Teaching math to gifted learners

[Pegs]

I'm taking a math education subject this semester, and I'm on the lookout for interesting articles on teaching mathematics to the highly able.

 

I'm aware of The Calculus Trap, and I've had some readings assigned already, but I thought I'd pop in here and ask for some additional input. If you know of any particularly interesting articles on maths/teaching/exceptional learners, please would you share with me here?

 

Thanking you in advance. :)

[Rosie_0801]

Interesting.

 

I wrote last semester on teaching remedial students, one of whom I very seriously suspected of being gifted.

 

Lambert, R. (2015). Constructing and resisting disability in mathematics classrooms: a case study exploring the impact of different pedagogies. Educational Studies in Mathematics, 89(1), 1-18.

 

Soooooo, not what you're asking for, but I thought I'd come and be conversational anyway.  :tongue_smilie:

[Pegs]

Ooooh! Thanks Rosie!

[Monica_in_Switzerland]

No help for OP, but wanted to just say thanks for mentioning the Calculus Trap.  I'd never heard of it, and reading the article on the AOPS site helped me resolve a question I didn't know I had about using the AOPS "optional" books or just moving through the standard alg-geo-alg2-preC-C sequence.  

 

Thanks!

[Loesje22000]

Not sure it fits your question,

But this book:

https://www.amazon.com/Teaching-Mastery-Mathematics-Modeling-Problem-solving/dp/9810168683/ref=sr_1_fkmr0_1?ie=UTF8&qid=1500289172&sr=8-1-fkmr0&keywords=math+bar+models+yeap

 

Explains how to do math 'the singapore way' without using 'singapore math books'.

[lewelma]

I have no articles, only experience. My ds refused all teaching or even the use of text books with direct instruction starting at the age of 8. He had to figure it out all by himself, just had to. Clearly he is not the only gifted math learner like this given that the AoPS textbooks are written with the discovery approach. So I'd be interested in what exactly "teaching" means in this context. I encouraged and listened and learned with him at times, but I never taught in the traditional sense. Just something to think about as you explore this topic.

 

Ruth in NZ

[nutella08]

Some books, and not necessarily for teaching gifted learners...

 

I found Liping Ma's Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States interesting when I read it years ago.

https://www.amazon.com/Knowing-Teaching-Elementary-Mathematics-Understanding/dp/0415873843/

 

Or maybe Maria Montessori's writings/methods or Moebius Noodles?

https://www.amazon.com/Moebius-Noodles-Natural-Yelena-McManaman/dp/0977693953

[debi21]

I'm very interested in this topic and am interested in what you find. I don't think the U.S. does a good job at all with this, generally. I don't know of any articles.

 

So I went to the state Math Kangaroo awards this year and I took a minute to talk to our state winner and runner up in 12th grade, who had represented our state in MathCounts in middle school, etc. They both live in the most populous county in our state, while I live in an adjoining one. I asked them if they knew if any high schools in my county that had a good reputation for math, competitions, etc. They didn't, and we talked about the "top" high schools in their county and they pointed out that even there, for math clubs and math competitions it was generally just students teaching other students. Basically, they implied no math teachers were up to the task.

 

I think somehow we just expect the really genius kids will just figure it out on their own. If they are not successful with the discovery method, AOPS, etc., what else is there for them? The bright and gifted, but not profoundly so, I think are really let down and may not reach their full potential.

 

 

Edit: Rosie, your article sounds great. I'm going to go read it.

 

More Edit: OP, would love it if you would share your assigned readings. Also, I had noticed that Cleo Borac had offered a "seminar for Parents of Gifted Mathematicians" on outschool.com and while I hadn't pursued it, it is still in the back of my mind. I wonder if she would have any useful input there.

Edited July 17, 2017 by debi21

[SoCal_Bear]

Maybe it depends on the area and the people involved in maths education? I would say the ones in my area are more than up to the task...but then again it is the San Diego Math Circle which has some AOPS contributors working there. The professor I have working with me our non-competitive SDSU math circle is really amazing with kids. Both of his son are highly gifted in maths.

In general, I would agree that those truly gifted in maths are not necessarily in maths education. We don't specialize like in Asia, and this is where I might get flack...I don't support teachers' unions because I absolutely think science and maths educators must be paid more in order to draw better talent. It makes zero sense to me that we pay them exactly the same.

Edited July 17, 2017 by calbear

[chocolate-chip chooky]

I have no articles, only experience. My ds refused all teaching or even the use of text books with direct instruction starting at the age of 8. He had to figure it out all by himself, just had to. Clearly he is not the only gifted math learner like this given that the AoPS textbooks are written with the discovery approach. So I'd be interested in what exactly "teaching" means in this context. I encouraged and listened and learned with him at times, but I never taught in the traditional sense. Just something to think about as you explore this topic.

 

Ruth in NZ

 

I can relate to this.

 

For some reason, my daughter (11) feels like she should already know things and gets upset sometimes when she actually needs some instruction for something new or particularly challenging.

I guess that this is because so much has already come so easily and naturally that not knowing something can feel new and uncomfortable for her.

 

 

This varies with mood though, and could be quite different with someone other than Mum, so please don't run away Pegs.  :)

 

Oh and another thing, Pegs, is the asynchrony. Simultaneous equations may be manipulated quite readily and then 8x7 needs to be stopped and thought about, for example.

[lewelma]

Good point, ds was still memorizing the subtraction facts while working independently through AoPS Intro Algebra.  We just made it two separate things.

 

I am absolutely sure that if ds had been in school he would have been labeled bad at math.  Grade level material (or even a grade or two up) was so obvious as to be mind-numbingly dull.  He generally would not do the work and when he did try, he made many careless errors. A half engaged brain (or less) just couldn't do the work, he just couldn't focus on something so boring to actually get the questions right. I have always compared it to proof reading an old-fashioned phone book, just because you want to, doesn't me you can actually do the work.

 

ETA: I will also add, that even if ds would have let me, I could not have taught him.  I am a high school math teacher with a PhD in mathematical biology, but there is a big difference between what I do/did and the problem solving that he does.  I just have no interest in learning that kind of material.  I did his first year *with* him to get him up to the level to get into the camp, and it broke me.  I was seriously burned out for 9 months after that.  Very few people with that level of skill are going to be teaching high school.

Edited July 17, 2017 by lewelma

[Pegs]

Cheers, folks.

 

I'll follow up on "teaching asynchronous learners" and "discovery vs explicit instruction", and I'll let you know what I find.

 

I'll be back with links and so forth when I get to my PC.

[daijobu]

This site has a number of excellent Math Circle materials with detailed instructions on pdf.  

 

I have reviewed Conway's Rational Tangles by Tom Davis and Set by Brian Conrey, and both are excellent.

[Pegs]

Thanks a lot. I'll be designing and implementing "fun and educational" activities for teaching middle school and high school students too, so I greatly appreciate anything which fits that bill also. :)

[ttt]

Developing Math Talent

 

https://www.amazon.com/Developing-Talent-Susan-Assouline-Ph-D/dp/159363496X/ref=pd_lpo_sbs_14_t_0?_encoding=UTF8&psc=1&refRID=DJV7RT1WPVVH7MSWCPGS

 

I'm currently reading it and am finding a lot of useful info re: advocating for my child at school.  Most everything they suggest is tied back to a research study.  I saw her speak at a conference re: acceleration, and later realized how focused she was on Math from her time at SMPY.

 

Susan Assouline's bio. 

 

 

Susan G. Assouline is a professor of school psychology at The University of Iowa and the director of the UI Belin-Blank Center.  She received her B. S. in general science with a teaching endorsement, her Ed.S. in School Psychology, and her Ph.D. in Psychological and Quantitative Foundations, all from The University of Iowa.  

Upon completion of her doctorate, she was awarded a two-year post-doctoral fellowship at the Study of Mathematically Precocious Youth (SMPY) at Johns Hopkins University and subsequently joined the Belin-Blank Center in 1990.  She is especially interested in academically talented elementary students and is co-author  (with Ann Shoplik) of both editions of Developing Math (2005, 2011).  As well, she is co-developer of The Iowa Acceleration Scale (2009), a tool designed to guide educators and parents through decisions about accelerating students.  In 2004, she co-authored, with Nicholas Colangelo and Miraca U. M. Gross, A Nation Deceived:  How Schools Hold Back America’s Brightest Students. Dr. Assouline serves on the editorial board of Gifted Child Quarterly. 

 

[seaben]

Thanks a lot. I'll be designing and implementing "fun and educational" activities for teaching middle school and high school students too, so I greatly appreciate anything which fits that bill also. :)

 

I have a bunch of writeups of pre-algebra level group activities and how they went.  If you're interested my year end summary is here: http://bit.ly/2sjuO2G and it has links to you can browse off of there. (I'm a bit free form in the summer so there are some more random recent posts.)

[quark]

Lockhart's Lament is a classic.

Not able to link on my phone but Advice to a Young Mathematician by Gowers also validated our journey.

Google to download a free PDF of both.

 

ETA: Adding links now from my laptop!

Edited July 18, 2017 by quark

[quark]

For activities, check out the nrich site put up by UK math educators. I have the link in one of my siggy threads.

 

High school students might enjoy the YouTube video on Erdos.

[4KookieKids]

Lockhart's Lament is a classic.

 

 

 

Ahh, I remember stumbling across this as an adult and feeling like someone *finally* understood!

[slackermom]

I cannot find a link to articles I read years ago; I think found them here at the National Association for Gifted Children: https://www.nagc.org/

 

It may not be precisely what you are interested in. The topic was how girls tend to mask their own giftedness intentionally starting around grade 4, so one should try to identify and hook them on higher-level material before that stage. So, not so much on specifically how to teach math to gifted kids, but trying to build awareness that social dynamics play a role. We ended up switching afterschool math circles (to this: http://www.girlsangle.org/)at one point because of those dynamics. 

 

eta: I still cannot find what I was looking for, but this is an interesting (to me, anyway!) interview with the founder of the Girls Angle group: 

https://girlsangle.wordpress.com/2013/01/03/interview-with-the-institute-of-mathematical-sciences-in-madrid/

 

editing again to add a snippit:

"There are also differences in modes of instruction. Again, acknowledging the ever present exception, roughly speaking, especially in grades 5-10, competitive events resonate more with boys than with girls. Yet, the US math educational landscape is flooded with math competitions. There are dozens upon dozens of math competitions, and many of them test for characteristics that are unimportant in mathematics, yet whose results, nevertheless, strongly influence participant’s self-perception of mathematical ability. At Girls’ Angle, we develop new modes of math instruction that are particularly effective for girls’ math education. Of course, there is great variety among girls, so one cannot point to a single such mode of instruction that works for all girls, but a good example of the kind of thing I’m referring to is our Math Treasure Hunt or Math Collaboration. The basic scenario for such events is that participants are thrown into a predicament from which they must extricate themselves by solving a collection of math problems. Because the participants all win together or lose together, there is no incentive to withhold observations or ideas from each other. "

 

 

 

Edited July 18, 2017 by slackermom

[Pegs]

I'm really appreciative of every single response in this thread. Thank you to each of you.

 

Please don't think me rude for not responding in full just yet - I mostly post from my phone and I struggle to write much from a tiny screen. I will get back here on the PC some time soon, though! :)