Help me understand 7-yo's Math thinking

[FreyaO]

I'm new here with plans to start HS our just-turned-7 yo DD. I feel uncertain about how to approach Math with her. So far she has been in B&M school performing just OK at grade level. She has shown understanding of math concepts at home and is doing a bit of BA whenever time allows - mostly during extended Covid breaks. Here is what confuses me:

- computational skills are consistently extremely variable. On a rare good day, she can do 3 digit addition and subtraction mentally. On a regular day, she will get maybe 70% of simpler arithmetic correct (let's day 2-digit addition/subtraction). On bad days/moments or when under scrutiny or time constraints, she will fail even simple tasks.

 

- She has an intuitive understanding of more abstract concepts. At various time points, she has come up with observations like "7-10 is a negative number. It's -3", "10 divided by 2 is 5, 5 divided by 2 is  2 and a half, 2 and a half divided by 2 is 1 and one quarter, 1 and one quarter divided by 2 is half and one eighth", or "1/8 is less than 1/6 but more than 1/12" (she was not taught fractions, it came up when cutting pancakes). She smiles at questions like "what is the smallest number you can subtract from 456 to get a two-digit number", but outright fights computational tasks. Last week, we came across a problem like this: if $ + @ = $ + 19, and $ + $ + @ = $ + 45, what is $ and @". I asked whether she can find @ from the first equation, she said "yeah, it's 19, and the second one gives me a hint, that $ + @ = 45, so $ is 26". 

 

At times, she seems to believe that she is bad at Math and I don't want this to become an established belief. She has mentioned that she often asked to go to the bathroom during Math class at school and purposefully delayed going back. We are planning to continue with BA next year, but I feel that there are discrepancies that I can't get my brain around. Has anyone had a similar experience? or can you point me to a resource that explains how mathematical thinking evolves? 

[Clarita]

Superficially, she's good at math and that's the problem at B&M school. If she is like me in my youth, she gets bored in class because somedays they start off teaching something she already knows, then zones out and then occasionally misses some pieces of information. I also had a hard time doing timed things and lots of problems; I would just make a lot of careless errors. I don't understand why but given a page of problems I will end up completely reading some of them wrong 2+4 becomes 5+3. Coupled together with my teachers occasionally talking about themselves being "bad at math" I would say that too. For you I think when you start teaching her and giving her a personalized education you can find there is nothing wrong with her and she is great at math. (Maybe there's a thing here or there that she didn't quite get but overall just fine.)

Even going to PS all my life, eventually I got to middle school and high school where I wasn't quite as bored because they started having different math classes things got a lot better. To the point where I went to University for an engineering degree. In university my experience got even better because the problems were hard and they would assign only a few and that helped me get my carelessness under control (double checking 5 problems was less daunting to me than 24).

Just squash the I'm bad at math (this is true for any subject). At least just change that into math is hard or better yet be specific like 2 digit addition is hard for me. Then add so I need to work on 2 digit addition. 

 

[HomeAgain]

I would need more information.

She may appear to be good at memorizing procedures when they look familiar (and looks like understanding), or she may struggle with place value's role in written problems, or she may have a boredom/interest issue.

I have a very dry book on my shelf about mathematical thinking and I wouldn't recommend it, but it moves from a concrete to abstract understanding as a general rule.  Every math program will develop individual skills differently, though.  DS12 used Gattegno and started with multiplying fractions after getting through 1-10 addition/subtraction. That said, with you using Beast Academy, I would absolutely harp on her being able to prove her answers in a more concrete way at this age.  I'd want to know exactly where the gaps in her understanding are and how she's working with them.  If she can't prove her math, then it points to more of understanding/memorizing procedure, not concept.

[Clemsondana]

I have one who became overwhelmed by having lots of problems, even if they are easy.  Kid still insists that they are bad at math *every time they miss a problem* even if it is a new concept.  They will also insist that they are bad at math *if problems can't be done as quickly as they expect* even if they are taking a completely reasonable amount of time to do them.  I'm not sure what causes this - we know that kid has a low frustration tolerance and we're looking at a potential ADHD other similar diagnosis for other reasons, so this could play in to it.  When kid was younger, we had good luck with Singapore Math, only doing the workbook and dividing most reviews into 2 days.  It has fewer problems than some books, explains different ways to do problems, and encourages mathmatical reasoning/mental math, so it was a good fit.  There are other similar programs that I'm sure other boardies will recommend that might be a good fit.  

[Malam]

She's good at math and bored with arithmetic. She seems to fit the mold of an underchallenged gifted child. Maybe 

If you really want her to practice basic arithmetic, try getting her some word problems from, say, CWP books 1 and 2. The act of turning the word problem into a math expression will satisfy her need for challenge, and she'll (hopefully) be more willing to do the arithmetic at the end to get the final answer.

You might also want to get her tested and read the similar experiences of parents on the davidson forum

[Malam]

On 7/9/2022 at 8:31 AM, Clemsondana said:

I have one who became overwhelmed by having lots of problems, even if they are easy.  Kid still insists that they are bad at math *every time they miss a problem* even if it is a new concept.  They will also insist that they are bad at math *if problems can't be done as quickly as they expect* even if they are taking a completely reasonable amount of time to do them.  I'm not sure what causes this

What was his early math education like? It's possible it consisted of quick, easy problems, and he grew accustomed to his level of proficiency as being normal for math, so now that problems are taking longer, he feels he's falling behind

[FreyaO]

On 7/9/2022 at 8:31 AM, Clemsondana said:

I have one who became overwhelmed by having lots of problems, even if they are easy.  Kid still insists that they are bad at math *every time they miss a problem* even if it is a new concept.  They will also insist that they are bad at math *if problems can't be done as quickly as they expect* even if they are taking a completely reasonable amount of time to do them.  I'm not sure what causes this - we know that kid has a low frustration tolerance and we're looking at a potential ADHD other similar diagnosis for other reasons, so this could play in to it.  When kid was younger, we had good luck with Singapore Math, only doing the workbook and dividing most reviews into 2 days.  It has fewer problems than some books, explains different ways to do problems, and encourages mathmatical reasoning/mental math, so it was a good fit.  There are other similar programs that I'm sure other boardies will recommend that might be a good fit.  

Thank you, yes, the low frustration tolerance, together with low tolerance for being corrected, is an issue for sure. I have spent some time thinking about ADHD and related diagnoses (for additional reasons) too. 

Edited July 11, 2022 by FreyaO

[FreyaO]

27 minutes ago, Malam said:

She's good at math and bored with arithmetic. She seems to fit the mold of an underchallenged gifted child. Maybe 

If you really want her to practice basic arithmetic, try getting her some word problems from, say, CWP books 1 and 2. The act of turning the word problem into a math expression will satisfy her need for challenge, and she'll (hopefully) be more willing to do the arithmetic at the end to get the final answer.

You might also want to get her tested and read the similar experiences of parents on the davidson forum

At some point, one needs to develop some automaticity, right? So that simple calculations do not hinder more complex procedures and thinking? 

She will cooperate with practicing to an acceptable level if someone shows her flash cards. Handing her a sheet of paper is a no go, and Math apps were a disaster too (I think it's the time element, there is a monster coming to you or a clock ticking). 

Testing will be nice indeed, but it's not cheap and I'm not sure she will cooperate... 

[FreyaO]

On 7/9/2022 at 7:15 AM, HomeAgain said:

I would need more information.

She may appear to be good at memorizing procedures when they look familiar (and looks like understanding), or she may struggle with place value's role in written problems, or she may have a boredom/interest issue.

I have a very dry book on my shelf about mathematical thinking and I wouldn't recommend it, but it moves from a concrete to abstract understanding as a general rule.  Every math program will develop individual skills differently, though.  DS12 used Gattegno and started with multiplying fractions after getting through 1-10 addition/subtraction. That said, with you using Beast Academy, I would absolutely harp on her being able to prove her answers in a more concrete way at this age.  I'd want to know exactly where the gaps in her understanding are and how she's working with them.  If she can't prove her math, then it points to more of understanding/memorizing procedure, not concept.

Thank you, that's an interesting point and something I should keep in mind, although right now it seems to me more like an inability or indifference or refusal to memorize and reproduce procedures.

[Malam]

23 minutes ago, FreyaO said:

At some point, one needs to develop some automaticity, right? So that simple calculations do not hinder more complex procedures and thinking? 

She will cooperate with practicing to an acceptable level if someone shows her flash cards. Handing her a sheet of paper is a no go, and Math apps were a disaster too (I think it's the time element, there is a monster coming to you or a clock ticking). 

Testing will be nice indeed, but it's not cheap and I'm not sure she will cooperate... 

Which level of Beast Academy has she been doing or placed into?

I think you'd be surprised on the testing front - intelligence and achievement tests don't ask students to do arithmetic worksheets because, among other reasons, children will be unlikely to cooperate. The types of questions are usually novel enough that children won't project their previous negative associations with academics onto them, and testing for younger kids does include frequent breaks.

If the goal is automaticity of basic math facts, then flashcards seem great. If anything, you'd be able to practice more facts faster with flashcards than with worksheets. For most students this runs the risk of skipping fundamental concepts like place value or *why* 17/3=9, but that's typically covered in 2nd and 3rd grade anyways, and concepts don't seem to be her weakness. If she gets bored of flashcard revision too, try Kate Snow's Math Facts that stick series or spacing out revision sessions by larger and larger intervals.

She might also find book with mental math to be engaging, like https://www.mathmammoth.com/add_subtract_3 or https://www.amazon.com/Mental-Math-Grade-Strategies-Calculation/dp/193602408X#customerReviews (the second one is light on practice)

Edited July 11, 2022 by Malam

[FreyaO]

On 7/8/2022 at 7:03 PM, Clarita said:

Superficially, she's good at math and that's the problem at B&M school. If she is like me in my youth, she gets bored in class because somedays they start off teaching something she already knows, then zones out and then occasionally misses some pieces of information. I also had a hard time doing timed things and lots of problems; I would just make a lot of careless errors. I don't understand why but given a page of problems I will end up completely reading some of them wrong 2+4 becomes 5+3. Coupled together with my teachers occasionally talking about themselves being "bad at math" I would say that too. For you I think when you start teaching her and giving her a personalized education you can find there is nothing wrong with her and she is great at math. (Maybe there's a thing here or there that she didn't quite get but overall just fine.)

Even going to PS all my life, eventually I got to middle school and high school where I wasn't quite as bored because they started having different math classes things got a lot better. To the point where I went to University for an engineering degree. In university my experience got even better because the problems were hard and they would assign only a few and that helped me get my carelessness under control (double checking 5 problems was less daunting to me than 24).

Just squash the I'm bad at math (this is true for any subject). At least just change that into math is hard or better yet be specific like 2 digit addition is hard for me. Then add so I need to work on 2 digit addition. 

 

Thank you, yes, what you described seems exactly like what I'm seeing! Except that the 2+4 becomes 2-4. 

[Malam]

13 minutes ago, FreyaO said:

Thank you, yes, what you described seems exactly like what I'm seeing! Except that the 2+4 becomes 2-4. 

Have you gotten her evaluated for a visual processing problem (not to be confused with poor eyesight)? They can be confused with ADHD due to similarities in symptoms.  

https://www.additudemag.com/adhd-and-vision-problems-understanding-symptoms/#:~:text=Vision disorders sometimes mimic symptoms,the root of the trouble.

https://www.thevisiontherapycenter.com/discovering-vision-therapy/adhd-misdiagnosis  

 

Edited July 11, 2022 by Malam

[Malam]

I just had another idea: you could the Miquon math series, and have her learn to use the C-Rods and regain her confidence using the first two books (which conveniently aren't labelled as being first grade) skipping whenever she gets bored (if she gets bored). Since it's manipulative-based and introduces many advanced concepts early, she'd hopefully like it more than a standard workbook approach like PS. You could use it as a supplement to BA, or use BA as a supplement to it.

Edited July 11, 2022 by Malam

[FreyaO]

1 hour ago, Malam said:

I just had another idea: you could the Miquon math series, and have her learn to use the C-Rods and regain her confidence using the first two books (which conveniently aren't labelled as being first grade) skipping whenever she gets bored (if she gets bored). Since it's manipulative-based and introduces many advanced concepts early, she'd hopefully like it more than a standard workbook approach like PS. You could use it as a supplement to BA, or use BA as a supplement to it.

Thanks for all the suggestions, Malam!

She is finishing up BA 2B. I think she likes the puzzle aspects. I will look into the Miquon math, she likes using her hands in general.

I haven't looked into functional vision at all. (I have considered auditory issues, but she claims she hears me perfectly fine and understands what is being asked). I will have to look into it in more detail. Her visual acuity is fine. But interestingly, although she is very physical and active, her eye-hand coordination in any kind of sport that involves a ball is ... let's say ... suboptimal (mentioned in the second link you provided). She reads very well, vocabulary, stamina, comprehension, etc, but when asked to read aloud she often skips small words, or reverses the order. Most times, this is insignificant, but sometimes it isn't. I used to think it's because she rushes through to find what will happen next, but maybe it isn't just that. 

[Malam]

Maybe try having her read random words to see if it's due to her rushing through or a vision issue?

[Clarita]

6 hours ago, Malam said:

Have you gotten her evaluated for a visual processing problem (not to be confused with poor eyesight)? They can be confused with ADHD due to similarities in symptoms.  

Oh my I think I have this. I mean the sports thing could be sports isn't my cup of tea but everything else is to a T.

4 hours ago, FreyaO said:

She reads very well, vocabulary, stamina, comprehension, etc, but when asked to read aloud she often skips small words, or reverses the order. Most times, this is insignificant, but sometimes it isn't. I used to think it's because she rushes through to find what will happen next, but maybe it isn't just that. 

I do all of this. I loved reading as a kid and if asked about main plot lines and such (general comprehension) I'd do great. What I really struggle with were directions especially on a "timed" test (this is a big culprit in a lot of my carelessness), reading aloud, and reading research papers or reading for information (like a textbook not just a simple can you find the information question).  

I only found out recently that putting as much effort as I had to (and still do) is not normal. Another boardie mentioned when I talked about what I needed to do to read a textbook or research paper. (Transcribe sections of the work and reading it probably 5-10 times before I could start using the information presented.)

I don't know if this is a normal thing, but when I was in school when I look up at the board from looking down at my notes, my vision is blurry for a few seconds as if my eyes have to readjust. So, I chunk my time between taking notes and looking up at the board (I zone the other one out). 

[Malam]

I believe there are eye focus exercises for this. Like adjusting your focus from the foreground to the background and back.

https://www.mayoclinic.org/diseases-conditions/convergence-insufficiency/diagnosis-treatment/drc-20352739#:~:text=In this exercise%2C you focus,or more days a week.

[Malam]

Oh and as for testing, check out the SIGS 2 home rating scale: https://www.routledge.com/Scales-for-Identifying-Gifted-Students-SIGS-2-Home-Rating-Scale-Forms/Ryser-McConnell-Sanguras-Kettler/p/book/9781646321742

It's affordable(-ish) and can be done by yourself.