how can I figure out where he "is" in math?

[Lucy the Valiant]

If anyone has a minute to help me with this, I would be truly grateful.

 

Short data: 8yo ds tests out of the standardized tests & is bored in math (I consider him bright but not gifted); he's currently "on-track" with Singapore (finished 2B). He knew this stuff at the end of last year, though; I feel as if we've been treading water in math, and I'm afraid that I am not directing his skills and abilities very well. When I tried to skip a book with him, he FREAKED OUT - in his world, things MUST be done sequentially, so I put him back in 1B and we just kept going.

 

He's bored, but I am uncertain of myself and not sure what to do - I think the main problem is that I don't know what he's capable of learning.

 

We bought Beast Academy 3A - he likes it, but the math is not challenging; he likes Penrose (the math *IS* challenging, but the book isn't really structured for practice & solidification of techniques); he likes Khan Academy (some of it is challenging, but again - not really an organized plan). He's bright, but quite lazy; in all honesty, the PRIMARY goal from my perspective is that he learn discipline in his studies, and the SECONDARY goal is that he enjoy them. I don't think those are mutually exclusive, but - I'm a bit lost in mathematics.

 

Should I accelerate him in Singapore and just force the non-sequential issue? Switch to a different program altogether? Could he start some pre-algebra stuff? If we do that, how do I make sure I"m not missing all those basics that he'd essentially be skipping?

 

I feel really lost here, and I feel like there's something super awesome for him that I am just too clueless to locate / identify.

[Targhee]

There's more than one way to accelerate - it doesn't just have to be skipping.  So you can accelerate his studies without skipping levels. Also, differentiation for high ability can be more than accelerating - you can go deep and wide, and delve into things that aren't typical in elementary arithmetic.  So, with that in mind some ideas might be:

 

- Continue sequentially with Singapore (which version are you using? I recommend US Edition or Standards Edition - MiF and the new common core stuff not so much), but eliminate the workbook and only do the textbook (making sure you are working on the Singapore method with him - there's a difference that using PM books and actually teaching Singapore methods.  You can easily accelerate this way.

 

- Continue sequentially with Singapore, but instead of the workbook use the Challenging Word Problems book or the Intensive Practice book 

 

- Switch to a different program (like Math Mammoth) and test him into the right book. Perhaps switching texts will fix the need to go through each book sequentially.

 

- Continue sequentially with any book of your choice, but add in enrichment books (like Challenge Math, Penrose books, logic puzzles, recreational mathematics, etc), get him into a Math Circle, and build a math culture (lots of games, looking for math in the world around you, watch great math you tubes, etc)

 

One thing about your primary goal being discipline and secondary goal being enjoyment - it is not impossible, but it is not common, that people who are forced into doing a task against their inclinations (which becomes "work") end up enjoying the task (which you might call "play").  Most people discipline themselves to study and complete things *because* they enjoy them (and not the other way around).  We all need to learn self-discipline, but it will continue to come with age (and just because a person has high ability does not equal high self-discipline or drive in that ability).  Both of those goals (being disciplined in his studies and enjoying mathematics) are great goals! I would propose, though, that the second engenders the first.  Also, going sequentially is in itself a form of discipline to his studies - good job to your DS! 

 

Oh, and pre-algebra is just the end of arithmetic.  Effectually it would be skipping over PM books 3-5 and starting in 6 (or another preA program).  If you think he's ready to skip three years of arithmetic then go for it (maybe get a book that doesn't have a level number on it though ;-))  If he currently is bored with arithmetic then start looking at high math concepts that are formatted to present to younger (concrete) thinkers.  Check our Moebiusnoodles and Letsplaymath and watch lots of great math videos online.  Play games (I don't mean games that help you learn math facts, but games that help you reason and problem solve).  

 

One last thought, because I am droning on.  Often children who have intuitively come to a subject/have ability and ease in it do not know how to handle frustrations and challenges when they come along.  This is a whole other topic in and of itself, but developing a frustration tolerance, having the perspective of "mistakes are an opportunity to learn," and relaxing as they interact with the material is just as important to their success as accelerating.  This comes to kids usually by working side-by-side in a non-critical way (you can even intentionally make mistakes so help them see it's normal), and having small challenges/frustrations first so that they can quickly get to the success/reinforcement before they are met with large challenges.  Best wishes!!

[Five More Minutes]

Listening in and bookmarking this thread. I was just wondering myself how to switch things up for a bright child who refuses to skip anything, so thanks for starting this! And Shannon, thanks for the advice you've shared here, which I'm copying into my "keep for frequent reference" notes.

[EKS]

I'd accelerate him in Singapore, but don't skip any of the books. 

 

Here is what I did with my son (right after 2B, in fact).  If he thought he could do the hardest problem in the lesson while explaining what he was doing and why without instruction (and without taking forever), he did it, and we moved on to the next lesson.  If he did need instruction, then I would have him do the textbook problems only.  I would frequently have him do the problems orally so that we could move to the next lesson the same day.  The reason I had him do the textbook problems rather than the workbook problems is that the textbook tended to have harder problems.  For the reviews (we used the Standards edition), I had him do a few problems each day alongside the regular lesson.  Occasionally he would have trouble with something and we would take several days on it (long division was one of those things).

 

He got through 3A/B and 4A/B in one year doing this and the next year we did 5A/B and 6A before moving to prealgebra.  He did Algebra I at a b&m school at age 10 (5th grade age).

[Lucy the Valiant]

Thank you so much, both Shannon and Kai, for those thoughts. He does (currently) do all the workbook + textbook + CWP in Singapore, and also eavesdrops on the 5A/5B lessons going on in the same house, so - yeah, I hadn't thought about just dropping the workbook as redundant.

 

I love this idea.

 

Much to chew on - THANK YOU again for taking the time to write it out. From me AND my son. :)

[dauphin]

Following thanks for a timely question OP and the great responses!!!

[Lucy the Valiant]

So . . . while I am chewing / digesting / thinking through these ideas, I have a few more questions:

 

- Is Singapore 6A/6B a pre-algebra class? (I have a different child doing that level next year, but it's my first time through - I'm thinking maybe if my DS is "in the same room" as the class, that might open some windows for him. (But, to be honest, I have not yet figured out "what comes after 6A/6B" for older child, though).

 

- That work-play love-tolerate balance . . . as it relates to a "mathy" kid . . . any tips? He sometimes doesn't want to do math (I think because it's boring to him), but he acknowledges that he LOVES math. His hand definitely slows him down (he can think / sum / figure much more quickly than he can write; I've been trying to balance this by doing SOME written numbers, and some orally). After a page of multiplication or addition problems, he tallies up the "odds" vs. the "evens" to see who won. LOVES problems that give an inverse to something else on the same page. But at some point, he has to learn the stuff that he needs for the higher math, right? (i.e., the times tables, so he can factor) Should I teach him factoring and just wait for him to realize that he needs the times tables? I'm aiming for that balance between giving him the tools he needs (and doesn't realize he needs) and just letting him fly solo.

 

- How necessary is it that he can explain to me what he is doing? For instance, right out of the gate, in 1A, he adds & subtracts left-to-right, not right-to-left. He does the regrouping Singapore-style, with the bonds / sets of 10, but he just carries the negatives in his head and adjusts as he goes, and 99% of the time comes up with the right answer. He understands the right-to-left way (I forced him), but prefers left-to-right; however, I don't think that even now he could adequately explain with words what his brain is doing. Is that ability to explain something I should push?

 

- And, Shannon, your point about frustration - how do I guide a child to increase his frustrate-a-bility? For instance, he "gets" base 2 and base 8 systems, so he loves them; he got initially quite frustrated with square roots, so has written them off. I don't care if he doesn't get square roots, but how do I persuade him to try again something that has initially been frustrating? (Sometimes it works in other content-areas (not skill-based areas) to just leave lying around the material I want him to read & he eventually reads it. Does that work with math, too?)

 

I feel like a young rookie sitting at the feet of wisdom here, and I appreciate your thoughts / ideas on this. Part of me thinks I'm over-thinking this, but the other part of me is SURE there's a golden thread for him that I just have to find. :) So, again, my thanks.

[Targhee]

So . . . while I am chewing / digesting / thinking through these ideas, I have a few more questions:

 

- Is Singapore 6A/6B a pre-algebra class? (I have a different child doing that level next year, but it's my first time through - I'm thinking maybe if my DS is "in the same room" as the class, that might open some windows for him. (But, to be honest, I have not yet figured out "what comes after 6A/6B" for older child, though).

 

- That work-play love-tolerate balance . . . as it relates to a "mathy" kid . . . any tips? He sometimes doesn't want to do math (I think because it's boring to him), but he acknowledges that he LOVES math. His hand definitely slows him down (he can think / sum / figure much more quickly than he can write; I've been trying to balance this by doing SOME written numbers, and some orally). After a page of multiplication or addition problems, he tallies up the "odds" vs. the "evens" to see who won. LOVES problems that give an inverse to something else on the same page. But at some point, he has to learn the stuff that he needs for the higher math, right? (i.e., the times tables, so he can factor) Should I teach him factoring and just wait for him to realize that he needs the times tables? I'm aiming for that balance between giving him the tools he needs (and doesn't realize he needs) and just letting him fly solo.

 

- How necessary is it that he can explain to me what he is doing? For instance, right out of the gate, in 1A, he adds & subtracts left-to-right, not right-to-left. He does the regrouping Singapore-style, with the bonds / sets of 10, but he just carries the negatives in his head and adjusts as he goes, and 99% of the time comes up with the right answer. He understands the right-to-left way (I forced him), but prefers left-to-right; however, I don't think that even now he could adequately explain with words what his brain is doing. Is that ability to explain something I should push?

 

- And, Shannon, your point about frustration - how do I guide a child to increase his frustrate-a-bility? For instance, he "gets" base 2 and base 8 systems, so he loves them; he got initially quite frustrated with square roots, so has written them off. I don't care if he doesn't get square roots, but how do I persuade him to try again something that has initially been frustrating? (Sometimes it works in other content-areas (not skill-based areas) to just leave lying around the material I want him to read & he eventually reads it. Does that work with math, too?)

 

I feel like a young rookie sitting at the feet of wisdom here, and I appreciate your thoughts / ideas on this. Part of me thinks I'm over-thinking this, but the other part of me is SURE there's a golden thread for him that I just have to find. :) So, again, my thanks.

There is some discussion on whether or not Singapore 6 is a "pre algebra" class.  There is some talk on this thread.  Here's a great blog post by mom4peace about what they did with a young math talent after 6B (they went into algebra! and other things as well).  I know there are more posts, these are just what I remember.  We decided after 5B to go into AoPS preA.

 

As far as learning things like times tables - give him a multiplication chart and lots of juicy problems that might use multiplication as part of the problem solving.  He will learn them by using them.  I'm surprised he found Penrose challenging and not BA - maybe look at the other books? - they teach factoring right alongside teaching multiplication. However, they do not drill it at all! They get interesting problems which happen to use multiplication or factoring. It seems, like many other people, he needs context and significance in order to enjoy the task.  

 

 Explaining what he is doing... I completely understand this! I would be so baffled and frustrated when dd would solve complex problems in her head and simply write the answer (not a full solution).  She still does this, but not as much.  And she never really could explain it fully to me.  I was so concerned about this.  But really, she didn't always have a way to explain her thinking process.  Using AoPS has been helpful, because they use full solutions so she can see how to write them.  It will be important to write some things down in order to correct any errors in the problem solving process.  But I wouldn't push this too much.  I would encourage it, and gently give occasional example. I would play dumb and say "can you explain to me how you got that, because I don't understand how to get it?"  And I would scribe and do oral work.  Don't conflate something that is difficult (writing) with math because then math becomes "difficult."  Think of it this way, would you want to paint a picture for every thing you wanted to tell someone about? No! Because that is laborious.  Neither does an immature writer want to write out a full solution.  Be patient with the developing writing, continue to encourage and model, and eventually his writing will catch up to his thinking (at least well enough to write things down).

 

Here is a great example of a way to increase frustration tolerance without forcing a task.  Here is another. More mistakes in math.  A big key to building frustration tolerance is self-talk - we get frustrated because of what we tell our selves.  There's an entire area of psychology (cognitive behavioral therapy) which deals with how we handle the stream of thoughts (positive and negative) which flow through our minds and you can look more into this.  Here's an informal blog post giving some basic examples of changing self-talk.  You can model this for your DS.  Another thing that helps kids grow frustration tolerance is free play.  Some kids are uncomfortable with this at first, but free play (outside preferably, and with other kids) is their opportunity to take risks (climbing, jumping, throwing, etc) and handle the results of their risks (successes and failures) without the pressure of external structures. I highly recommend Free to Learn for more on this.

 

Of course you want them to persist in things. But at what cost? It can be hard to find that sweet spot of pressure which helps them grow without increasing anxiety or frustration.  I believe that the younger they are the LESS pressure they need.  I would err on the side of too little.  You can "strew" math around your house as you suggested with other subjects - there are math trade books, there are math games, there are puzzles, there are manipulatives... Perhaps you need to try a different approach to a topic instead of persisting in the same approach, as well.  For square roots have him build squares with square tiles.  A square with side length 8 has 64 square tiles in it.  The square root of the number is the side length of the perfect square you can build with that number of tiles.  Although he's bright, most kids this age still need tangible or concrete things.  And he has plenty of time to revisit the concept of a square root.  It's ok to drop it right now.

 

I don't think I would have given the same advice I am giving now 4 years ago, because I didn't have as much faith in the process of trusting the child.  When oldest dd came home after three years in public school (we did homeschool K) she was almost a year behind in math.  I didn't understand, because when she entered school she was amazing with math and LOVED it.  One thing that destroyed her math love and confidence was timed drill sheets every day at school.  I was so anxious she didnt have her math facts memorized when I brought her home.  I was convinced she needed to learn them.  We tried several things (songs, flash cards, video games, picture stories of the facts, etc.) but nothing really helped out. So we went ahead and covered 6 Singapore books in 18 months, but stopped drilling math facts (we did do some mental math slips but not timed) and she began to soar again.  I gave her a multiplication table to refer to whenever she wanted.  She used it, then she redesigned it with a color system which made sense to her (each factor had a color - i.e. 2 is red background and the 7 is blue background - and the product was the result of combining those colors - ergo 2x7=14 (purple background).  I still don't understand her color system entirely, but it worked for her and she no longer needs the chart.  This, along with other things, has greatly increased my ability to be patient and have faith in my children's unique timelines and talents.

 

You, as your son's mother, have a unique position that no one else can replicate. Don't doubt yourself, or your son. Sometimes there's a golden thread with the key to understanding what to do, but more often you have to proceed with a bit of faith, relying on your observations and intuition and on those things your child communicates to you. Best wishes with everything!

[kiwik]

Ds7 looks at the sky and mutters to himself then gives the answer. If you ask him how he got it he says he guessed because it is easier. Unfortunately he goes to a b&m school!

 

could you just get him to work through the placement test and tell him that you are skipping a level because the rule is you do what the test says? Sometimes I say that certain things are part of my jib as his mother and it seems to sort of work - I get away with putting tge broccoli on his plate but it doesn't get eaten so only sort of.

[Crimson Wife]

Test him with the ADAM and figure out where the holes are. I would get something like the MM "blue" package if he dwells on the grade number. Print off the topics he needs, and go from there.

 

If he is "mathier" than his older sibling, you might want to have them in different programs to reduce the sibling rivalry aspect.

[EKS]

I forgot to mention a few things.  I did use the CWP with my son a year behind, so it served as a review sort of.

 

Also, to address your original question of how to find his level (which I forgot to do), he'll slow down once you find his level, though he might not slow down to a one level per year pace, though my son has.  My son just finished geometry and for the past three years (for prealgebra, Algebra I, and geometry) he has been moving at the standard pace.  I'm thinking that he may move more quickly through Algebra II because of the extensive review of Algebra I, but I could be wrong.