How to accelerate math?

[twoforjoy]

I'm wondering how I can accelerate DS in math without missing important information.

 

Background: I was hesitant to accelerate DS in math because he seemed to have such a hard time with his addition facts. He could do all sorts of addition problems in his head, but when drilled on his facts, he'd freeze. Now that he's had the summer break, I'm starting to think he was just bored. He has no more struggle with his basic facts at all. He gets frustrated going over material he already knows, and that tends to manifest itself in his not paying attention and then saying he doesn't know what he's doing. He does know what he's doing, he just has a hard time focusing if he feels like it's too easy. When we're covering new topics or more challenging topics, he does better.

 

So now I'm thinking I should accelerate him, but I'm not sure how, because I don't want to miss something vital. We're using CLE, if that matters. (The spiral approach is working very well for him, so I don't want to switch programs, just move him ahead faster.)

 

What I'm thinking is that I'll do two lessons with him a day, rather than one. So he doesn't get overwhelmed with the amount of problems, I thought I'd do all of the problems for each new concept in both lessons, but then only assign half of the "We Remember" problems. That way he'd be doing the same amount of review work he'd get if we did one lesson a day. He'd get through second grade math in half the time, and then we'd start third grade math after our winter break.

 

Does that sound like a reasonable plan? Any other ideas?

[galaxy]

Not sure if you've used Khan yet, but it's really increased my kids' ability in Math. A perfect supplement to any spine. Good luck.

[Spy Car]

I'm wondering how I can accelerate DS in math without missing important information.

 

Background: I was hesitant to accelerate DS in math because he seemed to have such a hard time with his addition facts. He could do all sorts of addition problems in his head, but when drilled on his facts, he'd freeze. Now that he's had the summer break, I'm starting to think he was just bored. He has no more struggle with his basic facts at all. He gets frustrated going over material he already knows, and that tends to manifest itself in his not paying attention and then saying he doesn't know what he's doing. He does know what he's doing, he just has a hard time focusing if he feels like it's too easy. When we're covering new topics or more challenging topics, he does better.

 

So now I'm thinking I should accelerate him, but I'm not sure how, because I don't want to miss something vital. We're using CLE, if that matters. (The spiral approach is working very well for him, so I don't want to switch programs, just move him ahead faster.)

 

What I'm thinking is that I'll do two lessons with him a day, rather than one. So he doesn't get overwhelmed with the amount of problems, I thought I'd do all of the problems for each new concept in both lessons, but then only assign half of the "We Remember" problems. That way he'd be doing the same amount of review work he'd get if we did one lesson a day. He'd get through second grade math in half the time, and then we'd start third grade math after our winter break.

 

Does that sound like a reasonable plan? Any other ideas?

 

I think you need to find a more challenging math program. Without more intellectual challenge he is going to be (rightfully) bored and "accelerating" the pace of unchallenging work probably isn't the answer.

 

Bill

[EKS]

Even though you said you want to stick with CLE, I think it's important to choose a program that is easily to accelerate. Singapore is a good example. To go more quickly, you can do just the textbook problems or just the Intensive Practice problems and do two lessons or more per day. Another program that is easy to accelerate, but that I wouldn't recommend for a strong math student is MUS. You can do just one worksheet per lesson instead of three. That way you won't miss anything and still go much faster.

 

But I do agree with Bill. The first thing I'd try is introducing more challenge.

 

FWIW, I did accelerate Saxon by doing two lessons per day and hand picking the review problems. I see now that that was a poor choice and my son could have been served better by moving to a more acceleration friendly program.

[TracyP]

I am accelerating CLE to get to a more challenging point for dd. I skip lessons 5, 10, 16, and 17 in each LU. Skipping these and the first LU will make it possible to finish a year in 20 weeks. I tried going the way you are thinking but the We Remember sections are so varied that I always felt like we were missing review of something we needed. I do cross off the parts that seem redundant to shorten each lesson and we also work in MM.

 

FWIW, this is not a "mathy" child. I highly doubt I will use CLE with my "mathy" son. If you really want to accelerate I agree with the others who suggested looking at other programs.

[catz]

I will also say you might want to look at the curriculum you are using. My kids just work on math an age appropriate time per day and they've accelerated themselves. I also treat drill separate from conceptual math and problem solving. So, yes my kids do maybe 10 minutes of boring math a day just using recall. But then the rest is more interesting.

 

We use Singapore as our core math curriculum (attempting to migrate to AoPS Algebra for my oldest)

[Aquinas Academy]

I think you need to find a more challenging math program. Without more intellectual challenge he is going to be (rightfully) bored and "accelerating" the pace of unchallenging work probably isn't the answer.

 

Bill

:iagree:

You might want to try Singapore's Challenging Word Problems, Ed Zaccaro books, and living math books (there are lots of ideas here).

[twoforjoy]

Hmm. Now I'm tempted to try Singapore, but I'm loathe to switch his curriculum again. We did Math Mammoth last year and he absolutely hated it. He called it "Math With Tears." He likes the spiral approach, but I do think CLE is presented in a way that may not be challenging enough for him.

[ElizaG]

We're not using CLE at the moment (we changed programs for non-academic reasons, and might switch back), but when we were, we accelerated it in the way you're describing. It worked fine. In addition to doing only one set of "We Remember," I also crossed out various other questions that seemed too simple. I've found it necessary to do that with most workbook-based curricula.

 

Whether or not it's a challenging program is a matter of opinion -- cf. a bazillion "math wars" threads. ;) It is above grade level, and there are some families on here who've chosen to use it with their mathematically accelerated DC. I know skaterbabs has mentioned that her daughter goes through two levels a year.

[LittleIzumi]

If there are post-tests in CLE (not familiar with it) you can give those to see what he already knows & what you still need to teach him, & skip what he knows.

[Whereneverever]

We're accelerating with Saxon- after DROPPING Singapore. We go through a lot of problems orally, skip pages it it's repetitious. It's not something that can just be done by tossing the book at the kid, but if you are willing to work with them to gauge where they are in understanding, I think you can accelerate any math program.

[ElizaG]

Another thought -- are you using the TM? I used to read ahead a few lessons and make note of the new concepts on an index card (which doubled as a bookmark). It helped me get a sense of how long we'd need to spend on each lesson, so I didn't have to figure it all out on the fly.

[serendipitous journey]

I think you need to find a more challenging math program. Without more intellectual challenge he is going to be (rightfully) bored and "accelerating" the pace of unchallenging work probably isn't the answer.

 

Bill

 

... is that true usually? I've moved Button quickly through Math-U-See and it hasn't been a problem; when he learns something, we move forward. Though there have been sticking points for facts (I stopped the worksheets and did other drills for a while) and also for the "regrouping" problems both addition and multiplication, just b/c he's still so young and all the accounting involved can get confusing; but we solved that with 1/2 inch graph paper and a gentle increments of difficulty.

 

MathUSee is "mastery" and not spiral, so in that sense he may not be accelerated at all, just progressing as he masters stuff ...

[chepyl]

We have been accelerating SM 2A. I started in this level because DS needs all of the intro to multiplication and a little more addition/subtraction practice. We should be done around Christmas, but right now, we are set to finish in mid NOV. As he continues to move fast, I can see us finishing in October.

 

I cut some of the repetition - we might do half the problems in a lesson and do two lessons in a day. I have not skipped any lessons, just a few of the text reviews. By cutting the reps and keeping all the lessons, I know he is not missing a concept. If he struggles with the problems, we can always do the rest the next day.

[Spy Car]

... is that true usually? I've moved Button quickly through Math-U-See and it hasn't been a problem; when he learns something, we move forward. Though there have been sticking points for facts (I stopped the worksheets and did other drills for a while) and also for the "regrouping" problems both addition and multiplication, just b/c he's still so young and all the accounting involved can get confusing; but we solved that with 1/2 inch graph paper and a gentle increments of difficulty.

 

MathUSee is "mastery" and not spiral, so in that sense he may not be accelerated at all, just progressing as he masters stuff ...

 

Speaking generally:

 

I think one is best teaching for depth and that math work should be challenging. I would rather not accelerate the pace and progression through "easy" work or through programs that do not challenge a child's cognitive skills or develop their mathematical reasoning.

 

Otherwise one be be "ahead" by some superficial measure of "level" without really developing deep mathematical skills and building the critical mental faculties that challenging math study is capable of doing.

 

For me a major goal I have for the study of mathematics as a subject is to incrementally build my child's upper-level cognitive skills (in fun and age appropriate ways) along with developing his procedural competence with arithmetic.

 

But critical-thinking, logic, the ability to manipulate numbers mentally, multi-step problem-solving, and development of mathematical reasoning and a real understanding of what is going on mathematically behind the procedures is more important to be than speeding up the progression through materials that are lacking in this regard.

 

Bill

[serendipitous journey]

Speaking generally:

... But critical-thinking, logic, the ability to manipulate numbers mentally, multi-step problem-solving, and development of mathematical reasoning and a real understanding of what is going on mathematically behind the procedures is more important to be than speeding up the progression through materials that are lacking in this regard.

 

Bill

 

:iagree: thank you for expanding that ... I would have to agree. We've supplemented the logical and critical-thinking aspects throughout, and have just begun adding multi-step problems a la Singapore's challenging word problems. Those have been a bit of a handful! but Button really enjoys them, presented at his level ...

[Spy Car]

:iagree: thank you for expanding that ... I would have to agree. We've supplemented the logical and critical-thinking aspects throughout, and have just begun adding multi-step problems a la Singapore's challenging word problems. Those have been a bit of a handful! but Button really enjoys them, presented at his level ...

 

That's all I'm saying. I also think that when one one pushes for depth (even when that appears to cut into the speed of progression in the short-term) that it ultimately leads to "natural acceleration"...because the children understand, and build understandings upon understandings, rather than hitting walls. And they are able to move through challenging materials at a good clip.

 

Would you agree?

 

I see "natural acceleration" (that flows from engaging in deep work) as something very different than on-going acceleration through light work. I hope that makes sense.

 

Bill

[serendipitous journey]

That's all I'm saying. I also think that when one one pushes for depth (even when that appears to cut into the speed of progression in the short-term) that it ultimately leads to "natural acceleration"...because the children understand, and build understandings upon understandings, rather than hitting walls. And they are able to move through challenging materials at a good clip.

 

Would you agree?

 

I see "natural acceleration" (that flows from engaging in deep work) as something very different than on-going acceleration through light work. I hope that makes sense.

 

Bill

 

... it's hard not to agree with that. ;) Rather the difference between skimming the surface, and plowing through.

[MissKNG]

My big girl "naturally accelerated" herself beyond SM 2a this past summer somehow. Now I seriously regret waiting for the fall to start it. So even though we are moving through it quickly and easily, we are still using other supplements and such to keep the depth and challenge going. I use materials (in all forms - books, workbooks, CDROMS) that span different "grade" levels (ie. Penrose the Mathematical Cat, Basher books, 'Key to' materials, JumpStart games and of course the IP and CWP books, etc). I also make sure we go into depth in areas of interest.

 

OP - do you use anything "extra" other than CLE?

[ElizaG]

Not the OP, but just to share some more ideas, we supplemented CLE with EPGY twice a week and The Verbal Math Lesson about 4 times a week. Every now and then we did something completely different, such as everyday problem-solving, the first bit of LOF, or a few of the Professor B tricks. The children also have ongoing access to base 10 materials, Montessori beads, Right Start games, fun math books, etc. Not saying it's necessary to do all of this, but there are many ways to approach the concepts and we enjoy getting different perspectives.

 

(Yes, we have a lot of math curricula. The decision to use CLE wasn't based on ignorance of the alternatives. :) It just seemed to be the one that worked best for my eldest. SM didn't go well at all, as it was too visually distracting for her. I know it's supposed to be wonderfully conceptual, but the only concept she retained was "funny clown." :D)

[Ritsumei]

I see "natural acceleration" (that flows from engaging in deep work) as something very different than on-going acceleration through light work. I hope that makes sense.

 

Bill

 

 

Could you give me an example of "deep work" vs. "light work"? I see this talked about in math threads pretty regularly, but I'm really struggling to figure it out, and know how to put it into practice. My boy is also working in work that's too easy for him, and I have done some speeding through too easy work, some doubling up, and some outright skipping, trying to get to work that is actually challenging. I keep seeing people talking about "going deeper" but how do you do that with arithmetic? How do you get deep with adding?? I'd like to change my thinking to a way that would serve him better - I've been at the edges of several conversations here at the Hive that make me think you guys are onto something, but I just can't quite wrap my head around it. :banghead:

[Moonbeam Jones]

Could you give me an example of "deep work" vs. "light work"? I keep seeing people talking about "going deeper" but how do you do that with arithmetic? How do you get deep with adding??

 

:iagree::bigear:

[jennynd]

It is interesting thread.

 

I seen quite a few people here doing 2/3 grades skipping here. I will really love to know how they did/do it

 

DS went light on the 1-3. We started formal math program just last fall when he started 1st grade. When he started 1st grade, he already have whole times table down solid. knows 3 digit X 2 Digit, 3 digit divide 1 digit and 4/5 digit add/sub and basic fraction operation. and he did it quite proficiently. So, there was really no reason stay in 1-3 too much, we quickly skim through 1-3. We went through 4 grade a bit slower to fill the holes (geometry mainly) and start to work more on word problem, and 5th grade is where we started going deep. We did all textbook (SM), workbooks and CWP questions. We are in 6A now and also adding IP. I personally think skipping here there at low grade is ok since they are more introduction than anything else. The low grade (1-3) focus is understand and efficient add/sub/multi/divide) but as u go higher grade, there are a lot more to play with. Fraction/decimal and that make the word problems a lot more fun and challenging.

[ChandlerMom]

Accelerating doesn't have to just mean "speeding up"!

 

t don't know how you'd do this in a spiral program, but what we did with dd#1 was work several strands of mathematics simultaneously. For example, in one day she would do a lesson in arithmetic (conceptual and drill), one in shapes/geometry, one in measurement, maybe one in probability or graphs.

 

Math really isn't ONE subject, so we just broke it down into independent "strands" and worked in each of them. I think the continuity of subjects really helped with retention (similar to what spiral tries to do) because she wasn't doing a couple weeks of one topic and then not seeing it until the next year. It also preserved more time for absorption of newer concepts and math facts, since she wasn't progressing thru them faster, just doing other stuff and not stopping the math facts to do the other strands. This approach will end up with the child grade levels ahead, but without speeding up the individual topics, which may be good or bad depending on your point of view.

 

I agree with working in extra word problems and puzzles, if they are interested. Few children that are good at math with become mathematicians, but good solid problem solving skills and confidence in math as a tool is useful in almost any profession!

 

I also think a big issue is WHY they are accelerating. A lot of kids will plateau, which is fine. IMO a lot of acceleration thru early grades is because SOME kids are naturally intuitive with math and abstract thinkers. Math curric assumes younger kids are concrete thinkers and teaches to that. A concrete thinker sees "2+3=5" as an independent thing to "3+2=5", whereas to an abstract thinker the whole fact family is immediately obvious.

 

This makes most curric a bad fit for the abstract thinker (or at least BORING), since a lot of time is spent teaching something that doesn't need to be taught. By the time you reach upper elementary, it's assumed kids are at least somewhat capable of abstraction and the gap/acceleration may disappear at that point. But grade levels 1-5 are painfully repetitious for some kids (same concepts, just more digits), and I don't see a problem moving at your child's speed thru it until you get to more meaty, interesting problems, or use some higher level problems and simplify the numbers for the younger child to supplement.

 

ETA: @jennynd: in our case we used K12 for K-2A (thru first semester of 2nd grade). She did ALL the lessons (didn't skip), but in K she did Math 1&2, in 1st she did Math 3 and first half of Math 4. In 2nd grade they changed math programs and we changed VA, so she restarted Math 4, completing 4th grade math plus some extra work. Even so, the redundancy in math was killing her enthusiasm (she looked at Math 5 and rolled her eyes saying, "I've done this already!"), and last year (2nd grade) she went from loving math to dreading it. So, now in 3rd grade she's doing AoPS preAlgebra plus Math Olympiad problems and LOVING math again.

 

I think that's a really important consideration, whatever the content, kids should ENJOY math in elementary school. If your kid is enjoying it AND retaining it, you're probably on a good path. If either of those isn't true, something is wrong.

Edited September 26, 2011 by ChandlerMom

[WinsomeCreek]

I just have to say that the best guidance I found on accelerating math was through reading Developing Math Talent by Assouline and Lupkowski-Shoplik. My main take-away was that moving through the material by testing out (not skipping content) and actually learning what needs to be learned is an okay strategy. I think this can be applied to any curriculum. I do think SM SE with CWP is perfectly suited for this. I’ve been told that the danger of acceleration is of having a kid who doesn’t want to look back and sees math as a race. We’ll allow acceleration as long as no math snobbery develops. Now we do work ahead, but it does not define math around here.

Ritsumei, my goodness, I know how you feel. “Go deep.†I’ve heard it, but how? I think I have an idea now as far as how to present problems. I think for elementary math you want to look for problems where the student doesn’t just solve the arithmetic. So, if the kid is working on surface area she can have light problems where she’s given a shape and asked to state the surface area. A (deeper?) problem can ask for how many bricks would be needed to build a townhouse, then 2, 3 and then n townhouses. It takes the problem and applies it to a situation without saying what arithmetic is to be used. Resources for this include Zaccaro’s books, CWP, Exemplars, Math Olympiads, etc. I’m still not sure if “deep†is the right word, but that’s what I’ve been able to gather for meaning. I'm certainly interested in hearing more clarification on the term.

[Beth in SW WA]

That's all I'm saying. I also think that when one one pushes for depth (even when that appears to cut into the speed of progression in the short-term) that it ultimately leads to "natural acceleration"...because the children understand, and build understandings upon understandings, rather than hitting walls. And they are able to move through challenging materials at a good clip.

 

Would you agree?

 

I see "natural acceleration" (that flows from engaging in deep work) as something very different than on-going acceleration through light work. I hope that makes sense.

 

Bill

 

I understand this perspective. It makes sense. In our reality it looks slightly different.

 

On-going acceleration has worked well here. We do plenty of challenging word problems/IP, etc. Accelerating through 'light' work helps some kids arrive to the 'fun stuff' sooner. (Only speaking on behalf of my kids and our experience.)

 

But grade levels 1-5 are painfully repetitious for some kids (same concepts, just more digits), and I don't see a problem moving at your child's speed thru it until you get to more meaty, interesting problems,

 

:iagree::iagree:

 

Those interesting problems have finally arrived for dd8. Solving multiplication/div challenging word problems are no where near as exciting as the problems she can do with fractions, balancing simple equations and working with negative numbers.

 

I'm not in the 'deeper-is-always-better-than-wider' camp. A balance btw deep & wide is our M.O.

 

My older dc didn't spend hours in challenging word problems and they have excellent math sense. Ds is loving college alg & trig. He was tutoring a friend in algebra yesterday. He loves math. It is his favorite subject -- despite having Saxon math & CD as his foundation (nod to Bill :)). I didn't know about Singapore or 'Asian' math when he was younger. Yet he thrives.

 

Just another perspective.

 

I just have to say that the best guidance I found on accelerating math was through reading Developing Math Talent by Assouline and Lupkowski-Shoplik. My main take-away was that moving through the material by testing out (not skipping content) and actually learning what needs to be learned is an okay strategy. I think this can be applied to any curriculum. I do think SM SE with CWP is perfectly suited for this. I’ve been told that the danger of acceleration is of having a kid who doesn’t want to look back and sees math as a race. We’ll allow acceleration as long as no math snobbery develops. Now we do work ahead, but it does not define math around here.

Ritsumei, my goodness, I know how you feel. “Go deep.” I’ve heard it, but how? I think I have an idea now as far as how to present problems. I think for elementary math you want to look for problems where the student doesn’t just solve the arithmetic. So, if the kid is working on surface area she can have light problems where she’s given a shape and asked to state the surface area. A (deeper?) problem can ask for how many bricks would be needed to build a townhouse, then 2, 3 and then n townhouses. It takes the problem and applies it to a situation without saying what arithmetic is to be used. Resources for this include Zaccaro’s books, CWP, Exemplars, Math Olympiads, etc. I’m still not sure if “deep” is the right word, but that’s what I’ve been able to gather for meaning. I'm certainly interested in hearing more clarification on the term.

 

When dh does math on the weekends with my dds he loves to find an actual problem they can solve 'in the real world' to give the girls a different level of challenge. I wish I had more time in the week to do more of this. I feel my girls have a balance of plug & chug along w/ word problems to stretch their minds. Cybershala.com has been a blessing.

 

 

:bigear:

Edited September 27, 2011 by Beth in SW WA

[ebunny]

What we did with dd#1 was work several strands of mathematics simultaneously. For example, in one day she would do a lesson in arithmetic (conceptual and drill), one in shapes/geometry, one in measurement, maybe one in probability or graphs.

 

Math really isn't ONE subject, so we just broke it down into independent "strands" and worked in each of them. I think the continuity of subjects really helped with retention (similar to what spiral tries to do) because she wasn't doing a couple weeks of one topic and then not seeing it until the next year. It also preserved more time for absorption of newer concepts and math facts, since she wasn't progressing thru them faster, just doing other stuff and not stopping the math facts to do the other strands. This approach will end up with the child grade levels ahead, but without speeding up the individual topics, which may be good or bad depending on your point of view.

:iagree:

 

By trial and error, I'm taking the same route with my DD. She is simultaneously doing the abstract ( for eg: equations with variables) and the concrete ( for eg: method of multi-digit multiplication).

 

It does get tricky at times trying to balance her strength (for complex problem solving) with her weakness (speed and accuracy)

I insist that she do a few problems in basic arithmetic and supplement it with pre-algebra/Word problems.

So far, so good.

[Spy Car]

Could you give me an example of "deep work" vs. "light work"? I see this talked about in math threads pretty regularly, but I'm really struggling to figure it out, and know how to put it into practice. My boy is also working in work that's too easy for him, and I have done some speeding through too easy work, some doubling up, and some outright skipping, trying to get to work that is actually challenging. I keep seeing people talking about "going deeper" but how do you do that with arithmetic? How do you get deep with adding?? I'd like to change my thinking to a way that would serve him better - I've been at the edges of several conversations here at the Hive that make me think you guys are onto something, but I just can't quite wrap my head around it. :banghead:

 

Ok, this is like a topic for a book, rather than a post :001_smile:

 

So these will be some fragmentary thoughts.

 

One way is to alter the form of the topic.

 

Let's say the child is working on sums of double digit numbers. Instead of just doing endless 89+73=[ ] type questions one might break out a protractor and draw some triangles. Then teach the child to measure angles, and to add their sums.

 

After you give them several triangles to measure for their interior angles and have them sum those 3 values they may begin to notice a theme going on. If they don't They get more triangles to measures. Sooner or later they discover that the sum of every triangle is 180 degrees. Which is an important concept to accidentally discover while practicing sums :D

 

Then once they sufficiently get that the sum of angles in a triangle is 180, one can give them two of the three angles and they have to find the third. This works the skills and stretches them a little.

 

Then you could do the same thing with quadrilaterals.

............

 

Or once could play around with replacing....zzzzzzzzzzzz.

 

I'm falling asleep at the keyboard (you too? :tongue_smilie:)

 

Bill (who wishes he could just talk with y'all sometimes rather than type)

[jennynd]

ETA: @jennynd: in our case we used K12 for K-2A (thru first semester of 2nd grade). She did ALL the lessons (didn't skip), but in K she did Math 1&2, in 1st she did Math 3 and first half of Math 4. In 2nd grade they changed math programs and we changed VA, so she restarted Math 4, completing 4th grade math plus some extra work. Even so, the redundancy in math was killing her enthusiasm (she looked at Math 5 and rolled her eyes saying, "I've done this already!"), and last year (2nd grade) she went from loving math to dreading it. So, now in 3rd grade she's doing AoPS preAlgebra plus Math Olympiad problems and LOVING math again.

 

I think that's a really important consideration, whatever the content, kids should ENJOY math in elementary school. If your kid is enjoying it AND retaining it, you're probably on a good path. If either of those isn't true, something is wrong.

 

 

That is quite interesting approach.

When I was a Child, I enjoy very much 5/6 grade math, For me, that was when my light bulbs went on and that is also when I had a solid understanding of math and I went on loving algebra and calculus and I went on become engineer. I always have a strong feel about 5/6 grade math is quite important. (Of course, this is Asian math we are talking about, and 6th grade math in SM and Taiwan are pre algebra) And that is why I insist that my children also to go through 5/6 "heavy load". I understand there are repeat topics, but this is the time everything comes together rather than every topic is isolated.

Even DS placed in Algebra in varies curriculum (When he just finished SM 5A ) and asking for it... I feel in the long run, it is better for him to stick with the SM scope and sequence . (We do using key to algebra as warm up)

 

But again, each child is different. And Mom knows the best what is best for their child. As for mine. he is stocked with me,

Edited September 27, 2011 by jennynd

[Beth in SW WA]

And that is why I insist that my children also to go through 5/6 "heavy load". I understand there are repeat topics, but this is the time everything comes together rather than every topic is isolated.

 

 

Thanks for sharing your experience, Jenny. I have been waffling on whether to continue with 5B after finishing 5A. Hmmmm..... Have you seen DM? Would that be another option or do you feel the PM series is sufficient? I absolutely agree that grade 6 math is a turning point. I want to optimize time, energy and enthusiasm for the new world that is opening up to dd (specifically regarding math). Thanks again for your perspective.

Edited September 27, 2011 by Beth in SW WA
typo

[Rivka]

Could you give me an example of "deep work" vs. "light work"? I see this talked about in math threads pretty regularly, but I'm really struggling to figure it out, and know how to put it into practice. My boy is also working in work that's too easy for him, and I have done some speeding through too easy work, some doubling up, and some outright skipping, trying to get to work that is actually challenging. I keep seeing people talking about "going deeper" but how do you do that with arithmetic? How do you get deep with adding?? I'd like to change my thinking to a way that would serve him better - I've been at the edges of several conversations here at the Hive that make me think you guys are onto something, but I just can't quite wrap my head around it. :banghead:

 

I think MEP is a great example of a program that requires "deep work" even in the earliest grades. It's free online, so you can look through and get an idea of what kinds of problems they ask. Some examples that only involve addition and subtraction, from Year 2:

 

 

Find the numbers which make the statements true.

40 + 33 < triangle < 100 - 23.

87 - 4 < 80 + circle < 92 - 5.

 

 

On Thursday, Mum bought 53g of mushrooms, 15g more than she bought on Monday. How many did she buy on Monday? By Thursday evening, she had used only 85g of mushrooms. What weight of mushrooms did she have left?

 

 

Find a rule, then complete the table. Write down the rule in different ways.

a: 12 8 23 25

b: 21 30 7 15 12

c: 17 12 19

[Edit: No matter how many times I try to fix the spacing of this, it strips the extra spaces out. The problem is a grid with three rows labeled a, b, and c. The first two columns are filled in, showing a=12, b=21, c=17, and then a=8, b=30, c=12. After that, only two numbers are filled in for each column. The child is supposed to deduce that a + b + c = 50, complete the table by filling in all the missing values, and then write out a + b+ c = 50, a = 50 - b - c, b = 50 - a - c, etc.

Edited September 27, 2011 by Rivka

[onaclairadeluna]

I think MEP is a great example of a program that requires "deep work" even in the earliest grades. It's free online, so you can look through and get an idea of what kinds of problems they ask.

 

 

Yes!!! The other day I went over to AOPS and took a peek at their pre-algebra videos. DD insisted on watching a few with me (she would have watched them all but I think we hit a point where she would have been lost). Anyhow I said "how about you do a little math now" so she got out MEP and lo and behold there it was the distributive property right smack in the middle of her second grade curriculum. It was taught exactly the same as in the rusczyk videos too. It was a very happy math moment.

 

You can go deep with arithmetic by teaching problem solving, by teaching properties of addition and also by generalizing concepts( ie. operational systems in the very esoteric "Elements of Mathematics" curriculum.) Or you can do wacky things like teach mini computers and line diagrams ala CSMP.

[Spy Car]

I think MEP is a great example of a program that requires "deep work" even in the earliest grades. It's free online, so you can look through and get an idea of what kinds of problems they ask. Some examples that only involve addition and subtraction, from Year 2:

 

 

Find the numbers which make the statements true.

40 + 33 < triangle < 100 - 23.

87 - 4 < 80 + circle < 92 - 5.

 

 

On Thursday, Mum bought 53g of mushrooms, 15g more than she bought on Monday. How many did she buy on Monday? By Thursday evening, she had used only 85g of mushrooms. What weight of mushrooms did she have left?

 

 

Find a rule, then complete the table. Write down the rule in different ways.

a: 12 8 23 25

b: 21 30 7 15 12

c: 17 12 19

[Edit: No matter how many times I try to fix the spacing of this, it strips the extra spaces out. The problem is a grid with three rows labeled a, b, and c. The first two columns are filled in, showing a=12, b=21, c=17, and then a=8, b=30, c=12. After that, only two numbers are filled in for each column. The child is supposed to deduce that a + b + c = 50, complete the table by filling in all the missing values, and then write out a + b+ c = 50, a = 50 - b - c, b = 50 - a - c, etc.

 

Good examples, and I agree 100% about MEP having a good deal of "deep work" at the outset.

 

I'm sorry I passed out last night (before I even got started :tongue_smilie:).

 

But some of the ways to go deep include:

 

Changing the form of problems

 

Maybe it is small changes in early levels. Things as simple as giving 2+[ ]=5 instead of only 2+3=[ ].

 

Later if might be replacing number values with shapes, and giving increasingly difficult if/then balancing equations a child that a child has to use to deduce what the values of the individual shapes are.

 

One might learn to do linear equations. They can go from very easy 2n=10, so n=[ ], to word problems like: Eric's brother is twice as old as Eric, his sister is 3 years older than Eric. His mother is seven times as old as Eric and his father is five years older than Eric's mother. If their total ages (including Eric) is 98, how old is Eric.

 

This last one "seems" hard, but requires nothing more than very basic arithmetic and a little algebraic logic to solve. Primary Grade Challenge Math has a lovely graded section on this topic.

 

One should teach explicit knowledge of the Mathematical Laws

 

It can be as simple as pointing out to the 4 year old that when they discover that a 3 Rod and a 2 Rod are the same length as a 2 rod and a 3 Rod, that they have "discovered" The Commutative Law!!!! Big hurays!!!!!

 

Then you see if other combinations work the same way? They do. It is proved. The child "owns" the Commutitive Law of Addition (and multiplication will follow).

 

When one introduces multiplication teach how the Distributive Law works. First with concrete objects, then with pictorial "arrays", and finally with abstract formulas like a(b+c)=ab+ac.

 

It is fun when a young child learning multiplication gets a problem like 7x3=[ ] and they don't know the answer, and instead of using serial addition, or skip counting, instead says: I know that 7x3 is the same as 5x3 plus 2x3, because that is the Distributive Law, and I know 5x3 is 15 and 2x3 is 6, so 7x3 has to be 21. That is cool, and that is deep.

 

Bill

[Rivka]

Yes!!! The other day I went over to AOPS and took a peek at their pre-algebra videos. DD insisted on watching a few with me (she would have watched them all but I think we hit a point where she would have been lost). Anyhow I said "how about you do a little math now" so she got out MEP and lo and behold there it was the distributive property right smack in the middle of her second grade curriculum. It was taught exactly the same as in the rusczyk videos too. It was a very happy math moment.

 

Last night at dinner, Alex started asking, in a worried sort of way, about how they used letters in advanced math. I showed her on the white board how it was exactly the same thing that she does now when she solves for triangle or circle.

 

"...But how do you know which letter to use?"

 

She was so relieved to hear that it can just be any number - it cleared up the whole issue for her, and she agreed that it's no different from what she already does.

 

As I kept thinking about it, I realized how much we've already been laying the groundwork for algebra. Multistep problems; solving for a symbol that represents a number; working systems of equations in which the same symbol means the same number throughout; solving problems with a range of potential solutions. The math's going to get more complicated as we go on, obviously (she's only in 2b), but the concepts are there from the start.

[Spy Car]

As I kept thinking about it, I realized how much we've already been laying the groundwork for algebra. Multistep problems; solving for a symbol that represents a number; working systems of equations in which the same symbol means the same number throughout; solving problems with a range of potential solutions. The math's going to get more complicated as we go on, obviously (she's only in 2b), but the concepts are there from the start.

 

Yep. We are taking little beings who can only think in concrete terms and slowly helping build minds that are capable of (and enjoy) abstract thought.

 

It is a process. It takes incremental stretching of the mind.

 

Bill

[Crimson Wife]

Thanks for sharing your experience, Jenny. I have been waffling on whether to continue with 5B after finishing 5A. Hmmmm..... Have you seen DM? Would that be another option or do you feel the PM series is sufficient? I absolutely agree that grade 6 math is a turning point. I want to optimize time, energy and enthusiasm for the new world that is opening up to dd (specifically regarding math). Thanks again for your perspective.

 

If you don't have me on "ignore" after the other thread ;), I would venture the opinion that jumping to DM 1 after finishing 5A appears do-able by a bright child. Many of the topics in 5B-6B SE were originally done in 7th grade Singapore Math (NEM 1 or DM 1) but got switched down in order to meet the CA state standards.

 

The one topic that appears in PM SE but not DM 1 is some of the probability stuff. DM 1B has a bit of it, but not everything that's in 6B SE. I have a copy of 6B that I got from our virtual charter's lending library, and I am planning on having DD complete that particular chapter. She has to take the state STAR test and I don't want any gaps due to her acceleration.

[Ritsumei]

Good examples, and I agree 100% about MEP having a good deal of "deep work" at the outset.

 

OK, I'll have a look. Though I need a *3rd* math program about like a need a hole in my head!! I like that it's online though. ;)

 

I'm sorry I passed out last night (before I even got started :tongue_smilie:).

I understand - some days are like that, and a big luncheon where we could all just sit around and pick eachother's brains.

 

But some of the ways to go deep include:

 

Changing the form of problems

 

Maybe it is small changes in early levels. Things as simple as giving 2+[ ]=5 instead of only 2+3=[ ].

 

Encouraging; our "main program," Math Expressions, does this. They introduce it in K, and it's one of the reasons that I really like the program.

 

Later if might be replacing number values with shapes, and giving increasingly difficult if/then balancing equations a child that a child has to use to deduce what the values of the individual shapes are.

 

So, are you talking about something like this:

If 2+3=[] then []+4=?

 

 

One might learn to do linear equations. They can go from very easy 2n=10, so n=[ ], to word problems like: Eric's brother is twice as old as Eric, his sister is 3 years older than Eric. His mother is seven times as old as Eric and his father is five years older than Eric's mother. If their total ages (including Eric) is 98, how old is Eric.

 

This last one "seems" hard, but requires nothing more than very basic arithmetic and a little algebraic logic to solve. Primary Grade Challenge Math has a lovely graded section on this topic.

 

Yer killing me!! I just hate this sort of problem! It still seems hard to me. :tongue_smilie::lol: Is there a cure for this sort of hardness? Something that I can understand to make this kind of problem less of a pain in my butt??

 

Seriously, it's hard not to squelch his love of math with my own lack of enthusiasm when I have this sort of reaction to a relatively large number of types of problems. I need some remediation, some experience with fun in my math. I've come to the conclusion that I was taught with some definite drill-n-kill/plug-n-chug kinds of methods. And I can clearly remember the 5-6th grade feeling of, "Really?? Addition again? We did that. Last year. And the year before. And the one before that. Can't we do something interesting?" I so badly want to avoid that for my son. Math is his favorite right now. We've got a good thing going with it: lots of hands-on, touchable stuff going on. He had is first multiplication lightbulb this morning with the c-rods we recently bought. That so cool!

 

One should teach explicit knowledge of the Mathematical Laws

 

It can be as simple as pointing out to the 4 year old that when they discover that a 3 Rod and a 2 Rod are the same length as a 2 rod and a 3 Rod, that they have "discovered" The Commutative Law!!!! Big hurays!!!!!

 

Then you see if other combinations work the same way? They do. It is proved. The child "owns" the Commutitive Law of Addition (and multiplication will follow).

 

We had this just this morning - the only reason I knew the name of the Law is because of conversations here at the Hive. But I was glad that I did. We were working with the "partners" of 7, doing one of those exercises-

 

7

/\

3 4

 

And I asked him what happens if you switch the numbers, is it still the same? Yeah. So, does it work for other numbers? Like, 5+2? He rolled his eyes at me. Yeah, of course it does. That was, in fact, about 5 minutes before that multiplication lightbulb. Funny that you should use a 4yo in your example: his 5th b-day was last week. (Tell me, why does multiplication follow?)

When one introduces multiplication teach how the Distributive Law works. First with concrete objects, then with pictorial "arrays", and finally with abstract formulas like a(b+c)=ab+ac.

 

Is there a list of these Laws somewhere? I don't know them, don't know what they mean, and may have to remediate on how they work as well, for some of them.

 

It is fun when a young child learning multiplication gets a problem like 7x3=[ ] and they don't know the answer, and instead of using serial addition, or skip counting, instead says: I know that 7x3 is the same as 5x3 plus 2x3, because that is the Distributive Law, and I know 5x3 is 15 and 2x3 is 6, so 7x3 has to be 21. That is cool, and that is deep.

 

That is deep. I had to think pretty hard about why it works. One of these days I hope that is a lot less true. C-rods are cool because they make some of this stuff so visually, touchably apparent to me. Math makes so much more visceral sense when I see them. Sure, I knew that you can switch the numbers in addition & it still works, but somehow seeing it in c-rods is so satisfying.

 

 

 

Bill

I never thought I was very mathy, but nobody ever showed me this cool stuff in the course of my education. I wonder how much difference it would have made for me.

[jennynd]

Thanks for sharing your experience, Jenny. I have been waffling on whether to continue with 5B after finishing 5A. Hmmmm..... Have you seen DM? Would that be another option or do you feel the PM series is sufficient? I absolutely agree that grade 6 math is a turning point. I want to optimize time, energy and enthusiasm for the new world that is opening up to dd (specifically regarding math). Thanks again for your perspective.

 

I asked same question a while ago, I had mind made at the time to finish 5B and go with NEM. A lot poeple think it is ok to go from 5B to algebra.

 

To be honest with you. I don't know. Maybe you can ask people on the high school board or college board to see if anybody have done so and what is the outcome.

 

I see you are working 5 and TT-pre-algebra.. why don't you keep working on 5 to 6 just IP or CWP and go on algebra? That way u have all front covered?

DS will work through 6B like I said before but I do supplement him with Key to algebra (light). when he done with 6B, my guess is that we will finish Key to algebra at the same time and start NEM with supplement AoPS

Edited September 28, 2011 by jennynd

[jennynd]

If you don't have me on "ignore" after the other thread ;), I would venture the opinion that jumping to DM 1 after finishing 5A appears do-able by a bright child. Many of the topics in 5B-6B SE were originally done in 7th grade Singapore Math (NEM 1 or DM 1) but got switched down in order to meet the CA state standards.

 

The one topic that appears in PM SE but not DM 1 is some of the probability stuff. DM 1B has a bit of it, but not everything that's in 6B SE. I have a copy of 6B that I got from our virtual charter's lending library, and I am planning on having DD complete that particular chapter. She has to take the state STAR test and I don't want any gaps due to her acceleration.

 

 

probability is one topic I will feel VERY comfortable to skip, I will much rather teaching it when the kid is at high school level.

[Spy Car]

One might learn to do linear equations. They can go from very easy 2n=10' date=' so n=[ '], to word problems like: Eric's brother is twice as old as Eric, his sister is 3 years older than Eric. His mother is seven times as old as Eric and his father is five years older than Eric's mother. If their total ages (including Eric) is 98, how old is Eric?

 

This last one "seems" hard, but requires nothing more than very basic arithmetic and a little algebraic logic to solve. Primary Grade Challenge Math has a lovely graded section on this topic.

 

OYer killing me!! I just hate this sort of problem! It still seems hard to me. Is there a cure for this sort of hardness? Something that I can understand to make this kind of problem less of a pain in my butt??

 

 

This looks hard, but it's not. I will show you how easy this really is.

 

One thing to remember: an equation (=) means the value of both sides are balanced. If you do something to one side of the equation you need to do the same thing to the other side to maintain that balance. We will use this later.

 

So we are looking to solve for Eric's age, right?

 

We will use the language of algebra and call Eric's age "n". Then we can work out everyone else's age relative to Eric's, or "n".

 

Eric is n.

Brother is 2n.

Sister is n+3

Mother is 7n

Father is 7n+5

 

Total ages equal 98

 

We could write it:

 

n+2n+n+3+7n+7n+5=98

 

Which we can simply to:

 

18n+8=98.

 

But we want only "n's" on the left side of the equation, what do we do?

 

Remember that if we do the same things to both sides of the equation it remainds "balanced?"

 

So we will subtract "8" from both sides of the equation. This leaves:

 

18n=90

 

And if 18n=90, then "n"=5.

 

Eric is 5

The brother is 10

The sister is 8

The mother is 35

The father is 40.

 

Easy huh?

 

Ed Zaccaro's Primary Grade Challenge Math has sections on just these sorts of problems and he breaks it down even more than I just did. making it really easy to do what look like "hard" problems (but really aren't).

 

Bill

Edited September 28, 2011 by Spy Car

[poetic license]

Hmm... I think *I* need to be the one doing Zaccaro's challenge math and Khan academy before I have to get to this stuff... :001_huh:

[Beth in SW WA]

If you don't have me on "ignore" after the other thread ;),

 

Never! I value your opinions tooooo much to ever do that! :001_smile:

 

I would venture the opinion that jumping to DM 1 after finishing 5A appears do-able by a bright child. Many of the topics in 5B-6B SE were originally done in 7th grade Singapore Math (NEM 1 or DM 1) but got switched down in order to meet the CA state standards.

 

The one topic that appears in PM SE but not DM 1 is some of the probability stuff. DM 1B has a bit of it, but not everything that's in 6B SE. I have a copy of 6B that I got from our virtual charter's lending library, and I am planning on having DD complete that particular chapter. She has to take the state STAR test and I don't want any gaps due to her acceleration.

 

Thanks for the feedback! Lots to chew on! We have a while. We won't be 'officially' starting pre-alg for months. We're just 'dabbling' a bit for now.

 

I asked same question a while ago, I had mind made at the time to finish 5B and go with NEM. A lot poeple think it is ok to go from 5B to algebra.

 

To be honest with you. I don't know. Maybe you can ask people on the high school board or college board to see if anybody have done so and what is the outcome.

 

I see you are working 5 and TT-pre-algebra.. why don't you keep working on 5 to 6 just IP or CWP and go on algebra? That way u have all front covered?

DS will work through 6B like I said before but I do supplement him with Key to algebra (light). when he done with 6B, my guess is that we will finish Key to algebra at the same time and start NEM with supplement AoPS

 

Thank you!

Edited September 29, 2011 by Beth in SW WA

[catz]

I asked same question a while ago, I had mind made at the time to finish 5B and go with NEM. A lot poeple think it is ok to go from 5B to algebra.

 

 

I went from 6B to NEM with my oldest (and am now doing AoPS Algebra not pre-alg with him). We did the algebra portions of NEM last year over the entire year.

 

I am really glad I did not skip 6A and 6B with him. This really was a bunch of deep problem solving that required extensive writing and showing a work flow. However if you do additional problem solving like the harder Singapore books through the series, maybe that would be redundant (we did them on and off and took some side trips. Tried Fred - he hated it. Did some Zaccarro too). NEM is a challenging curriculum and it was still frustrating for a while after moving to this curriculum. Even if 6A/6B only bought me a some months of maturity, I think it was worthwhile. To me NEM takes some conceptual leaps that AoPS is laying out more clearly. We are moving through AoPS slowly, but we're finding it easier and more clear if that makes any sense. If you have a super accurate child that can very clearly lay on problems on a page through multiple steps, this may not apply to you! :D

 

I think with my next child I will go through 6B and then do AoPS pre-alg or DM. The writing and accuracy in the 10 year old still isn't always there, but we've come a long way. Conceptually, there's no problems at all. FWIW, I don't think NEM was written as well as the elementary series. Maybe if there was a teacher's guide, some accompanying videos (we did often use Khan academy) or something. I do have a math degree and spent way too much time investigating this topic.

[Poke Salad Annie]

This looks hard, but it's not. I will show you how easy this really is.

 

One thing to remember: an equation (=) means the value of both sides are balanced. If you do something to one side of the equation you need to do the same thing to the other side to maintain that balance. We will use this later.

 

So we are looking to solve for Eric's age, right?

 

We will use the language of algebra and call Eric's age "n". Then we can work out everyone else's age relative to Eric's, or "n".

 

Eric is n.

Brother is 2n.

Sister is n+3

Mother is 7n

Father is 7n+5

 

Total ages equal 98

 

We could write it:

 

n+2n+n+3+7n+7n+5=98

 

Which we can simply to:

 

18n+8=98.

 

But we want only "n's" on the left side of the equation, what do we do?

 

Remember that if we do the same things to both sides of the equation it remainds "balanced?"

 

Bill

 

:iagree:

 

This is exactly the way I teach equations. We use MEP and a text from 1970 which expands upon the topics taught in the MEP lessons.

 

I have hammered in from the start the need to *balance* equations. I even stand up and illustrate the point with my arms outstretched to both sides. If the equation is unbalanced, I tip my arm on one side over, and the opposite side goes up. (I also make a silly noise like an alarm when this happens. That gets a few laughs, but it really illustrates the point. :D) We work these problems on the large white board, and I make a big deal out of the fact that whatever is done to one side of the equation, must be done to the other to maintain the *balance*.

 

What I love about the 1970 text is that it continually brings into play the mathematical laws. The child is asked frequently in a day's lesson which law is being represented. I very much like this, and it is expanding upon the lessons taught in MEP. The two are working together quite well so far.

[Spy Car]

:iagree:

 

This is exactly the way I teach equations. We use MEP and a text from 1970 which expands upon the topics taught in the MEP lessons.

 

I have hammered in from the start the need to *balance* equations. I even stand up and illustrate the point with my arms outstretched to both sides. If the equation is unbalanced, I tip my arm on one side over, and the opposite side goes up. (I also make a silly noise like an alarm when this happens. That gets a few laughs, but it really illustrates the point. :D) We work these problems on the large white board, and I make a big deal out of the fact that whatever is done to one side of the equation, must be done to the other to maintain the *balance*.

 

What I love about the 1970 text is that it continually brings into play the mathematical laws. The child is asked frequently in a day's lesson which law is being represented. I very much like this, and it is expanding upon the lessons taught in MEP. The two are working together quite well so far.

 

Which 70s text, pray tell?

 

Bill

[poetic license]

Which 70s text, pray tell?

 

Bill

 

:lurk5:

 

You know that you can't just throw a hint like that and not spill the title! :lol:

[Beth in SW WA]

 

I think with my next child I will go through 6B and then do AoPS pre-alg or DM.

 

:bigear:

[TracyP]

Which 70s text, pray tell?

 

Bill

 

Check out this thread. I'm guessing this is the same text.

[twoforjoy]

Wow. Thanks for all of the input. This has been really interesting, especially since, while I'm not bad at math, I'm not a "mathy" person at all.

 

I think we're going to continue to work through CLE at a faster pace and with fewer problems, because I feel like it's covering all the bases in terms of the basics. But, I'm going to be more consistent about supplementing with Math Mammoth and with Miquon than I have been, and may also start using MEP to supplement as well.