? Take those out, use the flashcards instead. If the game has a spinner have her spin it. Then pick up the flashcard and if she answers right , she gets to move that many spaces. If not. She can't move until its her next turn and she answers correctly. Of course when I learn new math facts I give them a 2nd or 3rd chance to answer. But once I know they know the answers its a one time answer, or wait your next turn.

 

3. If your weather is nice outside, and you have access to a sidewalk and have sidewalk chalk. Write the problems on the sidewalk with the chalk. If you have a dice roll it. Or you can print one out, or print, or write out some number cards for 1-5. Once you roll it she can jump onto the sidewalk blocks and when she lands she can answer the math fact.

 

4. If your weather isn't so nice like ours is right now you can make a human game board from the flashcards on the floor. Just lay them on the floor while making a ''game board" on the floor. Then do the rest that is mentioned above. My girls love being able to move and grove to a human game.

 

5. Group up your cards into cards that equal 2, 3,4,5,etc. Make those number into square cards, and stick them to the floor. Then give her the equation. For instance you can ask her 3+1 equals what? Have her run to the right answer on the floor.

 

6. If she likes food like my 5yr old does. You can do something similar with Fruit Loops, or Cheerios. Give her a mound of cereal, show her the card and have her show you the answer in cereal.

 

7. You can play Flashlight Tag. Stick the flashcards in her room, on her bed, dresser, in places she can reach with a flashlight. You want the room to be dark. Give her a flashlight and have her flash the light on the cards and answer the question.

 

That would break up the monotony of flashcards. There is also the FlashMaster. I don't own this but it reminds me of Speak and Math. Something you can actually still get. I bought one off of Ebay quite a few years ago and my daughters LOVE to play with it. I have heard good things about the 2+2 does not equal 5 math books. I haven't gotten them yet but plan to do so eventually just to see what they are like. My 5yr old loves math and does really well with it.

 

But as for memorizing it is a completely age appropriate thing to do. If you follow the Trivium , this is considered the Grammar Stage. One in which children can learn to memorize facts. Just sometimes you have to tweak what you do to keep the interest, but it CAN be done.

[squirtymomma]

Thanks for your response. I am familiar with the trivium. ;)

 

I'm not saying that I'm going to let her keep counting on her fingers forever. I'm just saying that maybe we can continue on in learning new concepts as we drill the facts. The Singapore HIG says to not move into the next unit until all of the addition/subtraction facts to 10 are mastered. I think that could be torture for a lot of kids... would have been for me. I happened to be one of those kids who had a hard time learning my math facts (ask my mother about multiplication rap!). I also got a BS in math in college and worked in microprocessor design at IBM. I did ok.

 

That Two Plus Two is Not Five book is intriguing. Have people had good success with that?

[nono]

But as for memorizing it is a completely age appropriate thing to do. If you follow the Trivium , this is considered the Grammar Stage. One in which children can learn to memorize facts. Just sometimes you have to tweak what you do to keep the interest, but it CAN be done.

 

Yes, but the grammar stage is a lot longer the length of Singapore 1A!

 

I find the HIG unnecessarily draconian in this regard of stopping dead until the facts are rote. Love your list, and think that using it, along with continued, methodical progression through Singapore, makes a lot more sense.

[Down_the_Rabbit_Hole]

I don't think learning math facts at this age is developmentally inappropriate at all. Actually they need to learn them. I made that horrible mistake with my oldest daughter. I remember many years ago asking the same question and being told. Don't worry about it. Keep moving on. She'll get it.

 

Well as she got older , though she understood the steps to math , her computation got slower and slower. Making math time drag terribly. I finally last year had to go through them all just to see where she was at because math time was just crazy and she was still counting on her fingers to get the answer.

 

My middle two have learned their math facts early on and I can honestly say math is fun for them. They take a reasonable amount of time to get their math done and that's it.

 

Instead of NOT doing drill. You can make it fun for you both. I remember those flashcard days. I learned after doing this for so long that you tend to neglect the things you both don't enjoy doing. I've come up with some fun games that you can do in the meantime.

 

1. Go fish. Use either index cards, or if your a crafty person, cut out some fish from construction paper. Write the math problems on them. Then use a wooden spoon with yarn at the end and a magnet as your ' fishing rod'. Put some paper clips on the index cards/fish and have her go fishing. Have her pick up a fish and when she does have her answer the math fact. If she gets it right she gets to keep her fish. If not , throw it back into the pond (floor).

 

2. Have board games? Take those out, use the flashcards instead. If the game has a spinner have her spin it. Then pick up the flashcard and if she answers right , she gets to move that many spaces. If not. She can't move until its her next turn and she answers correctly. Of course when I learn new math facts I give them a 2nd or 3rd chance to answer. But once I know they know the answers its a one time answer, or wait your next turn.

 

3. If your weather is nice outside, and you have access to a sidewalk and have sidewalk chalk. Write the problems on the sidewalk with the chalk. If you have a dice roll it. Or you can print one out, or print, or write out some number cards for 1-5. Once you roll it she can jump onto the sidewalk blocks and when she lands she can answer the math fact.

 

4. If your weather isn't so nice like ours is right now you can make a human game board from the flashcards on the floor. Just lay them on the floor while making a ''game board" on the floor. Then do the rest that is mentioned above. My girls love being able to move and grove to a human game.

 

5. Group up your cards into cards that equal 2, 3,4,5,etc. Make those number into square cards, and stick them to the floor. Then give her the equation. For instance you can ask her 3+1 equals what? Have her run to the right answer on the floor.

 

6. If she likes food like my 5yr old does. You can do something similar with Fruit Loops, or Cheerios. Give her a mound of cereal, show her the card and have her show you the answer in cereal.

 

7. You can play Flashlight Tag. Stick the flashcards in her room, on her bed, dresser, in places she can reach with a flashlight. You want the room to be dark. Give her a flashlight and have her flash the light on the cards and answer the question.

 

That would break up the monotony of flashcards. There is also the FlashMaster. I don't own this but it reminds me of Speak and Math. Something you can actually still get. I bought one off of Ebay quite a few years ago and my daughters LOVE to play with it. I have heard good things about the 2+2 does not equal 5 math books. I haven't gotten them yet but plan to do so eventually just to see what they are like. My 5yr old loves math and does really well with it.

 

But as for memorizing it is a completely age appropriate thing to do. If you follow the Trivium , this is considered the Grammar Stage. One in which children can learn to memorize facts. Just sometimes you have to tweak what you do to keep the interest, but it CAN be done.

:iagree:

For my dd, when it came time to learn math facts I pulled out the flash cards and we worked with them but kept advancing in the the book. Each lesson got slower and more tear filled. She felt pressure in trying to get the math fact while doing a new math step. Finally I said enough and put the book on the shelf and we worked on just math facts. I pulled out all the math fact cards and told her the goal was to move the facts from the "I don't know" pile to the "I Know" pile. We drilled, played games, made stories and drew pictures. When she had them pretty much down we began her lessons again. They went faster and her focus was not on the math facts but on the lesson. No tears and faster classes, worth the month it took to learn the facts.

[poetic license]

ditto to the suggestions for activities. It doesn't have to be flash cards. You want the memory of the number relationships to be cemented in her mind, not just a mindless memorization.

 

This book has some great ideas for developing number sense:

http://www.amazon.com/Developing-Number-Concepts-Book-Subtraction/dp/0769000592/ref=pd_sim_b_6

 

Keep in mind that as you practice facts up to 20 and beyond, the facts up to 10 will be used over and over, so you are getting practice in them even if you move beyond.

 

Also, as you focus on the 1-10 facts, just do a batch at a time for more intensive play/study. 1-5 first (or even fewer if necessary) then 6-7, 8-9, and 10 last (faster students may be able to do more at a time). Don't try to hit 1-10 if she's still mixing up at 1-5.

[zenjenn]

I don't think learning math facts at this age is developmentally inappropriate at all. Actually they need to learn them. I made that horrible mistake with my oldest daughter. I remember many years ago asking the same question and being told. Don't worry about it. Keep moving on. She'll get it.

 

We do both. We keep moving, but we practice facts.

 

Every. Single. Day.

 

I have one that is getting them way faster than the other. Ironically, the younger one has far greater mastery than her older sister.

[Spy Car]

The acquisition of skills should be on-going. One of the greatest strengths of the Singapore math approach is the re-grouping skills taught in the program. These should be practiced and practiced and practiced.

 

No one is suggesting these should not be "worked" (even if some of the practice involves activity-based and playful means.

 

But practicing mental math and re-grouping strategies is not the same thing as simply "memorizing" math-facts absent acquisition of the fundamentally important re-grouping skills a child needs to learn on this level.

 

The next levels of Singapore math will hinge on the ability of a child to be able to deconstruct numbers into part and reconstruct them into units that help facilitate mental math. These skills take practice.

 

"Memorization" alone doesn't cut it. Yes, the child should become highly fascile with basic addition and subtraction but it should come organically thought working out the parts and whole relationships in a methodical fashion, and not from "memorizing" flash-cards.

 

It is far better to have the child "explain" his or her answers. How did you solve that? What is your reasoning? What strategy did you employ? Rather than trying to train a parrot.

 

As to finger counting, it has to stop! The OP needs to find other ways for her child to "see" groups, and to learn to find sums and differences without finger-counting. Where "memorization" can be one way to leap-frog over learning the fundamental re-grouping skills, "finger-counting" is another.

 

Bill

[Milknhoney]

My son has this problem too. One thing that helped was the book A Fair Bear Share. It really helped him visualize the whole concept of regrouping. While he can't memorize his math facts, he does understand that to come up with 8+5, he can turn it into 8+2=10, +3=13. He just has to learn how to do it in his head more quickly. We were getting very frustrated because his inability to do this was impeding his progress through the lessons, which he otherwise had perfect conceptual understanding of (we're doing Miquon). I finally let him use an addition and multiplication chart so that it won't be a block in getting through the lesson. But then every day he has to do an addition drill sheet that I print off from http://www.math-drills.com/addition.shtml. Our deal is that when he can complete a 100-problem page in 10 minutes with no errors, then he doesn't have to do it any more.

[squirtymomma]

As to finger counting, it has to stop! The OP needs to find other ways for her child to "see" groups, and to learn to find sums and differences without finger-counting. Where "memorization" can be one way to leap-frog over learning the fundamental re-grouping skills, "finger-counting" is another.

 

Bill

 

Ok, tell me exactly what you mean by finger counting. Basically, she has to "count on" or "count back" (and I remind her to use these skills learned from Singapore). She just sometimes uses her fingers to keep track (only up to 4). Is that the same as finger counting?

[zenjenn]

He's probably going to tell you c-rods. And they DO work.

 

We move forward with math topics, but my girl who struggles with fact mastery does review work each and every day. She has access to c-rods.

 

In this way, even if she is doing another topic like multiplication or geometry in her main curriculum, she is still getting daily practice with addition and subtraction (using c-rods.)

 

She is improving - at her pace - but the improvement over time has been dramatic since using c-rods.

[Spy Car]

Ok, tell me exactly what you mean by finger counting. Basically, she has to "count on" or "count back" (and I remind her to use these skills learned from Singapore). She just sometimes uses her fingers to keep track (only up to 4). Is that the same as finger counting?

 

If you are talking about having 4+3=[ ] and she's starting with 4 fingers and "counting up" to 7 using her fingers, then yes, I would call that "finger-counting." I would (gently) try to discourage this practice.

 

If she needs an aid for doing her sums you might consider a set of Cuisenaire Rods. They can help bridge the developmental needs while encouraging the child to see values in discrete parts and combinations rather than being reliant on "counting" up or down.

 

This skill will be needed in an on-going fashion as you progress in Singapore math. With the C Rods she could show you all the ways one can make "7" including 4+3 and 3+4 while at the same time learning that the difference between 7 and 4 is 3 and the difference between 7 and 3 is 4.

 

These sorts of exercises are like doing "number-bonds" in a concrete form. This really is an essential skill to cultivate.

 

Bill

[Spy Car]

He's probably going to tell you c-rods.

 

Prescient! :D

 

And they DO work.

 

Yes, they do work.

 

We move forward with math topics, but my girl who struggles with fact mastery does review work each and every day. She has access to c-rods.

 

In this way, even if she is doing another topic like multiplication or geometry in her main curriculum, she is still getting daily practice with addition and subtraction (using c-rods.)

 

She is improving - at her pace - but the improvement over time has been dramatic since using c-rods.

 

This tool allows the child to figure out the mathematical combinations and re-groupings for themselves in a way that is hands-on, and friendly, and they can control. It makes the Singapore method very approachable to a young child.

 

Everywhere one looks in official Singapore Math documents one can see they extoll a "concrete>pictorial>abstract" development of math knowledge. But, unfortunately, the otherwise outstanding program tends to skip over the "concrete" stage of learning that children need and jumps right to the "pictorial."

 

The C Rods are a perfect "concrete" manipulative, as they perfectly stand in as physical "number-bonds" and build a fore-understanding of bar-diagrams (which function pretty much like C Rods in use, just with more viable values).

 

Short answer, the C Rods work.

 

Without an outstanding concrete manipulative a child may turn to the concrete manipulative they have at hand, their fingers. While there are programs that attempt to use fingers to show "groupings" (as opposed to counting) IMO it is just better to use C Rods, as finger counting is not going to develop the grouping skill necessary for success in Singapore-style math.

 

Which I know is agreeing with you (some of above aimed generally) :001_smile:

 

Bill

[ErinE]

I don't think learning math facts at this age is developmentally inappropriate at all. Actually they need to learn them.

 

I'm not advocating that children shouldn't learn their math facts. I think recalling answers quickly and accurately is important. But I don't think forward progress on math learning should stop because working with a newly learned concept, a child can't instantly recall the answer to 4+5. There are many chapters in SM1 that don't require addition and subtraction facts and the op's child can move on.

 

I learned a lot from reading this forum and added in a play time before the SM lesson. Whether it's Miquon, a game, or rolling dice to fill out a fact family worksheet, my dd is constantly working on her math facts. I'm just not drilling her to the point of frustration and tears. In her SM lesson, she gets to learn something new and different; it's not drill and computation all the time.

 

For my eldest, we're actually working on speeding up his addition/subtraction. He knows his facts well enough that working on speed is now fun. He likes trying to beat me, so I play against him. Honestly, I do stretch my time a bit so I'm not constantly winning, but it is getting to the point where he's beaten me without any handicapping. We'll do something similar in a few months for multiplication speed.

 

I don't think anyone is saying memorizing facts isn't important. There just saying it takes time and not to rush a process than can often happen naturally with the right activities.

[go_go_gadget]

I fully agree with the exhortation to discourage finger-counting in any form, and replace it with some kind of manipulative. Miquon uses C-rods; RS uses an abacus. Once the number bonds (all the addition facts for each number, or ways to add numbers together to make, say, five) are solid, you can play games or use game software to increase speed.

[Spy Car]

I'm not advocating that children shouldn't learn their math facts. I think recalling answers quickly and accurately is important. But I don't think forward progress on math learning should stop because working with a newly learned concept, a child can't instantly recall the answer to 4+5. There are many chapters in SM1 that don't require addition and subtraction facts and the op's child can move on.

 

I learned a lot from reading this forum and added in a play time before the SM lesson. Whether it's Miquon, a game, or rolling dice to fill out a fact family worksheet, my dd is constantly working on her math facts. I'm just not drilling her to the point of frustration and tears. In her SM lesson, she gets to learn something new and different; it's not drill and computation all the time.

 

For my eldest, we're actually working on speeding up his addition/subtraction. He knows his facts well enough that working on speed is now fun. He likes trying to beat me, so I play against him. Honestly, I do stretch my time a bit so I'm not constantly winning, but it is getting to the point where he's beaten me without any handicapping. We'll do something similar in a few months for multiplication speed.

 

I don't think anyone is saying memorizing facts isn't important. There just saying it takes time and not to rush a process than can often happen naturally with the right activities.

 

:iagree:

 

These are important things to learn, but one does not want to create anxiety in either the child or the parent (because kids know when parents are getting stressed;)).

 

Further, while everyone want to reach an end-goal of automaticity the means to that end are critical.

 

To use an analogy. We all want reading fluency, yes? So do we take a book write out the words on flash-cards, and have the child memorize the sight-words, and then think the child can read "fluently?" Of course not.

 

As with reading and language acquisition there are skills that need to be cultivated. Math has a "grammar" of it own, just like English. That grammar need to be learned in the grammar stage. Math is no more an assemblage of memorized "math facts" than reading is an assemblage of memorized "sight-words, and a failure to understand that in either field will lead to big problems down the road.

 

Flash-cards are a siren-song that can lead to an unjustified illusion of competence and mathematical understanding when no such understanding exists. Better to teach for understanding. It takes more patience, and it does take work and practice, but it pays off.

 

Bill

Edited December 8, 2011 by Spy Car

[QueenieReighn]

We moved on but I made sure my daughter did DAILY practice of her facts at the xtramath website. It is amazing and really got her to memorize her facts nicely. You should try it!

[squirtymomma]

Everywhere one looks in official Singapore Math documents one can see they extoll a "concrete>pictorial>abstract" development of math knowledge. But, unfortunately, the otherwise outstanding program tends to skip over the "concrete" stage of learning that children need and jumps right to the "pictorial."

 

The C Rods are a perfect "concrete" manipulative, as they perfectly stand in as physical "number-bonds" and build a fore-understanding of bar-diagrams (which function pretty much like C Rods in use, just with more viable values).

 

Short answer, the C Rods work.

 

Without an outstanding concrete manipulative a child may turn to the concrete manipulative they have at hand, their fingers. While there are programs that attempt to use fingers to show "groupings" (as opposed to counting) IMO it is just better to use C Rods, as finger counting is not going to develop the grouping skill necessary for success in Singapore-style math.

 

Which I know is agreeing with you (some of above aimed generally) :001_smile:

 

Bill

 

I can see what you mean about not spending enough time on the concrete step in SM. And I see how the C rods are an excellent tool. We did some work with them today, making "trains" and then writing the corresponding number bonds, and vice versa. I also tried to connect them with the dot cards (from the back of the HIG) for the 5+_ bonds and with an abacus (although we don't have the RS-style one). She enjoyed it, and I do think it's helpful.

 

I guess there are also other ways to "see" what is happening with basic addition and subtraction. To me, counting on (and other methods) involve basically visualizing a timeline, don't they? Isn't that another legitimate way to understand the relationships between numbers (and one that will be particularly helpful when we get to decimals and negative numbers)? We've done some Miquon (it's been about a year, though), and it uses timelines too.

 

Also, aren't fingers the perfect 5+_ manipulative? She recognizes numbers 6-10 by the number of fingers her second hand is holding up.

 

I'm definitely sympathetic with the suggestion to use a more conceptual means to master the facts. I was the bane of all of my math teachers because I always wanted to know "why" something worked the way it did. I didn't give up easily. :tongue_smilie: But I also know that there were times that concepts solidified with use over time, and rote work can be helpful to make calculations simpler in the meantime. Can't you go at it from both directions?

 

I really appreciate you sharing your ideas. They've helped me think through this better.

[Spy Car]

I can see what you mean about not spending enough time on the concrete step in SM. And I see how the C rods are an excellent tool. We did some work with them today, making "trains" and then writing the corresponding number bonds, and vice versa. I also tried to connect them with the dot cards (from the back of the HIG) for the 5+_ bonds and with an abacus (although we don't have the RS-style one). She enjoyed it, and I do think it's helpful.

 

Great!

 

I guess there are also other ways to "see" what is happening with basic addition and subtraction. To me, counting on (and other methods) involve basically visualizing a timeline, don't they? Isn't that another legitimate way to understand the relationships between numbers (and one that will be particularly helpful when we get to decimals and negative numbers)? We've done some Miquon (it's been about a year, though), and it uses timelines too.

 

Yes, a timeline can be helpful to understand concepts like negative numbers. However, "visualizing a timeline" is not a "scaleable" skill as numbers get larger. One does not want to be "counting up" when you move into 3-Digit numbers. It is fine as a tool for showing the concept, but not fine as a means of problem-solving or computing—as it is a dead-end. Not to mention it causes one to neglect the skills on needs to build at this level. Skills that are scaleable.

 

Also, aren't fingers the perfect 5+_ manipulative? She recognizes numbers 6-10 by the number of fingers her second hand is holding up.

 

It is a natural manipulative that has some upsides (theory are always there) and some downsides (they are always there). This can lead to adding and subtracting via "finger-counting" and that's not so good.

 

I'm definitely sympathetic with the suggestion to use a more conceptual means to master the facts. I was the bane of all of my math teachers because I always wanted to know "why" something worked the way it did. I didn't give up easily. :tongue_smilie: But I also know that there were times that concepts solidified with use over time, and rote work can be helpful to make calculations simpler in the meantime. Can't you go at it from both directions?

 

I think it is harder (maybe not improssible) to teach basic skills when a child already knows how to "do it." Think of trying to teach basic phonics to a child whose already sight-reading.

 

Teaching re-grouping skills (and making them walk you through it again, and again, and again) if they keep saying, "but Mom I know 8+7 is 15" because they have "memorized" the math fact.

 

What they need to master now are the re-grouping strategies and mathematical concepts. As they work these skills they will master the math facts through working them, and understanding them.

 

I really appreciate you sharing your ideas. They've helped me think through this better.

 

I hope you find it useful.

 

Best wishes!

 

Bill

[ErinE]

I feel like I should get a gold star: Bill agreed with something I said about math...

 

 

 

 

One more (last) thing, please don't give your child timed drills. I went this route early in my eldest's math instruction with very easy addition/subtraction problems. He is a bright kid who loves math. He finished every math section of his standardized test in less than half the time allotted. These timed drills brought him to tears. It kills me now just thinking about the damage I might have done had I persisted. His friends are being subjected to timed tests weekly in PS and I've had many conversations with parents that began: "My child came home telling me he thought he was good at math and now he feels stupid."

[Embassy]

 

Teaching re-grouping skills (and making them walk you through it again, and again, and again) if they keep saying, "but Mom I know 8+7 is 15" because they have "memorized" the math fact.

 

What they need to master now are the re-grouping strategies and mathematical concepts. As they work these skills they will master the math facts through working them, and understanding them.

 

 

:iagree: I'd much rather have my child mentally add 8+2+5 than have 8+7 memorized. With repeated practice and use in everyday math the 8+2+5 becomes automatic.

 

I do timed drills once or twice a week, but at a much lower level than where my kids are working so they are essentially improving speed of already understood and practiced math facts.

[squirtymomma]

:iagree: I'd much rather have my child mentally add 8+2+5 than have 8+7 memorized. With repeated practice and use in everyday math the 8+2+5 becomes automatic.

 

I do timed drills once or twice a week, but at a much lower level than where my kids are working so they are essentially improving speed of already understood and practiced math facts.

 

But, we're talking about addition/subtraction facts to 10. You can't mentally add 8+2+5 when you see 8+7 unless you know that 2+5=7. I'm totally on board with how Singapore teaches addition past 10, but they have to know the facts to 10 first to be able to use those strategies.

[squirtymomma]

Yes, a timeline can be helpful to understand concepts like negative numbers. However, "visualizing a timeline" is not a "scaleable" skill as numbers get larger. One does not want to be "counting up" when you move into 3-Digit numbers. It is fine as a tool for showing the concept, but not fine as a means of problem-solving or computing—as it is a dead-end. Not to mention it causes one to neglect the skills on needs to build at this level. Skills that are scaleable.

 

It is a natural manipulative that has some upsides (theory are always there) and some downsides (they are always there). This can lead to adding and subtracting via "finger-counting" and that's not so good.

 

I think it is harder (maybe not improssible) to teach basic skills when a child already knows how to "do it." Think of trying to teach basic phonics to a child whose already sight-reading.

 

Teaching re-grouping skills (and making them walk you through it again, and again, and again) if they keep saying, "but Mom I know 8+7 is 15" because they have "memorized" the math fact.

 

What they need to master now are the re-grouping strategies and mathematical concepts. As they work these skills they will master the math facts through working them, and understanding them.

 

Ack! I meant number line, not timeline. LOL I do see what you mean about regrouping being scaleable. And I appreciate the comparison to phonics/sight-reading. That makes a lot of sense.

 

Like I mentioned in the above post, though, we're only trying to master the facts up to 10, not beyond. Could that be comparable to having a few sight words learned, so that you can read a small book that makes sense before you learn every single sound for every single letter? LOL Really, I'm just playing devil's advocate now.

[Alice]

I've only skimmed the thread so I may be repeating what's already been said.

 

We use Singapore and my 5 yr old is at about the same stage. For him and for my oldest what has worked is to play a lot of games for drill. We do some of the Right Start Games (Go to the Dump) and some from Peggy Kaye's book (Fast Track is a big hit) and Math War and Math Dice and some we make up. I do occasional flashcards as a game I call the "fast game". He sees how many he can get right in 2 minutes. If he beats his record he gets a prize (usually something like a lollipop or some gum or sometimes he gets to play a math game on the computer for the rest of the time he'd being doing math). I will say that both my boys seem to thrive on competition so the timed drill works for us. I wouldn't do it if they were kids that found it stressful. This has worked for us to cement facts without getting too bogged down in drill.

 

At the same time I move forward in other concepts. In Singapore I've found that we can skip ahead to the very end of the book and do the chapters on geometry and time and money while we are working on the facts. I do that if I don't think they are ready to move on to the next topic conceptually. I also find that while we are parked in one spot we can review facts and also take the time to do extra problems in the IP books or read math literature books (like Greg Tang's books) or do other things to play with math.

 

My oldest is only in 3B so I'm not an expert but I have found our general pattern to be that we go through a few chapters fairly quickly and then get to a point where they need to slow down and work on mastery of facts or a concept. While we do that I add in some of the other things (games, books, word problems that are challenging for the problem solving aspect but not the computation).

[stm4him]

I have a daughter who struggles with Math facts. She is the kind of child that needs to do repetition ad nauseum to retain it long term. What has helped her the most in the past was to do pages and pages of math facts. Now before you say that is the most boring thing you ever heard of which would qualify as exasperating your children, let me say that the resources I'm going to suggest were her favorite of all the resources we have tried (and we have tried quite a few, including games). What she loved the most was Lifepac Math b/c of the Bible verse and the little characters in it (though there really weren't that many....I didn't find them distracting). We don't use that as our main program, but it was something I bought in a time where we were off of school and I was doing planning. She needed to work on her facts so I picked those up cheap and she loved them sooo much that literally she cried when I tried to sell the ones we didn't do and keeps them in her room and pulls them out sometimes to work on for fun. So if you can find some units of Lifepacs that are focused on the facts, your child might really enjoy them.

 

The other program we used and (I want to add back in for this very reason) is Rod and Staff Math. The whole reason that Memoria Press chose it is that it masters the basics, especially math facts. They asked the upper level math teachers at Highlands Latin School what they would like the students to be able to do and what they really wanted was for the kids to be grounded in their facts. It has nice drawings to add interest without being loud and distracting. It has a Bible theme to it which I like. It groups the facts together the way SM and RightStart does (whole and two parts). And it has a ton of practice to it b/c it is mastery-based.

 

Flashcards are nice and we use them with Saxon, but it is harder for me to tell how she is doing with them unless I am doing them with her. When she does them on paper it is easier to see the progress and I think it does a better job of increasing speed drill speed. And its is amazing what adding a sticker to a page will do for motivation with some kids :-)

 

Anyway, we are using Saxon and while I really, really am sold on its benefits I also think that a program like Rod and Staff can help solidify those facts to automaticity and increase confidence. It is easy to pull out on days when we aren't doing a Saxon lesson, on car trips, etc. and the answer keys are easy for the kids to use to correct their work. And they are a cheap!

 

Just my two cents...

 

stm4him

[Spy Car]

Ack! I meant number line, not timeline. LOL

 

Worst of all you got me doing it too :lol:

 

I do see what you mean about regrouping being scaleable. And I appreciate the comparison to phonics/sight-reading. That makes a lot of sense.

 

Like I mentioned in the above post, though, we're only trying to master the facts up to 10, not beyond. Could that be comparable to having a few sight words learned, so that you can read a small book that makes sense before you learn every single sound for every single letter? LOL Really, I'm just playing devil's advocate now.

 

I know you a joking a bit, but really, imagine sitting with flash-cards and having a non-reader "memorize" Sam, Cat, Sat and Mat by their shapes. And then "reading" the first Bob Book (Sam sat. Mat sat. Cat sat.) and getting all excited because "baby can read!"

 

It would be an illusion.

 

Instead one need to do the same sort of spade-work in math that one does in phonics. The good news is much of it can be gone in fun ways and you already have many of the recourses at hand to help you.

 

Bill

[Spy Car]

I feel like I should get a gold star: Bill agreed with something I said about math...

 

I was thinking two gold stars :001_smile:

 

 

One more (last) thing, please don't give your child timed drills. I went this route early in my eldest's math instruction with very easy addition/subtraction problems. He is a bright kid who loves math. He finished every math section of his standardized test in less than half the time allotted. These timed drills brought him to tears. It kills me now just thinking about the damage I might have done had I persisted. His friends are being subjected to timed tests weekly in PS and I've had many conversations with parents that began: "My child came home telling me he thought he was good at math and now he feels stupid."

 

Make it 3!

 

Bill